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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Extra Assignments and MLM Samples are required and Graded.They are part of the participation points ",null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"TODAY()-1","v":"2025-11-27"},null,"TC","No"]
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[null,null,null,null,null,"Master Quizzes MQ 5%",null,null,null,null,null,null,null,"MyLab Math MLM 15%",null,null,null,null,null,null,null,"Extra Assignments "]
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[null,null,{"$f":"IF(AND(YEAR(JanM)=$N$2,MONTH(JanM)=1),JanM, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+1)=$N$2,MONTH(JanM+1)=1),JanM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+2)=$N$2,MONTH(JanM+2)=1),JanM+2, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+3)=$N$2,MONTH(JanM+3)=1),JanM+3, \"\")","v":"2025-01-01"},{"$f":"IF(AND(YEAR(JanM+4)=$N$2,MONTH(JanM+4)=1),JanM+4, \"\")","v":"2025-01-02"},{"$f":"IF(AND(YEAR(JanM+5)=$N$2,MONTH(JanM+5)=1),JanM+5, \"\")","v":"2025-01-03"},{"$f":"IF(AND(YEAR(JanM+6)=$N$2,MONTH(JanM+6)=1),JanM+6, \"\")","v":"2025-01-04"},null,{"$f":"IF(AND(YEAR(FebM)=$N$2,MONTH(FebM)=2),FebM, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+1)=$N$2,MONTH(FebM+1)=2),FebM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+2)=$N$2,MONTH(FebM+2)=2),FebM+2, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+3)=$N$2,MONTH(FebM+3)=2),FebM+3, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+4)=$N$2,MONTH(FebM+4)=2),FebM+4, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+5)=$N$2,MONTH(FebM+5)=2),FebM+5, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+6)=$N$2,MONTH(FebM+6)=2),FebM+6, \"\")","v":"2025-02-01"},null,{"$f":"IF(AND(YEAR(MarM)=$N$2,MONTH(MarM)=3),MarM, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+1)=$N$2,MONTH(MarM+1)=3),MarM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+2)=$N$2,MONTH(MarM+2)=3),MarM+2, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+3)=$N$2,MONTH(MarM+3)=3),MarM+3, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+4)=$N$2,MONTH(MarM+4)=3),MarM+4, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+5)=$N$2,MONTH(MarM+5)=3),MarM+5, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+6)=$N$2,MONTH(MarM+6)=3),MarM+6, \"\")","v":"2025-03-01"},null,{"$f":"IF(AND(YEAR(AprM)=$N$2,MONTH(AprM)=4),AprM, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+1)=$N$2,MONTH(AprM+1)=4),AprM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+2)=$N$2,MONTH(AprM+2)=4),AprM+2, \"\")","v":"2025-04-01"},{"$f":"IF(AND(YEAR(AprM+3)=$N$2,MONTH(AprM+3)=4),AprM+3, \"\")","v":"2025-04-02"},{"$f":"IF(AND(YEAR(AprM+4)=$N$2,MONTH(AprM+4)=4),AprM+4, \"\")","v":"2025-04-03"},{"$f":"IF(AND(YEAR(AprM+5)=$N$2,MONTH(AprM+5)=4),AprM+5, \"\")","v":"2025-04-04"},{"$f":"IF(AND(YEAR(AprM+6)=$N$2,MONTH(AprM+6)=4),AprM+6, \"\")","v":"2025-04-05"},null,null,null,null,"MLK day, third Monday in January",null,null,null,{"$f":"AQ7","v":"2025-01-20"},{"$f":"DATE(CA6,1,1)+IF(2<WEEKDAY(DATE(CA6,1,1)),7-WEEKDAY(DATE(CA6,1,1))+2,2-WEEKDAY(DATE(CA6,1,1)))+((3-1)*7)","v":"2025-01-20"},null,{"$f":"AQ7","v":"2025-01-20"},null,null,null,null,null,null,null,null,"2011 Election Day, Primary","2011-05-03",{"$f":"BC7","v":"2011-05-03"},null,2011,{"$f":"BF7&\"a\"","v":"2011a"},"Christmas Day  (Washington Birthday)","2011-12-23",{"$f":"BI7","v":"2011-12-23"},null,2013,"2013-03-29","2013-03-29","2013-01-01","2013-01-01","2013-07-04","2013-07-04","2013-11-11","2013-11-11",null,4,"Apr"]
[null,null,{"$f":"IF(AND(YEAR(JanM+7)=$N$2,MONTH(JanM+7)=1),JanM+7, \"\")","v":"2025-01-05"},{"$f":"IF(AND(YEAR(JanM+8)=$N$2,MONTH(JanM+8)=1),JanM+8, \"\")","v":"2025-01-06"},{"$f":"IF(AND(YEAR(JanM+9)=$N$2,MONTH(JanM+9)=1),JanM+9, \"\")","v":"2025-01-07"},{"$f":"IF(AND(YEAR(JanM+10)=$N$2,MONTH(JanM+10)=1),JanM+10, \"\")","v":"2025-01-08"},{"$f":"IF(AND(YEAR(JanM+11)=$N$2,MONTH(JanM+11)=1),JanM+11, \"\")","v":"2025-01-09"},{"$f":"IF(AND(YEAR(JanM+12)=$N$2,MONTH(JanM+12)=1),JanM+12, \"\")","v":"2025-01-10"},{"$f":"IF(AND(YEAR(JanM+13)=$N$2,MONTH(JanM+13)=1),JanM+13, \"\")","v":"2025-01-11"},null,{"$f":"IF(AND(YEAR(FebM+7)=$N$2,MONTH(FebM+7)=2),FebM+7, \"\")","v":"2025-02-02"},{"$f":"IF(AND(YEAR(FebM+8)=$N$2,MONTH(FebM+8)=2),FebM+8, \"\")","v":"2025-02-03"},{"$f":"IF(AND(YEAR(FebM+9)=$N$2,MONTH(FebM+9)=2),FebM+9, \"\")","v":"2025-02-04"},{"$f":"IF(AND(YEAR(FebM+10)=$N$2,MONTH(FebM+10)=2),FebM+10, \"\")","v":"2025-02-05"},{"$f":"IF(AND(YEAR(FebM+11)=$N$2,MONTH(FebM+11)=2),FebM+11, \"\")","v":"2025-02-06"},{"$f":"IF(AND(YEAR(FebM+12)=$N$2,MONTH(FebM+12)=2),FebM+12, \"\")","v":"2025-02-07"},{"$f":"IF(AND(YEAR(FebM+13)=$N$2,MONTH(FebM+13)=2),FebM+13, \"\")","v":"2025-02-08"},null,{"$f":"IF(AND(YEAR(MarM+7)=$N$2,MONTH(MarM+7)=3),MarM+7, \"\")","v":"2025-03-02"},{"$f":"IF(AND(YEAR(MarM+8)=$N$2,MONTH(MarM+8)=3),MarM+8, \"\")","v":"2025-03-03"},{"$f":"IF(AND(YEAR(MarM+9)=$N$2,MONTH(MarM+9)=3),MarM+9, \"\")","v":"2025-03-04"},{"$f":"IF(AND(YEAR(MarM+10)=$N$2,MONTH(MarM+10)=3),MarM+10, \"\")","v":"2025-03-05"},{"$f":"IF(AND(YEAR(MarM+11)=$N$2,MONTH(MarM+11)=3),MarM+11, \"\")","v":"2025-03-06"},{"$f":"IF(AND(YEAR(MarM+12)=$N$2,MONTH(MarM+12)=3),MarM+12, \"\")","v":"2025-03-07"},{"$f":"IF(AND(YEAR(MarM+13)=$N$2,MONTH(MarM+13)=3),MarM+13, \"\")","v":"2025-03-08"},null,{"$f":"IF(AND(YEAR(AprM+7)=$N$2,MONTH(AprM+7)=4),AprM+7, \"\")","v":"2025-04-06"},{"$f":"IF(AND(YEAR(AprM+8)=$N$2,MONTH(AprM+8)=4),AprM+8, \"\")","v":"2025-04-07"},{"$f":"IF(AND(YEAR(AprM+9)=$N$2,MONTH(AprM+9)=4),AprM+9, \"\")","v":"2025-04-08"},{"$f":"IF(AND(YEAR(AprM+10)=$N$2,MONTH(AprM+10)=4),AprM+10, \"\")","v":"2025-04-09"},{"$f":"IF(AND(YEAR(AprM+11)=$N$2,MONTH(AprM+11)=4),AprM+11, \"\")","v":"2025-04-10"},{"$f":"IF(AND(YEAR(AprM+12)=$N$2,MONTH(AprM+12)=4),AprM+12, \"\")","v":"2025-04-11"},{"$f":"IF(AND(YEAR(AprM+13)=$N$2,MONTH(AprM+13)=4),AprM+13, \"\")","v":"2025-04-12"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2011 Election Day, General","2011-11-08",{"$f":"BC8","v":"2011-11-08"},null,2011,{"$f":"BF8&\"b\"","v":"2011b"},"Christmas Day  ","2011-12-26",{"$f":"BI8","v":"2011-12-26"},null,2014,"2014-04-18","2014-04-18","2014-01-01","2014-01-01","2014-07-04","2014-07-04","2014-11-11","2014-11-11",null,5,"May"]
[null,null,{"$f":"IF(AND(YEAR(JanM+14)=$N$2,MONTH(JanM+14)=1),JanM+14, \"\")","v":"2025-01-12"},{"$f":"IF(AND(YEAR(JanM+15)=$N$2,MONTH(JanM+15)=1),JanM+15, \"\")","v":"2025-01-13"},{"$f":"IF(AND(YEAR(JanM+16)=$N$2,MONTH(JanM+16)=1),JanM+16, \"\")","v":"2025-01-14"},{"$f":"IF(AND(YEAR(JanM+17)=$N$2,MONTH(JanM+17)=1),JanM+17, \"\")","v":"2025-01-15"},{"$f":"IF(AND(YEAR(JanM+18)=$N$2,MONTH(JanM+18)=1),JanM+18, \"\")","v":"2025-01-16"},{"$f":"IF(AND(YEAR(JanM+19)=$N$2,MONTH(JanM+19)=1),JanM+19, \"\")","v":"2025-01-17"},{"$f":"IF(AND(YEAR(JanM+20)=$N$2,MONTH(JanM+20)=1),JanM+20, \"\")","v":"2025-01-18"},null,{"$f":"IF(AND(YEAR(FebM+14)=$N$2,MONTH(FebM+14)=2),FebM+14, \"\")","v":"2025-02-09"},{"$f":"IF(AND(YEAR(FebM+15)=$N$2,MONTH(FebM+15)=2),FebM+15, \"\")","v":"2025-02-10"},{"$f":"IF(AND(YEAR(FebM+16)=$N$2,MONTH(FebM+16)=2),FebM+16, \"\")","v":"2025-02-11"},{"$f":"IF(AND(YEAR(FebM+17)=$N$2,MONTH(FebM+17)=2),FebM+17, \"\")","v":"2025-02-12"},{"$f":"IF(AND(YEAR(FebM+18)=$N$2,MONTH(FebM+18)=2),FebM+18, \"\")","v":"2025-02-13"},{"$f":"IF(AND(YEAR(FebM+19)=$N$2,MONTH(FebM+19)=2),FebM+19, \"\")","v":"2025-02-14"},{"$f":"IF(AND(YEAR(FebM+20)=$N$2,MONTH(FebM+20)=2),FebM+20, \"\")","v":"2025-02-15"},null,{"$f":"IF(AND(YEAR(MarM+14)=$N$2,MONTH(MarM+14)=3),MarM+14, \"\")","v":"2025-03-09"},{"$f":"IF(AND(YEAR(MarM+15)=$N$2,MONTH(MarM+15)=3),MarM+15, \"\")","v":"2025-03-10"},{"$f":"IF(AND(YEAR(MarM+16)=$N$2,MONTH(MarM+16)=3),MarM+16, \"\")","v":"2025-03-11"},{"$f":"IF(AND(YEAR(MarM+17)=$N$2,MONTH(MarM+17)=3),MarM+17, \"\")","v":"2025-03-12"},{"$f":"IF(AND(YEAR(MarM+18)=$N$2,MONTH(MarM+18)=3),MarM+18, \"\")","v":"2025-03-13"},{"$f":"IF(AND(YEAR(MarM+19)=$N$2,MONTH(MarM+19)=3),MarM+19, \"\")","v":"2025-03-14"},{"$f":"IF(AND(YEAR(MarM+20)=$N$2,MONTH(MarM+20)=3),MarM+20, \"\")","v":"2025-03-15"},null,{"$f":"IF(AND(YEAR(AprM+14)=$N$2,MONTH(AprM+14)=4),AprM+14, \"\")","v":"2025-04-13"},{"$f":"IF(AND(YEAR(AprM+15)=$N$2,MONTH(AprM+15)=4),AprM+15, \"\")","v":"2025-04-14"},{"$f":"IF(AND(YEAR(AprM+16)=$N$2,MONTH(AprM+16)=4),AprM+16, \"\")","v":"2025-04-15"},{"$f":"IF(AND(YEAR(AprM+17)=$N$2,MONTH(AprM+17)=4),AprM+17, \"\")","v":"2025-04-16"},{"$f":"IF(AND(YEAR(AprM+18)=$N$2,MONTH(AprM+18)=4),AprM+18, \"\")","v":"2025-04-17"},{"$f":"IF(AND(YEAR(AprM+19)=$N$2,MONTH(AprM+19)=4),AprM+19, \"\")","v":"2025-04-18"},{"$f":"IF(AND(YEAR(AprM+20)=$N$2,MONTH(AprM+20)=4),AprM+20, \"\")","v":"2025-04-19"},null,null,null,null,"Spring Break",null,{"$f":"IF(CA6=2029,DATE(CA6,3,1)+IF(4<WEEKDAY(DATE(CA6,3,1)),7-WEEKDAY(DATE(CA6,3,1))+1,1-WEEKDAY(DATE(CA6,3,1)))+((1)*7),DATE(CA6,3,1)+IF(4<WEEKDAY(DATE(CA6,3,1)),7-WEEKDAY(DATE(CA6,3,1))+1,1-WEEKDAY(DATE(CA6,3,1)))+((2)*7))","v":"2025-03-16"},null,"Until",{"$f":"AN9+7","v":"2025-03-23"},null,null,null,null,null,null,null,null,null,null,"2012 Election Day, Primary","2012-05-08","2012-05-08",null,2012,{"$f":"BF9&\"a\"","v":"2012a"},"Christmas Day  (Washington Birthday)","2012-12-24",{"$f":"BI9","v":"2012-12-24"},null,2015,"2015-04-03","2015-04-03","2015-01-01","2015-01-01","2015-07-03","2015-07-03","2015-11-11","2015-11-11",null,6,"Jun"]
[null,null,{"$f":"IF(AND(YEAR(JanM+21)=$N$2,MONTH(JanM+21)=1),JanM+21, \"\")","v":"2025-01-19"},{"$f":"IF(AND(YEAR(JanM+22)=$N$2,MONTH(JanM+22)=1),JanM+22, \"\")","v":"2025-01-20"},{"$f":"IF(AND(YEAR(JanM+23)=$N$2,MONTH(JanM+23)=1),JanM+23, \"\")","v":"2025-01-21"},{"$f":"IF(AND(YEAR(JanM+24)=$N$2,MONTH(JanM+24)=1),JanM+24, \"\")","v":"2025-01-22"},{"$f":"IF(AND(YEAR(JanM+25)=$N$2,MONTH(JanM+25)=1),JanM+25, \"\")","v":"2025-01-23"},{"$f":"IF(AND(YEAR(JanM+26)=$N$2,MONTH(JanM+26)=1),JanM+26, \"\")","v":"2025-01-24"},{"$f":"IF(AND(YEAR(JanM+27)=$N$2,MONTH(JanM+27)=1),JanM+27, \"\")","v":"2025-01-25"},null,{"$f":"IF(AND(YEAR(FebM+21)=$N$2,MONTH(FebM+21)=2),FebM+21, \"\")","v":"2025-02-16"},{"$f":"IF(AND(YEAR(FebM+22)=$N$2,MONTH(FebM+22)=2),FebM+22, \"\")","v":"2025-02-17"},{"$f":"IF(AND(YEAR(FebM+23)=$N$2,MONTH(FebM+23)=2),FebM+23, \"\")","v":"2025-02-18"},{"$f":"IF(AND(YEAR(FebM+24)=$N$2,MONTH(FebM+24)=2),FebM+24, \"\")","v":"2025-02-19"},{"$f":"IF(AND(YEAR(FebM+25)=$N$2,MONTH(FebM+25)=2),FebM+25, \"\")","v":"2025-02-20"},{"$f":"IF(AND(YEAR(FebM+26)=$N$2,MONTH(FebM+26)=2),FebM+26, \"\")","v":"2025-02-21"},{"$f":"IF(AND(YEAR(FebM+27)=$N$2,MONTH(FebM+27)=2),FebM+27, \"\")","v":"2025-02-22"},null,{"$f":"IF(AND(YEAR(MarM+21)=$N$2,MONTH(MarM+21)=3),MarM+21, \"\")","v":"2025-03-16"},{"$f":"IF(AND(YEAR(MarM+22)=$N$2,MONTH(MarM+22)=3),MarM+22, \"\")","v":"2025-03-17"},{"$f":"IF(AND(YEAR(MarM+23)=$N$2,MONTH(MarM+23)=3),MarM+23, \"\")","v":"2025-03-18"},{"$f":"IF(AND(YEAR(MarM+24)=$N$2,MONTH(MarM+24)=3),MarM+24, \"\")","v":"2025-03-19"},{"$f":"IF(AND(YEAR(MarM+25)=$N$2,MONTH(MarM+25)=3),MarM+25, \"\")","v":"2025-03-20"},{"$f":"IF(AND(YEAR(MarM+26)=$N$2,MONTH(MarM+26)=3),MarM+26, \"\")","v":"2025-03-21"},{"$f":"IF(AND(YEAR(MarM+27)=$N$2,MONTH(MarM+27)=3),MarM+27, \"\")","v":"2025-03-22"},null,{"$f":"IF(AND(YEAR(AprM+21)=$N$2,MONTH(AprM+21)=4),AprM+21, \"\")","v":"2025-04-20"},{"$f":"IF(AND(YEAR(AprM+22)=$N$2,MONTH(AprM+22)=4),AprM+22, \"\")","v":"2025-04-21"},{"$f":"IF(AND(YEAR(AprM+23)=$N$2,MONTH(AprM+23)=4),AprM+23, \"\")","v":"2025-04-22"},{"$f":"IF(AND(YEAR(AprM+24)=$N$2,MONTH(AprM+24)=4),AprM+24, \"\")","v":"2025-04-23"},{"$f":"IF(AND(YEAR(AprM+25)=$N$2,MONTH(AprM+25)=4),AprM+25, \"\")","v":"2025-04-24"},{"$f":"IF(AND(YEAR(AprM+26)=$N$2,MONTH(AprM+26)=4),AprM+26, \"\")","v":"2025-04-25"},{"$f":"IF(AND(YEAR(AprM+27)=$N$2,MONTH(AprM+27)=4),AprM+27, \"\")","v":"2025-04-26"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2012 Election Day, General","2012-11-06","2012-11-06",null,2012,{"$f":"BF10&\"b\"","v":"2012b"},"Christmas Day  ","2012-12-25",{"$f":"BI10","v":"2012-12-25"},null,2016,"2016-03-25","2016-03-25","2016-01-01","2016-01-01","2016-07-04","2016-07-04","2016-11-11","2016-11-11",null,7,"Jul"]
[null,null,{"$f":"IF(AND(YEAR(JanM+28)=$N$2,MONTH(JanM+28)=1),JanM+28, \"\")","v":"2025-01-26"},{"$f":"IF(AND(YEAR(JanM+29)=$N$2,MONTH(JanM+29)=1),JanM+29, \"\")","v":"2025-01-27"},{"$f":"IF(AND(YEAR(JanM+30)=$N$2,MONTH(JanM+30)=1),JanM+30, \"\")","v":"2025-01-28"},{"$f":"IF(AND(YEAR(JanM+31)=$N$2,MONTH(JanM+31)=1),JanM+31, \"\")","v":"2025-01-29"},{"$f":"IF(AND(YEAR(JanM+32)=$N$2,MONTH(JanM+32)=1),JanM+32, \"\")","v":"2025-01-30"},{"$f":"IF(AND(YEAR(JanM+33)=$N$2,MONTH(JanM+33)=1),JanM+33, \"\")","v":"2025-01-31"},{"$f":"IF(AND(YEAR(JanM+34)=$N$2,MONTH(JanM+34)=1),JanM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(FebM+28)=$N$2,MONTH(FebM+28)=2),FebM+28, \"\")","v":"2025-02-23"},{"$f":"IF(AND(YEAR(FebM+29)=$N$2,MONTH(FebM+29)=2),FebM+29, \"\")","v":"2025-02-24"},{"$f":"IF(AND(YEAR(FebM+30)=$N$2,MONTH(FebM+30)=2),FebM+30, \"\")","v":"2025-02-25"},{"$f":"IF(AND(YEAR(FebM+31)=$N$2,MONTH(FebM+31)=2),FebM+31, \"\")","v":"2025-02-26"},{"$f":"IF(AND(YEAR(FebM+32)=$N$2,MONTH(FebM+32)=2),FebM+32, \"\")","v":"2025-02-27"},{"$f":"IF(AND(YEAR(FebM+33)=$N$2,MONTH(FebM+33)=2),FebM+33, \"\")","v":"2025-02-28"},{"$f":"IF(AND(YEAR(FebM+34)=$N$2,MONTH(FebM+34)=2),FebM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(MarM+28)=$N$2,MONTH(MarM+28)=3),MarM+28, \"\")","v":"2025-03-23"},{"$f":"IF(AND(YEAR(MarM+29)=$N$2,MONTH(MarM+29)=3),MarM+29, \"\")","v":"2025-03-24"},{"$f":"IF(AND(YEAR(MarM+30)=$N$2,MONTH(MarM+30)=3),MarM+30, \"\")","v":"2025-03-25"},{"$f":"IF(AND(YEAR(MarM+31)=$N$2,MONTH(MarM+31)=3),MarM+31, \"\")","v":"2025-03-26"},{"$f":"IF(AND(YEAR(MarM+32)=$N$2,MONTH(MarM+32)=3),MarM+32, \"\")","v":"2025-03-27"},{"$f":"IF(AND(YEAR(MarM+33)=$N$2,MONTH(MarM+33)=3),MarM+33, \"\")","v":"2025-03-28"},{"$f":"IF(AND(YEAR(MarM+34)=$N$2,MONTH(MarM+34)=3),MarM+34, \"\")","v":"2025-03-29"},null,{"$f":"IF(AND(YEAR(AprM+28)=$N$2,MONTH(AprM+28)=4),AprM+28, \"\")","v":"2025-04-27"},{"$f":"IF(AND(YEAR(AprM+29)=$N$2,MONTH(AprM+29)=4),AprM+29, \"\")","v":"2025-04-28"},{"$f":"IF(AND(YEAR(AprM+30)=$N$2,MONTH(AprM+30)=4),AprM+30, \"\")","v":"2025-04-29"},{"$f":"IF(AND(YEAR(AprM+31)=$N$2,MONTH(AprM+31)=4),AprM+31, \"\")","v":"2025-04-30"},{"$f":"IF(AND(YEAR(AprM+32)=$N$2,MONTH(AprM+32)=4),AprM+32, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+33)=$N$2,MONTH(AprM+33)=4),AprM+33, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+34)=$N$2,MONTH(AprM+34)=4),AprM+34, \"\")","v":""},null,null,null,null,"Good Friday (varies per year)",null,null,null,{"$f":"AQ11","v":"2025-04-18"},{"$f":"IF($CD$5=1,VLOOKUP($CA$6,BL1:BT60,2,FALSE),\"\")","v":"2025-04-18"},null,null,null,null,null,null,null,null,null,null,"2013 Election Day, Primary","None","Non",null,2013,{"$f":"BF11&\"a\"","v":"2013a"},"Christmas Day  (Washington Birthday)","2013-12-24",{"$f":"BI11","v":"2013-12-24"},null,2017,"2017-04-14","2017-04-14","2017-01-02","2017-01-02","2017-07-04","2017-07-04","2017-11-10","2017-11-10",null,8,"Aug"]
[null,null,{"$f":"IF(AND(YEAR(JanM+35)=$N$2,MONTH(JanM+35)=1),JanM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+36)=$N$2,MONTH(JanM+36)=1),JanM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+37)=$N$2,MONTH(JanM+37)=1),JanM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+38)=$N$2,MONTH(JanM+38)=1),JanM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+39)=$N$2,MONTH(JanM+39)=1),JanM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+40)=$N$2,MONTH(JanM+40)=1),JanM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(JanM+41)=$N$2,MONTH(JanM+41)=1),JanM+41, \"\")","v":""},null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(YEAR(MarM+35)=$N$2,MONTH(MarM+35)=3),MarM+35, \"\")","v":"2025-03-30"},{"$f":"IF(AND(YEAR(MarM+36)=$N$2,MONTH(MarM+36)=3),MarM+36, \"\")","v":"2025-03-31"},{"$f":"IF(AND(YEAR(MarM+37)=$N$2,MONTH(MarM+37)=3),MarM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+38)=$N$2,MONTH(MarM+38)=3),MarM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+39)=$N$2,MONTH(MarM+39)=3),MarM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+40)=$N$2,MONTH(MarM+40)=3),MarM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(MarM+41)=$N$2,MONTH(MarM+41)=3),MarM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(AprM+35)=$N$2,MONTH(AprM+35)=4),AprM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+36)=$N$2,MONTH(AprM+36)=4),AprM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+37)=$N$2,MONTH(AprM+37)=4),AprM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+38)=$N$2,MONTH(AprM+38)=4),AprM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+39)=$N$2,MONTH(AprM+39)=4),AprM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+40)=$N$2,MONTH(AprM+40)=4),AprM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(AprM+41)=$N$2,MONTH(AprM+41)=4),AprM+41, \"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2013 Election Day, General","None","Non",null,2013,{"$f":"BF12&\"b\"","v":"2013b"},"Christmas Day  ","2013-12-25",{"$f":"BI12","v":"2013-12-25"},null,2018,"2018-03-30","2018-03-30","2018-01-01","2018-01-01","2018-07-04","2018-07-04","2018-11-12","2018-11-12",null,9,"Sep"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Memorial Day, Last Monday in May",null,null,null,{"$f":"AQ13","v":"2025-05-26"},{"$f":"DATE(CA6,6,1)+IF(2<WEEKDAY(DATE(CA6,6,1)),7-WEEKDAY(DATE(CA6,6,1))+2,2-WEEKDAY(DATE(CA6,6,1)))+((1-1)*7)-7","v":"2025-05-26"},null,{"$f":"AQ13","v":"2025-05-26"},null,null,null,null,null,null,null,null,"2014 Election Day, Primary","2014-05-06","2014-05-06",null,2014,{"$f":"BF13&\"a\"","v":"2014a"},"Christmas Day  (Washington Birthday)","2014-12-26",{"$f":"BI13","v":"2014-12-26"},null,2019,"2019-04-19","2019-04-19","2019-01-01","2019-01-01","2019-07-04","2019-07-04","2019-11-11","2019-11-11",null,10,"Oct"]
[null,null,"May",null,null,null,null,null,null,null,"June",null,null,null,null,null,null,null,"July",null,null,null,null,null,null,null,"August",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2014 Election Day, General","2014-11-04","2014-11-04",null,2014,{"$f":"BF14&\"b\"","v":"2014b"},"Christmas Day  ","2014-12-25","2014-12-25",null,2020,"2020-04-10","2020-04-10","2020-01-01","2020-01-01","2020-07-03","2020-07-03","2020-11-11","2020-11-11",null,11,"Nov"]
[null,null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,null,null,null,"Independence Day ",null,null,null,{"$f":"AQ15","v":"2025-07-04"},{"$f":"IF($CD$5=1,VLOOKUP($CA$6,BL1:BT60,6,FALSE),DATE(CA6,7,4))","v":"2025-07-04"},null,{"$f":"AQ15","v":"2025-07-04"},null,null,null,null,null,null,null,null,"2015 Election Day, Primary","2015-05-05","2015-05-05",null,2015,{"$f":"BF15&\"a\"","v":"2015a"},"Christmas Day  (Washington Birthday)","2015-12-24","2015-12-24",null,2021,"2021-04-02","2021-04-02","2021-01-01","2021-01-01","2021-07-05","2021-07-05","2021-11-11","2021-11-11",null,12,"Dec"]
[null,null,{"$f":"IF(AND(YEAR(MayM)=$N$2,MONTH(MayM)=5),MayM, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+1)=$N$2,MONTH(MayM+1)=5),MayM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+2)=$N$2,MONTH(MayM+2)=5),MayM+2, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+3)=$N$2,MONTH(MayM+3)=5),MayM+3, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+4)=$N$2,MONTH(MayM+4)=5),MayM+4, \"\")","v":"2025-05-01"},{"$f":"IF(AND(YEAR(MayM+5)=$N$2,MONTH(MayM+5)=5),MayM+5, \"\")","v":"2025-05-02"},{"$f":"IF(AND(YEAR(MayM+6)=$N$2,MONTH(MayM+6)=5),MayM+6, \"\")","v":"2025-05-03"},null,{"$f":"IF(AND(YEAR(JunM)=$N$2,MONTH(JunM)=6),JunM, \"\")","v":"2025-06-01"},{"$f":"IF(AND(YEAR(JunM+1)=$N$2,MONTH(JunM+1)=6),JunM+1, \"\")","v":"2025-06-02"},{"$f":"IF(AND(YEAR(JunM+2)=$N$2,MONTH(JunM+2)=6),JunM+2, \"\")","v":"2025-06-03"},{"$f":"IF(AND(YEAR(JunM+3)=$N$2,MONTH(JunM+3)=6),JunM+3, \"\")","v":"2025-06-04"},{"$f":"IF(AND(YEAR(JunM+4)=$N$2,MONTH(JunM+4)=6),JunM+4, \"\")","v":"2025-06-05"},{"$f":"IF(AND(YEAR(JunM+5)=$N$2,MONTH(JunM+5)=6),JunM+5, \"\")","v":"2025-06-06"},{"$f":"IF(AND(YEAR(JunM+6)=$N$2,MONTH(JunM+6)=6),JunM+6, \"\")","v":"2025-06-07"},null,{"$f":"IF(AND(YEAR(JulM)=$N$2,MONTH(JulM)=7),JulM, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+1)=$N$2,MONTH(JulM+1)=7),JulM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+2)=$N$2,MONTH(JulM+2)=7),JulM+2, \"\")","v":"2025-07-01"},{"$f":"IF(AND(YEAR(JulM+3)=$N$2,MONTH(JulM+3)=7),JulM+3, \"\")","v":"2025-07-02"},{"$f":"IF(AND(YEAR(JulM+4)=$N$2,MONTH(JulM+4)=7),JulM+4, \"\")","v":"2025-07-03"},{"$f":"IF(AND(YEAR(JulM+5)=$N$2,MONTH(JulM+5)=7),JulM+5, \"\")","v":"2025-07-04"},{"$f":"IF(AND(YEAR(JulM+6)=$N$2,MONTH(JulM+6)=7),JulM+6, \"\")","v":"2025-07-05"},null,{"$f":"IF(AND(YEAR(AugM)=$N$2,MONTH(AugM)=8),AugM, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+1)=$N$2,MONTH(AugM+1)=8),AugM+1, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+2)=$N$2,MONTH(AugM+2)=8),AugM+2, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+3)=$N$2,MONTH(AugM+3)=8),AugM+3, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+4)=$N$2,MONTH(AugM+4)=8),AugM+4, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+5)=$N$2,MONTH(AugM+5)=8),AugM+5, \"\")","v":"2025-08-01"},{"$f":"IF(AND(YEAR(AugM+6)=$N$2,MONTH(AugM+6)=8),AugM+6, \"\")","v":"2025-08-02"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2015 Election Day, General","2015-11-03","2015-11-03",null,2015,{"$f":"BF16&\"b\"","v":"2015b"},"Christmas Day  ","2015-12-25","2015-12-25",null,2022,"2022-04-15","2022-04-15","2021-12-31","2021-12-31","2022-07-04","2022-07-04","2022-11-11","2022-11-11"]
[null,null,{"$f":"IF(AND(YEAR(MayM+7)=$N$2,MONTH(MayM+7)=5),MayM+7, \"\")","v":"2025-05-04"},{"$f":"IF(AND(YEAR(MayM+8)=$N$2,MONTH(MayM+8)=5),MayM+8, \"\")","v":"2025-05-05"},{"$f":"IF(AND(YEAR(MayM+9)=$N$2,MONTH(MayM+9)=5),MayM+9, \"\")","v":"2025-05-06"},{"$f":"IF(AND(YEAR(MayM+10)=$N$2,MONTH(MayM+10)=5),MayM+10, \"\")","v":"2025-05-07"},{"$f":"IF(AND(YEAR(MayM+11)=$N$2,MONTH(MayM+11)=5),MayM+11, \"\")","v":"2025-05-08"},{"$f":"IF(AND(YEAR(MayM+12)=$N$2,MONTH(MayM+12)=5),MayM+12, \"\")","v":"2025-05-09"},{"$f":"IF(AND(YEAR(MayM+13)=$N$2,MONTH(MayM+13)=5),MayM+13, \"\")","v":"2025-05-10"},null,{"$f":"IF(AND(YEAR(JunM+7)=$N$2,MONTH(JunM+7)=6),JunM+7, \"\")","v":"2025-06-08"},{"$f":"IF(AND(YEAR(JunM+8)=$N$2,MONTH(JunM+8)=6),JunM+8, \"\")","v":"2025-06-09"},{"$f":"IF(AND(YEAR(JunM+9)=$N$2,MONTH(JunM+9)=6),JunM+9, \"\")","v":"2025-06-10"},{"$f":"IF(AND(YEAR(JunM+10)=$N$2,MONTH(JunM+10)=6),JunM+10, \"\")","v":"2025-06-11"},{"$f":"IF(AND(YEAR(JunM+11)=$N$2,MONTH(JunM+11)=6),JunM+11, \"\")","v":"2025-06-12"},{"$f":"IF(AND(YEAR(JunM+12)=$N$2,MONTH(JunM+12)=6),JunM+12, \"\")","v":"2025-06-13"},{"$f":"IF(AND(YEAR(JunM+13)=$N$2,MONTH(JunM+13)=6),JunM+13, \"\")","v":"2025-06-14"},null,{"$f":"IF(AND(YEAR(JulM+7)=$N$2,MONTH(JulM+7)=7),JulM+7, \"\")","v":"2025-07-06"},{"$f":"IF(AND(YEAR(JulM+8)=$N$2,MONTH(JulM+8)=7),JulM+8, \"\")","v":"2025-07-07"},{"$f":"IF(AND(YEAR(JulM+9)=$N$2,MONTH(JulM+9)=7),JulM+9, \"\")","v":"2025-07-08"},{"$f":"IF(AND(YEAR(JulM+10)=$N$2,MONTH(JulM+10)=7),JulM+10, \"\")","v":"2025-07-09"},{"$f":"IF(AND(YEAR(JulM+11)=$N$2,MONTH(JulM+11)=7),JulM+11, \"\")","v":"2025-07-10"},{"$f":"IF(AND(YEAR(JulM+12)=$N$2,MONTH(JulM+12)=7),JulM+12, \"\")","v":"2025-07-11"},{"$f":"IF(AND(YEAR(JulM+13)=$N$2,MONTH(JulM+13)=7),JulM+13, \"\")","v":"2025-07-12"},null,{"$f":"IF(AND(YEAR(AugM+7)=$N$2,MONTH(AugM+7)=8),AugM+7, \"\")","v":"2025-08-03"},{"$f":"IF(AND(YEAR(AugM+8)=$N$2,MONTH(AugM+8)=8),AugM+8, \"\")","v":"2025-08-04"},{"$f":"IF(AND(YEAR(AugM+9)=$N$2,MONTH(AugM+9)=8),AugM+9, \"\")","v":"2025-08-05"},{"$f":"IF(AND(YEAR(AugM+10)=$N$2,MONTH(AugM+10)=8),AugM+10, \"\")","v":"2025-08-06"},{"$f":"IF(AND(YEAR(AugM+11)=$N$2,MONTH(AugM+11)=8),AugM+11, \"\")","v":"2025-08-07"},{"$f":"IF(AND(YEAR(AugM+12)=$N$2,MONTH(AugM+12)=8),AugM+12, \"\")","v":"2025-08-08"},{"$f":"IF(AND(YEAR(AugM+13)=$N$2,MONTH(AugM+13)=8),AugM+13, \"\")","v":"2025-08-09"},null,null,null,null,"Labor Day, first Monday in September",null,null,null,{"$f":"AQ17","v":"2025-09-01"},{"$f":"DATE(CA6,9,1)+IF(2<WEEKDAY(DATE(CA6,9,1)),7-WEEKDAY(DATE(CA6,9,1))+2,2-WEEKDAY(DATE(CA6,9,1)))+((1-1)*7)","v":"2025-09-01"},null,{"$f":"AQ17","v":"2025-09-01"},null,null,null,null,null,null,null,null,"2016 Election Day, Primary","2016-05-03","2016-05-03",null,2016,{"$f":"BF17&\"a\"","v":"2016a"},"Christmas Day  (Washington Birthday)","2016-12-23","2016-12-23",null,2023,"2023-04-07","2023-04-07","2023-01-02","2023-01-02","2023-07-04","2023-07-04","2023-11-10","2023-11-10"]
[null,null,{"$f":"IF(AND(YEAR(MayM+14)=$N$2,MONTH(MayM+14)=5),MayM+14, \"\")","v":"2025-05-11"},{"$f":"IF(AND(YEAR(MayM+15)=$N$2,MONTH(MayM+15)=5),MayM+15, \"\")","v":"2025-05-12"},{"$f":"IF(AND(YEAR(MayM+16)=$N$2,MONTH(MayM+16)=5),MayM+16, \"\")","v":"2025-05-13"},{"$f":"IF(AND(YEAR(MayM+17)=$N$2,MONTH(MayM+17)=5),MayM+17, \"\")","v":"2025-05-14"},{"$f":"IF(AND(YEAR(MayM+18)=$N$2,MONTH(MayM+18)=5),MayM+18, \"\")","v":"2025-05-15"},{"$f":"IF(AND(YEAR(MayM+19)=$N$2,MONTH(MayM+19)=5),MayM+19, \"\")","v":"2025-05-16"},{"$f":"IF(AND(YEAR(MayM+20)=$N$2,MONTH(MayM+20)=5),MayM+20, \"\")","v":"2025-05-17"},null,{"$f":"IF(AND(YEAR(JunM+14)=$N$2,MONTH(JunM+14)=6),JunM+14, \"\")","v":"2025-06-15"},{"$f":"IF(AND(YEAR(JunM+15)=$N$2,MONTH(JunM+15)=6),JunM+15, \"\")","v":"2025-06-16"},{"$f":"IF(AND(YEAR(JunM+16)=$N$2,MONTH(JunM+16)=6),JunM+16, \"\")","v":"2025-06-17"},{"$f":"IF(AND(YEAR(JunM+17)=$N$2,MONTH(JunM+17)=6),JunM+17, \"\")","v":"2025-06-18"},{"$f":"IF(AND(YEAR(JunM+18)=$N$2,MONTH(JunM+18)=6),JunM+18, \"\")","v":"2025-06-19"},{"$f":"IF(AND(YEAR(JunM+19)=$N$2,MONTH(JunM+19)=6),JunM+19, \"\")","v":"2025-06-20"},{"$f":"IF(AND(YEAR(JunM+20)=$N$2,MONTH(JunM+20)=6),JunM+20, \"\")","v":"2025-06-21"},null,{"$f":"IF(AND(YEAR(JulM+14)=$N$2,MONTH(JulM+14)=7),JulM+14, \"\")","v":"2025-07-13"},{"$f":"IF(AND(YEAR(JulM+15)=$N$2,MONTH(JulM+15)=7),JulM+15, \"\")","v":"2025-07-14"},{"$f":"IF(AND(YEAR(JulM+16)=$N$2,MONTH(JulM+16)=7),JulM+16, \"\")","v":"2025-07-15"},{"$f":"IF(AND(YEAR(JulM+17)=$N$2,MONTH(JulM+17)=7),JulM+17, \"\")","v":"2025-07-16"},{"$f":"IF(AND(YEAR(JulM+18)=$N$2,MONTH(JulM+18)=7),JulM+18, \"\")","v":"2025-07-17"},{"$f":"IF(AND(YEAR(JulM+19)=$N$2,MONTH(JulM+19)=7),JulM+19, \"\")","v":"2025-07-18"},{"$f":"IF(AND(YEAR(JulM+20)=$N$2,MONTH(JulM+20)=7),JulM+20, \"\")","v":"2025-07-19"},null,{"$f":"IF(AND(YEAR(AugM+14)=$N$2,MONTH(AugM+14)=8),AugM+14, \"\")","v":"2025-08-10"},{"$f":"IF(AND(YEAR(AugM+15)=$N$2,MONTH(AugM+15)=8),AugM+15, \"\")","v":"2025-08-11"},{"$f":"IF(AND(YEAR(AugM+16)=$N$2,MONTH(AugM+16)=8),AugM+16, \"\")","v":"2025-08-12"},{"$f":"IF(AND(YEAR(AugM+17)=$N$2,MONTH(AugM+17)=8),AugM+17, \"\")","v":"2025-08-13"},{"$f":"IF(AND(YEAR(AugM+18)=$N$2,MONTH(AugM+18)=8),AugM+18, \"\")","v":"2025-08-14"},{"$f":"IF(AND(YEAR(AugM+19)=$N$2,MONTH(AugM+19)=8),AugM+19, \"\")","v":"2025-08-15"},{"$f":"IF(AND(YEAR(AugM+20)=$N$2,MONTH(AugM+20)=8),AugM+20, \"\")","v":"2025-08-16"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2016 Election Day, General","2016-11-08","2016-11-08",null,2016,{"$f":"BF18&\"b\"","v":"2016b"},"Christmas Day  ","2016-12-26","2016-12-26",null,2024,"2024-03-29","2024-03-29","2024-01-01","2024-01-01","2024-07-04","2024-07-04","2024-11-11","2024-11-11"]
[null,null,{"$f":"IF(AND(YEAR(MayM+21)=$N$2,MONTH(MayM+21)=5),MayM+21, \"\")","v":"2025-05-18"},{"$f":"IF(AND(YEAR(MayM+22)=$N$2,MONTH(MayM+22)=5),MayM+22, \"\")","v":"2025-05-19"},{"$f":"IF(AND(YEAR(MayM+23)=$N$2,MONTH(MayM+23)=5),MayM+23, \"\")","v":"2025-05-20"},{"$f":"IF(AND(YEAR(MayM+24)=$N$2,MONTH(MayM+24)=5),MayM+24, \"\")","v":"2025-05-21"},{"$f":"IF(AND(YEAR(MayM+25)=$N$2,MONTH(MayM+25)=5),MayM+25, \"\")","v":"2025-05-22"},{"$f":"IF(AND(YEAR(MayM+26)=$N$2,MONTH(MayM+26)=5),MayM+26, \"\")","v":"2025-05-23"},{"$f":"IF(AND(YEAR(MayM+27)=$N$2,MONTH(MayM+27)=5),MayM+27, \"\")","v":"2025-05-24"},null,{"$f":"IF(AND(YEAR(JunM+21)=$N$2,MONTH(JunM+21)=6),JunM+21, \"\")","v":"2025-06-22"},{"$f":"IF(AND(YEAR(JunM+22)=$N$2,MONTH(JunM+22)=6),JunM+22, \"\")","v":"2025-06-23"},{"$f":"IF(AND(YEAR(JunM+23)=$N$2,MONTH(JunM+23)=6),JunM+23, \"\")","v":"2025-06-24"},{"$f":"IF(AND(YEAR(JunM+24)=$N$2,MONTH(JunM+24)=6),JunM+24, \"\")","v":"2025-06-25"},{"$f":"IF(AND(YEAR(JunM+25)=$N$2,MONTH(JunM+25)=6),JunM+25, \"\")","v":"2025-06-26"},{"$f":"IF(AND(YEAR(JunM+26)=$N$2,MONTH(JunM+26)=6),JunM+26, \"\")","v":"2025-06-27"},{"$f":"IF(AND(YEAR(JunM+27)=$N$2,MONTH(JunM+27)=6),JunM+27, \"\")","v":"2025-06-28"},null,{"$f":"IF(AND(YEAR(JulM+21)=$N$2,MONTH(JulM+21)=7),JulM+21, \"\")","v":"2025-07-20"},{"$f":"IF(AND(YEAR(JulM+22)=$N$2,MONTH(JulM+22)=7),JulM+22, \"\")","v":"2025-07-21"},{"$f":"IF(AND(YEAR(JulM+23)=$N$2,MONTH(JulM+23)=7),JulM+23, \"\")","v":"2025-07-22"},{"$f":"IF(AND(YEAR(JulM+24)=$N$2,MONTH(JulM+24)=7),JulM+24, \"\")","v":"2025-07-23"},{"$f":"IF(AND(YEAR(JulM+25)=$N$2,MONTH(JulM+25)=7),JulM+25, \"\")","v":"2025-07-24"},{"$f":"IF(AND(YEAR(JulM+26)=$N$2,MONTH(JulM+26)=7),JulM+26, \"\")","v":"2025-07-25"},{"$f":"IF(AND(YEAR(JulM+27)=$N$2,MONTH(JulM+27)=7),JulM+27, \"\")","v":"2025-07-26"},null,{"$f":"IF(AND(YEAR(AugM+21)=$N$2,MONTH(AugM+21)=8),AugM+21, \"\")","v":"2025-08-17"},{"$f":"IF(AND(YEAR(AugM+22)=$N$2,MONTH(AugM+22)=8),AugM+22, \"\")","v":"2025-08-18"},{"$f":"IF(AND(YEAR(AugM+23)=$N$2,MONTH(AugM+23)=8),AugM+23, \"\")","v":"2025-08-19"},{"$f":"IF(AND(YEAR(AugM+24)=$N$2,MONTH(AugM+24)=8),AugM+24, \"\")","v":"2025-08-20"},{"$f":"IF(AND(YEAR(AugM+25)=$N$2,MONTH(AugM+25)=8),AugM+25, \"\")","v":"2025-08-21"},{"$f":"IF(AND(YEAR(AugM+26)=$N$2,MONTH(AugM+26)=8),AugM+26, \"\")","v":"2025-08-22"},{"$f":"IF(AND(YEAR(AugM+27)=$N$2,MONTH(AugM+27)=8),AugM+27, \"\")","v":"2025-08-23"},null,null,null,null,"Columbus Day",null,null,null,{"$f":"AQ19","v":"2025-10-13"},{"$f":"(DATE(CA6,10,1)+IF(2<WEEKDAY(DATE(CA6,10,1)),7-WEEKDAY(DATE(CA6,10,1))+2,2-WEEKDAY(DATE(CA6,10,1)))+((2-1)*7))","v":"2025-10-13"},null,{"$f":"AQ19","v":"2025-10-13"},null,null,null,null,null,null,null,null,"2017 Election Day, Primary","None","None",null,2017,{"$f":"BF19&\"a\"","v":"2017a"},"Christmas Day  (Washington Birthday)","2017-12-25","2017-12-25",null,2025,"2025-04-18","2025-04-18","2025-01-01","2025-01-01","2025-07-04","2025-07-04","2025-11-11","2025-11-11"]
[null,null,{"$f":"IF(AND(YEAR(MayM+28)=$N$2,MONTH(MayM+28)=5),MayM+28, \"\")","v":"2025-05-25"},{"$f":"IF(AND(YEAR(MayM+29)=$N$2,MONTH(MayM+29)=5),MayM+29, \"\")","v":"2025-05-26"},{"$f":"IF(AND(YEAR(MayM+30)=$N$2,MONTH(MayM+30)=5),MayM+30, \"\")","v":"2025-05-27"},{"$f":"IF(AND(YEAR(MayM+31)=$N$2,MONTH(MayM+31)=5),MayM+31, \"\")","v":"2025-05-28"},{"$f":"IF(AND(YEAR(MayM+32)=$N$2,MONTH(MayM+32)=5),MayM+32, \"\")","v":"2025-05-29"},{"$f":"IF(AND(YEAR(MayM+33)=$N$2,MONTH(MayM+33)=5),MayM+33, \"\")","v":"2025-05-30"},{"$f":"IF(AND(YEAR(MayM+34)=$N$2,MONTH(MayM+34)=5),MayM+34, \"\")","v":"2025-05-31"},null,{"$f":"IF(AND(YEAR(JunM+28)=$N$2,MONTH(JunM+28)=6),JunM+28, \"\")","v":"2025-06-29"},{"$f":"IF(AND(YEAR(JunM+29)=$N$2,MONTH(JunM+29)=6),JunM+29, \"\")","v":"2025-06-30"},{"$f":"IF(AND(YEAR(JunM+30)=$N$2,MONTH(JunM+30)=6),JunM+30, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+31)=$N$2,MONTH(JunM+31)=6),JunM+31, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+32)=$N$2,MONTH(JunM+32)=6),JunM+32, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+33)=$N$2,MONTH(JunM+33)=6),JunM+33, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+34)=$N$2,MONTH(JunM+34)=6),JunM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(JulM+28)=$N$2,MONTH(JulM+28)=7),JulM+28, \"\")","v":"2025-07-27"},{"$f":"IF(AND(YEAR(JulM+29)=$N$2,MONTH(JulM+29)=7),JulM+29, \"\")","v":"2025-07-28"},{"$f":"IF(AND(YEAR(JulM+30)=$N$2,MONTH(JulM+30)=7),JulM+30, \"\")","v":"2025-07-29"},{"$f":"IF(AND(YEAR(JulM+31)=$N$2,MONTH(JulM+31)=7),JulM+31, \"\")","v":"2025-07-30"},{"$f":"IF(AND(YEAR(JulM+32)=$N$2,MONTH(JulM+32)=7),JulM+32, \"\")","v":"2025-07-31"},{"$f":"IF(AND(YEAR(JulM+33)=$N$2,MONTH(JulM+33)=7),JulM+33, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+34)=$N$2,MONTH(JulM+34)=7),JulM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(AugM+28)=$N$2,MONTH(AugM+28)=8),AugM+28, \"\")","v":"2025-08-24"},{"$f":"IF(AND(YEAR(AugM+29)=$N$2,MONTH(AugM+29)=8),AugM+29, \"\")","v":"2025-08-25"},{"$f":"IF(AND(YEAR(AugM+30)=$N$2,MONTH(AugM+30)=8),AugM+30, \"\")","v":"2025-08-26"},{"$f":"IF(AND(YEAR(AugM+31)=$N$2,MONTH(AugM+31)=8),AugM+31, \"\")","v":"2025-08-27"},{"$f":"IF(AND(YEAR(AugM+32)=$N$2,MONTH(AugM+32)=8),AugM+32, \"\")","v":"2025-08-28"},{"$f":"IF(AND(YEAR(AugM+33)=$N$2,MONTH(AugM+33)=8),AugM+33, \"\")","v":"2025-08-29"},{"$f":"IF(AND(YEAR(AugM+34)=$N$2,MONTH(AugM+34)=8),AugM+34, \"\")","v":"2025-08-30"},null,null,null,null,"Fall Break",null,{"$f":"(DATE(CA6,10,1)+IF(2<WEEKDAY(DATE(CA6,10,1)),7-WEEKDAY(DATE(CA6,10,1))+2,2-WEEKDAY(DATE(CA6,10,1)))+((2-1)*7)+7)","v":"2025-10-20"},null,"Until",{"$f":"AN20+1","v":"2025-10-21"},null,null,null,null,null,null,null,null,null,null,"2017 Election Day, General","None","None",null,2017,{"$f":"BF20&\"b\"","v":"2017b"},"Christmas Day  ","2017-12-26","2017-12-26",null,2026,"2026-04-03","2026-04-03","2026-01-01","2026-01-01","2026-07-03","2026-07-03","2026-11-11","2026-11-11"]
[null,null,{"$f":"IF(AND(YEAR(MayM+35)=$N$2,MONTH(MayM+35)=5),MayM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+36)=$N$2,MONTH(MayM+36)=5),MayM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+37)=$N$2,MONTH(MayM+37)=5),MayM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+38)=$N$2,MONTH(MayM+38)=5),MayM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+39)=$N$2,MONTH(MayM+39)=5),MayM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+40)=$N$2,MONTH(MayM+40)=5),MayM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(MayM+41)=$N$2,MONTH(MayM+41)=5),MayM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(JunM+35)=$N$2,MONTH(JunM+35)=6),JunM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+36)=$N$2,MONTH(JunM+36)=6),JunM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+37)=$N$2,MONTH(JunM+37)=6),JunM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+38)=$N$2,MONTH(JunM+38)=6),JunM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+39)=$N$2,MONTH(JunM+39)=6),JunM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+40)=$N$2,MONTH(JunM+40)=6),JunM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(JunM+41)=$N$2,MONTH(JunM+41)=6),JunM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(JulM+35)=$N$2,MONTH(JulM+35)=7),JulM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+36)=$N$2,MONTH(JulM+36)=7),JulM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+37)=$N$2,MONTH(JulM+37)=7),JulM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+38)=$N$2,MONTH(JulM+38)=7),JulM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+39)=$N$2,MONTH(JulM+39)=7),JulM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+40)=$N$2,MONTH(JulM+40)=7),JulM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(JulM+41)=$N$2,MONTH(JulM+41)=7),JulM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(AugM+35)=$N$2,MONTH(AugM+35)=8),AugM+35, \"\")","v":"2025-08-31"},{"$f":"IF(AND(YEAR(AugM+36)=$N$2,MONTH(AugM+36)=8),AugM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+37)=$N$2,MONTH(AugM+37)=8),AugM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+38)=$N$2,MONTH(AugM+38)=8),AugM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+39)=$N$2,MONTH(AugM+39)=8),AugM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+40)=$N$2,MONTH(AugM+40)=8),AugM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(AugM+41)=$N$2,MONTH(AugM+41)=8),AugM+41, \"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2018 Election Day, Primary","2018-05-08","2018-05-08",null,2018,{"$f":"BF21&\"a\"","v":"2018a"},"Christmas Day  (Washington Birthday)","2018-12-24","2018-12-24",null,2027,"2027-03-26","2027-03-26","2027-01-01","2027-01-01","2027-07-05","2027-07-05","2027-11-11","2027-11-11"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Veterans Day",null,null,null,{"$f":"AQ22","v":"2025-11-11"},{"$f":"IF($CD$5=1,VLOOKUP($CA$6,BL1:BT60,8,FALSE),DATE(CA6,11,11))","v":"2025-11-11"},null,{"$f":"AQ22","v":"2025-11-11"},null,null,null,null,null,null,null,null,"2018 Election Day, General","2018-11-06","2018-11-06",null,2018,{"$f":"BF22&\"b\"","v":"2018b"},"Christmas Day  ","2018-12-25","2018-12-25",null,2028,"2028-04-14","2028-04-14","2027-12-31","2027-12-31","2028-07-04","2028-07-04","2028-11-10","2028-11-10"]
[null,null,"September",null,null,null,null,null,null,null,"October",null,null,null,null,null,null,null,"November",null,null,null,null,null,null,null,"December",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2019 Election Day, Primary","2019-05-07","2019-05-07",null,2019,{"$f":"BF23&\"a\"","v":"2019a"},"Christmas Day  (Washington Birthday)","2019-12-24","2019-12-24",null,2029,"2029-03-30","2029-03-30","2029-01-01","2029-01-01","2029-07-04","2029-07-04","2029-11-12","2029-11-12"]
[null,null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,"Su","Mo","Tu","We","Th","Fr","Sa",null,null,null,null,"Thanksgiving Day",null,null,null,{"$f":"AQ24","v":"2025-11-27"},{"$f":"DATE(CA6,11,1)+IF(5<WEEKDAY(DATE(CA6,11,1)),7-WEEKDAY(DATE(CA6,11,1))+5,5-WEEKDAY(DATE(CA6,11,1)))+((3)*7)","v":"2025-11-27"},null,null,null,null,null,null,null,null,null,null,"2019 Election Day, General","2019-11-05","2019-11-05",null,2019,{"$f":"BF24&\"b\"","v":"2019b"},"Christmas Day  ","2019-12-25","2019-12-25",null,2030,"2030-04-19","2030-04-19","2030-01-01","2030-01-01","2030-07-04","2030-07-04","2030-11-11","2030-11-11"]
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[null,null,{"$f":"IF(AND(YEAR(SepM+14)=$N$2,MONTH(SepM+14)=9),SepM+14, \"\")","v":"2025-09-14"},{"$f":"IF(AND(YEAR(SepM+15)=$N$2,MONTH(SepM+15)=9),SepM+15, \"\")","v":"2025-09-15"},{"$f":"IF(AND(YEAR(SepM+16)=$N$2,MONTH(SepM+16)=9),SepM+16, \"\")","v":"2025-09-16"},{"$f":"IF(AND(YEAR(SepM+17)=$N$2,MONTH(SepM+17)=9),SepM+17, \"\")","v":"2025-09-17"},{"$f":"IF(AND(YEAR(SepM+18)=$N$2,MONTH(SepM+18)=9),SepM+18, \"\")","v":"2025-09-18"},{"$f":"IF(AND(YEAR(SepM+19)=$N$2,MONTH(SepM+19)=9),SepM+19, \"\")","v":"2025-09-19"},{"$f":"IF(AND(YEAR(SepM+20)=$N$2,MONTH(SepM+20)=9),SepM+20, \"\")","v":"2025-09-20"},null,{"$f":"IF(AND(YEAR(OctM+14)=$N$2,MONTH(OctM+14)=10),OctM+14, \"\")","v":"2025-10-12"},{"$f":"IF(AND(YEAR(OctM+15)=$N$2,MONTH(OctM+15)=10),OctM+15, \"\")","v":"2025-10-13"},{"$f":"IF(AND(YEAR(OctM+16)=$N$2,MONTH(OctM+16)=10),OctM+16, \"\")","v":"2025-10-14"},{"$f":"IF(AND(YEAR(OctM+17)=$N$2,MONTH(OctM+17)=10),OctM+17, \"\")","v":"2025-10-15"},{"$f":"IF(AND(YEAR(OctM+18)=$N$2,MONTH(OctM+18)=10),OctM+18, \"\")","v":"2025-10-16"},{"$f":"IF(AND(YEAR(OctM+19)=$N$2,MONTH(OctM+19)=10),OctM+19, \"\")","v":"2025-10-17"},{"$f":"IF(AND(YEAR(OctM+20)=$N$2,MONTH(OctM+20)=10),OctM+20, \"\")","v":"2025-10-18"},null,{"$f":"IF(AND(YEAR(NovM+14)=$N$2,MONTH(NovM+14)=11),NovM+14, \"\")","v":"2025-11-09"},{"$f":"IF(AND(YEAR(NovM+15)=$N$2,MONTH(NovM+15)=11),NovM+15, \"\")","v":"2025-11-10"},{"$f":"IF(AND(YEAR(NovM+16)=$N$2,MONTH(NovM+16)=11),NovM+16, \"\")","v":"2025-11-11"},{"$f":"IF(AND(YEAR(NovM+17)=$N$2,MONTH(NovM+17)=11),NovM+17, \"\")","v":"2025-11-12"},{"$f":"IF(AND(YEAR(NovM+18)=$N$2,MONTH(NovM+18)=11),NovM+18, \"\")","v":"2025-11-13"},{"$f":"IF(AND(YEAR(NovM+19)=$N$2,MONTH(NovM+19)=11),NovM+19, \"\")","v":"2025-11-14"},{"$f":"IF(AND(YEAR(NovM+20)=$N$2,MONTH(NovM+20)=11),NovM+20, \"\")","v":"2025-11-15"},null,{"$f":"IF(AND(YEAR(DecM+14)=$N$2,MONTH(DecM+14)=12),DecM+14, \"\")","v":"2025-12-14"},{"$f":"IF(AND(YEAR(DecM+15)=$N$2,MONTH(DecM+15)=12),DecM+15, \"\")","v":"2025-12-15"},{"$f":"IF(AND(YEAR(DecM+16)=$N$2,MONTH(DecM+16)=12),DecM+16, \"\")","v":"2025-12-16"},{"$f":"IF(AND(YEAR(DecM+17)=$N$2,MONTH(DecM+17)=12),DecM+17, \"\")","v":"2025-12-17"},{"$f":"IF(AND(YEAR(DecM+18)=$N$2,MONTH(DecM+18)=12),DecM+18, \"\")","v":"2025-12-18"},{"$f":"IF(AND(YEAR(DecM+19)=$N$2,MONTH(DecM+19)=12),DecM+19, \"\")","v":"2025-12-19"},{"$f":"IF(AND(YEAR(DecM+20)=$N$2,MONTH(DecM+20)=12),DecM+20, \"\")","v":"2025-12-20"},null,null,null,null,"Christmas Day  ",null,null,null,{"$f":"AQ27","v":"2025-12-25"},{"$f":"IF($CD$5=1,VLOOKUP($AZ$26,BG1:BI60,3,FALSE),DATE(CA6,12,25))","v":"2025-12-25"},null,{"$f":"AQ27","v":"2025-12-25"},null,null,null,null,null,null,null,null,"2021 Election Day, Primary","2021-05-04","2021-05-04",null,2021,{"$f":"BF27&\"a\"","v":"2021a"},"Christmas Day  (Washington Birthday)","2021-12-23","2021-12-23",null,2033,"2033-04-15","2033-04-15","2032-12-31","2032-12-31","2033-07-04","2033-07-04","2033-11-11","2033-11-11"]
[null,null,{"$f":"IF(AND(YEAR(SepM+21)=$N$2,MONTH(SepM+21)=9),SepM+21, \"\")","v":"2025-09-21"},{"$f":"IF(AND(YEAR(SepM+22)=$N$2,MONTH(SepM+22)=9),SepM+22, \"\")","v":"2025-09-22"},{"$f":"IF(AND(YEAR(SepM+23)=$N$2,MONTH(SepM+23)=9),SepM+23, \"\")","v":"2025-09-23"},{"$f":"IF(AND(YEAR(SepM+24)=$N$2,MONTH(SepM+24)=9),SepM+24, \"\")","v":"2025-09-24"},{"$f":"IF(AND(YEAR(SepM+25)=$N$2,MONTH(SepM+25)=9),SepM+25, \"\")","v":"2025-09-25"},{"$f":"IF(AND(YEAR(SepM+26)=$N$2,MONTH(SepM+26)=9),SepM+26, \"\")","v":"2025-09-26"},{"$f":"IF(AND(YEAR(SepM+27)=$N$2,MONTH(SepM+27)=9),SepM+27, \"\")","v":"2025-09-27"},null,{"$f":"IF(AND(YEAR(OctM+21)=$N$2,MONTH(OctM+21)=10),OctM+21, \"\")","v":"2025-10-19"},{"$f":"IF(AND(YEAR(OctM+22)=$N$2,MONTH(OctM+22)=10),OctM+22, \"\")","v":"2025-10-20"},{"$f":"IF(AND(YEAR(OctM+23)=$N$2,MONTH(OctM+23)=10),OctM+23, \"\")","v":"2025-10-21"},{"$f":"IF(AND(YEAR(OctM+24)=$N$2,MONTH(OctM+24)=10),OctM+24, \"\")","v":"2025-10-22"},{"$f":"IF(AND(YEAR(OctM+25)=$N$2,MONTH(OctM+25)=10),OctM+25, \"\")","v":"2025-10-23"},{"$f":"IF(AND(YEAR(OctM+26)=$N$2,MONTH(OctM+26)=10),OctM+26, \"\")","v":"2025-10-24"},{"$f":"IF(AND(YEAR(OctM+27)=$N$2,MONTH(OctM+27)=10),OctM+27, \"\")","v":"2025-10-25"},null,{"$f":"IF(AND(YEAR(NovM+21)=$N$2,MONTH(NovM+21)=11),NovM+21, \"\")","v":"2025-11-16"},{"$f":"IF(AND(YEAR(NovM+22)=$N$2,MONTH(NovM+22)=11),NovM+22, \"\")","v":"2025-11-17"},{"$f":"IF(AND(YEAR(NovM+23)=$N$2,MONTH(NovM+23)=11),NovM+23, \"\")","v":"2025-11-18"},{"$f":"IF(AND(YEAR(NovM+24)=$N$2,MONTH(NovM+24)=11),NovM+24, \"\")","v":"2025-11-19"},{"$f":"IF(AND(YEAR(NovM+25)=$N$2,MONTH(NovM+25)=11),NovM+25, \"\")","v":"2025-11-20"},{"$f":"IF(AND(YEAR(NovM+26)=$N$2,MONTH(NovM+26)=11),NovM+26, \"\")","v":"2025-11-21"},{"$f":"IF(AND(YEAR(NovM+27)=$N$2,MONTH(NovM+27)=11),NovM+27, \"\")","v":"2025-11-22"},null,{"$f":"IF(AND(YEAR(DecM+21)=$N$2,MONTH(DecM+21)=12),DecM+21, \"\")","v":"2025-12-21"},{"$f":"IF(AND(YEAR(DecM+22)=$N$2,MONTH(DecM+22)=12),DecM+22, \"\")","v":"2025-12-22"},{"$f":"IF(AND(YEAR(DecM+23)=$N$2,MONTH(DecM+23)=12),DecM+23, \"\")","v":"2025-12-23"},{"$f":"IF(AND(YEAR(DecM+24)=$N$2,MONTH(DecM+24)=12),DecM+24, \"\")","v":"2025-12-24"},{"$f":"IF(AND(YEAR(DecM+25)=$N$2,MONTH(DecM+25)=12),DecM+25, \"\")","v":"2025-12-25"},{"$f":"IF(AND(YEAR(DecM+26)=$N$2,MONTH(DecM+26)=12),DecM+26, \"\")","v":"2025-12-26"},{"$f":"IF(AND(YEAR(DecM+27)=$N$2,MONTH(DecM+27)=12),DecM+27, \"\")","v":"2025-12-27"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$CA$6&\"a\"","v":"2025a"},null,"2021 Election Day, General","2021-11-02","2021-11-02",null,2021,{"$f":"BF28&\"b\"","v":"2021b"},"Christmas Day  ","2021-12-24","2021-12-24",null,2034,"2034-04-07","2034-04-07","2034-01-02","2034-01-02","2034-07-04","2034-07-04","2034-11-10","2034-11-10"]
[null,null,{"$f":"IF(AND(YEAR(SepM+28)=$N$2,MONTH(SepM+28)=9),SepM+28, \"\")","v":"2025-09-28"},{"$f":"IF(AND(YEAR(SepM+29)=$N$2,MONTH(SepM+29)=9),SepM+29, \"\")","v":"2025-09-29"},{"$f":"IF(AND(YEAR(SepM+30)=$N$2,MONTH(SepM+30)=9),SepM+30, \"\")","v":"2025-09-30"},{"$f":"IF(AND(YEAR(SepM+31)=$N$2,MONTH(SepM+31)=9),SepM+31, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+32)=$N$2,MONTH(SepM+32)=9),SepM+32, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+33)=$N$2,MONTH(SepM+33)=9),SepM+33, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+34)=$N$2,MONTH(SepM+34)=9),SepM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(OctM+28)=$N$2,MONTH(OctM+28)=10),OctM+28, \"\")","v":"2025-10-26"},{"$f":"IF(AND(YEAR(OctM+29)=$N$2,MONTH(OctM+29)=10),OctM+29, \"\")","v":"2025-10-27"},{"$f":"IF(AND(YEAR(OctM+30)=$N$2,MONTH(OctM+30)=10),OctM+30, \"\")","v":"2025-10-28"},{"$f":"IF(AND(YEAR(OctM+31)=$N$2,MONTH(OctM+31)=10),OctM+31, \"\")","v":"2025-10-29"},{"$f":"IF(AND(YEAR(OctM+32)=$N$2,MONTH(OctM+32)=10),OctM+32, \"\")","v":"2025-10-30"},{"$f":"IF(AND(YEAR(OctM+33)=$N$2,MONTH(OctM+33)=10),OctM+33, \"\")","v":"2025-10-31"},{"$f":"IF(AND(YEAR(OctM+34)=$N$2,MONTH(OctM+34)=10),OctM+34, \"\")","v":""},null,{"$f":"IF(AND(YEAR(NovM+28)=$N$2,MONTH(NovM+28)=11),NovM+28, \"\")","v":"2025-11-23"},{"$f":"IF(AND(YEAR(NovM+29)=$N$2,MONTH(NovM+29)=11),NovM+29, \"\")","v":"2025-11-24"},{"$f":"IF(AND(YEAR(NovM+30)=$N$2,MONTH(NovM+30)=11),NovM+30, \"\")","v":"2025-11-25"},{"$f":"IF(AND(YEAR(NovM+31)=$N$2,MONTH(NovM+31)=11),NovM+31, \"\")","v":"2025-11-26"},{"$f":"IF(AND(YEAR(NovM+32)=$N$2,MONTH(NovM+32)=11),NovM+32, \"\")","v":"2025-11-27"},{"$f":"IF(AND(YEAR(NovM+33)=$N$2,MONTH(NovM+33)=11),NovM+33, \"\")","v":"2025-11-28"},{"$f":"IF(AND(YEAR(NovM+34)=$N$2,MONTH(NovM+34)=11),NovM+34, \"\")","v":"2025-11-29"},null,{"$f":"IF(AND(YEAR(DecM+28)=$N$2,MONTH(DecM+28)=12),DecM+28, \"\")","v":"2025-12-28"},{"$f":"IF(AND(YEAR(DecM+29)=$N$2,MONTH(DecM+29)=12),DecM+29, \"\")","v":"2025-12-29"},{"$f":"IF(AND(YEAR(DecM+30)=$N$2,MONTH(DecM+30)=12),DecM+30, \"\")","v":"2025-12-30"},{"$f":"IF(AND(YEAR(DecM+31)=$N$2,MONTH(DecM+31)=12),DecM+31, \"\")","v":"2025-12-31"},{"$f":"IF(AND(YEAR(DecM+32)=$N$2,MONTH(DecM+32)=12),DecM+32, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+33)=$N$2,MONTH(DecM+33)=12),DecM+33, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+34)=$N$2,MONTH(DecM+34)=12),DecM+34, \"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$CA$6&\"b\"","v":"2025b"},null,"2022 Election Day, Primary","2022-05-03","2022-05-03",null,2022,{"$f":"BF29&\"a\"","v":"2022a"},"Christmas Day  (Washington Birthday)","2022-12-23","2022-12-23",null,2035,"2035-03-23","2035-03-23","2035-01-01","2035-01-01","2035-07-04","2035-07-04","2035-11-12","2035-11-12"]
[null,null,{"$f":"IF(AND(YEAR(SepM+35)=$N$2,MONTH(SepM+35)=9),SepM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+36)=$N$2,MONTH(SepM+36)=9),SepM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+37)=$N$2,MONTH(SepM+37)=9),SepM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+38)=$N$2,MONTH(SepM+38)=9),SepM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+39)=$N$2,MONTH(SepM+39)=9),SepM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+40)=$N$2,MONTH(SepM+40)=9),SepM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(SepM+41)=$N$2,MONTH(SepM+41)=9),SepM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(OctM+35)=$N$2,MONTH(OctM+35)=10),OctM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+36)=$N$2,MONTH(OctM+36)=10),OctM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+37)=$N$2,MONTH(OctM+37)=10),OctM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+38)=$N$2,MONTH(OctM+38)=10),OctM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+39)=$N$2,MONTH(OctM+39)=10),OctM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+40)=$N$2,MONTH(OctM+40)=10),OctM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(OctM+41)=$N$2,MONTH(OctM+41)=10),OctM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(NovM+35)=$N$2,MONTH(NovM+35)=11),NovM+35, \"\")","v":"2025-11-30"},{"$f":"IF(AND(YEAR(NovM+36)=$N$2,MONTH(NovM+36)=11),NovM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(NovM+37)=$N$2,MONTH(NovM+37)=11),NovM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(NovM+38)=$N$2,MONTH(NovM+38)=11),NovM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(NovM+39)=$N$2,MONTH(NovM+39)=11),NovM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(NovM+40)=$N$2,MONTH(NovM+40)=11),NovM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(NovM+41)=$N$2,MONTH(NovM+41)=11),NovM+41, \"\")","v":""},null,{"$f":"IF(AND(YEAR(DecM+35)=$N$2,MONTH(DecM+35)=12),DecM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+36)=$N$2,MONTH(DecM+36)=12),DecM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+37)=$N$2,MONTH(DecM+37)=12),DecM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+38)=$N$2,MONTH(DecM+38)=12),DecM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+39)=$N$2,MONTH(DecM+39)=12),DecM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+40)=$N$2,MONTH(DecM+40)=12),DecM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(DecM+41)=$N$2,MONTH(DecM+41)=12),DecM+41, \"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2022 Election Day, General","2022-11-08","2022-11-08",null,2022,{"$f":"BF30&\"b\"","v":"2022b"},"Christmas Day  ","2022-12-26","2022-12-26"]
[null,null,null,null,null,"Holiday",null,null,null,"School Break",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2023 Election Day, Primary","2023-05-02","2023-05-02",null,2023,{"$f":"BF31&\"a\"","v":"2023a"},"Christmas Day  (Washington Birthday)","2023-12-25","2023-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2023 Election Day, General","2023-11-07","2023-11-07",null,2023,{"$f":"BF32&\"b\"","v":"2023b"},"Christmas Day  ","2023-12-26","2023-12-26"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2024 Election Day, Primary","2024-05-07","2024-05-07",null,2024,{"$f":"BF33&\"a\"","v":"2024a"},"Christmas Day  (Washington Birthday)","2024-12-24","2024-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2024 Election Day, General","2024-11-05","2024-11-05",null,2024,{"$f":"BF34&\"b\"","v":"2024b"},"Christmas Day  ","2014-12-25","2014-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2025 Election Day, Primary","2025-05-06","2025-05-06",null,2025,{"$f":"BF35&\"a\"","v":"2025a"},"Christmas Day  (Washington Birthday)","2025-12-24","2025-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"DATE(CA6,10,1)+IF(2<WEEKDAY(DATE(CA6,10,1)),7-WEEKDAY(DATE(CA6,10,1))+2,2-WEEKDAY(DATE(CA6,10,1)))+((2-1)*7)","v":"2025-10-13"},null,null,null,null,2026,"2026-03-15",null,null,null,null,null,null,null,null,null,null,"2025 Election Day, General","2025-11-04","2025-11-04",null,2025,{"$f":"BF36&\"b\"","v":"2025b"},"Christmas Day  ","2025-12-25","2025-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2023,"2026-03-12",null,null,null,null,null,null,null,null,null,null,"2026 Election Day, Primary","2026-05-05","2026-05-05",null,2026,{"$f":"BF37&\"a\"","v":"2026a"},"Christmas Day  (Washington Birthday)","2026-12-24","2026-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2026 Election Day, General","2026-11-03","2026-11-03",null,2026,{"$f":"BF38&\"b\"","v":"2026b"},"Christmas Day  ","2026-12-25","2026-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2027 Election Day, Primary","2027-05-04","2027-05-04",null,2027,{"$f":"BF39&\"a\"","v":"2027a"},"Christmas Day  (Washington Birthday)","2027-12-23","2027-12-23"]
[null,null,{"$f":"IF(AND(YEAR(FebM+35)=$N$2,MONTH(FebM+35)=2),FebM+35, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+36)=$N$2,MONTH(FebM+36)=2),FebM+36, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+37)=$N$2,MONTH(FebM+37)=2),FebM+37, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+38)=$N$2,MONTH(FebM+38)=2),FebM+38, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+39)=$N$2,MONTH(FebM+39)=2),FebM+39, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+40)=$N$2,MONTH(FebM+40)=2),FebM+40, \"\")","v":""},{"$f":"IF(AND(YEAR(FebM+41)=$N$2,MONTH(FebM+41)=2),FebM+41, \"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2027 Election Day, General","2027-11-02","2027-11-02",null,2027,{"$f":"BF40&\"b\"","v":"2027b"},"Christmas Day  ","2027-12-24","2027-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2028 Election Day, Primary","2028-05-02","2028-05-02",null,2028,{"$f":"BF41&\"a\"","v":"2028a"},"Christmas Day  (Washington Birthday)","2028-12-25","2028-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2028 Election Day, General","2028-11-07","2028-11-07",null,2028,{"$f":"BF42&\"b\"","v":"2028b"},"Christmas Day  ","2028-12-26","2028-12-26"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2029 Election Day, Primary","2029-05-08","2029-05-08",null,2029,{"$f":"BF43&\"a\"","v":"2029a"},"Christmas Day  (Washington Birthday)","2029-12-24","2029-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2029 Election Day, General","2029-11-06","2029-11-06",null,2029,{"$f":"BF44&\"b\"","v":"2029b"},"Christmas Day  ","2029-12-25","2029-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2030 Election Day, Primary","2030-05-07","2030-05-07",null,2030,{"$f":"BF45&\"a\"","v":"2030a"},"Christmas Day  (Washington Birthday)","2030-12-24","2030-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2030 Election Day, General","2030-11-05","2030-11-05",null,2030,{"$f":"BF46&\"b\"","v":"2030b"},"Christmas Day  ","2030-12-25","2030-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2031 Election Day, Primary","2031-05-06","2031-05-06",null,2031,{"$f":"BF47&\"a\"","v":"2031a"},"Christmas Day  (Washington Birthday)","2031-12-24","2031-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2031 Election Day, General","2031-11-04","2031-11-04",null,2031,{"$f":"BF48&\"b\"","v":"2031b"},"Christmas Day  ","2031-12-25","2031-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2032 Election Day, Primary","2032-05-04","2032-05-04",null,2032,{"$f":"BF49&\"a\"","v":"2032a"},"Christmas Day  (Washington Birthday)","2032-12-23","2032-12-23"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2032 Election Day, General","2032-11-02","2032-11-02",null,2032,{"$f":"BF50&\"b\"","v":"2032b"},"Christmas Day  ","2032-12-24","2032-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2033 Election Day, Primary","2033-05-03","2033-05-03",null,2033,{"$f":"BF51&\"a\"","v":"2033a"},"Christmas Day  (Washington Birthday)","2033-12-23","2033-12-23"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2033 Election Day, General","2033-11-08","2033-11-08",null,2033,{"$f":"BF52&\"b\"","v":"2033b"},"Christmas Day  ","2033-12-26","2033-12-26"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2034 Election Day, Primary","2034-05-02","2034-05-02",null,2034,{"$f":"BF53&\"a\"","v":"2034a"},"Christmas Day  (Washington Birthday)","2034-12-25","2034-12-25"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2034 Election Day, General","2034-11-07","2034-11-07",null,2034,{"$f":"BF54&\"b\"","v":"2034b"},"Christmas Day  ","2034-12-26","2034-12-26"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2035 Election Day, Primary","2035-05-08","2035-05-08",null,2035,{"$f":"BF55&\"a\"","v":"2035a"},"Christmas Day  (Washington Birthday)","2035-12-24","2035-12-24"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2035 Election Day, General","2034-11-07","2034-11-07",null,2035,{"$f":"BF56&\"b\"","v":"2035b"},"Christmas Day  ","2035-12-25","2035-12-25"]

{"sheet":"5) Logic","index":5,"n_rows":69,"n_cols":31,"rows_kept":69,"cut":false,"hidden":false,"merged":[[7,3,7,4],[7,5,7,8],[7,11,7,12],[7,13,7,17],[8,3,8,4],[8,5,8,8],[8,11,8,12],[8,13,8,17]]}
[]
[null,null,null,null,null,null," Logical Equivalence: When two statements have identical last column in the truth tables",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Yes",null,null,"No","No",null,"T",null,null,"No"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No",null,null,"Yes","Yes",null,"F",null,null,"Yes"]
[null,null,"Tautology  =  valid argument: the elements of the last column are all T",null,null,null,null,null,null,null,null,"Contradiction: The elements of the last column are all F"]
[]
[]
[]
[null,null,"Conjunction","∧  (And)",null,"it is true only when both are true",null,null,null,null,"Conditional","→       (If...then)",null,"it is always true unless the first is T and the second is F"]
[null,null,"Disjunction","∨  (Or)",null,"it is true when either one or both are true",null,null,null,null,"Biconditional","↔    (If and only if)",null,"it is  true when both are true or both are false"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"T"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"F"]
[]
[]
[null,null,null,null,"Not p","Not q","p And q","p Or q","p",null,null,null,"if p then q","if q then p","if and only if ","p","(p → q)","(p → q)"]
[null,null,"p","q","¬ p","¬ q","p ∧ q","p ∨ q","∨ (p ∧ q)",null,"p","q","p → q","q → p","p ↔ q","∧ (q → p)","∧ (q → p)","∨  (q → p)"]
[null,null,"T","T","F","F","T","T","T",null,"T","T","T","T","T","T","T","T"]
[null,null,"T","F","F","T","F","T","T",null,"T","F","F","T","F","T","F","T"]
[null,null,"F","T","T","F","F","T","F",null,"F","T","T","F","F","F","F","T"]
[null,null,"F","F","T","T","F","F","F",null,"F","F","T","T","T","F","T","T"]
[]
[]
[]
[]
[null,null,"A) Fill the following truth table (errors will be in red)",null,null,null,null,null,"(¬ p ∧ q)",null,"(¬ p ∧ q)",null,null," q ",null,null,"(¬ p → q)","(¬ p → q)"]
[null,null,"p","q","¬p","¬q","¬ p ∧ q","p ∨ ¬ q"," ∧ (p ∨ ¬ q)","¬ p ∧ ¬ q","V (¬ p ∧ ¬ q)","¬ p →  q","q → p"," ∧  (¬ p →  q)","¬ p ↔ q","p ↔ ¬ p","V  (q → p)","∧  ( q → p)"]
[null,null,"T","T"]
[null,null,"T","F"]
[null,null,"F","T"]
[null,null,"F","F"]
[null,null,"Highlight? Yes, No",null,null,null,null,null,null,null,null,"Highlight? Yes, No",null,null,"Highlight? Yes, No"]
[null,null,"Yes","Yes","No","No","No","No",null,"No",null,"No","Yes",null,"No","No"]
[]
[]
[]
[]
[]
[]
[null,null,"B) Fill the following truth table (errors will be in red)",null,null,null,null,null,"(p ∨ q)",null,null,null,null," q ",null,null,"(p → r)","(p → r)"]
[null,null,"p","q","r","p ∧ q","p ∨ q","p ∧ r"," ∧ (p ∧ r)","p → q","p → r","r → q","q → r"," ∧  ( p → q)","p ↔ r","q↔ r","∧ (r → q)","V (r → q)"]
[null,null,"T","T","T"]
[null,null,"T","T","F"]
[null,null,"T","F","T"]
[null,null,"T","F","F"]
[null,null,"F","T","T"]
[null,null,"F","T","F"]
[null,null,"F","F","T"]
[null,null,"F","F","F"]
[null,null,"Highlight? Yes, No",null,null,null,null,null,null,"Highlight? Yes, No",null,null,null,null,"Highlight? Yes, No",null,null,{"$f":"IF(COUNTIF(R40:R47,\"T\")=8,\"Tautology\",\"\")","v":""}]
[null,null,"Yes","Yes","Yes","No","No","No",null,"No","No","No","No",null,"No","No",null,{"$f":"IF(COUNTIF(R40:R47,\"T\")=8,\"Valid Argument\",\"\")","v":""}]
[]
[null,null,null,null,null,null,null,null,"(¬ p ∧ q)",null,null,null,null,"(¬ p ∧ ¬ q)",null,null,"(¬ p ∧ q)","(¬ p → q)"]
[null,null,"p","q","¬p","¬q","¬ p ∧ q","p ∨ ¬ q"," ∧ (p ∨ ¬ q)","¬ p ∧ ¬ q","¬ p → q","¬ p →  q","q → p","(¬ q → p)","¬ p ↔ q","p ↔ ¬ p","V (¬ p ∨ ¬ q)","∧  (¬ q → p)"]
[null,null,"T","T","F","F","F","T","F","F","F","T","T","T","F","F","T","T"]
[null,null,"T","F","F","T","F","T","F","F","F","T","T","F","T","F","T","T"]
[null,null,"F","T","T","F","T","F","F","F","T","T","F","T","T","F","T","F"]
[null,null,"F","F","T","T","F","T","F","T","T","F","T","F","F","F","T","F"]
[null,null,4,4,4,4,4,4,4,4,4,4,4,4,4,4]
[]
[null,null,null,null,null,null,null,null,"(p ∨ q)",null,null,null,null,"p → ",null,null,"(p → r)","(p → r)"]
[null,null,"p","q","r","p ∧ q","p ∨ q","p ∧ r"," ∧ (p ∧ r)","p → q","p → r","r → q","q → r"," (q → r)","p ↔ r","q↔ r","∧ (r → q)","V (r → q)"]
[null,null,"T","T","T","T","T","T","T","T","T","T","T","T","T","T","T","T"]
[null,null,"T","T","F","T","T","F","F","T","F","T","F","T","F","F","F","T"]
[null,null,"T","F","T","F","T","T","T","F","T","F","T","F","T","F","F","T"]
[null,null,"T","F","F","F","T","F","F","F","F","T","T","F","F","T","F","T"]
[null,null,"F","T","T","F","T","F","F","T","T","T","T","T","F","T","T","T"]
[null,null,"F","T","F","F","T","F","F","T","T","T","F","T","T","F","T","T"]
[null,null,"F","F","T","F","F","F","F","T","T","F","T","F","F","F","F","T"]
[null,null,"F","F","F","F","F","F","F","T","T","T","T","F","T","T","T","T"]
[null,null,8,8,8,8,8,8,8,8,8,8,8,8,8,8]

{"sheet":"6) Calc","index":6,"n_rows":33,"n_cols":75,"rows_kept":33,"cut":false,"hidden":false,"merged":[[26,24,26,25],[21,24,21,25],[22,24,22,25],[23,24,23,25],[21,28,21,29],[9,44,9,46],[9,30,9,31],[9,25,9,27],[10,25,10,27],[10,30,10,31],[28,8,28,9],[31,16,31,17],[31,18,31,19],[31,20,31,21],[29,7,29,9],[29,16,29,17],[29,18,29,19],[29,20,29,21],[30,7,30,9],[30,16,30,17],[30,18,30,19],[30,20,30,21],[27,16,27,17],[27,18,27,19],[27,20,27,21],[28,16,28,17],[28,18,28,19],[28,20,28,21],[25,16,25,17],[25,18,25,19],[25,20,25,21],[26,5,26,7],[26,10,26,11],[26,16,26,17],[26,18,26,19],[26,20,26,21],[24,16,24,17],[24,18,24,19],[24,20,24,21],[23,16,23,17],[20,5,20,7],[21,16,21,17],[21,18,21,19],[21,20,21,21],[22,16,22,17],[22,18,22,19],[22,20,22,21],[23,18,23,19],[23,20,23,21],[17,16,17,17],[17,18,17,19],[17,20,17,21],[18,5,18,6],[18,16,18,17],[18,18,18,19],[18,20,18,21],[19,16,19,17],[19,18,19,19],[19,20,19,21],[20,10,20,11],[20,16,20,17],[20,18,20,19],[20,20,20,21],[9,8,9,10],[14,1,14,24],[15,16,15,17],[15,18,15,19],[15,20,15,21],[15,3,16,8],[16,16,16,17],[16,18,16,19],[16,20,16,21],[9,19,9,21],[7,65,7,66],[4,1,4,2],[4,13,4,14],[8,1,8,2],[8,13,8,14],[4,7,4,9],[4,19,4,21],[28,28,28,29],[22,28,22,29],[31,24,31,25],[15,24,15,25],[27,24,27,25],[28,24,28,25],[29,24,29,25],[30,24,30,25],[24,24,24,25],[25,24,25,25],[16,24,16,25],[17,24,17,25],[18,24,18,25],[19,24,19,25],[20,24,20,25],[27,28,27,29]]}
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Permutation ",null,null,null,null,"Combination "]
[null,null,"Enter in the Green cells only. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"n =","r =",null,"Ans",null,"n =","r =","Ans"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(Z3=\"\",Z3=\"\",),\"\",PERMUT(Y3,Z3))","v":""},false,null,null,{"$f":"IF(OR(AE3=\"\",AE3=\"\",),\"\",COMBIN(AD3,AE3))","v":""},false,null,null,null,null,null,{"$f":"IF(AC3=TRUE,AB3,0)","v":0},{"$f":"IF(AC3=FALSE,1,IF(AC3=TRUE,IF(AB3=\"\",1,AB3)))","v":1},null,{"$f":"IF(AG3=TRUE,AF3,0)","v":0},{"$f":"IF(AG3=FALSE,1,IF(AG3=TRUE,IF(AF3=\"\",1,AF3)))","v":1},null,"Sum"]
[null,"Permutation ",null,"n","r",null,null,null,null,null,null,null,null,"Combination ",null,"n","r",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(Z4=\"\",Z4=\"\",),\"\",COMBIN(Y4,Z4))","v":""},false,null,null,"",false,null,null,null,null,null,0,{"$f":"IF(AC4=FALSE,1,IF(AC4=TRUE,IF(AB4=\"\",1,AB4)))","v":1},null,{"$f":"IF(AG4=TRUE,AF4,0)","v":0},{"$f":"IF(AG4=FALSE,1,IF(AG4=TRUE,IF(AF4=\"\",1,AF4)))","v":1},null,"Mult",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"or P (",{"$f":"IF(AND(D5=\"\",E5=\"\"),\"\",D5)","v":""},",",{"$f":"IF(AND(D5=\"\",E5=\"\"),\"\",E5)","v":""},") "]
[null,"P(n, r)",null,null,null,null,"=",{"$f":"IF(OR(D5=\"\",E5=\"\"),\"\",PERMUT(D5,E5))","v":""},null,null,null,null,null,"C(n, r)",null,null,null,null,"=",{"$f":"IF(OR(P5=\"\",Q5=\"\",),\"\",COMBIN(P5,Q5))","v":""},null,null,null,null,null,null,null,"",false,null,null,"",false,null,null,null,null,null,0,1,null,{"$f":"IF(AG5=TRUE,AF5,0)","v":0},{"$f":"IF(AG5=FALSE,1,IF(AG5=TRUE,IF(AF5=\"\",1,AF5)))","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",false,null,null,"",false,null,null,null,null,null,0,1,{"$f":"IF(AC7=TRUE,AB7,1)","v":1},{"$f":"IF(AG6=TRUE,AF6,0)","v":0},{"$f":"IF(AG6=FALSE,1,IF(AG6=TRUE,IF(AF6=\"\",1,AF6)))","v":1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"or C (",{"$f":"IF(AND(P5=\"\",Q5=\"\"),\"\",P5)","v":""},",",{"$f":"IF(AND(P5=\"\",Q5=\"\"),\"\",Q5)","v":""},") "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",false,null,null,"",false,null,null,null,null,null,0,1,null,0,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",false,null,null,"",false,null,null,null,null,null,0,1,null,{"$f":"IF(AG8=TRUE,AF8,0)","v":0},1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"or ",{"$f":"IF(P10=\"\",\"\",P10)","v":""},null,{"$f":"IF(Q10=\"\",\"\",Q10)","v":""}]
[null,"Factorial x!",null,"x =","Factorial",null,null,null,null,null,null,null,null,"Power",null,"x","to the power",null,null,null,null,null,null,null,null,null,null,"",false,null,null,"",false,null,null,null,null,null,0,1,null,{"$f":"IF(AG9=TRUE,AF9,0)","v":0},1]
[null,null,null,null,"!",null,"=",{"$f":"IF(D10=\"\",\"\",\"! =\")","v":""},{"$f":"IF(D10=\"\",\"\",FACT(D10))","v":""},null,null,null,null,null,null,null,null,null,"=",{"$f":"IF(OR(P10=\"\",Q10=\"\"),\"\",POWER(P10,Q10))","v":""},null,null,null,null,"Sum",{"$f":"IF(Y10=\"Sum\",AM10,\"\")","v":""},null,null,null,"Sum",{"$f":"IF(AD10=\"Sum\",AP10,\"\")","v":""},null,null,null,null,null,null,null,{"$f":"IF(MAX(AM3:AM9)=0,\"\",SUM(AM3:AM9))","v":""},{"$f":"IF(MAX(AN3:AN9)=1,\"\",AN3*AN4*AN5*AN6*AN7*AN8*AN9)","v":""},null,{"$f":"IF(MAX(AP3:AP9)=0,\"\",SUM(AP3:AP9))","v":""},{"$f":"IF(MAX(AQ3:AQ9)=1,\"\",AQ3*AQ4*AQ5*AQ6*AQ7*AQ8*AQ9)","v":""},null,{"$f":"AQ3*AQ4*AQ5*AQ6*AQ7*AQ8*AQ9","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mult",{"$f":"IF(Y11=\"Mult\",AN10,\"\")","v":""},null,null,null,"Mult",{"$f":"IF(AD11=\"Mult\",AQ10,\"\")","v":""}]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AE14=TRUE,AD14,0)","v":0}]
[null,"Bernoulli Trials:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MAX(AP3:AP13)=0,\"\",SUM(AP3:AP13))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"BP16","v":""},null,null,{"$f":"IF(OR(BN16=\"\",BP16=\"\"),\"\",BN16-BP16)","v":""}]
[null,null,null,"P = C(n , r). pr.qn-r",null,null,null,null,null,null,null,null,null,null,"n =","r =","p =",null,"q =",null,"Ans.",null,null,null,"1-  Ans.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"C (",{"$f":"IF(F19=\"\",\"\",F19)","v":""},",",{"$f":"IF(J19=\"\",\"\",J19)","v":""},")",". (",{"$f":"IF(F21=\"\",\"\",F21)","v":""},") .","(",{"$f":"K21","v":""},")"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Q17=\"\",\"\",1-Q17)","v":""},null,{"$f":"IF(OR(O17=\"\",P17=\"\",Q17=\"\"),\"\",COMBIN(O17,P17)*$Q17^P17*(1-$Q17)^(O17-P17))","v":""},null,null,false,{"$f":"IF(OR(U17=0,U17=\"\"),\"\",1-U17)","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(X17=TRUE,U17,0)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Q18=\"\",\"\",1-Q18)","v":""},null,{"$f":"IF(OR(O18=\"\",P18=\"\",Q18=\"\"),\"\",COMBIN(O18,P18)*$Q18^P18*(1-$Q18)^(O18-P18))","v":""},null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,"Enter n, r and p in each. ",null,null,"n =",null,null,null,"r =",null,null,null,null,null,null,null,null,null,"",null,{"$f":"IF(OR(O19=\"\",P19=\"\",Q19=\"\"),\"\",COMBIN(O19,P19)*$Q19^P19*(1-$Q19)^(O19-P19))","v":""},null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,"Sum of the checked ",null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,"p =",null,null,null,null,"Then q =",{"$f":"IF(F21=\"\",\"\",1-F21)","v":""},null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,"Bernoulli probabilities:",null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,"Ans.",null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,{"$f":"AP33","v":""},null,"Or",{"$f":"AC23","v":""},null,null,null,null,null,null,null,null,null,0]
[null,{"$f":"IF(OR(J19=\"\",F19=\"\",F21=\"\"),\"\",\"looks like:\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,"Decimal",null,null,null,null,"Percentage",null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,"Answer",null,"P =",{"$f":"IF(OR(J19=\"\",F19=\"\",F21=\"\"),\"\",COMBIN(F19,J19)*F21^J19*(1-F21)^(F19-J19))","v":""},null,null,null,null,{"$f":"IF(F27=\"\",\"\",F27)","v":""},null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,"1 - Sum Above: ",null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,"1 - Ans.",null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,{"$f":"IF(OR(F27=0,F27=\"\"),\"\",\"All except above: \")","v":""},null,null,{"$f":"IF(OR(F27=0,F27=\"\"),\"\",1)","v":""},{"$f":"IF(OR(F27=0,F27=\"\"),\"\",\" - \")","v":""},{"$f":"IF(OR(F27=0,F27=\"\",J19=\"\",F19=\"\",F21=\"\"),\"\",F27)","v":""},null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,{"$f":"IF(OR(AC23=0,AC23=\"\"),\"\",1-AC23)","v":""},null,"Or",{"$f":"AC29","v":""},null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,{"$f":"IF(OR(F27=0,F27=\"\"),\"\",\" = \")","v":""},{"$f":"IF(OR(F27=0,F27=\"\",J19=\"\",F19=\"\",F21=\"\"),\"\",1-F27)","v":""},null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,{"$f":"IF(OR(F27=0,F27=\"\"),\"\",\" = \")","v":""},{"$f":"IF(OR(F27=0,F27=\"\",J19=\"\",F19=\"\",F21=\"\"),\"\",H30)","v":""},null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"",null,"",null,null,false,"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(MAX(AP17:AP32)=0,\"\",SUM(AP17:AP32))","v":""}]

{"sheet":"7) 5.2","index":7,"n_rows":56,"n_cols":31,"rows_kept":56,"cut":false,"hidden":false,"merged":[[32,17,32,18],[37,12,37,13],[37,21,37,22],[8,13,8,14],[46,21,47,21],[46,18,47,18],[46,19,47,19],[46,20,47,20],[3,3,3,5],[20,2,21,2],[20,3,21,3],[20,4,21,4],[20,5,21,5],[16,3,17,3],[16,4,17,4],[16,5,17,5],[6,3,7,3],[6,4,7,4],[6,5,7,5],[46,9,47,9],[46,10,47,10],[46,11,47,11],[46,12,47,12],[1,6,1,9],[3,9,3,10]]}
[]
[null,null,null,null,null,null,"Fill Green Cells Only"]
[]
[null,null,null,"Section 5.1 Main Points",null,null,null,null,null,"Section 5.2",null,null,null,null,null,null,null,null,"Question from MLM, section 5.2 :"]
[null,null,"Mean, Average",null,null,null,null,null,"Expected Value Only"]
[null,null,null,"Example:","The scores in one exam",null,null,null,null,"x","p","x.p",null,null,null,null,null,"One option in a roulette game is to bet  $11  on red. ​ "]
[null,null,null,"N of \nStudents","Score","Total Points",null,null,null,null,null,{"$f":"IF(K7=\"\",\"\",K7*J7)","v":""},null,null,null,null,null,"(There are 18 red​ compartments, 18 black​ compartments, "]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K8=\"\",\"\",K8*J8)","v":""},null,null,null,null,null,"and 2 compartments that are neither red nor​ black.)"]
[null,null,null,1,95,{"$f":"D9*E9","v":95},null,null,null,null,null,{"$f":"IF(K9=\"\",\"\",K9*J9)","v":""},null,"Fill Green Cells Only",null,null,null,"If the ball lands on​ red, you get to keep the  $11  you paid to play the​ game, and you are awarded  $12."]
[null,null,null,3,93,{"$f":"D10*E10","v":279},null,null,null,null,null,{"$f":"IF(K10=\"\",\"\",K10*J10)","v":""},null,null,null,null,null,"If the ball lands​ elsewhere, you are awarded​ nothing, and the  $11 that you bet is collected."]
[null,null,null,5,91,455,null,null,null,null,null,{"$f":"IF(K11=\"\",\"\",K11*J11)","v":""}]
[null,null,null,4,86,344,null,null,null,null,null,{"$f":"IF(K12=\"\",\"\",K12*J12)","v":""},null,null,null,null,null,"Write down the probability distribution for the earnings from this type of bet and find the expected value."]
[null,null,null,5,80,400,null,null,null,null,null,""]
[null,null,null,8,70,560,null,null,null,null,null,{"$f":"IF(K14=\"\",\"\",K14*J14)","v":""},null,null,null,null,null,null,"Case","$ Earning","Prob","Mult"]
[null,null,null,11,60,660,null,null,null,null,"µ",{"$f":"SUM(L7:L14)","v":0},null,null,null,null,null,null,"18 Red",12,"18/38 = 9/19",{"$f":"T15*AE18","v":5.6842105263157894}]
[null,null,"Total",{"$f":"SUM(D9:D15)","v":37},null,{"$f":"SUM(F9:F15)","v":2793},null,null,null,null,null,null,null,null,null,null,null,null,"18 Black & 2 neither",-11,"20/38 = 10/19",{"$f":"T16*AE19","v":-5.7894736842105257}]
[null,null,null,"Average = ",{"$f":"F16&\" / \"&D16 &\" =\"","v":"2793 / 37 ="},{"$f":"F16/D16","v":75.486486486486484},null,null,"Variance and Standard Deviation",null,null,null,null,null,null,null,null,null,"Total: 38 Compartments",null,"Sum",{"$f":"SUM(V15:V16)","v":-0.10526315789473628}]
[null,null,null,null,null,null,null,null,null,"x","p","x.p","x - µ","(x - µ)2","p*(x - µ )2",null,null,null,null,null,"Or Expected value :","$ -0.11",null,null,null,null,null,null,null,null,{"$f":"9/19","v":0.47368421052631576}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(J19=\"\",\"\",K19*J19)","v":""},{"$f":"IF(J19=\"\",\"\",J19-$L$27)","v":""},{"$f":"IF(J19=\"\",\"\",M19^2)","v":""},{"$f":"IF(K19=\"\",\"\",K19*N19)","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"10/19","v":0.52631578947368418}]
[null,null,"GPA",null,null,null,null,null,null,null,null,{"$f":"IF(J20=\"\",\"\",K20*J20)","v":""},"",{"$f":"IF(J20=\"\",\"\",M20^2)","v":""},{"$f":"IF(K20=\"\",\"\",K20*N20)","v":""}]
[null,null,"Grade","Value"," Credits of Grade","Points",null,null,null,null,null,{"$f":"IF(J21=\"\",\"\",K21*J21)","v":""},"",{"$f":"IF(J21=\"\",\"\",M21^2)","v":""},{"$f":"IF(K21=\"\",\"\",K21*N21)","v":""},null,null,"Similar Examples: You can change the numbers in the green cells"]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(J22=\"\",\"\",K22*J22)","v":""},"",{"$f":"IF(J22=\"\",\"\",M22^2)","v":""},{"$f":"IF(K22=\"\",\"\",K22*N22)","v":""},null,null,"(There are 18 red​ compartments, 18 black​ compartments, "]
[null,null,"A",4,5,{"$f":"D23*E23","v":20},null,null,null,null,null,{"$f":"IF(J23=\"\",\"\",K23*J23)","v":""},"",{"$f":"IF(J23=\"\",\"\",M23^2)","v":""},{"$f":"IF(K23=\"\",\"\",K23*N23)","v":""},null,null,"and 2 compartments that are neither red nor​ black.)"]
[null,null,"B",3,15,{"$f":"D24*E24","v":45},null,null,null,null,null,{"$f":"IF(J24=\"\",\"\",K24*J24)","v":""},"",{"$f":"IF(J24=\"\",\"\",M24^2)","v":""},{"$f":"IF(K24=\"\",\"\",K24*N24)","v":""},null,null,null,"You pay:",19,"to play the game"]
[null,null,"C",2,22,44,null,null,null,null,null,"","","","",null,null,null,"You get:",20,"If you bet on Red"]
[null,null,"D",1,6,6,null,null,null,null,null,"","","",""]
[null,null,"F",0,3,0,null,null,null,null,"µ",{"$f":"SUM(L19:L26)","v":0},null,"Var",{"$f":"SUM(O19:O26)","v":0},null,null,null,"Case","$ Earning","Prob","Mult"]
[null,null,null,"Total",{"$f":"SUM(E23:E27)","v":51},{"$f":"SUM(F23:F27)","v":115},null,null,null,null,null,null,null,"Std Dev",{"$f":"SQRT(O27)","v":0},null,null,null,"18 Red",{"$f":"T25","v":20},"18/38 = 9/19",{"$f":"T28*AE31","v":9.473684210526315}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"18 Black & 2 neither",{"$f":"-1*T24","v":-19},"20/38 = 10/19",{"$f":"T29*AE34","v":-10}]
[null,null,null,{"$f":"E28&\" Credits with \"&F28&\" points\"","v":"51 Credits with 115 points"},null,null,null,null,null,null,null,null,null,"or:",{"$f":"O28","v":0},null,null,null,"Total: 38 Compartments",null,"Sum",{"$f":"SUM(V28:V29)","v":-0.52631578947368496}]
[null,null,"GPA = ",{"$f":"F28&\" / \"&E28& \" =\"","v":"115 / 51 ="},{"$f":"F28/E28","v":2.2549019607843137},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"9/19","v":0.47368421052631576}]
[]
[null,null,null,null,null,null,null,null,null,null,"Common Question, If:",5000,"Tickets",null,null,null,null,"Common Question, If:",null,2000," Tckets"]
[null,null,"Median: number at the midpoint of a ranked data.",null,null,null,null,null,null,"are sold at​ $1 each for a charity raffle. Tickets are to be drawn ",null,null,null,null,null,null,null,null,"are sold at​ $1 each for a charity raffle. Tickets are to be drawn ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"10/19","v":0.52631578947368418}]
[null,null,"Data must be ranked from smallest to largest. ",null,null,null,null,null,null,"at random and monetary prizes awarded as​ follows: ",null,null,null,null,null,null,null,null,"at random and monetary prizes awarded as​ follows: "]
[null,null,null,2]
[null,null,null,3,null,null,null,null,null,"# of prizes","$",null,null,null,null,null,null,null,"# of prizes","$"]
[null,null,null,4,null,null,null,null,null,1,600,null,"Fill Green Cells Only",null,null,null,null,null,1,1200,null,"Fill Green Cells Only"]
[null,null,null,4,null,null,null,null,null,3,200,null,null,null,null,null,null,null,3,400]
[null,null,null,5,null,null,null,null,null,5,10,null,null,null,null,null,null,null,5,60]
[null,null,null,6,null,null,null,null,null,20,5,null,null,null,null,null,null,null,20,5]
[null,null,null,8,"Median=",{"$f":"MEDIAN(D36:D43)","v":4.5}]
[null,null,null,9]
[null,null,null,null,null,null,null,null,null,"What is the expected value of this raffle if you buy 1​ ticket?",null,null,null,null,null,null,null,null,"What is the expected value of this raffle if you buy 1​ ticket?"]
[null,null,null,null,null,null,null,null,null,"Total number of tickets is:",null,{"$f":"L33","v":5000},null,null,null,null,null,null,"Total number of tickets is:",{"$f":"T33","v":2000}]
[null,null,"Mode: the number or numbers that occur most often"]
[null,null,null,1,null,null,null,null,null,"X","N number of each",{"$f":"\"Prob  =  N/\"&L33","v":"Prob  =  N/5000"},"X.P",null,null,null,null,null,"X","N number of each",{"$f":"\"Prob  =  N/\"&T33","v":"Prob  =  N/2000"},"X.P"]
[null,null,null,2]
[null,null,null,3,null,null,null,null,null,{"$f":"K38","v":600},{"$f":"J38","v":1},{"$f":"K49/$L$33","v":2.0000000000000001E-4},{"$f":"L49*J49","v":0.12000000000000001},null,null,null,null,null,{"$f":"T38","v":1200},{"$f":"S38","v":1},{"$f":"T49/2000","v":5.0000000000000001E-4},{"$f":"U49*S49","v":0.6}]
[null,null,null,4,null,null,null,null,null,{"$f":"K39","v":200},{"$f":"J39","v":3},{"$f":"K50/$L$33","v":5.9999999999999995E-4},{"$f":"L50*J50","v":0.12},null,null,null,null,null,{"$f":"T39","v":400},{"$f":"S39","v":3},{"$f":"T50/2000","v":1.5E-3},{"$f":"U50*S50","v":0.6}]
[null,null,null,7,null,null,null,null,null,{"$f":"K40","v":10},{"$f":"J40","v":5},{"$f":"K51/$L$33","v":1E-3},{"$f":"L51*J51","v":0.01},null,null,null,null,null,{"$f":"T40","v":60},{"$f":"S40","v":5},{"$f":"T51/2000","v":2.5000000000000001E-3},{"$f":"U51*S51","v":0.15}]
[null,null,null,7,null,null,null,null,null,{"$f":"K41","v":5},{"$f":"J41","v":20},{"$f":"K52/$L$33","v":4.0000000000000001E-3},{"$f":"L52*J52","v":0.02},null,null,null,null,null,{"$f":"T41","v":5},{"$f":"S41","v":20},{"$f":"T52/2000","v":0.01},{"$f":"U52*S52","v":0.05}]
[null,null,null,9,"Mode =",{"$f":"IFERROR(_xlfn.MODE.MULT(D47:D56),\"No Mode\")","v":9},null,null,null,{"$f":"K42","v":0},{"$f":"J42","v":0},{"$f":"K53/$L$33","v":0},{"$f":"L53*J53","v":0},null,null,null,null,null,{"$f":"T42","v":0},{"$f":"S42","v":0},{"$f":"T53/2000","v":0},{"$f":"U53*S53","v":0}]
[null,null,null,9,null,null,null,null,null,null,null,"E(X)",{"$f":"SUM(M49:M53)","v":0.27},null,null,null,null,null,null,null,"E(X)",{"$f":"SUM(V49:V53)","v":1.4}]
[null,null,null,9]
[null,null,null,13,null,null,null,null,"      You paid $1, you get back :",null,null,{"$f":"M54","v":0.27},"gain/Loss: ",{"$f":"M54-1","v":-0.73},"(Loss )",null,null,null,"You paid $1, and you get back :",{"$f":"V54","v":1.4},"Your gain/Loss: ",{"$f":"V54-1","v":0.39999999999999991},"(profit)"]

{"sheet":"7) 5.2b","index":8,"n_rows":37,"n_cols":47,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Section 5.2, #9",null,null,null,null,null,null,null,"Section 5.5, similar to #5",null,null,null,null,null,null,"Value of X","P"]
[null,"Two coins are randomly selected from two quarters and two dimes.  A random variable",null,null,null,null,null,null,null,"Find the expected value and the standard deviation for the probability density function:",null,null,null,null,null,null,1,0.4]
[null," is defined as the value of the coins (in cents). Find the expected value of X.",null,null,null,null,null,null,null,"Solution:",null,null,null,null,null,null,2,0.3]
[null,"Outcomes","x =Cents","p",null,"x.p",null,null,null,"Value of X","P","x.p",null,null,null,null,4,0.2]
[null,"2 Q",50,"C(2,2)  / C(4,2)  =",{"$f":"1/6","v":0.16666666666666666},{"$f":"IF(B6=\"\",\"\",E6*C6)","v":8.3333333333333321},null,null,null,1,0.4,{"$f":"IF(K6=\"\",\"\",K6*J6)","v":0.4},null,null,null,null,6,0.1]
[null,"1 Q. 1 D",35,"C(2,1). C(2,1)  / C(4,2)  =",{"$f":"4/6","v":0.66666666666666663},{"$f":"IF(B7=\"\",\"\",E7*C7)","v":23.333333333333332},null,null,null,2,0.3,{"$f":"IF(K7=\"\",\"\",K7*J7)","v":0.6}]
[null,"2 D",20,"C(2,2)  / C(4,2)  =",{"$f":"1/6","v":0.16666666666666666},3.333333333333333,null,null,null,4,0.2,0.8]
[null,null,null,null,"µ",{"$f":"SUM(F6:F8)","v":35},"cents",null,null,6,0.1,0.60000000000000009]
[null,null,null,null,null,null,null,null,null,null,"Expected Value   µ",{"$f":"SUM(L6:L9)","v":2.4000000000000004}]
[null,"Similar Example:"]
[null,"Two coins are randomly selected from two nickels and six quarters. A random variable ",null,null,null,null,null,null,null,"x","p","x.p","x - µ","(x - µ)2","p.(x - µ )2"]
[null,"is defined as the value of the coins (in cents). Find the expected value of X.",null,null,null,null,null,null,null,1,0.4,{"$f":"IF(J13=\"\",\"\",K13*J13)","v":0.4},{"$f":"IF(J13=\"\",\"\",J13-$L$17)","v":-1.4000000000000004},{"$f":"IF(J13=\"\",\"\",M13^2)","v":1.9600000000000011},{"$f":"IF(K13=\"\",\"\",K13*N13)","v":0.78400000000000047}]
[null,"Outcomes","x =Cents","p",null,"x.p",null,null,null,2,0.3,{"$f":"IF(J14=\"\",\"\",K14*J14)","v":0.6},{"$f":"IF(J14=\"\",\"\",J14-$L$17)","v":-0.40000000000000036},{"$f":"IF(J14=\"\",\"\",M14^2)","v":0.16000000000000028},{"$f":"IF(K14=\"\",\"\",K14*N14)","v":4.8000000000000084E-2}]
[null,"2 Q",50,"C(6,2)  / C(8,2)  =",{"$f":"15/28","v":0.5357142857142857},{"$f":"IF(B15=\"\",\"\",E15*C15)","v":26.785714285714285},null,null,null,4,0.2,{"$f":"IF(J15=\"\",\"\",K15*J15)","v":0.8},{"$f":"IF(J15=\"\",\"\",J15-$L$17)","v":1.5999999999999996},{"$f":"IF(J15=\"\",\"\",M15^2)","v":2.5599999999999987},{"$f":"IF(K15=\"\",\"\",K15*N15)","v":0.51199999999999979}]
[null,"1 Q. 1 N",30,"C(6,1). C(2,1)  / C(8,2)  =",{"$f":"12/28","v":0.42857142857142855},{"$f":"IF(B16=\"\",\"\",E16*C16)","v":12.857142857142856},null,null,null,6,0.1,{"$f":"IF(J16=\"\",\"\",K16*J16)","v":0.60000000000000009},{"$f":"IF(J16=\"\",\"\",J16-$L$17)","v":3.5999999999999996},{"$f":"IF(J16=\"\",\"\",M16^2)","v":12.959999999999997},{"$f":"IF(K16=\"\",\"\",K16*N16)","v":1.2959999999999998}]
[null,"2 N",10,"C(2,2)  / C(8,2)  =",{"$f":"1/28","v":3.5714285714285712E-2},0.3571428571428571,null,null,null,null,"µ",{"$f":"SUM(L13:L16)","v":2.4000000000000004},null,"Var",{"$f":"SUM(O13:O16)","v":2.64}]
[null,null,null,null,"µ",{"$f":"SUM(F15:F17)","v":39.999999999999993},"cents",null,null,null,null,null,null,"Std Dev",{"$f":"SQRT(O17)","v":1.6248076809271921}]
[]
[]
[null,"Section 5.5, #3",null,null,null,null,null,null,null,"Full Example"]
[null,"Two coins are selected at random from a pocket containing three quarters, two dimes,",null,null,null,null,null,null,null,"An experiment consists of flipping a coin with P(H) = 1/3 until a total of two heads occur or two tails occur."]
[null,"and one nickel. What is the expected amount in cents of the two coins selected?",null,null,null,null,null,null,null,"A random variable X is defined as the number of times the coin was flipped. Find the expected value of X"]
[null,"Outcomes","x =Cents","p",null,"x.p",null,null,null,"Outcomes","x = N ","p",null,"x.p"]
[null,"2 Q",50,"C(3,2)  / C(6,2)  =",{"$f":"3/15","v":0.2},{"$f":"IF(B25=\"\",\"\",E25*C25)","v":10},null,null,null,"2 H",2," 1/3.1/3 =",{"$f":"1/9","v":0.1111111111111111},{"$f":"IF(J25=\"\",\"\",M25*K25)","v":0.22222222222222221}]
[null,"2 D",20,"C(2,2)  / C(6,2)  =",{"$f":"1/15","v":6.6666666666666666E-2},{"$f":"IF(B26=\"\",\"\",E26*C26)","v":1.3333333333333333},null,null,null,"2 H, 1T",3,"2.(1/3.1/3.2/3) =",{"$f":"4/27","v":0.14814814814814814},{"$f":"IF(J26=\"\",\"\",M26*K26)","v":0.44444444444444442}]
[null,"1 Q, 1 D",35,"C(3,1). C(2,1)  / C6,2)  =",{"$f":"6/15","v":0.4},14,null,null,null,"2 T, 1 H",3,"2.(2/3.2/3.1/3) =",{"$f":"8/27","v":0.29629629629629628},0.88888888888888884]
[null,"1 Q, 1 N",30,"C(2,1). C(1,1)  / C6,2)  =",{"$f":"3/15","v":0.2},6,null,null,null,"2 T",2,"2/3 . 2/3  =",{"$f":"4/9","v":0.44444444444444442},0.88888888888888884]
[null,"1 D, 1 N",15,"C(3,1). C(1,1)  / C6,2)  =",{"$f":"2/15","v":0.13333333333333333},2,null,null,null,null,null,null,"µ",{"$f":"SUM(N25:N28)","v":2.4444444444444442}]
[null,null,null,null,"µ",{"$f":"SUM(F25:F29)","v":33.333333333333336},"cents"]
[null,null,null,null,null,null,null,null,null,"To find the variance and Standard deviation:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x","p","x.p","x - µ","(x - µ)2","p.(x - µ )2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,{"$f":"1/9","v":0.1111111111111111},{"$f":"IF(AP32=\"\",\"\",AQ32*AP32)","v":0.22222222222222221},{"$f":"IF(AP32=\"\",\"\",AP32-$N$29)","v":-0.4444444444444442},{"$f":"IF(AP32=\"\",\"\",AS32^2)","v":0.19753086419753063},{"$f":"IF(AQ32=\"\",\"\",AQ32*AT32)","v":2.1947873799725626E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"4/27","v":0.14814814814814814},{"$f":"IF(AP33=\"\",\"\",AQ33*AP33)","v":0.44444444444444442},{"$f":"IF(AP33=\"\",\"\",AP33-$N$29)","v":0.5555555555555558},{"$f":"IF(AP33=\"\",\"\",AS33^2)","v":0.30864197530864224},{"$f":"IF(AQ33=\"\",\"\",AQ33*AT33)","v":4.5724737082761813E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,{"$f":"8/27","v":0.29629629629629628},{"$f":"IF(AP34=\"\",\"\",AQ34*AP34)","v":0.88888888888888884},0.5555555555555558,{"$f":"IF(AP34=\"\",\"\",AS34^2)","v":0.30864197530864224},{"$f":"IF(AQ34=\"\",\"\",AQ34*AT34)","v":9.1449474165523625E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,{"$f":"4/9","v":0.44444444444444442},{"$f":"IF(AP35=\"\",\"\",AQ35*AP35)","v":0.88888888888888884},-0.4444444444444442,{"$f":"IF(AP35=\"\",\"\",AS35^2)","v":0.19753086419753063},{"$f":"IF(AQ35=\"\",\"\",AQ35*AT35)","v":8.7791495198902503E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Note: if it was a fair coin,  then",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"µ",{"$f":"SUM(AR32:AR35)","v":2.4444444444444442},null,"Var",{"$f":"SUM(AU32:AU35)","v":0.24691358024691357}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(H) and P(T) are equal to 1/2.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Std Dev",{"$f":"SQRT(AU36)","v":0.49690399499995325}]

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[]
[null,"First, read the example below, then use the template to solve a problem.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fill Green Cells Only"]
[null,"Example:",null,null,"Let X to be a normal variable with mean 400 and standard deviation 40. Find the following cases:",null,null,null,null,null,null,null,null,"Section 5.3: Random Variable Template",null,null,null,null,null,null,null,null,null,null,null,"Example 1:","A teacher says that the top",0.15,"  will received an A on the last test. "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If the mean is:",75,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"100-(AB3*100)","v":85},{"$f":"AQ4/100","v":0.85}]
[null,"Given:",null,null,null,null,null,null,null,null,null,null,null,"Given:",null,null,null,null,"Fill",null,null,null,null,null,null,null,"and standard deviation",8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AB3=\"\",\"\",IF(OR(AR4>0.97,AR4<0.05,AR4=19),NORMSINV(AR4+0.0001),IF(AR4<>0,NORMSINV(AR4+0.001),NORMSINV(AR4+0.0007))))","v":1.040731886467543},null,{"$f":"IF(AR8<0,LEFT(AR8,4),LEFT(AR8,3))","v":"1.0"}]
[null,null,null,"Expected Value, Mean =",null,null,400,null,null,null,null,null,null,null,null,"Expected Value, Mean =",null,null,100,null,null,null,null,null,null,null,"Find the minimum score required to get an A.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,null,{"$f":"IF(AND(AR8>=0,AR4=3),0,IF(AND(AR8<0,AR4=5),0,IF(AND(AR8>=0,AR4=1),0,IF(AND(AR8<0,AR4=3),0,RIGHT(AR8,1)))))","v":"4"}]
[null,null,null,"Standard Deviation =",null,null,40,null,null,null,null,null,null,null,null,"Standard Deviation =",null,null,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solution:","We usually use the Z-score table to find the probability (area to the left)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(AR4=\"\",AR4>=100%,AR4<=0,AR6<>AR7),\"\",ROUND(AR5,2))","v":1.04}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Given, the right area or top:",{"$f":"AB3","v":0.15},null,"So, the left area is:",{"$f":"1-AB3","v":0.85},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AB3=\"\",\"\",IF(OR(AR4>0.97,AR4<0.05,AR4=19),NORMSINV(AR4+0.0001),IF(AR4<>0,NORMSINV(AR4+0.002),NORMSINV(AR4+0.0007))))","v":1.0450496996583867}]
[null,null,null,"To find Z-score:"," If x  =",350,{"$f":"  \" Then  Z =  (\"&F10&\" - \"&G6&\") / \"&G7","v":" Then  Z =  (350 - 400) / 40"},null,null,null,null,null,null,null,null,"To find Z-score:"," If x  =",120,{"$f":"IF(OR(S6=\"\",S7=\"\",R10=\"\"),\"\", \" Then  Z =  (\"&R10&\" - \"&S6&\") / \"&S7)","v":" Then  Z =  (120 - 100) / 10"}]
[null,null,null,null,null,null,"Z =",{"$f":"(F10-G6)/G7","v":-1.25},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(T11=\"\",\"\",\" Z = \")","v":" Z = "},{"$f":"IF(OR(S6=\"\",S7=\"\",R10=\"\"),\"\",(R10-S6)/S7)","v":2},null,null,null,null,null,null,null,"Using the table backward, the closest to:",{"$f":"AE9","v":0.85},"is:",{"$f":"ROUND(NORMSDIST(AR8),4)","v":0.8508}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"is in row:",{"$f":"AT5","v":"1.0"}]
[null,null,"Case 1: ",null,"Pr ( x < 350)",null,null,null,null,null,null,null,null,null,"Case 1: at most",null,"Pr( x < a)  ",null,null,null,null,null,null,null,null,null,null,null,null,"Column:",{"$f":"AT6/100","v":0.04}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,null,null,null,null,"Or, Z-score:",{"$f":"IF(OR(AR4=\"\",AR4>=100%,AR4<=0,AR6<>AR7),\"\",ROUND(AR5,2))","v":1.04},null,null,null,{"$f":"IF(S15=\"\",\"\",ROUND(S15,2))","v":2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Pr( x < ",null,120,"or","P ( Z <",{"$f":"IF(OR(S6=\"\",S7=\"\",P15=\"\"),\"\",(P15-S6)/S7)","v":2},"P =",null,{"$f":"IF(OR(S6=\"\",S7=\"\",P15=\"\"),\"\",NORMSDIST(AI14))","v":0.97724986805182079},null,null,null,null,"The Z-Score formula is: "]
[null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,null,null,null,null,null,null,null,null,{"$f":"V15","v":0.97724986805182079}]
[null,null,null,"Pr( x < ",350," or P ( Z <",-1.25,"P =",null,0.1056]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AE14&\" = (x - \"&AB4&\" ) / \"&AB5","v":"1.04 = (x - 75 ) / 8"},"Solve for x :",null,{"$f":"AE14*AB5+AB4","v":83.32}]
[]
[null,null,"Case 2:",null,"Pr (x > 420)",null,null,null,null,null,null,null,null,null,"Case 2: at least",null,"Pr( x > b) "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,"Example 2:","Assume that the readings on the thermometers are normally distributed with:"]
[]
[null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,"Pr( x > ",null,120,"or","P( Z >",{"$f":"IF(OR(S6=\"\",S7=\"\",P23=\"\"),\"\",(P23-S6)/S7)","v":2},"P =",null,{"$f":"IF(OR(S6=\"\",S7=\"\",P23=\"\"),\"\",1-NORMSDIST(AI23))","v":2.2750131948179209E-2},null,null,null,null,"If the mean is:",0,null,null,null,null,null,null,{"$f":"IF(S23=\"\",\"\",ROUND(S23,2))","v":2}]
[null,null,null,"Pr( x > ",420," or P ( Z >",0.5,"P =",null,0.3085,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V23","v":2.2750131948179209E-2},null,null,null,null,"and standard deviation",1]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"    A thermometer is randomly selected and tested. find the temperature reading corresponding "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"to  ",0.89,"percentile."]
[null,null,"Case 3:",null,"Pr (360 < x < 410)",null,null,null,null,null,null,null,null,null,"Case 3: between",null,"Pr( a < x < b) ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(AB27*100)","v":89},{"$f":"AQ28/100","v":0.89}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solution:",null,"Using the table backward, the closest to:",{"$f":"AB27","v":0.89},"is:",{"$f":"ROUND(NORMSDIST(AR32),4)","v":0.89070000000000005},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AB27=\"\",\"\",IF(OR(AR28>0.97,AR28<0.05,AR28=19),NORMSINV(AR28+0.0001),IF(AR28<>0,NORMSINV(AR28+0.001),NORMSINV(AR28+0.0007))))","v":1.2318637087349826},null,{"$f":"IF(AR32<0,LEFT(AR32,4),LEFT(AR32,3))","v":"1.2"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,75,"< x <",105,{"$f":"IF(OR(S6=\"\",S7=\"\",O30=\"\"),\"\",(O30-S6)/S7)","v":-2.5}," < Z <",{"$f":"IF(OR(S6=\"\",S7=\"\",Q30=\"\"),\"\",(Q30-S6)/S7)","v":0.5},null,null,null,null,null,null,null,null,null,"is in row:",{"$f":"AT29","v":"1.2"},null,null,null,{"$f":"IF(R30=\"\",\"\",ROUND(R30,2))","v":-2.5},{"$f":"IF(T30=\"\",\"\",ROUND(T30,2))","v":0.5},null,null,null,null,null,null,null,0,null,{"$f":"IF(AND(AR32>=0,AR28=3),0,IF(AND(AR32<0,AR28=5),0,IF(AND(AR32>=0,AR28=1),0,IF(AND(AR32<0,AR28=3),0,RIGHT(AR32,1)))))","v":"3"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Column:",{"$f":"AT30/100","v":0.03},null,null,null,null,null,null,null,null,null,null,null,null,0]
[null,360,null,"< x <",410,-1," < Z <",0.25,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(S6=\"\",S7=\"\",O30=\"\",Q30=\"\"),\"\",NORMSDIST(AI30))","v":6.2096653257761331E-3}," < P <",{"$f":"IF(OR(S6=\"\",S7=\"\",O30=\"\",Q30=\"\"),\"\",NORMSDIST(AJ30))","v":0.69146246127401312},null,null,null,null,null,null,null,null,null,"Or, Z-score:",{"$f":"IF(OR(AR28=\"\",AR28>=100%,AR28<=0,AR30<>AR31),\"\",ROUND(AR29,2))","v":1.23},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(AR28=\"\",AR28>=100%,AR28<=0,AR30<>AR31),\"\",ROUND(AR29,2))","v":1.23}]
[null,null,null,null,null,0.15865525393145707," < P <",0.5987063256829237,null,"Answer:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The Z-Score formula is: ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AB27=\"\",\"\",IF(OR(AR28>0.97,AR28<0.05,AR28=19),NORMSINV(AR28+0.0001),IF(AR28<>0,NORMSINV(AR28+0.002),NORMSINV(AR28+0.0007))))","v":1.2372345991628275}]
[null,null,null,null,null,null,null,"P =",null,0.44009999999999999,null,null,null,null,null,{"$f":"IF(V34<0,\"Error, negative answer\",\"\")","v":""},null,null,"Answer:","P =",null,{"$f":"IF(OR(R32=\"\",T32=\"\"),\"\",(T32-R32))","v":0.68525279594823696}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V34","v":0.68525279594823696},null,null,null,null,{"$f":"AE32&\" = (x - \"&AB23&\" ) / \"&AB24","v":"1.23 = (x - 0 ) / 1"},"Solve for x :",null,{"$f":"AE32*AB24+AB23","v":1.23}]
[]
[null,null,null,"The above is just an example already filled and solved"]

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[null,"First, read the example below, then use the template on the right ",null,null,null,null,null,null,null,null,null,null,null,"Fill the Green cell only."]
[null,"Example:",null,"A coin with Pr(Tails) = 0.4 flipped 200 times. Find the probability of the 4 cases below:",null,null,null,null,null,null,null,null,null,"Section 5.4: The Normal Approximation Method Template"]
[]
[null,"Given:",null,null,null,null,null,"Then:",null,null,null,null,null,"Given:",null,null,"Fill",null,null,"Then:"]
[null,null,null,"n =",200,null,null,"q = 1- p ",null,0.6,null,null,null,null,null,"n =",null,null,null,"q = 1- p ","=",{"$f":"IF(Q6=\"\",\"\",1-Q6)","v":""}]
[null,null,null,"Pr = ",0.4,null,null,null,null,80,null,null,null,null,null,"Pr = ",null,null,null,null,"=",{"$f":"IF(OR(Q5=\"\",Q6=\"\"),\"\",Q5*Q6)","v":""}]
[null,null,null,null,null,null,null,null,null,6.9279999999999999,null,null,null,null,null,null,{"$f":"IF(Q6>1,\"Pr error\",\"\")","v":""},null,null,null,"=",{"$f":"IF(OR(Q5=\"\",Q6=\"\"),\"\",SQRT(Q5*Q6*(1-Q6)))","v":""}]
[]
[]
[null,null,"Case 1:",null,"Getting at Most 65 tails",null,null,null,null,null,null,null,null,null,"Case 1:",null,"At Most"]
[]
[null,null,null,"Original",null,"Approximation",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x < ",65," x <",65.5,null,null,"Answer:",null,null,null,null,null,"Pr( x < ",null," x <",{"$f":"IF(Q13=\"\",\"\",Q13+0.5)","v":""},null,null,"Answer:"]
[null,null,null,null,null," Z <",-2.0928947258123936,null,"P =",1.7999999999999999E-2,null,null,null,null,null,null,null," Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q13=\"\"),\"\",(S13-V6)/V7)","v":""},null,"P =",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q13=\"\"),\"\",NORMSDIST(Z14))","v":""},null,null,null,{"$f":"IF(S14=\"\",\"\",ROUND(S14,2))","v":""}]
[]
[]
[null,null,"Case 2:",null,"Getting at Least 65 tails",null,null,null,null,null,null,null,null,null,"Case 2:",null,"At Least"]
[]
[null,null,null,"Original",null,"Approximation",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x > ",65,"x >",64.5,null,null,"Answer:",null,null,null,null,null,"Pr( x > ",null,"x >",{"$f":"IF(Q20=\"\",\"\",Q20-0.5)","v":""},null,null,"Answer:"]
[null,null,null,null,null," Z >",-2.2372322931098001,null,"P =",0.98699999999999999,null,null,null,null,null,null,null," Z >",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q20=\"\"),\"\",(S20-V6)/V7)","v":""},null,"P =",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q20=\"\"),\"\",1-NORMSDIST(Z21))","v":""},null,null,null,{"$f":"IF(S21=\"\",\"\",ROUND(S21,2))","v":""}]
[]
[]
[null,null,"Case 3:",null,"Getting Exactly 65 tails",null,null,null,null,null,null,null,null,null,"Case 3:",null,"Exactly"]
[]
[null,null,null,"Original",null,"Approximation",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x =",65,64.5," < x <",65.5,null,null,null,null,null,null,null,"Pr( x =",null,{"$f":"IF(Q27=\"\",\"\",Q27-0.5)","v":""}," < x <",{"$f":"IF(Q27=\"\",\"\",Q27+0.5)","v":""}]
[null,null,null,null,null,-2.2372322931098001," < Z <",-2.0928947258123936,null,"Answer:",null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",(R27-V6)/V7)","v":""}," < Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",(T27-V6)/V7)","v":""},null,"Answer:",null,null,null,{"$f":"IF(R28=\"\",\"\",ROUND(R28,2))","v":""},null,{"$f":"IF(T28=\"\",\"\",ROUND(T28,2))","v":""}]
[null,null,null,null,null,1.2635580888435305E-2," < P <",1.8179276586395399E-2,"P =",6.0000000000000001E-3,null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",Z28=\"\"),\"\",NORMSDIST(R28))","v":""}," < P <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",NORMSDIST(AB28))","v":""},"P =",{"$f":"IF(OR(R29=\"\",T29=\"\"),\"\",ABS(R29-T29))","v":""}]
[]
[]
[null,null,"Case 4:",null,"Getting Between 65 and 100 tails",null,null,null,null,null,null,null,null,null,"Case 4:",null,"Between",null,null,null,null,{"$f":"IF(V37<0,\"Error, negative answer\",\"\")","v":""}]
[]
[null,null,"Original",null,null,"Approximation",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,65,"< x <",100,64.5," < x <",100.5,null,null,null,null,null,null,null,"< x <",null,{"$f":"IF(O36=\"\",\"\",O36-0.5)","v":""}," < x <",{"$f":"IF(Q36=\"\",\"\",Q36+0.5)","v":""}]
[null,null,null,null,null,-2.2372322931098001," < Z <",2.9589201295968324,null,"Answer:",null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",O36=\"\"),\"\",(R35-V6)/V7)","v":""}," < Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q36=\"\"),\"\",(T35-V6)/V7)","v":""},null,"Answer:",null,null,null,{"$f":"IF(R36=\"\",\"\",ROUND(R36,2))","v":""},null,{"$f":"IF(T36=\"\",\"\",ROUND(T36,2))","v":""}]
[null,null,null,null,null,1.2635580888435305E-2," < P <",0.9984564044790033,"P =",0.98599999999999999,null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",O36=\"\"),\"\",NORMSDIST(Z36))","v":""}," < P <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q36=\"\"),\"\",NORMSDIST(AB36))","v":""},"P =",{"$f":"IF(OR(R37=\"\",T37=\"\"),\"\",(T37-R37))","v":""}]
[]
[]
[null,null,null,"The above is just an example already filled and solved"]

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[null,"First, read the example below, then use the template on the right ",null,null,null,null,null,null,null,null,null,null,null,"Fill the Green cell only."]
[null,"Example:",null,null,"A coin with Pr(Tails) = 0.4 flipped 200 times. Find the probability of the 4 cases below:",null,null,null,null,null,null,null,null,"Section 5.4: The Normal Approximation Method Template"]
[]
[null,"Given:",null,null,null,null,null,"Then:",null,null,null,null,null,"Given:",null,null,"Fill",null,null,"Then:"]
[null,null,null,"n =",200,null,null,"q = 1- p ",null,0.6,null,null,null,null,null,"n =",null,null,null,"q = 1- p ","=",{"$f":"IF(Q6=\"\",\"\",1-Q6)","v":""}]
[null,null,null,"Pr = ",0.4,null,null,null,null,80,null,null,null,null,null,"Pr = ",null,null,null,null,"=",{"$f":"IF(OR(Q5=\"\",Q6=\"\"),\"\",Q5*Q6)","v":""}]
[null,null,null,null,null,null,null,null,null,6.9279999999999999,null,null,null,null,null,null,{"$f":"IF(Q6>1,\"Pr error\",\"\")","v":""},null,null,null,"=",{"$f":"IF(OR(Q5=\"\",Q6=\"\"),\"\",SQRT(Q5*Q6*(1-Q6)))","v":""}]
[]
[]
[null,null,"Case 1:",null,"getting at most 65 tails;\nPr ( x < 65) or Pr( x < 65.5)",null,null,null,null,null,null,null,null,null,"Case 1:",null,"At Most"]
[]
[null,null,null,null,null,"Probability Of:",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x < ",65," x <",65.5,null,null,"Answer:",null,null,null,null,null,"Pr( x < ",null," x <",{"$f":"IF(Q13=\"\",\"\",Q13+0.5)","v":""},null,null,"Answer:"]
[null,null,null,null,null," Z <",-2.0928947258123936,null,"P =",1.7999999999999999E-2,null,null,null,null,null,null,null," Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q13=\"\"),\"\",(S13-V6)/V7)","v":""},null,"P =",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q13=\"\"),\"\",NORMSDIST(Z14))","v":""},null,null,null,{"$f":"IF(S14=\"\",\"\",ROUND(S14,2))","v":""}]
[]
[]
[null,null,"Case 2:",null,"getting at least 65 tails;\nPr ( x > 65) or Pr( x > 64.5)",null,null,null,null,null,null,null,null,null,"Case 2:",null,"At Least"]
[]
[null,null,null,null,null,"Normal Approx.",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x > ",65,"x >",64.5,null,null,"Answer:",null,null,null,null,null,"Pr( x > ",null,"x >",{"$f":"IF(Q20=\"\",\"\",Q20-0.5)","v":""},null,null,"Answer:"]
[null,null,null,null,null," Z >",-2.2372322931098001,null,"P =",0.98699999999999999,null,null,null,null,null,null,null," Z >",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q20=\"\"),\"\",(S20-V6)/V7)","v":""},null,"P =",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q20=\"\"),\"\",1-NORMSDIST(Z21))","v":""},null,null,null,{"$f":"IF(S21=\"\",\"\",ROUND(S21,2))","v":""},null,null,null,"Example 1 : A coin with Pr[Tails] = 0.4 is flipped 200 times.  Find the probabilty:"]
[]
[]
[null,null,"Case 3:",null,"getting 65 tails;\nPr ( x = 65) or Pr( 64.5 < x < 65.5)",null,null,null,null,null,null,null,null,null,"Case 3:",null,"Exactly",null,null,null,null,null,null,null,null,null,null,null,null,"a) of getting between 65 and 100 tails \nb) of getting exactly 65 tails",null,null,null,"Answer:\nAnswer:","0.9859\n0.0057"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"c) of getting at least 65 tails",null,null,null,"Answer:",0.98750000000000004]
[null,null,null,null,null,"Normal Approx.",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr( x =",65,64.5," < x <",65.5,null,null,null,null,null,null,null,"Pr( x =",null,{"$f":"IF(Q27=\"\",\"\",Q27-0.5)","v":""}," < x <",{"$f":"IF(Q27=\"\",\"\",Q27+0.5)","v":""},null,null,null,null,null,null,null,null,null,"d) of getting at most 100 tails ",null,null,null,"Answer:",0.99850000000000005]
[null,null,null,null,null,-2.2372322931098001," < Z <",-2.0928947258123936,null,"Answer:",null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",(R27-V6)/V7)","v":""}," < Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",(T27-V6)/V7)","v":""},null,"Answer:",null,null,null,{"$f":"IF(R28=\"\",\"\",ROUND(R28,2))","v":""},null,{"$f":"IF(T28=\"\",\"\",ROUND(T28,2))","v":""},null,"Example 2 : Assume that IQ scores are normally distributed with mean 100 and standard deviation 15. What is  the probability that a randomly chosen person will have an IQ at most 105?\n\n  Answer:  Expected value and standard deviation are given. Therefore No approximation to be used. Find Z-score, then use the table, and you will get   0.6293"]
[null,null,null,null,null,1.2635580888435305E-2," < P <",1.8179276586395399E-2,"P =",6.0000000000000001E-3,null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",Z28=\"\"),\"\",NORMSDIST(R28))","v":""}," < P <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q27=\"\"),\"\",NORMSDIST(AB28))","v":""},"P =",{"$f":"IF(OR(R29=\"\",T29=\"\"),\"\",ABS(R29-T29))","v":""}]
[]
[]
[null,null,"Case 4:",null,"getting between 65 and 100 tails;\nPr ( 65 < x < 100) or Pr( 64.5 < x < 100.5)",null,null,null,null,null,null,null,null,null,"Case 4:",null,"Between",null,null,null,null,{"$f":"IF(V37<0,\"Error, negative answer\",\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Example 3. A fair pair of dice is rolled 138 times. Find the probability that the same point comes up on both dice at least 28 times.     (Answer: 0.1515)"]
[null,null,null,null,null,"Normal Approx.",null,null,null,null,null,null,null,null,null,"Original",null,"Approximation"]
[null,null,null,"Pr of:",null,64.5," < x <",100.5,null,null,null,null,null,null,null,"< x <",null,{"$f":"IF(O36=\"\",\"\",O36-0.5)","v":""}," < x <",{"$f":"IF(Q36=\"\",\"\",Q36+0.5)","v":""}]
[null,null,65,"< x <",100,-2.2372322931098001," < Z <",2.9589201295968324,null,"Answer:",null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",O36=\"\"),\"\",(R35-V6)/V7)","v":""}," < Z <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q36=\"\"),\"\",(T35-V6)/V7)","v":""},null,"Answer:",null,null,null,{"$f":"IF(R36=\"\",\"\",ROUND(R36,2))","v":""},null,{"$f":"IF(T36=\"\",\"\",ROUND(T36,2))","v":""},null,"Example 4. A fair die is rolled 140 times. Find the probability that itt comes up larger than 4 at least 55 times.   (Answer: 0.0808)"]
[null,null,null,null,null,1.2635580888435305E-2," < P <",0.9984564044790033,"P =",0.98599999999999999,null,null,null,null,null,null,null,{"$f":"IF(OR(Q5=\"\",Q6=\"\",O36=\"\"),\"\",NORMSDIST(Z36))","v":""}," < P <",{"$f":"IF(OR(Q5=\"\",Q6=\"\",Q36=\"\"),\"\",NORMSDIST(AB36))","v":""},"P =",{"$f":"IF(OR(R37=\"\",T37=\"\"),\"\",(T37-R37))","v":""}]
[]
[]
[null,null,null,"The above is just an example already filled and solved"]

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[]
[null,"Section 6.1 : Solving Graphically",null,null,null,null,null,null,{"$f":"IF(AND(C9=0,D9=0,F9=0),\"\",\"Line 1\")","v":"Line 1"},null,null,null,null,null,{"$f":"IF(AND(C21=0,D21=0,F21=0),\"\",\"Line 2\")","v":"Line 2"},null,null,null,null,null,{"$f":"IF(OR(I2=\"\",O2=\"\"),\"\",\"Line 1 & 2\")","v":"Line 1 & 2"},null,null,"Select a Point"]
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{"sheet":"11) All Int.","index":13,"n_rows":92,"n_cols":36,"rows_kept":92,"cut":false,"hidden":false,"merged":[[75,29,79,34],[40,7,40,8],[41,7,41,8],[32,2,32,22],[34,3,34,12],[34,15,34,22],[63,35,64,39],[66,35,69,40],[70,35,74,40],[13,1,17,6],[13,15,17,20],[63,29,67,34],[69,29,73,34]]}
[]
[null,null,"Solving 2 Equations, 2 Unknowns Using the All-Integer Method.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solving 3 Equations, 3 Unknowns Using the All-Integer Method."]
[null,null,"(Not to be used for special cases such as: no solution or dependent)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(Not to be used for special cases such as: no solution or dependent)"]
[]
[null,"   Setup the initial table without decimals or fractions",null,null,null,null,null,null,null,null,null,null,null,null,null,"   Setup the initial table without decimals or fractions"]
[null,"  (see example below):",null,null,null,null,null,null,null,null,null,null,null,null,null,"   (see example below):"]
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[null,null,2,2,2,null,null,null,{"$f":"IF(AND($D$11=1,$L$8=0),C10,\"\")","v":1},{"$f":"IF(AND($D$11=1,$L$8=0),D10,\"\")","v":3},{"$f":"IF(AND($D$11=1,$L$8=0),E10,\"\")","v":5},{"$f":"IF(AND(I9=0,J9=0,K9=0),1,IF(AND(I9=0,J9=0,K9<>0),2,0))","v":0},{"$f":"IF(L9=1,\"Linearly Dependent\",IF(L9=2,\"No Solution\",IF(L9=3,\"Pivot = 0\",\"\")))","v":""},null,null,null,1,2,3,4,null,null,{"$f":"IF(AND($R$12=1,$AA$8=0),Q10,\"\")","v":5},4,6,5,{"$f":"IF(AND(W9=0,X9=0,Y9=0,Z9=0),1,IF(AND(W9=0,X9=0,Y9=0,Z9<>0),2,0))","v":0},{"$f":"IF(AA9=1,\"Linearly Dependent\",IF(AA9=2,\"No Solution\",IF(AA9=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,1,3,5,null,null,null,null,null,null,{"$f":"SUM(L8:L9)","v":0},null,null,null,null,5,4,6,5,null,null,5,7,8,9,{"$f":"IF(AND(W10=0,X10=0,Y10=0,Z10=0),1,IF(AND(W10=0,X10=0,Y10=0,Z10<>0),2,0))","v":0},{"$f":"IF(AA10=1,\"Linearly Dependent\",IF(AA10=2,\"No Solution\",IF(AA10=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,null,{"$f":"IF(COUNT(C9:E10)<=2,0,1)","v":1},null,null,null,null,{"$f":"IF(AND($D$11=1,$L$10=0),I8,\"\")","v":2},{"$f":"IF(AND($D$11=1,$L$10=0),J8,\"\")","v":2},{"$f":"IF(AND($D$11=1,$L$10=0),K8,\"\")","v":2},{"$f":"IF(AND(I11=0,J11=0,K11=0),1,IF(AND(I11=0,J11=0,K11<>0),2,0))","v":0},{"$f":"IF(L11=1,\"Linearly Dependent\",IF(L11=2,\"No Solution\",IF(L11=3,\"Pivot = 0\",\"\")))","v":""},null,null,null,5,7,8,9,null,null,null,null,null,null,{"$f":"SUM(AA8:AA10)","v":0}]
[null,null,null,null,null,null,null,null,{"$f":"IF(AND($D$11=1,$L$10=0),0,\"\")","v":0},{"$f":"IF(AND($D$11=1,$L$10=0),((J9*I8)-(I9*J8)),\"\")","v":4},{"$f":"IF(AND($D$11=1,$L$10=0),((I8*K9)-(I9*K8)),\"\")","v":8},{"$f":"IF(AND(I12=0,J12=0,K12=0),1,IF(AND(I12=0,J12=0,K12<>0),2,IF(J12=0,3,0)))","v":0},{"$f":"IF(L12=1,\"Linearly Dependent\",IF(L12=2,\"No Solution\",IF(L12=3,\"Pivot = 0\",\"\")))","v":""},null,null,null,null,{"$f":"IF(COUNT(Q9:T11)<=7,0,1)","v":1},null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$11=0),W8,\"\")","v":1},{"$f":"IF(AND($R$12=1,$AA$11=0),X8,\"\")","v":2},{"$f":"IF(AND($R$12=1,$AA$11=0),Y8,\"\")","v":3},{"$f":"IF(AND($R$12=1,$AA$11=0),Z8,\"\")","v":4},{"$f":"IF(AND(W12=0,X12=0,Y12=0,Z12=0),1,IF(AND(W12=0,X12=0,Y12=0,Z12<>0),2,0))","v":0},{"$f":"IF(AA12=1,\"Linearly Dependent\",IF(AA12=2,\"No Solution\",IF(AA12=3,\"Pivot = 0\",\"\")))","v":""}]
[null,{"$f":"IF(B14=\"\",\"\",\" Comment:\")","v":""},null,null,null,null,null,null,null,null,null,{"$f":"SUM(L7:L12)","v":0},null,null,null,{"$f":"IF(P14=\"\",\"\",\" Comment:\")","v":""},null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$11=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$11=0),((X9*W8)-(W9*X8)),\"\")","v":-6},{"$f":"IF(AND($R$12=1,$AA$11=0),((W8*Y9)-(W9*Y8)),\"\")","v":-9},{"$f":"IF(AND($R$12=1,$AA$11=0),((W8*Z9)-(W9*Z8)),\"\")","v":-15},{"$f":"IF(AND(W13=0,X13=0,Y13=0,Z13=0),1,IF(AND(W13=0,X13=0,Y13=0,Z13<>0),2,IF(X13=0,3,0)))","v":0},{"$f":"IF(AA13=1,\"Linearly Dependent\",IF(AA13=2,\"No Solution\",IF(AA13=3,\"Pivot = 0\",\"\")))","v":""}]
[null,{"$f":"IF(OR(L10=1,L13=1,L16=1),AD64,IF(OR(L10=2,L13=2,L16=2),AD70,IF(OR(L10=3,L13=3,L16=3),AD76,\"\")))","v":""},null,null,null,null,null,null,{"$f":"IF(AND($D$11=1,$L$13=0),J12,\"\")","v":4},{"$f":"IF(AND($D$11=1,$L$13=0),0,\"\")","v":0},{"$f":"IF(AND($D$11=1,$L$13=0),(((J12*K11)-(J11*K12))/I8),\"\")","v":-4},{"$f":"IF(AND(I14=0,J14=0,K14=0),1,IF(AND(I14=0,J14=0,K14<>0),2,0))","v":0},{"$f":"IF(L14=1,\"Linearly Dependent\",IF(L14=2,\"No Solution\",IF(L14=3,\"Pivot = 0\",\"\")))","v":""},null,null,{"$f":"IF(OR(AA11=1,AA15=1,AA19=1,AA23=1),AD64,IF(OR(AA11=2,AA15=2,AA19=2,AA23=2),AD70,IF(OR(AA11=3,AA15=3,AA19=3,AA23=3),AD76,\"\")))","v":""},null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$11=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$11=0),((W8*X10)-(W10*X8)),\"\")","v":-3},{"$f":"IF(AND($R$12=1,$AA$11=0),((W8*Y10)-(W10*Y8)),\"\")","v":-7},{"$f":"IF(AND($R$12=1,$AA$11=0),((W8*Z10)-(W10*Z8)),\"\")","v":-11},{"$f":"IF(AND(W14=0,X14=0,Y14=0,Z14=0),1,IF(AND(W14=0,X14=0,Y14=0,Z14<>0),2,0))","v":0},{"$f":"IF(AA14=1,\"Linearly Dependent\",IF(AA14=2,\"No Solution\",IF(AA14=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"IF(AND($D$11=1,$L$13=0),0,\"\")","v":0},{"$f":"IF(AND($D$11=1,$L$13=0),J12,\"\")","v":4},{"$f":"IF(AND($D$11=1,$L$13=0),K12,\"\")","v":8},{"$f":"IF(AND(I15=0,J15=0,K15=0),1,IF(AND(I15=0,J15=0,K15<>0),2,0))","v":0},{"$f":"IF(L15=1,\"Linearly Dependent\",IF(L15=2,\"No Solution\",IF(L15=3,\"Pivot = 0\",\"\")))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AA8:AA14)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(L7:L15)","v":0},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$15=0),X13,\"\")","v":-6},{"$f":"IF(AND($R$12=1,$AA$15=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$15=0),(((X13*Y12)-(X12*Y13))/W8),\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$15=0),(((X13*Z12)-(X12*Z13))/W8),\"\")","v":6},{"$f":"IF(AND(W16=0,X16=0,Y16=0,Z16=0),1,IF(AND(W16=0,X16=0,Y16=0,Z16<>0),2,0))","v":0},{"$f":"IF(AA16=1,\"Linearly Dependent\",IF(AA16=2,\"No Solution\",IF(AA16=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"IF(AND($D$11=1,$L$16=0),I14/J12,\"\")","v":1},{"$f":"IF(AND($D$11=1,$L$16=0),0,\"\")","v":0},{"$f":"IF(AND($D$11=1,$L$16=0),K14/J12,\"\")","v":-1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$15=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$15=0),X13,\"\")","v":-6},{"$f":"IF(AND($R$12=1,$AA$15=0),Y13,\"\")","v":-9},{"$f":"IF(AND($R$12=1,$AA$15=0),Z13,\"\")","v":-15},{"$f":"IF(AND(W17=0,X17=0,Y17=0,Z17=0),1,IF(AND(W17=0,X17=0,Y17=0,Z17<>0),2,0))","v":0},{"$f":"IF(AA17=1,\"Linearly Dependent\",IF(AA17=2,\"No Solution\",IF(AA17=3,\"Pivot = 0\",\"\")))","v":""},{"$f":"IF(X13=0,3,\"\")","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"IF(AND($D$11=1,$L$16=0),0,\"\")","v":0},{"$f":"IF(AND($D$11=1,$L$16=0),J15/J12,\"\")","v":1},{"$f":"IF(AND($D$11=1,$L$16=0),K15/J12,\"\")","v":2},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$15=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$15=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$15=0),(((X13*Y14)-(X14*Y13))/W8),\"\")","v":15},{"$f":"IF(AND($R$12=1,$AA$15=0),(((X13*Z14)-(X14*Z13))/W8),\"\")","v":21},{"$f":"IF(AND(W18=0,X18=0,Y18=0,Z18=0),1,IF(AND(W18=0,X18=0,Y18=0,Z18<>0),2,IF(Y18=0,3,0)))","v":0},{"$f":"IF(AA18=1,\"Linearly Dependent\",IF(AA18=2,\"No Solution\",IF(AA18=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AA8:AA18)","v":0}]
[null,"  Example:","For the following set of equations:",null,null,null,null,null,null,null,null,null,null,null,null,"Example: For the following set of equations:",null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$19=0),Y18,\"\")","v":15},{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),(((Y18*Z16)-(Y16*Z18))/X13),\"\")","v":-15},{"$f":"IF(AND(W20=0,X20=0,Y20=0,Z20=0),1,IF(AND(W20=0,X20=0,Y20=0,Z20<>0),2,0))","v":0},{"$f":"IF(AA20=1,\"Linearly Dependent\",IF(AA20=2,\"No Solution\",IF(AA20=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,"   0.2x - 0.1y = 0.4",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2x + y - 3z =5",null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),Y18,\"\")","v":15},{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),(((Y18*Z17)-(Y17*Z18))/X13),\"\")","v":6},{"$f":"IF(AND(W21=0,X21=0,Y21=0,Z21=0),1,IF(AND(W21=0,X21=0,Y21=0,Z21<>0),2,0))","v":0},{"$f":"IF(AA21=1,\"Linearly Dependent\",IF(AA21=2,\"No Solution\",IF(AA21=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,"0.1x + 0.1y = 0.5",null,null,null,null,null,null,null,"x =",null,{"$f":"IF(AND($D$11=1,$M$19=0),K17,\"\")","v":-1},null,null,null,null,"2y - z = 5",null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$19=0),Y18,\"\")","v":15},{"$f":"IF(AND($R$12=1,$AA$19=0),Z18,\"\")","v":21},{"$f":"IF(AND(W22=0,X22=0,Y22=0,Z22=0),1,IF(AND(W22=0,X22=0,Y22=0,Z22<>0),2,0))","v":0},{"$f":"IF(AA22=1,\"Linearly Dependent\",IF(AA22=2,\"No Solution\",IF(AA22=3,\"Pivot = 0\",\"\")))","v":""}]
[null,null,null,null,null,null,null,null,null,null,"y =",null,{"$f":"IF(AND($D$11=1,$M$19=0),K18,\"\")","v":2},null,null,null,null,"2x + y + 2z = 6",null,null,null,null,null,null,null,null,{"$f":"SUM(AA8:AA22)","v":0}]
[null,"    Multiply each equation by 10 to remove decimals:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$23=0),W20/Y18,\"\")","v":1},{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),Z20/Y18,\"\")","v":-1}]
[null,"   Setup table:",null,null,null,null,null,null,null,null,null,null,null,null,null,"The setup table is:",null,null,null,null,null,null,{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),X21/Y18,\"\")","v":1},{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),Z21/Y18,\"\")","v":0.4}]
[null,null,"x","y",null,null,null,null,null,null,null,null,null,null,null,null,"x","y","z",null,null,null,{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),0,\"\")","v":0},{"$f":"IF(AND($R$12=1,$AA$23=0),Y22/Y18,\"\")","v":1},{"$f":"IF(AND($R$12=1,$AA$23=0),Z22/Y18,\"\")","v":1.4}]
[null,null,2,-1,4,null,null,null,null,null,null,null,null,null,null,null,2,1,3,5]
[null,null,1,1,5,null,null,null,null,null,null,null,null,null,null,null,0,2,-1,5,null,null,null,null,null,"x =",{"$f":"IF(AB28<>\"\",\"=\",\"\")","v":"="},{"$f":"IF(AND($R$12=1,$AA$23=0),Z24,\"\")","v":-1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,1,2,6,null,null,null,null,null,"y =",{"$f":"IF(AB29<>\"\",\"=\",\"\")","v":"="},{"$f":"IF(AND($R$12=1,$AA$23=0),Z25,\"\")","v":0.4}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"z =",{"$f":"IF(AB30<>\"\",\"=\",\"\")","v":"="},{"$f":"IF(AND($R$12=1,$AA$23=0),Z26,\"\")","v":1.4}]
[]
[]
[null,null,"Note: First Pivot cannot be = 0. Try to rearrange the original set of equations by switching rows in the setup table. Switch between rows 1 and 2."]
[]
[null,null,null,"Linear Dependent because the row is all 0s.",null,null,null,null,null,null,null,null,null,null,null,"No Solution because the row is all 0s on the left,\nand nonzero number in the right."]
[]
[]
[null,null,null,null,null,null,null,null,"Regular Calculator to solve 2 or 3 linear equations:"]
[]
[null,null,"x","y","=",null,null,null,null,null,null,null,null,null,null,null,"x","y","z","="]
[null,null,5,3,3,null,"x =",{"$f":"IF(OR(L41<3,L42<3),\"\",VLOOKUP(C40,$D$85:$E$86,2,FALSE))","v":0},null,null,null,{"$f":"COUNT(C41:E41)","v":3},null,null,null,null,4,2,3,7,null,"x =",{"$f":"IF(OR(Z41<4,Z42<4,Z43<4),\"\",VLOOKUP(Q40,$R$85:$S$88,2,FALSE))","v":0.91666666666666652},null,null,{"$f":"COUNT(Q41:T41)","v":4}]
[null,null,2,3,3,null,"y = ",{"$f":"IF(OR(L41<3,L42<3),\"\",VLOOKUP(D40,$D$85:$E$86,2,FALSE))","v":1},null,null,null,{"$f":"COUNT(C42:E42)","v":3},null,null,null,null,4,2,7,4,null,"y = ",{"$f":"IF(OR(Z41<4,Z42<4,Z43<4),\"\",VLOOKUP(R40,$R$85:$S$88,2,FALSE))","v":2.791666666666667},null,null,{"$f":"COUNT(Q42:T42)","v":4}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9,0,3,6,null,"z =",{"$f":"IF(OR(Z41<4,Z42<4,Z43<4),\"\",VLOOKUP(S40,$R$85:$S$88,2,FALSE))","v":-0.75},null,null,{"$f":"COUNT(Q43:T43)","v":4}]
[null,null,null,null,null,null,null,{"$f":"+IFERROR(H41,\"None Unique Solution\")","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"+IFERROR(W41,\"None Unique Solution\")","v":0.91666666666666652}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Linear Dependent because the row is all 0s.",null,null,null,null,null,"Linear Dependent because the row is all 0s."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No Solution because the row is all 0s on the left,\nand nonzero number in the right."]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"No Solution because the row is all 0s on the left,\nand nonzero number in the right."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pivot cannot be = 0. Try to rearrange the original set of equations by switching rows in the setup table. Switch between rows 1 and 2."]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pivot cannot be = 0. Try to rearrange the original \nset of equations by switching rows in the setup table. \nSwitch between rows 1 and 2 or between rows 2 and 3…etc."]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"2 Eq",null,null,null,null,null,null,null,null,null,null,null,null,null,"3 Eq"]
[null,null,null,null,"Variables",{"$f":"C40","v":"x"},{"$f":"D40","v":"y"},null,null,null,null,null,null,null,null,null,null,null,"Variables",{"$f":"Q40","v":"x"},{"$f":"R40","v":"y"},{"$f":"S40","v":"z"}]
[null,null,null,"x",{"$f":"MMULT(F89:G90,H85:H86)","v":0},{"$f":"IF(COUNT($C41:$E41)=0,1,C41)","v":5},{"$f":"IF(COUNT($C41:$E41)=0,0,D41)","v":3},{"$f":"E41","v":3},null,{"$f":"IF(ISERROR(E85),\"\",E85)","v":0},null,null,null,null,null,null,null,"x",{"$f":"MMULT(T89:V91,W85:W87)","v":0.91666666666666652},{"$f":"IF(COUNT($Q41:$T41)=0,1,Q41)","v":4},{"$f":"IF(COUNT($Q41:$T41)=0,0,R41)","v":2},{"$f":"IF(COUNT($Q41:$T41)=0,0,S41)","v":3},{"$f":"T41","v":7},{"$f":"IF(ISERROR(S85),\"\",S85)","v":0.91666666666666652},null,{"$f":"IF(ISERROR(S85),\"\",S85)","v":0.91666666666666652}]
[null,null,null,"y",1,{"$f":"IF(COUNT($C42:$E42)=0,0,C42)","v":2},{"$f":"IF(COUNT($C42:$E42)=0,1,D42)","v":3},{"$f":"E42","v":3},null,{"$f":"IF(ISERROR(E86),\"\",E86)","v":1},null,null,null,null,null,null,null,"y",2.791666666666667,{"$f":"IF(COUNT($Q42:$T42)=0,0,Q42)","v":4},{"$f":"IF(COUNT($Q42:$T42)=0,1,R42)","v":2},{"$f":"IF(COUNT($Q42:$T42)=0,0,S42)","v":7},{"$f":"T42","v":4},{"$f":"IF(ISERROR(S86),\"\",S86)","v":2.791666666666667},null,{"$f":"IF(ISERROR(S86),\"\",S86)","v":2.791666666666667}]
[null,null,null,null,{"$error":"#N/A"},null,null,null,null,{"$f":"IF(ISERROR(E87),\"\",#REF!)","v":""},null,null,null,null,null,null,null,"z",-0.75,{"$f":"IF(COUNT($Q43:$T43)=0,0,Q43)","v":9},{"$f":"IF(COUNT($Q43:$T43)=0,0,R43)","v":0},{"$f":"IF(COUNT($Q43:$T43)=0,1,S43)","v":3},{"$f":"T43","v":6},-0.75,null,{"$f":"IF(ISERROR(S87),\"\",S87)","v":-0.75}]
[null,null,null,null,{"$error":"#N/A"},null,null,null,null,{"$f":"IF(ISERROR(E88),\"\",#REF!)","v":""},null,null,null,null,null,null,null,null,{"$error":"#N/A"},null,null,null,null,{"$f":"IF(ISERROR(S88),\"\",#REF!)","v":""}]
[null,null,null,null,null,{"$f":"MINVERSE(F85:G86)","v":0.33333333333333337},-0.33333333333333337,{"$error":"#N/A"},{"$error":"#N/A"},null,null,null,null,null,null,null,null,null,null,{"$f":"MINVERSE(T85:V87)","v":8.3333333333333329E-2},-8.3333333333333329E-2,0.1111111111111111,{"$error":"#N/A"}]
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[null,null,null,null,null,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},null,null,null,null,null,null,null,null,null,null,{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"},{"$error":"#N/A"}]

{"sheet":"11) 3 Eq","index":14,"n_rows":67,"n_cols":125,"rows_kept":67,"cut":false,"hidden":false,"merged":[[13,9,13,10],[21,24,21,25],[21,26,21,27],[22,26,22,27],[26,21,26,23],[18,22,19,23],[18,31,19,35],[16,36,16,37],[13,35,13,37],[14,35,14,37],[13,20,13,22],[14,20,14,22],[26,30,26,31],[26,34,26,38],[18,42,18,43],[19,39,19,40],[18,39,18,40],[19,24,19,25],[18,24,18,25],[22,24,22,25],[19,27,19,28],[18,37,19,38],[22,41,22,42],[22,43,22,44],[21,41,21,42],[21,43,21,44],[34,25,34,26],[34,32,34,33],[34,39,34,40],[34,27,34,29],[34,34,34,36],[34,41,34,43],[0,14,0,21],[24,9,24,11],[26,28,26,29],[26,26,26,27],[26,43,26,44],[26,41,26,42],[26,39,26,40],[30,32,30,36],[29,30,29,31],[29,32,29,33],[29,34,29,35],[29,36,29,38],[28,32,28,33],[28,36,28,38],[26,32,26,33],[26,24,26,25],[28,34,28,35],[28,30,28,31],[47,78,47,79],[45,73,45,74],[46,73,46,74],[47,73,47,74],[44,67,44,68],[44,69,44,70],[44,71,44,72],[44,73,44,74],[47,67,47,68],[47,69,47,70],[46,69,46,70],[45,69,45,70],[45,71,45,72],[46,71,46,72],[47,71,47,72],[45,67,45,68],[46,67,46,68],[36,82,36,83],[36,87,36,88],[32,80,32,81],[33,80,33,81],[34,80,34,81],[32,82,32,83],[33,82,33,83],[45,78,45,79],[46,78,46,79],[1,28,1,30],[34,82,34,83],[32,84,32,85],[33,84,33,85],[34,84,34,85],[22,39,22,40],[21,28,21,29],[22,28,22,29],[21,30,21,31],[22,30,22,31],[21,39,21,40],[31,38,31,39],[2,28,2,30],[21,55,21,57],[22,55,22,57],[27,32,27,37],[26,45,26,46],[22,45,22,46],[21,45,21,46],[31,33,31,34],[18,27,18,28],[7,25,7,27],[8,25,8,27],[19,42,19,43],[1,31,1,33],[1,34,1,36],[2,34,2,36],[3,34,3,36],[4,34,4,36],[1,37,1,39],[2,37,2,39],[3,37,3,39],[4,37,4,39],[3,28,3,30],[4,28,4,30],[2,31,2,33],[3,31,3,33],[4,31,4,33],[6,31,6,32],[7,31,7,32],[8,31,8,32],[6,37,6,39],[7,37,7,39],[8,37,8,39],[6,34,6,35],[7,34,7,35],[6,28,6,29],[7,28,7,29],[8,28,8,29],[8,34,8,35],[1,4,1,6],[1,7,1,9],[1,10,1,12],[2,4,2,6],[2,7,2,9],[2,10,2,12],[3,4,3,6],[3,7,3,9],[3,10,3,12],[2,1,3,3],[2,25,3,27],[22,5,22,6],[22,7,22,8],[22,9,22,11],[13,4,14,5],[26,9,26,11],[26,12,26,14],[6,2,6,3],[6,4,6,5],[6,7,6,8],[7,4,7,5],[7,7,7,8],[7,2,7,3],[13,6,13,7],[14,9,14,10],[14,6,14,7],[16,5,16,6],[16,7,16,8],[16,9,16,10],[18,5,18,6],[18,7,18,8],[18,9,18,10],[6,25,6,27]]}
[null,null,null,null,"Solving 2 Equations",null,null,null,null,null,null,null,null,null,"Fill Green Cells",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solving 3 Equations",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 1",null,null,"Eq 1",null,null,null,"x"]
[null,null,null,null,"x",null,null,"y",null,null,"=",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x",null,null,"y",null,null,"z",null,null,"=",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 2",null,null,"Eq 2",null,null,null,"y",null,"+"]
[null,"Enter Values",null,null,2,null,null,3,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Enter Values",null,null,2,null,null,1,null,null,3,null,null,5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 3",null,null,"Eq 3",null,null,null,"z",null,"-"]
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[null,null,"Eq 1",null,{"$f":"E3&\" x\"","v":"2 x"},null,{"$f":"IF(H3>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(H3)&\" y\"","v":"3 y"},null,"=",null,{"$f":"K3","v":3},null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 1",null,null,{"$f":"AC3&\" x\"","v":"2 x"},null,{"$f":"IF(AF3>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(AF3)&\" y\"","v":"1 y"},null,{"$f":"IF(AI3>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(AL3)&\" z\"","v":"5 z"},null,"=",{"$f":"AL3","v":5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"E3","v":2},{"$f":"H3","v":3},{"$f":"K3","v":3},null,null,null,null,null,null,null,null,null,{"$f":"AC3","v":2},null,{"$f":"AF3","v":1},null,{"$f":"AI3","v":3},{"$f":"AL3","v":5}]
[null,null,"Eq 2",null,{"$f":"E4&\" x\"","v":"4 x"},null,{"$f":"IF(H4>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(H4)&\" y\"","v":"2 y"},null,"=",null,{"$f":"K4","v":6},null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 2",null,null,{"$f":"AC4&\" x\"","v":"0 x"},null,{"$f":"IF(AF4>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(AF4)&\" y\"","v":"2 y"},null,{"$f":"IF(AI4>0,\"+\",\"-\")","v":"-"},{"$f":"ABS(AL4)&\" z\"","v":"5 z"},null,"=",{"$f":"AL4","v":5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"E4","v":4},{"$f":"H4","v":2},{"$f":"K4","v":6},null,null,null,null,null,null,null,null,null,{"$f":"AC4","v":0},null,{"$f":"AF4","v":2},null,{"$f":"AI4","v":-1},{"$f":"AL4","v":5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Eq 3",null,null,{"$f":"AC5&\" x\"","v":"2 x"},null,{"$f":"IF(AF5>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(AF5)&\" y\"","v":"1 y"},null,{"$f":"IF(AI5>0,\"+\",\"-\")","v":"+"},{"$f":"ABS(AL5)&\" z\"","v":"6 z"},null,"=",{"$f":"AL5","v":6},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC5","v":2},null,{"$f":"AF5","v":1},null,{"$f":"AI5","v":2},{"$f":"AL5","v":6}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a) Select Two different pairs of equations:"]
[null,"a) Eliminate one variable:"]
[]
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[null,null,null,null,"Mult ",null,{"$f":"C7","v":"Eq 1"},null,"by",-2,null,null,null,null,null,null,null,null,null,null,"Eq 1",null,null,{"$f":"IF($U$14=$BP$1,AC3,IF($U$14=$BP$2,AC4,AC5))","v":2},"x",{"$f":"IF($U$14=$BP$1,AE7,IF($U$14=$BP$2,AE8,AE9))","v":"+"},{"$f":"IF($U$14=$BP$1,ABS(AF3),IF($U$14=$BP$2,ABS(AF4),ABS(AF5)))","v":1},"y",{"$f":"IF($U$14=$BP$1,AH7,IF($U$14=$BP$2,AH8,AH9))","v":"+"},{"$f":"IF($U$14=$BP$1,ABS(AI3),IF($U$14=$BP$2,ABS(AI4),ABS(AI5)))","v":3},"z","=",{"$f":"IF($U$14=$BP$1,AL3,IF($U$14=$BP$2,AL4,AL5))","v":5},null,null,"Eq 2",null,null,{"$f":"IF($AJ$14=$BP$1,AC3,IF($AJ$14=$BP$2,AC4,AC5))","v":0},"x",{"$f":"IF($AJ$14=$BP$1,AE7,IF($AJ$14=$BP$2,AE8,AE9))","v":"+"},{"$f":"IF($AJ$14=$BP$1,ABS(AF3),IF($AJ$14=$BP$2,ABS(AF4),ABS(AF5)))","v":2},"y",{"$f":"IF($AJ$14=$BP$1,AH7,IF($AJ$14=$BP$2,AH8,AH9))","v":"-"},{"$f":"IF($AJ$14=$BP$1,ABS(AI3),IF($AJ$14=$BP$2,ABS(AI4),ABS(AI5)))","v":1},"z","=",{"$f":"IF($AJ$14=$BP$1,AL3,IF($AJ$14=$BP$2,AL4,AL5))","v":5},null,null,null,null,null,null,null,null,null,"x","y",null,null,null,null,null,null,null,null,null,null,{"$f":"X14","v":2},null,{"$f":"IF(Z14=\"+\",AA14,-1*AA14)","v":1},null,{"$f":"IF(AC14=\"+\",AD14,-1*AD14)","v":3},{"$f":"AG14","v":5},null,null,{"$f":"AM14","v":0},null,{"$f":"IF(AO14=\"+\",AP14,-1*AA14)","v":2},null,{"$f":"IF(AR14=\"+\",AS14,-1*AS14)","v":-1},{"$f":"AV14","v":5}]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"J15*E4","v":4},{"$f":"J15*H4","v":2},{"$f":"J15*K4","v":6}]
[null,null,null,null,{"$f":"J14&\" * \"&G14","v":"-2 * Eq 1"},{"$f":"IF(BF15=0,\"\",IF(BF15<>0,IF(BF15>0,\" \"&BF15&\" x\",\"- \"&ABS(BF15)&\" x\")))","v":"- 4 x"},null,{"$f":"IF(BG15=0,\"\",IF(BG15<>0,IF(BG15>0,\" + \"&BG15&\" x\",\"- \"&ABS(BG15)&\" x\")))","v":"- 6 x"},null,{"$f":"\" = \"&BH15","v":" = -6"},null,null,null,null,null,null,null,null,null,null,"b) Eliminate SAME variable in both pairs. To remove:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"BF15+BF16","v":0},{"$f":"BG15+BG16","v":-4},0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(COUNTIF(BF18:BG18,\"x\")>=1,COUNTIF(BF18:BG18,\"y\")>=1),\"2 variables\",\"\")","v":""},{"$f":"IF(BF17=0,\"\",BF14)","v":""},{"$f":"IF(BG17=0,\"\",BG14)","v":"y"}]
[null,null,null,null,{"$f":"J15&\" * \"&G15","v":"1 * Eq 2"},{"$f":"IF(BF16=0,\"\",IF(BF16<>0,IF(BF16>0,\" \"&BF16&\" x\",\"- \"&ABS(BF16)&\" x\")))","v":" 4 x"},null,{"$f":"IF(BG16=0,\"\",IF(BG16<>0,IF(BG16>0,\" + \"&BG16&\" x\",\"- \"&ABS(BG16)&\" x\")))","v":" + 2 x"},null,{"$f":"\" = \"&BH16","v":" = 6"},null,null,null,null,null,null,null,null,null,null,null,null,"Mult ",null,{"$f":"U14","v":"Eq 1"},null,"by",-2,null,null,null,{"$f":"IF(CH25=\"\",\"\",IF(CH25=AK17,CH25 &\" is removed\",\"\"))","v":"y is removed"},null,null,null,null,null,"Mult ",null,{"$f":"AJ14","v":"Eq 2"},null,"by",1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"U15","v":"Eq 2"},null,"by",1,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AJ15","v":"Eq 3"},null,"by",-2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"2 Eq"]
[null,"b) Add the two equations",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Variables",{"$f":"#REF!","v":{"$error":"#REF!"}},{"$f":"#REF!","v":{"$error":"#REF!"}},null,null,null,null,null,null,null,"x",null,"y",null,"z",null,null,null,"x",null,"y",null,"z"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Solution",null,"x =",null,{"$f":"IF(AG31<>\"\",\"\",IFERROR(CA46,\"\"))","v":3},null,null,null,null,"y = ",null,{"$f":"IF(AG31<>\"\",\"\",IFERROR(CA47,\"\"))","v":2},null,null,null,null,"z =",null,{"$f":"IF(AG31<>\"\",\"\",IFERROR(CA48,\"\"))","v":-1},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"BZ24","v":-4},{"$f":"CB24","v":0},{"$f":"CD24","v":-5},{"$f":"CE24","v":-7},null,null,null,{"$f":"HLOOKUP(1,$BV$32:$BX$35,4,FALSE)","v":-4},null,{"$f":"HLOOKUP(2,$BV$32:$BX$35,4,FALSE)","v":-5},null,{"$f":"BY35","v":-7},null,{"$f":"COUNT(CC35:CG35)","v":3}]
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[]
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[null,null,null,"C) Multiplication Example: Fill the left and the right matrices to be multiplied:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"F52","v":4},null,null,{"$f":"M52","v":3}]
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[]
[null,null,null,"First Matrix Dimensions:",null,null,null,null,null,null,null,"Second  Matrix Dimensions:"]
[]
[]
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[null,null,null,null,null,null,null,null,null,null,null,null,"To see Mult Steps, Select:",null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF($F$52<>$K$52,\"\",HLOOKUP($O$57,$BM$40:$BS$45,2,FALSE))","v":3},null,{"$f":"IF(OR(S58=\"\",Y54=\"\"),\"\",S58&\" x \"&Y54)","v":"2 x 3"},{"$f":"IF(AA54=\"\",\"\",\"=\")","v":"="},{"$f":"IF(OR(Y54=\"\",S58=\"\"),\"\",S58*Y54)","v":6}]
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[null,null,"A) Finding the Inverse Matrix, Method 1 Using the All Integers ",null,null,null,null,null,null,null,null,null,null,"   B) Finding Inverse Method 2  (for 2  by 2 matrix only)",null,null,null,null,null,null,null,"    C)  To Solve Equations using the Inverse Matrix",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"-"]
[null,"   Setup the initial matrix without decimals or fractions",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fill the green cells including the middle signs",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"COUNT(C7:D8)","v":4}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Original Setup","a","b","A =",{"$f":"C7","v":2},{"$f":"D7","v":3},"Same Matrix",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AM7:AM17)","v":0}]
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[null,null,"Fill the green cells",null,null,null,"Matrix A",null," Matrix I",null,"Comment",null,null,"    Re-arrange: Switch a and d, negate b and c:",null,null,null,null,null,null,null,null,4,"y","+",null,7,"y","=",3,null,null,null,null,null,null,null,null,{"$f":"SUM(AM7:AM20)","v":0},null,{"$f":"X11","v":4},{"$f":"AA11","v":7}]
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[null,null,null,null,null,null,{"$f":"IF(AND($AM$5=1,$AM$10=0),0,\"\")","v":0},{"$f":"IF(AND($AM$5=1,$AM$10=0),((H8*G7)-(G8*H7)),\"\")","v":2},{"$f":"IF(AND($AM$5=1,$AM$10=0),((G7*I8)-(G8*I7)),\"\")","v":-4},{"$f":"IF(AND($AM$5=1,$AM$10=0),((G7*J8)-(G8*J7)),\"\")","v":2},{"$f":"IF(AM12=1,\"No Inverse\",IF(AM12=3,\"Pivot = 0\",\"\"))","v":""},null,null,"Find T :","T = (d) x (a ) - (-c) x (-b)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G12=0,H12=0),1,IF(H12=0,3,0))","v":0},null,null,{"$f":"(AO8*AP10)  - (AO10*AP8)","v":2}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AM13=1,\"No Inverse\",IF(AM13=3,\"Pivot = 0\",\"\"))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"T = (\"&R8& \" x \" &S10& \") - (\"&R10&\" x \"&S8&\" ) =\"","v":"T = (7 x 2) - (-4 x -3 ) ="},null,null,{"$f":"(R8*S10)  - (R10*S8)","v":2},null,null,null,null,"Find A -1",null,null,null,"A-1 =",null,null,{"$f":"AS16","v":3.5},null,{"$f":"AT16","v":-1.5},null,null,null,null,null,null,{"$f":"SUM(AM7:AM13)","v":0},null,null,{"$f":"IF(AP12=0,\"\",1/AP12)","v":0.5},null,null,{"$f":"IF(OR(W5=0,AA5=0,AD5=0),\"\",IF(AND(W6/W5=AA6/AA5,AA6/AA5=AD6/AD5),\"One Line\",\"\"))","v":""}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$5=1,$AM$14=0),H12,\"\")","v":2},{"$f":"IF(AND($AM$5=1,$AM$14=0),0,\"\")","v":0},{"$f":"IF(AND($AM$5=1,$AM$14=0),(((H12*I11)-(H11*I12))/G7),\"\")","v":7},{"$f":"IF(AND($AM$5=1,$AM$14=0),(((H12*J11)-(H11*J12))/G7),\"\")","v":-3},{"$f":"IF(AM15=1,\"No Inverse\",IF(AM15=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AS17","v":-2},null,{"$f":"AT17","v":1},null,null,null,null,null,null,{"$f":"IF(AND(G15=0,H15=0),1,0)","v":0},null,null,null,null,null,{"$f":"IF(AND(W5=\"\",AA5=\"\",W6=\"\",AA6=\"\"),1,COUNT(AS16:AT17))","v":4}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$5=1,$AM$14=0),0,\"\")","v":0},{"$f":"IF(AND($AM$5=1,$AM$14=0),H12,\"\")","v":2},{"$f":"IF(AND($AM$5=1,$AM$14=0),I12,\"\")","v":-4},{"$f":"IF(AND($AM$5=1,$AM$14=0),J12,\"\")","v":2},"",null,null,"Find 1/T:","1 / T =",{"$f":"IF(COUNTA(C7:D8)=0,\"\",\"1 / \"&R14)","v":"1 / 2"},"=",{"$f":"IF(R14=0,\"\",1/R14)","v":0.5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G16=0,H16=0),1,0)","v":0},null,{"$f":"IF(AP12=0,\"\",1/AP12)","v":0.5},{"$f":"AO8","v":7},{"$f":"AP8","v":-3},"=",{"$f":"IFERROR(IF(AP14=0,\"\",AO16*AP16),\"\")","v":3.5},{"$f":"IFERROR(IF(AP12=0,\"\",AO16*AQ16),\"\")","v":-1.5}]
[null,null,null,null,null,null,null,null,null,null,"",null,null,null,null,null,null,null,null,null,null,"Solution :",null,null,"A-1  .  B =",null,null,null,null,{"$f":"AD14","v":3.5},null,{"$f":"AF14","v":-1.5},null,".",{"$f":"AH10","v":5},null,null,null,null,null,null,{"$f":"AO10","v":-4},{"$f":"AP10","v":2},null,{"$f":"IFERROR(IF(AP14=0,\"\",AO16*AP17),\"\")","v":-2},{"$f":"IFERROR(IF(AP14=0,\"\",AO16*AQ17),\"\")","v":1}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$5=1,$AM$4=0),G15/H12,\"\")","v":1},{"$f":"IF(AND($AM$5=1,$AM$4=0),0,\"\")","v":0},{"$f":"IF(AND($AM$5=1,$AM$4=0),(I15/H12),\"\")","v":3.5},{"$f":"IF(AND($AM$5=1,$AM$4=0),J15/H12,\"\")","v":-1.5},"",null,null,null,"A -1  =  ( 1 / T ) x  R  ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AD15","v":-2},null,{"$f":"AF15","v":1},null,null,{"$f":"AH11","v":3},null,null,null,{"$f":"IF(AND(G18=0,H18=0,H17=0),1,IF(G18=0,3,0))","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$5=1,$AM$4=0),0,\"\")","v":0},{"$f":"IF(AND($AM$5=1,$AM$4=0),H16/H12,\"\")","v":1},{"$f":"IF(AND($AM$5=1,$AM$4=0),(I16/H12),\"\")","v":-2},{"$f":"IF(AND($AM$5=1,$AM$4=0),J16/H12,\"\")","v":1},"",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G19=0,H19=0,H17=0),1,0)","v":0}]
[null,null,null,null,null,null,"I",null,"A -1",null,"",null,null,"=",{"$f":"IF(R14=0,\"\",1/R14)","v":0.5},{"$f":"IF(R14=0,\"\",R8)","v":7},{"$f":"IF(R14=0,\"\",S8)","v":-3},"=",{"$f":"IF(R14=0,\"\",O20*P20)","v":3.5},{"$f":"IF(R14=0,\"\",O20*Q20)","v":-1.5},null,null,{"$f":"IF(AS14=\"One Line\",\"One Line\",IF(AS15=0,\"No Solution\",\"\"))","v":""},null,null,null,null," X =",null,{"$f":"IF(AS15=1,\"\",IF(OR(AS15=0,AS14=\"One Line\"),\"\",AD17*AI17+AF17*AI18))","v":13},null,"x =",{"$f":"AD20","v":13}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(R14=0,\"\",R10)","v":-4},{"$f":"IF(R14=0,\"\",S10)","v":2},null,{"$f":"IF(R14=0,\"\",O20*P21)","v":-2},{"$f":"IF(R14=0,\"\",O20*Q21)","v":1},null,null,null,null,null,null,null,null,null,{"$f":"IF(AS15=1,\"\",IF(OR(AS15=0,AS14=\"One Line\"),\"\",AD18*AI17+AF18*AI18))","v":-7},null,"y =",{"$f":"AD21","v":-7}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"#REF!*AG20+#REF!*AG21","v":{"$error":"#REF!"}}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"#REF!*AG21+#REF!*AI22","v":{"$error":"#REF!"}}]
[]
[null,"   Setup the initial matrix without decimals or fractions",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     To Solve 3 Equations using the Inverse Matrix"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(COUNT(C31:E33)>=6,1,0)","v":1}]
[null,null,"3 by 3 matrix",null,null,null,"Original Matrix A",null,null,"Identity matrix I",null,null,"Comment",null,null,null,null,null,"Fill the green cells ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G30=0,H30=0,I30=0),1,IF(G30=0,3,0))","v":0},null,"2x - 1y  = 4"]
[null,null,"Fill the green cells",null,null,null,{"$f":"IF($AM$28=1,C31,\"\")","v":2},{"$f":"IF($AM$28=1,D31,\"\")","v":1},{"$f":"IF($AM$28=1,E31,\"\")","v":3},{"$f":"IF($AM$28=1,1,\"\")","v":1},{"$f":"IF($AM$28=1,0,\"\")","v":0},{"$f":"IF($AM$28=1,0,\"\")","v":0},{"$f":"IF(AM29=1,\"No Inverse\",IF(AM29=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,"x","y","z",null,"=",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G31=0,H31=0,I31=0),1,0)","v":0},null,"1x +y = 5"]
[null,null,2,1,3,null,{"$f":"IF(AND($AM$28=1,$AM$29=0),C32,\"\")","v":0},2,-1,{"$f":"IF($AM$28=1,0,\"\")","v":0},{"$f":"IF($AM$28=1,1,\"\")","v":1},{"$f":"IF($AM$28=1,0,\"\")","v":0},{"$f":"IF(AM30=1,\"No Inverse\",IF(AM30=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,2,1,3,null,5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G32=0,H32=0,I32=0),1,0)","v":0}]
[null,"A =",0,2,-1,null,2,1,2,null,{"$f":"IF($AM$28=1,0,\"\")","v":0},{"$f":"IF($AM$28=1,1,\"\")","v":1},{"$f":"IF(AM31=1,\"No Inverse\",IF(AM31=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,0,2,-1,null,5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AM29:AM31)","v":0}]
[null,null,2,1,2,null,null,null,null,{"$f":"IF($AM$28=1,0,\"\")","v":0},null,null,null,null,null,null,null,null,2,1,2,null,5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G34=0,H34=0,I34=0),1,0)","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$32=0),G30,\"\")","v":2},1,3,1,0,0,{"$f":"IF(AM33=1,\"No Inverse\",IF(AM33=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G35=0,H35=0,I35=0),1,IF(H35=0,3,0))","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$32=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$32=0),((H31*G30)-(G31*H30)),\"\")","v":4},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*I31)-(G31*I30)),\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*J31)-(G31*J30)),\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*K31)-(G31*K30)),\"\")","v":2},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*L31)-(G31*L30)),\"\")","v":0},{"$f":"IF(AM34=1,\"No Inverse\",IF(AM34=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,{"$f":"S31","v":2},1,3,null,null,"x",null,null,null,{"$f":"W31","v":5},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G36=0,H36=0,I36=0),1,0)","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$32=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*H32)-(G32*H30)),\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*I32)-(G32*I30)),\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*J33)-(G32*J30)),\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*K32)-(G32*K30)),\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$32=0),((G30*L32)-(G32*L30)),\"\")","v":2},{"$f":"IF(AM35=1,\"No Inverse\",IF(AM35=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,"A =",0,2,-1,"X =",null,"y","B =",null,null,{"$f":"W32","v":5},null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AM29:AM35)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2,1,2,null,null,"z",null,null,null,{"$f":"W33","v":5},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G38=0,H38=0,I38=0),1,0)","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$36=0),H35,\"\")","v":4},{"$f":"IF(AND($AM$28=1,$AM$36=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*I34)-(H34*I35))/G30),\"\")","v":7},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*J34)-(H34*J35))/G30),\"\")","v":2},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*K34)-(H34*K35))/G30),\"\")","v":-1},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*L34)-(H34*L35))/G30),\"\")","v":0},{"$f":"IF(AM37=1,\"No Inverse\",IF(AM37=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G39=0,H39=0,I39=0),1,0)","v":0}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$36=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),H35,\"\")","v":4},{"$f":"IF(AND($AM$28=1,$AM$36=0),I35,\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$36=0),J35,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),K35,\"\")","v":2},{"$f":"IF(AND($AM$28=1,$AM$36=0),L35,\"\")","v":0},{"$f":"IF(AM38=1,\"No Inverse\",IF(AM38=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,{"$f":"IFERROR(AQ45,\"\")","v":-1.25},-0.25,1.75,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G40=0,H40=0,I40=0),1,IF(I40=0,3,0))","v":0},{"$f":"IF(H35=0,3,\"\")","v":""},null,null,{"$f":"COUNT(R45:T47)","v":9}]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$36=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*I36)-(H36*I35))/G30),\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*J36)-(H36*J35))/G30),\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*K36)-(H36*K35))/G30),\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$36=0),(((H35*L36)-(H36*L35))/G30),\"\")","v":4},{"$f":"IF(AM39=1,\"No Inverse\",IF(AM39=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,"A -1 =",0.5,0.5,-0.5,null,{"$f":"IFERROR(AQ45,\"No Inverse\")","v":-1.25},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AM29:AM39)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1,0,-1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G42=0,H42=0,I42=0),1,IF(G42=0,3,0))","v":0},null,null,null,{"$f":"R35","v":2},1,3]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$40=0),I40,\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*J38)-(I38*J40))/H35),\"\")","v":5},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*K38)-(I38*K40))/H35),\"\")","v":1},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*L38)-(I38*L40))/H35),\"\")","v":-7},{"$f":"IF(AM41=1,\"No Inverse\",IF(AM41=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,"Note: If the inverse matrix is not given, then you need to find  it.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G43=0,H43=0,I43=0),1,0)","v":0},null,null,null,0,2,-1]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),I40,\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*J39)-(I39*J40))/H35),\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*K39)-(I39*K40))/H35),\"\")","v":-2},{"$f":"IF(AND($AM$28=1,$AM$40=0),(((I40*L39)-(I39*L40))/H35),\"\")","v":2},{"$f":"IF(AM42=1,\"No Inverse\",IF(AM42=3,\"Pivot = 0\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND(G44=0,H44=0,I44=0),1,0)","v":0},null,null,null,2,1,2]
[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),I40,\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$40=0),J40,\"\")","v":-4},{"$f":"IF(AND($AM$28=1,$AM$40=0),K40,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$40=0),L40,\"\")","v":4},{"$f":"IF(AM43=1,\"No Inverse\",IF(AM43=3,\"Pivot = 0\",\"\"))","v":""},null,null,{"$f":"IF(AQ39=0,\"\",\"Solution : \")","v":"Solution : "},null,null,null,null,null,null,null,null,null,null,null,null,"Then",null,null,null,null,null,null,null,null,null,{"$f":"SUM(AM29:AM43)","v":0}]
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[null,null,null,null,null,null,{"$f":"IF(AND($AM$28=1,$AM$44=0),G42/I40,\"\")","v":1},{"$f":"IF(AND($AM$28=1,$AM$44=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$44=0),0,\"\")","v":0},{"$f":"IF(AND($AM$28=1,$AM$44=0),J42/I40,\"\")","v":-1.25},{"$f":"IF(AND($AM$28=1,$AM$44=0),K42/I40,\"\")","v":-0.25},{"$f":"IF(AND($AM$28=1,$AM$44=0),L42/I40,\"\")","v":1.75},null,null,null,"A-1  .  B   =",null,0.5,0.5,-0.5,".",{"$f":"IF($AQ$39=0,\"\",AA36)","v":5},null,null,"=",null,{"$f":"IF(AQ39=0,\"\",R46*V45+S46*V46+T46*V47)","v":2.5},null,null,"y =",{"$f":"AA46","v":2.5},null,null,null,null,null,null,null,null,null,null,null,0.5,0.5,-0.5,{"$error":"#N/A"}]
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[null,"Section 7.1, 7.2 Template",null,null,"Fill Green Cells",null,null,null,null,"Line 1",{"$f":"AK13&\" \"&AL13&\" \"&AM13","v":"-1 x +  4 y = 4"},null,null,null,"Line 2",{"$f":"AK14&\" \"&AL14&\" \"&AM14","v":"3 x +  5 y = 10"},null,"Line 3",{"$f":"AK15&\" \"&AL15&\" \"&AM15","v":"0  x +  1 y = 2"},null,"Line 4",{"$f":"AK16&\" \"&AL16&\" \"&AM16","v":"  "},null,"Objective \nFunction",null,null,{"$f":"IF(AND($X$4=0,$Y$4=0),\"\",IF($X$4=\"\",\"0 x\",ROUND($X$4,2)&\" x\"))","v":"3 x"},{"$f":"IF(AND($X$4=0,$Y$4=0),\"\",IF($Y$4=\"\",\"+ 0 y\",IF($Y$4<0,ROUND($Y$4,2)&\" y\",\"+  \"&ROUND($Y$4,2)&\" y\")))","v":"+  2 y"},null,null,null,null,null,null,null,null,null,null,null,null,null,"Line 1",null,null,null,null,"Line 2",null,null,null,"Line 3",null,null,null,"Line 4",null,null,null,null,null,null,null,null,null,null,null,"Line 2"]
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[]
[]
[]
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[null,{"$f":"IF(AND(C10=0,D10=0,F10=0),\"\",IF(AND(C10=0,F10=0),\"\",IF(AND(C10=0,D10=0,F10<>0),\"\",IF(AND(D10=0,F10=0),\"\",IF(D10=0,\"Isolate x:\",\"Isolate y:\")))))","v":"Isolate y:"},{"$f":"IF(AND(C10=0,D10=0,F10=0),\"\",IF(AND(C10=0,F10=0),\"\",IF(AND(D10=0,F10=0),\"\",IF(AND(C10=0,D10=0,F10<>0),\"\",IF(C10=0,\"y = \"&F10&\"/\"&D10&\" = \"&ROUND(F10/D10,2),IF(D10=0,\"x = \"&F10&\"/\"&C10&\" = \"&ROUND(F10/C10,2),IF(F10<0,\"y = (\"&-C10&\" x  \"&F11&\") / \"&D10,\"y = (\"&-C10&\" x + \"&F11&\") / \"&D10)))))))","v":"y = (1 x + 4) / 4"},null,null,"y-intcpt",{"$f":"IF(AZ21=\"V\",\"\",IF(AND(C10=0,D10=0,F10=0),\"\",\"( 0, \" &ROUND(AR4,2)&\")\"))","v":"( 0, 1)"},null,null,{"$f":"RIGHT(J9,1)&\",\"&RIGHT(J10,1)","v":"1,2"},null,null,null,null,null,{"$f":"RIGHT(P9,1)&\",\"&RIGHT(P10,1)","v":"1,3"},null,null,null,null,null,{"$f":"RIGHT(U9,1)&\",\"&RIGHT(U10,1)","v":"2,3"},null,null,null,null,null,null,"",null,null,null,null,null,null,"Line 1",{"$f":"IF(AV13+AW13+AX13=0,\"\",IF(OR(AV13=0,AV13=\"\"),\"0  x\",ROUND(AV13,2)&\" x\"))","v":"-1 x"},{"$f":"IF(AV13+AW13+AX13=0,\"\",IF(OR(AW13=0,AW13=\"\"),\"+ 0 y =\",IF(AW13>0,\"+  \"&ROUND(AW13,2)&\" y =\",AW13&\" y =\")))","v":"+  4 y ="},{"$f":"IF(AV13+AW13+AX13=0,\"\",AX13)","v":4},null,null,null,"Line 1",null,null,null,"Line 1",{"$f":"C10","v":-1},{"$f":"D10","v":4},{"$f":"F10","v":4},null,{"$f":"C10","v":-1},{"$f":"D10","v":4},{"$f":"F10","v":4},null,null,null,"2,1",{"$f":"BG12","v":1.1764705882352937},{"$f":"BH12","v":1.2941176470588236},2,{"$f":"$C$22","v":3},{"$f":"$D$22","v":5},{"$f":"$F$22","v":10}]
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[null,"To use the Template, you need to add : Solver as Add-Ins into your Excel",null,null,null,null,null,null,null,null,null,null,"To Allow Macros",null,"https://www.youtube.com/watch?v=joaC7QyRAPs"]
[]
[null,null,"Video Instruction:"]
[null,null,"https://www.youtube.com/watch?v=LKV6fT8xApA"]
[]
[]
[null,"Next, you need to do the following 2 steps:"]
[]
[null,"Step 1:  press Alt+F11 to open up VBA."]
[]
[null,"Step 2: Add the Solver reference in visual basic"]
[null,null,"Tools > References..., then make sure that SOLVER is checked"]
[null,null,"Check then click OK"]
[]
[]
[null,null,"Save the file, and you don't have to do that again"]

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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.83222784000000027,0,0.16777216000000014]

{"sheet":"15) Markov","index":22,"n_rows":63,"n_cols":28,"rows_kept":63,"cut":false,"hidden":false,"merged":[[56,26,56,27],[57,26,57,27],[58,26,58,27],[55,26,55,27],[56,24,56,25],[57,24,57,25],[58,24,58,25],[53,8,53,9],[54,8,54,9],[52,8,52,9],[16,17,16,26],[21,17,22,17],[21,18,22,18],[21,19,22,19],[21,20,22,20],[21,21,22,21],[21,22,22,22],[21,23,22,23],[21,24,22,24],[20,15,22,16],[21,1,22,2],[3,8,3,9],[4,8,4,9],[16,3,16,9],[2,24,2,25],[3,24,3,25],[4,24,4,25]]}
[null,null,"Fill the green cells only",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fill the green cells only"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.3,0.7,0,{"$f":"IF(AND(COUNT(V3:X3)=3,SUM(V3:X3)<>1),\"Error\",\"\")","v":""}]
[null,null,"Fill:",null,null,null,0.3,0.7,{"$f":"IF(AND(COUNT(G4:H4)=2,SUM(G4:H4)<>1),\"Error\",\"\")","v":""},null,null,null,null,null,null,null,null,"Fill:",null,null,null,0,0,1,{"$f":"IF(AND(COUNT(V4:X4)=3,SUM(V4:X4)<>1),\"Error\",\"\")","v":""}]
[null,"Step 1: ","Transition Matrix",null,null,"T =",0.8,0.2,{"$f":"IF(AND(COUNT(G5:H5)=2,SUM(G5:H5)<>1),\"Error\",\"\")","v":""},null,null,null,null,null,null,"Step 1: ",null,"Transition Matrix",null,null,"T =",0.2,0,0.8,""]
[]
[null,{"$f":"IF(C7=\"\",1,0)","v":1},{"$f":"IF(COUNT(G4:H5)=0,\"\",IF(AND(G4+H4=1,G5+H5=1),\"\",\"Error: Sum Per Row is not = 1 in the Transition Matrix\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(R7=\"\",1,0)","v":1},{"$f":"IF(COUNT(V3:X5)=0,\"\",IF(AND(V3+W3+X3=1,V4+W4+X4=1,V5+W5+X5=1),\"\",\"Error: Sum Per Row is not = 1 in the Transition Matrix\"))","v":""}]
[null,null,null,null,null,null,null,null,{"$f":"IF(OR(I4<>\"\",I5<>\"\"),\"Sum must be =1\",\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(Y3<>\"\",Y4<>\"\",Y5<>\"\"),\"Sum must be =1\",\"\")","v":""}]
[null,null,null,null,null,null,{"$f":"IF(B7=0,\"\",G4)","v":0.3},{"$f":"IF(B7=0,\"\",H4)","v":0.7},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Q7=0,\"\",V3)","v":0.3},{"$f":"IF(Q7=0,\"\",W3)","v":0.7},{"$f":"IF(Q7=0,\"\",X3)","v":0}]
[null,"Step 2: ",null,"x","y",".",{"$f":"IF(B7=0,\"\",G5)","v":0.8},{"$f":"IF(B7=0,\"\",H5)","v":0.2},"=","x","y",null,null,null,null,"Step 2: ",null,"x","y","z",".",{"$f":"IF(Q7=0,\"\",V4)","v":0},{"$f":"IF(Q7=0,\"\",W4)","v":0},{"$f":"IF(Q7=0,\"\",X4)","v":1},"=","x","y","z"]
[null,"Theory",null,null,null,null,null,null,null,null,null,null,null,null,null,"Theory",null,null,null,null,null,{"$f":"IF(Q7=0,\"\",V5)","v":0.2},{"$f":"IF(Q7=0,\"\",W5)","v":0},{"$f":"IF(Q7=0,\"\",X5)","v":0.8}]
[]
[]
[null,"Step 3:",null,{"$f":"G9","v":0.3},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"G10","v":0.8},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},null,null,null,null,null,"Step 3:",null,{"$f":"V9","v":0.3},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"V10","v":0},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"V11","v":0.2},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"}]
[null,"Multiply",null,{"$f":"H9","v":0.7},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"H10","v":0.2},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},null,null,null,null,null,"Multiply",null,{"$f":"W9","v":0.7},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"W10","v":0},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"W11","v":0},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"X9","v":0},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"X10","v":1},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"X11","v":0.8},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"}]
[null,null,null,"Note 1:  Sum of each column  above = 1",null,null,null,null,null,null,null,null,null,null,null,null,null,"Note 1:  Sum of each of the three columns above = 1"]
[]
[null,"Step 4:",null,{"$f":"IF(B7=0,\"\",D14-1)","v":-0.7},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"G14","v":0.8},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",0)","v":0},null,null,null,null,null,"Step 4:",null,{"$f":"IF(Q7=0,\"\",R14-1)","v":-0.7},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"U14","v":0},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"X14","v":0.2},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",0)","v":0}]
[null,"Simplify",null,{"$f":"D15","v":0.7},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"-\")","v":"-"},{"$f":"IF(B7=0,\"\",ABS(G15-1))","v":0.8},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",0)","v":0},null,null,null,null,null,"Simplify",null,{"$f":"R15","v":0.7},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"-\")","v":"-"},{"$f":"IF(Q7=0,\"\",ABS(U15-1))","v":1},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"X15","v":0},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",0)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bring x, y and z to one side",null,{"$f":"R16","v":0},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"U16","v":1},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"-\")","v":"-"},{"$f":"IF(Q7=0,\"\",ABS(X16-1))","v":0.19999999999999996},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",0)","v":0}]
[null,"Bring x and y to one side",null,{"$f":"IF(B7=0,\"\",\"And:\")","v":"And:"},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},null,{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",\"1\")","v":"1"},null,null,null,null,null,null,null,{"$f":"IF($Q$7=0,\"\",\"And:\")","v":"And:"},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",1)","v":1}]
[]
[]
[null,null,"Removind Decimals:",null,null,null,null,null,"Enter:",null,null,null,null,null,null,null,"Removind Decimals:",null,null,null,null,null,null,null,"Enter:"]
[null,null,"Mutiply the first equation by (10 or 100): ",null,null,null,null,null,10,null,null,null,null,null,null,null,"Mutiply the first equation by (10 or 100): ",null,null,null,null,null,null,null,10]
[null,null,"By default, the second equation is deleted.",null,null,null,null,null,null,null,null,null,null,null,null,null,"Mutiply the second equation by (10 or 100): ",null,null,null,null,null,null,null,10]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"By default, the third equation is deleted."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Q7=0,\"\",R19*Y26)","v":-7},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF(Q7=0,\"\",U19*Y26)","v":0},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF(Q7=0,\"\",X19*Y26)","v":2},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",0)","v":0}]
[null,null,null,{"$f":"IF(B7=0,\"\",D19*I26)","v":-7},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"IF(B7=0,\"\",G19*I26)","v":8},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",0)","v":0},null,null,null,null,null,null,null,{"$f":"IF(Q7=0,\"\",R20*Y27)","v":7},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"-\")","v":"-"},{"$f":"IF(Q7=0,\"\",U20*Y27)","v":10},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF(Q7=0,\"\",X20*Y27)","v":0},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",0)","v":0}]
[null,null,null,{"$f":"IF(B7=0,\"\",\"1\")","v":"1"},{"$f":"IF(B7=0,\"\",\"x\")","v":"x"},{"$f":"IF(B7=0,\"\",\"+\")","v":"+"},{"$f":"IF(B7=0,\"\",\"1\")","v":"1"},{"$f":"IF(B7=0,\"\",\"y\")","v":"y"},{"$f":"IF(B7=0,\"\",\"=\")","v":"="},{"$f":"IF(B7=0,\"\",\"1\")","v":"1"},null,null,null,null,null,null,null,{"$f":"IF(Q7=0,\"\",1)","v":1},{"$f":"IF($Q$7=0,\"\",\"x\")","v":"x"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF(Q7=0,\"\",1)","v":1},{"$f":"IF($Q$7=0,\"\",\"y\")","v":"y"},{"$f":"IF($Q$7=0,\"\",\"+\")","v":"+"},{"$f":"IF(Q7=0,\"\",1)","v":1},{"$f":"IF($Q$7=0,\"\",\"z\")","v":"z"},{"$f":"IF($Q$7=0,\"\",\"=\")","v":"="},{"$f":"IF(Q7=0,\"\",1)","v":1}]
[]
[]
[null,null,null,null,"x","y",null,null,null,null,null,null,null,null,null,null,null,null,"x","y","z"]
[null,null,null,null,{"$f":"D30","v":-7},{"$f":"G30","v":8},{"$f":"IF(B7=0,\"\",0)","v":0},null,null,null,null,null,null,null,null,null,null,null,{"$f":"R29","v":-7},{"$f":"U29","v":0},{"$f":"X29","v":2},{"$f":"AA29","v":0}]
[null,null,null,null,{"$f":"IF(B7=0,\"\",1)","v":1},{"$f":"IF(B7=0,\"\",1)","v":1},{"$f":"IF(B7=0,\"\",1)","v":1},null,null,null,null,null,null,null,null,null,null,null,{"$f":"R30","v":7},{"$f":"IF(Q7=0,\"\",-U30)","v":-10},{"$f":"X30","v":0},{"$f":"AA30","v":0}]
[null,null,null,"You can use any method to solve the 2 equations.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"R31","v":1},{"$f":"U31","v":1},{"$f":"X31","v":1},{"$f":"IF(Q7=0,\"\",1)","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"You can use any method to solve the 3 equations."]
[null,null,null,"Using the All Integer:",null,null,null,null,null,null,null,null,null,null,null,null,null,"Using the All Integer:"]
[null,null,null,null,"x","y",null,null,null,null,null,null,null,null,null,null,null,null,"x","y","z"]
[null,null,null,null,{"$f":"IF($B$7=1,E35,\"\")","v":-7},{"$f":"IF($B$7=1,F35,\"\")","v":8},{"$f":"IF($B$7=1,G35,\"\")","v":0},{"$f":"IF(AND(E41=0,F41=0,G41=0),1,IF(AND(E41=0,F41=0,G41<>0),2,IF(E41=0,3,0)))","v":0},null,null,null,null,null,null,null,null,null,null,{"$f":"IF($Q$7=1,S35,\"\")","v":-7},{"$f":"IF($Q$7=1,T35,\"\")","v":0},{"$f":"IF($Q$7=1,U35,\"\")","v":2},{"$f":"IF($Q$7=1,V35,\"\")","v":0},{"$f":"IF(AND(S41=0,T41=0,U41=0,V41=0),1,IF(AND(S41=0,T41=0,U41=0,V41<>0),2,IF(S41=0,3,0)))","v":0}]
[null,null,null,null,{"$f":"IF(AND($B$7=1,$H$41=0),E36,\"\")","v":1},{"$f":"IF(AND($B$7=1,$H$41=0),F36,\"\")","v":1},{"$f":"IF(AND($B$7=1,$H$41=0),G36,\"\")","v":1},{"$f":"IF(AND(E42=0,F42=0,G42=0),1,IF(AND(E42=0,F42=0,G42<>0),2,0))","v":0},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($Q$7=1,$W$41=0),S36,\"\")","v":7},-10,0,0,{"$f":"IF(AND(S42=0,T42=0,U42=0,V42=0),1,IF(AND(S42=0,T42=0,U42=0,V42<>0),2,0))","v":0}]
[null,null,null,null,null,null,null,{"$f":"SUM(H41:H42)","v":0},null,null,null,null,null,null,null,null,null,null,1,1,1,1,{"$f":"IF(AND(S43=0,T43=0,U43=0,V43=0),1,IF(AND(S43=0,T43=0,U43=0,V43<>0),2,0))","v":0}]
[null,null,null,null,{"$f":"IF(AND($B$7=1,$H$43=0),E41,\"\")","v":-7},{"$f":"IF(AND($B$7=1,$H$43=0),F41,\"\")","v":8},{"$f":"IF(AND($B$7=1,$H$43=0),G41,\"\")","v":0},{"$f":"IF(AND(E44=0,F44=0,G44=0),1,IF(AND(E44=0,F44=0,G44<>0),2,0))","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(W41:W43)","v":0}]
[null,null,null,null,{"$f":"IF(AND($B$7=1,$H$43=0),0,\"\")","v":0},{"$f":"IF(AND($B$7=1,$H$43=0),((F42*E41)-(E42*F41)),\"\")","v":-15},{"$f":"IF(AND($B$7=1,$H$43=0),((E41*G42)-(E42*G41)),\"\")","v":-7},{"$f":"IF(AND(E45=0,F45=0,G45=0),1,IF(AND(E45=0,F45=0,G45<>0),2,IF(F45=0,3,0)))","v":0},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($Q$7=1,$W$44=0),S41,\"\")","v":-7},{"$f":"IF(AND($Q$7=1,$W$44=0),T41,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$44=0),U41,\"\")","v":2},{"$f":"IF(AND($Q$7=1,$W$44=0),V41,\"\")","v":0},{"$f":"IF(AND(S45=0,T45=0,U45=0,V45=0),1,IF(AND(S45=0,T45=0,U45=0,V45<>0),2,0))","v":0}]
[null,null,null,null,null,null,null,{"$f":"SUM(H40:H45)","v":0},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($Q$7=1,$W$44=0),0,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$44=0),((T42*S41)-(S42*T41)),\"\")","v":70},{"$f":"IF(AND($Q$7=1,$W$44=0),((S41*U42)-(S42*U41)),\"\")","v":-14},{"$f":"IF(AND($Q$7=1,$W$44=0),((S41*V42)-(S42*V41)),\"\")","v":0},{"$f":"IF(AND(S46=0,T46=0,U46=0,V46=0),1,IF(AND(S46=0,T46=0,U46=0,V46<>0),2,IF(T46=0,3,0)))","v":0}]
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[null,null,null,null,null,null,"Note 2: The final answers:","The Sum = 1",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($Q$7=1,$W$60=0),0,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$60=0),T54/U51,\"\")","v":1},{"$f":"IF(AND($Q$7=1,$W$60=0),0,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$60=0),V54/U51,\"\")","v":0.13461538461538461},null,"y = ",{"$f":"IF(AND($Q$7=1,$W$60=0),V58,\"\")","v":0.13461538461538461},null,{"$f":"Y58","v":0.13461538461538461}]
[null,null,null,null,null,null,null,"None is Negative",null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AND($Q$7=1,$W$60=0),0,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$60=0),0,\"\")","v":0},{"$f":"IF(AND($Q$7=1,$W$60=0),U55/U51,\"\")","v":1},{"$f":"IF(AND($Q$7=1,$W$60=0),V55/U51,\"\")","v":0.67307692307692313},null,"z =",{"$f":"IF(AND($Q$7=1,$W$60=0),V59,\"\")","v":0.67307692307692313},null,{"$f":"Y59","v":0.67307692307692313}]
[null,null,null,null,null,null,null,"Neither is > 1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(W41:W55)","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Note 2: The final answers:","The Sum = 1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"None is Negative"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"None is > 1"]

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[]
[null,null,null,null,null,null,"Chapter","Sections"]
[null,null,null,null,null,null,"Chapter 1: Introduction to Logic","Section 1.1: Propositions and Truth Tables"]
[null,"Chapter #","Title","Duration","# of video",null,null,"Section 1.2: Conditional Statements and Arguments"]
[null,null,null,"(hrs:min:sec)","Files",null,"Chapter 2: Set Theory","Section 2.1: Sets and Subsets"]
[null,null,null,null,null,null,null,"Section 2.2: Set Operations"]
[null,"Chapter 1","Introduction to Logic","00:47:10",5,null,"Chapter 3: Combinatorics","Section 2.3: Venn Diagrams"]
[null,null,null,null,null,null,null,"Section 3.1: Trees and Equally Likely Outcomes"]
[null,"Chapter 2","Set Theory ","01:16:28",9,null,null,"Section 3.2: Permutations"]
[null,null,null,null,null,null,null,"Section 3.3: Combinations"]
[null,"Chapter 3","Combinatorics","02:07:50",15,null,"Chapter 4: Probability","Section 4.1: Basic Concepts"]
[null,null,null,null,null,null,null,"Section 4.2: Conditional Probability and Independence"]
[null,"Chapter 4","Probability","01:53:07",11,null,null,"Section 4.3: Bayes' Theorem"]
[null,null,null,null,null,null,null,"Section 4.4: Bernoulli Trials"]
[null,"Chapter 5","Introduction to Statistics ","01:37:04",11,null,"Chapter 5: Statistic","Section 5.1: Central Tendency"]
[null,null,null,null,null,null,null,"Section 5.2: Expected Value and Standard Deviation"]
[null,"Chapter 6","Linear Equations and Matrix Algebra","01:25:37",7,null,null,"Section 5.3: Normal Random Variable"]
[null,null,null,null,null,null,null,"Section 5.4: The Normal Approximation to a Binomial Random Variable"]
[null,"Chapter 7","Linear Programming, Graphic Solutions","None","None",null,"Chapter 6:  Linear Equations and  Matrix Algebra","Section 6.1: Systems of Linear Equations in \nTwo Variables"]
[null,"Chapter 9","Markov Chains ","01:46:22",11,null,null,"Section 6.2: Matrices and Systems of Linear Equations"]
[null,null,null,null,null,null,null,"Section 6.3: Matrix Notation, Algebra, and Inverses"]
[null,null,"                                          Total","10:53:38",69,null,"Chapter 7: Linear Programing, graphic Solution","Section 7.1: System of Linear Inequalities"]
[null,null,null,null,null,null,null,"Section 7.2: Finding an Optimal Value"]
[null,null,null,null,null,null,"Chapter 9: Markov Chains","Section 9.1: Introduction, Transition Matrix"]
[null,null,null,null,null,null,null,"Section 9.2: Regular Markov Chains"]
[]
[null,null,null,"My Youtube site","https://www.youtube.com/@FiniteMath-pd5up/playlists"]
[null,null,null,"Helpful Graphing Program","http://www.graphmatica.com/"]
[null,null,null,"Web Graphing Site","https://www.desmos.com/calculator"]
[null,null,null,"How to use calculator","https://www.youtube.com/watch?v=0SfIIkiR6RA"]
[null,null,null,"Algebra in Youtube","https://www.youtube.com/watch?v=4BNcAjKcazc"]
[null,null,null,null,"https://www.youtube.com/watch?v=Q8HJHjARMVs&t=578s"]
[null,null,null,null,"https://www.youtube.com/@gotutormaths"]
[null,null,null,"Algebra Site","https://www.solve-variable.com/systems-of-linear-equations-and-problem-solving.html"]
[null,null,null,"To Allow Macros","https://www.youtube.com/watch?v=NdsndEtaG98"]
[null,null,null,"To add Development Tool","https://www.youtube.com/watch?v=bizIf264GIk"]
[null,null,null,"To add Data Analysis","https://www.youtube.com/watch?v=LZnBlQKZVdY"]
[null,null,null,"To add Solver","https://www.youtube.com/watch?v=LKV6fT8xApA"]

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[]
[null,null,"Click to Get your Scores from Tableau, Summary Sheet (HonerLock Class)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"Class","v":"TC"}]
[null,null,"Click to Get your Scores from Tableau, Summary Sheet (Testing Center class)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Image in Tableau of the Summary Sheet"]
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[null,null,"Enter your scores from Summary Sheet",null,null,null,"Enter your Midterm 1 Score",null,null,null,null,null,null,{"$f":"MQ_G*100+MLM_G*100+Part_G*100+Mid_G*100+Mid_G*100","v":75}]
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[null,null,"if your score is 92.3%, enter 92.3,",null,null,null,null,null,null,"Grade After Midterm 2",null,null,null,{"$f":"MIN('Grade Template'!Q28:R28)","v":0},null,null,null,null,null,null,null,null,"Points Distrubution"]
[null,null," Do not enter in decimal form as  0.923",null,null,null,"Enter your Midterm 2 Score",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mastery Quizzes, MQ: 5% of Total"]
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[null,null,null,null,null,null,null,null,"Total",null,null,null,null,"Mastery Quizzes\n MQ, (10 %)","MyLab Math\nMLM, (15 %)","Participation & MLM Samples\n (10 %)","Midterm #1 \n(20 %)",null,null,null,null,null,"Participation: 15% of Total"]
[null,null,null,null,null,null,null,null,{"$f":"IF(OR(N19=\"\",N19=0,O19=\"\",O19=0,P19=\"\",P19=0),\"\",MQ_G*N19+MLM_G*O19+Part_G*P19+Mid_G*Q19+Mid_G*G18)","v":""},{"$f":"IF(OR(N19=\"\",N19=0,O19=\"\",O19=0,P19=\"\",P19=0,G18=\"\"),\"\",I18/N6)","v":""},{"$f":"IF(J18=\"\",\"\",LOOKUP(J18,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"}))","v":""},null,null,null,null,null,null,null,null,null,null,null,"5%  Extra Work assignments, plus 1 point for each MLM or MQ with at least 40%."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C10=\"\",0,C10)","v":0},{"$f":"IF(D10=\"\",0,D10)","v":0},{"$f":"IF(E10=\"\",0,E10)","v":0},{"$f":"G10","v":0},null,null,null,null,null,{"$f":"IF(AE2=\"OL\",\"10% from Practice Exam and  Online MLM Sample Exam scores (6 samples)\",\"10% from Online Sample Exam scores (6 samples)  in MLM page.\")","v":"10% from Online Sample Exam scores (6 samples)  in MLM page."}]
[]
[]
[null,null,"Final Exam Cannot be missed, and it is 25% of your final grade",null,null,null,null,null,null,"Grade After Final Exam",null,null,null,null,null,null,null,null,null,null,null,null,"Midterm 1: 20% of Total,  Covering Chapters 1, 2, 3, and 4"]
[null,null,"You must pass the final exam with a score of 50% or higher to pass the course.",null,null,null,null,null,null,null,"Enter Final Exam",null,null,null,null,null,null,null,null,null,null,null,"Midterm 2: 20% of Total,  Covering Chapters 5. 6 and 7"]
[null,null,"However, I will modified  it to be:"]
[null,null,"MLM is Less than 75%  . Then the min final exam score accepted s is 50",null,null,null,null,null,null,null,null,null,null,"A","B","C","D","E",null,null,null,null,"Final Exam: 25%  of Total, Covering chapters 1, 2, 3, 4, 5, 6, 7, and 9"]
[null,null,"MLM Between 75% and 85%, then the min final exam score accepted is 45",null,null,null,null,null,null,"Average After Final","Semester \nGrade",null,null,"Mastery Quizzes\n MQ, (10 %)","MyLab Math\nMLM, (15 %)","Participation & MLM Samples\n (10 %)","Midterm #1 \n(20 %)","Midterm #2\n(20 %)",null,null,null,null,{"$f":"IF(Class=\"TC\",\"Testing Center Hours\",\"\")","v":"Testing Center Hours"}]
[null,null,"MLM is greater than  85%, then the min final exam score accepted is 40",null,null,null,null,null,"Total",{"$f":"IF(OR(I28=0,COUNTA(N28:R28)<>5,K24=\"\"),\"\",I32/100)","v":""},{"$f":"IF(OR(J27=0,COUNTA(N26:R26)<>5,K24=\"\"),\"\",IF(K24<50,\"F*\",LOOKUP(J27,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"})))","v":""},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Class=\"TC\",\"Monday – Friday  9 AM – 7 PM\",\"\")","v":"Monday – Friday  9 AM – 7 PM"}]
[null,null,null,null,null,null,null,null,{"$f":"MQ_G*N28+MLM_G*O28+Part_G*P28+Mid_G*Q28+Mid_G*R28","v":0},null,null,null,null,{"$f":"IF(N19=\"\",\"\",N19)","v":0},{"$f":"IF(O19=\"\",\"\",O19)","v":0},{"$f":"IF(P19=\"\",\"\",P19)","v":0},{"$f":"IF(Q19=\"\",\"\",Q19)","v":0},{"$f":"IF(G18=\"\",0,G18)","v":0},null,null,null,null,"Closed Saturdays and Sundays"]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(I32=0,COUNTA(N28:R28)<>5,K24=\"\"),\"\",IF(AND(O28>='Grade Template OL'!N9,K24>'Grade Template OL'!N11),(MQ_G*N28+MLM_G*O28+Part_G*P28+Mid_G*MAX(Q28,R28)+Mid_G*K24+Final_G*K24)/100,J27))","v":""},{"$f":"IF(OR(K24=\"\",K24=0,J29=\"\"),\"\",IF(K24<N31,\"F*\",LOOKUP(J29,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"})))","v":""},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(Class=\"TC\",\"Closed university holidays\",\"\")","v":"Closed university holidays"}]
[null,null,"(Regardless, aim to get the highest score you can in the final)",null,null,null,null,null,null,{"$f":"IF(AND(SUM(N28:R28)=0,K24>1),\"Enter Scores in Columns A,B,C,D and E\",\"\")","v":""}]
[null,null,null,null,null,null,null,{"$f":"IF(OR(I28=0,COUNTA(N28:R28)<>5,K24=\"\"),\"\",IF(AND(SUM(N28:R28)>10,K24<N31),\"* Failed the final exam\",IF(O28<N11,\"Final Exam did not replace lowest score\",IF(K24>MIN(Q28,R28),\"Final Exam Replaced Lowest score of : \"&MIN(Q28,R28),\"Final Exam did not replace lowest score\"))))","v":""},"Total",null,null,null,null,{"$f":"IF(O28>=85,40,IF(O28>=75,45,50))","v":50},null,null,null,null,null,null,null,null,{"$f":"IF(Class=\"TC\",\"Engineering Science and Technology Building\n723 W. Michigan Street\",\"\")","v":"Engineering Science and Technology Building\n723 W. Michigan Street"}]
[null,null,null,null,null,null,null,null,{"$f":"MQ_G*N28+MLM_G*O28+Part_G*P28+Mid_G*Q28+Mid_G*R28+Final_G*K24","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,"SL070 (Basement)"]

{"sheet":"Grade Template OL","index":28,"n_rows":30,"n_cols":23,"rows_kept":30,"cut":false,"hidden":true,"merged":[[23,17,24,17],[14,15,15,15],[14,16,15,16],[23,13,24,13],[23,14,24,14],[23,15,24,15],[23,16,24,16],[14,14,15,14],[5,10,6,10],[13,6,14,6],[13,9,14,9],[13,10,14,10],[14,13,15,13],[0,2,0,9],[5,2,6,2],[5,3,6,3],[5,4,6,4],[5,6,6,6],[5,9,6,9]]}
[null,null,"Click to Get your Scores from Tableau, Summary Sheet",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Image in Tableau of the Summary Sheet"]
[]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(G16=\"\",\"Grade After Midterm 1\",\"\")","v":""},null,null,null,{"$f":"MQ_P*100+MLM_P*100+Part_P*100+Mid_P*100","v":55},null,null,null,null,"Revised Summer 2025"]
[null,null,"Enter your scores from Summary Sheet",null,null,null,"Enter your Midterm 1 Score",null,null,null,null,null,null,{"$f":"MQ_P*100+MLM_P*100+Part_P*100+Mid_P*100+Mid_P*100","v":75}]
[null,null,"A","B","C",null,"D",null,null,{"$f":"IF(G16=\"\",\"Calculated Average after Midterm 1\",\"\")","v":""},null,null,null,null,null,"MQ",0.05]
[null,null,"Mastery Quizzes\n MQ, (5 %)","MyLab Math\nMLM, (15 %)","Participation \n (15 %)",null,"Midterm #1 \n(20 %)",null,null,{"$f":"IF(G16=\"\",\"Average\",\"\")","v":""},{"$f":"IF(G16=\"\",\"Grade\",\"\")","v":""},null,null,"L…..",null,"MLM",0.15]
[null,null,null,null,null,null,null,null,"Total",null,null,null,null,null,null,"Part",0.15]
[null,null,65,76,84,null,74,null,{"$f":"IF(OR(C8=\"\",C8=0,D8=\"\",D8=0,E8=\"\",E8=0),\"\",MQ_P*C8+MLM_P*D8+Part_P*E8+Mid_P*G8)","v":42.05},{"$f":"IF(OR(C8=\"\",C8=0,D8=\"\",D8=0,E8=\"\",E8=0,G16<>\"\"),\"\",I8/N3)","v":""},{"$f":"IF(J8=\"\",\"\",LOOKUP(J8,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"}))","v":""},null,null,null,null,"Mid",0.2]
[null,null,null,{"$f":"IF(O26<2,\"\",IF(O26<N9,\"MLM is Too Low\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,74,null,"Final",0.25]
[]
[null,null,"if your score is 92.3%, enter 92.3,",null,null,null,null,null,null,"Grade After Midterm 2",null,null,null,{"$f":"MIN('Grade Template OL'!Q26:R26)","v":45},null,null,null,null,null,null,null,null,"Points Distrubution"]
[null,null," Do not enter in decimal form as  0.923",null,null,null,"Enter your Midterm 2 Score",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mastery Quizzes, MQ: 5% of Total"]
[null,null,null,null,null,null,"E",null,null,"Calculated Average after Midterm 2",null,null,null,null,null,null,null,null,null,null,null,null,"MyLab Math , MLM: 15% of Total"]
[null,null,null,null,null,null,"Midterm #2\n(20 %)",null,null,"Average","Grade",null,null,"A","B","C","D"]
[null,null,null,null,null,null,null,null,"Total",null,null,null,null,"Mastery Quizzes\n MQ, (10 %)","MyLab Math\nMLM, (15 %)","Participation & MLM Samples\n (10 %)","Midterm #1 \n(20 %)",null,null,null,null,null,"Participation: 15% of Total"]
[null,null,null,null,null,null,45,null,{"$f":"IF(OR(N17=\"\",N17=0,O17=\"\",O17=0,P17=\"\",P17=0),\"\",MQ_P*N17+MLM_P*O17+Part_P*P17+Mid_P*Q17+Mid_P*G16)","v":51.05},{"$f":"IF(OR(N17=\"\",N17=0,O17=\"\",O17=0,P17=\"\",P17=0,G16=\"\"),\"\",I16/N4)","v":0.68066666666666664},{"$f":"IF(J16=\"\",\"\",LOOKUP(J16,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"}))","v":"D+"},null,null,null,null,null,null,null,null,null,null,null,"5%  Extra Work assignments, plus 1 point for each MLM or MQ with at least 40%."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(C8=\"\",0,C8)","v":65},{"$f":"IF(D8=\"\",0,D8)","v":76},{"$f":"IF(E8=\"\",0,E8)","v":84},{"$f":"G8","v":74},null,null,null,null,null,"10% from Practice Exam and  Online MLM Sample Exam scores (6 samples)"]
[]
[]
[null,null,"Final Exam Cannot be missed, and it is 25% of your final grade",null,null,null,null,null,null,"Grade After Final Exam",null,null,null,null,null,null,null,null,null,null,null,null,"Midterm 1: 20% of Total,  Covering Chapters 1, 2, 3, and 4"]
[null,null,"You must pass the final exam with a score of 50% or higher to pass the course.",null,null,null,null,null,null,null,"Enter Final Exam",null,null,null,null,null,null,null,null,null,null,null,"Midterm 2: 20% of Total,  Covering Chapters 5. 6 and 7"]
[null,null,"However, I will modified  it to be:",null,null,null,null,null,null,null,90]
[null,null,"MLM is Less than 75%  . Then the min final exam score accepted s is 50",null,null,null,null,null,null,null,null,null,null,"A","B","C","D","E",null,null,null,null,"Final Exam: 25%  of Total, Covering chapters 1, 2, 3, 4, 5, 6, 7, and 9"]
[null,null,"MLM Between 75% and 85%, then the min final exam score accepted is 45",null,null,null,null,null,null,"Average After Final","Semester \nGrade",null,null,"Mastery Quizzes\n MQ, (10 %)","MyLab Math\nMLM, (15 %)","Participation & MLM Samples\n (10 %)","Midterm #1 \n(20 %)","Midterm #2\n(20 %)"]
[null,null,"MLM is greater than  85%, then the min final exam score accepted is 40",null,null,null,null,null,"Total",{"$f":"IF(OR(I30=0,COUNTA(N26:R26)<>5,K22=\"\"),\"\",I30/100)","v":0.73549999999999993},{"$f":"IF(OR(I30=0,COUNTA(N26:R26)<>5,K22=\"\"),\"\",IF(K22<50,\"F*\",LOOKUP(J25,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"})))","v":"C-"}]
[null,null,null,null,null,null,null,null,{"$f":"MQ_P*N26+MLM_P*O26+Part_P*P26+Mid_P*Q26+Mid_P*R26","v":51.05},null,null,null,null,{"$f":"IF(N17=\"\",\"\",N17)","v":65},{"$f":"IF(O17=\"\",\"\",O17)","v":76},{"$f":"IF(P17=\"\",\"\",P17)","v":84},{"$f":"IF(Q17=\"\",\"\",Q17)","v":74},{"$f":"IF(G16=\"\",0,G16)","v":45}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(OR(I30=0,COUNTA(N26:R26)<>5,K22=\"\"),\"\",IF(AND(O26>='Grade Template OL'!N9,K22>'Grade Template OL'!N11),(MQ_P*N26+MLM_P*O26+Part_P*P26+Mid_P*MAX(Q26,R26)+Mid_P*K22+Final_P*K22)/100,J25))","v":0.82550000000000001},{"$f":"IF(OR(K22=\"\",K22=0,J27=\"\"),\"\",IF(K22<N29,\"F*\",LOOKUP(J27,{0,\"F\";0.6,\"D-\";0.64,\"D\";0.67,\"D+\";0.7,\"C-\";0.74,\"C\";0.77,\"C+\";0.8,\"B-\";0.84,\"B\";0.87,\"B+\";0.895,\"A-\";0.94,\"A\";0.98,\"A+\"})))","v":"B-"}]
[null,null,"(Regardless, aim to get the highest score you can in the final)",null,null,null,null,null,null,{"$f":"IF(AND(SUM(N26:R26)=0,K22>1),\"Enter Scores in Columns A,B,C,D and E\",\"\")","v":""}]
[null,null,null,null,null,null,null,null,"Total",{"$f":"IF(OR(I26=0,COUNTA(N26:R26)<>5,K22=\"\"),\"\",IF(AND(SUM(N26:R26)>10,K22<N29),\"* Failed the final exam\",IF(O26<N9,\"Final Exam did not replace lowest score\",IF(K22>MIN(Q26,R26),\"Final Exam Replaced Lowest score of : \"&MIN(Q26,R26),\"Final Exam did not replace lowest score\"))))","v":"Final Exam Replaced Lowest score of : 45"},null,null,null,{"$f":"IF(O26>=85,40,IF(O26>=75,45,50))","v":45}]
[null,null,null,null,null,null,null,null,{"$f":"MQ_P*N26+MLM_P*O26+Part_P*P26+Mid_P*Q26+Mid_P*R26+Final_P*K22","v":73.55}]

{"sheet":"Grading System","index":29,"n_rows":28,"n_cols":30,"rows_kept":28,"cut":false,"hidden":false,"merged":[[14,4,17,7],[19,4,20,7]]}
[]
[null,null,"A) Mastery Quizzes, MQ 5%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,98,90,80,70,60,50,40,30,20,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,102,100,95,85,75,65,55,45,35]
[null,null,"B) MyLab Math , MLM 15% "]
[]
[null,null,"C) Participation 15%"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"     MLM Sample  are Open until Final exam"]
[null,null,null,"1) 5% by doing Extra Work assignments on paper showing work. ",null,null,null,null,null,null,null,null,null,null,null,"If you get: "]
[null,null,null,"2) Plus 1 point for each MLM or MQ with at least 40%. ",null,null,null,null,null,null,null,null,null,null,null,null,"(98 - 100 ), then it will be adjusted to 102"]
[null,null,null,"3) 10% from Online MLM Sample Exam scores (6 samples)  in MLM page. ",null,null,null,null,null,null,null,null,null,null,null,null,"(91 - 97 ), then it will be adjusted to 100"]
[null,null,null," You have 10 attempts for each sample.The higher you get, the higher participation points.",null,null,null,null,null,null,null,null,null,null,null,null,"(81 – 90 ), then it will be adjusted to 95"]
[null,null,null,"  (They are essentials in preparing for the real exams, and will stay open until the final exam)",null,null,null,null,null,null,null,null,null,null,null,null,"(71 – 80), then it will be adjusted to 85"]
[null,null,null,{"$f":"IF(Class=\"OL\",\"4) Practice Exam proctored by HonerLock (2 attempts).\",\"\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,"(61 – 70 ) , then it will be adjusted to 75"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(51 –60 ), then it will be adjusted to 65"]
[null,null,null,null,"Will be counted in the participation points when Midterm 1 is given:",null,null,null,null,"MLM Sample , chapter 1",null,null,null,null,null,null,"(41 - 50 ), then it will be adjusted to 55"]
[null,null,null,null,null,null,null,null,null,"MLM Sample , chapter 2",null,null,null,null,null,null,"(31 – 40 ), then it will be adjusted to 45 "]
[null,null,null,null,null,null,null,null,null,"MLM Sample , chapter 3",null,null,null,null,null,null,"(21 – 30 ), then it will be adjusted to 35 "]
[null,null,null,null,null,null,null,null,null,"MLM Sample , chapter 4",null,null,null,null,null,"(0 – 20 ), then it will not be adjusted "]
[]
[null,null,null,null,"Will be counted in the participation points when Midterm 2 is given",null,null,null,null,"MLM Sample , chapter 5"]
[null,null,null,null,null,null,null,null,null,"MLM Sample , chapter 6, 7",null,null,null,null,null,null,"Enter your MLM Score: ",55]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Will be Converted to",{"$f":"IF(R21>=$U$2,$U$3,IF(R21>=$V$2,$V$3,IF(R21>=$W$2,$W$3,IF(R21>=$X$2,$X$3,IF(R21>=$Y$2,$Y$3,IF(R21>=$Z$2,$Z$3,IF(R21>=$AA$2,$AA$3,IF(R21>=$AB$2,$AB$3,R21))))))))","v":65}]
[null,null,"D) Midterm 1:  20% , Covering Chapters 1, 2, 3 and 4"]
[]
[null,null,"E) Midterm 2:  20% , Covering Chapters 5, 6 and 7"]
[]
[null,null,"F) Final Exam:  25% Covering the materials of Midterms 1 and 2 plus chapter 9"]

{"sheet":"Example 1","index":30,"n_rows":126,"n_cols":43,"rows_kept":126,"cut":false,"hidden":false,"merged":[[29,4,31,6],[36,10,37,12],[46,6,46,8],[10,8,11,8],[10,9,11,9],[12,8,13,8],[12,9,13,9],[12,10,13,13],[23,4,24,6],[3,17,4,27],[1,24,1,25],[4,8,5,9],[5,1,6,1],[5,2,6,2],[5,4,6,4],[5,5,6,5],[5,6,6,6]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Area Under the Curve from Left","Z = ",{"$f":"I34","v":1.96},"Area =",{"$f":"NORMSDIST(W2)","v":0.97500210485177952},null,null,null,null,null,null,null,null,null,null,null,null,"Round","Left","last"]
[]
[null,null,null,null,"The following are 12 different scores in a final exam for 32 students:",null,null,null,null,null,null,null,null,null,null,null,null,"Used : Area Under The Standard Normal Curve (Area From the Center)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"ABS(AE12)","v":1.96},{"$f":"AH4*100","v":196},null,null,{"$f":"IF(AI4<100,0,LEFT(AI4,1))","v":"1"},{"$f":"IF(AI4<10,0,IF(AND(AI4>10,AI4<100),LEFT(AI4,1)/10,AQ5*1))","v":1.9},{"$f":"RIGHT(AI4,1)/100","v":0.06},{"$f":"LEN(AL4)","v":1},{"$f":"LEFT(AI4,2)","v":"19"},{"$f":"MID(AI4,2,1)","v":"9"}]
[null,"Detailed Data",null,null,"Data Summarized",null,null,null,"Data Summary",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AL6>=-1*$AE$12,AM6,\"\")","v":""},null,null,{"$f":"IF(AI4<10,0,IF(AI4>=100,AL4&\".\"&AQ4,\"\"))","v":"1.9"}]
[null,"Students","Scores",null,"Score","Weight Of Each Score","Total",null,null,null,null,null,null,null,null,null,null,"Z",0,0.01,0.02,0.03,0.04,0.05,0.06,7.0000000000000007E-2,0.08,0.09,null,null,null,null,null,null,null,null,null,-3,{"$f":"_xlfn.NORM.S.DIST(AL6,FALSE)","v":4.4318484119380075E-3}]
[null,null,null,null,null,null,null,null,"Minimum",{"$f":"MIN($C$8:$C$107)","v":56},null,null,null,null,null,null,null,0,{"$f":"NORMSDIST(R7+$S$6)-0.5","v":0},{"$f":"NORMSDIST(R7+$T$6)-0.5","v":3.989356314631598E-3},{"$f":"NORMSDIST(R7+$U$6)-0.5","v":7.9783137169020524E-3},{"$f":"NORMSDIST(R7+$V$6)-0.5","v":1.1966473414112722E-2},{"$f":"NORMSDIST(R7+$W$6)-0.5","v":1.5953436852830682E-2},{"$f":"NORMSDIST(R7+$X$6)-0.5","v":1.9938805838372486E-2},{"$f":"NORMSDIST(R7+$Y$6)-0.5","v":2.3922182654106838E-2},{"$f":"NORMSDIST(R7+$Z$6)-0.5","v":2.7903170180521131E-2},{"$f":"NORMSDIST(R7+$AA$6)-0.5","v":3.1881372013987441E-2},{"$f":"NORMSDIST(R7+$AB$6)-0.5","v":3.5856392585172037E-2},null,null,null,null,{"$f":"LEN(AF12)","v":4},null,null,null,null,-2.95,{"$f":"_xlfn.NORM.S.DIST(AL7,FALSE)","v":5.1426409230539392E-3},{"$f":"IF(AL7>-1*$AE$12,AM7,IF(AL7=0,0,\"\"))","v":""},{"$f":"IF(AL7<=1*$AE$12,AM7,\"\")","v":5.1426409230539392E-3}]
[null,"Student 1",100,null,100,{"$f":"COUNTIF($C$8:$C$42,E8)","v":1},{"$f":"E8*F8","v":100},null,"Maximum",{"$f":"MAX($C$8:$C$107)","v":100},null,null,null,null,null,null,null,0.1,{"$f":"NORMSDIST(R8+$S$6)-0.5","v":3.9827837277028988E-2},4.3795312542316722E-2,4.7758426020583888E-2,5.1716786654561142E-2,5.5670004805906448E-2,5.9617692370242503E-2,6.3559462891432883E-2,6.7494931675038394E-2,7.1423715900900797E-2,7.5345434734795491E-2,null,null,null,null,null,null,null,null,null,-2.9,5.9525324197758538E-3,{"$f":"IF(AL8>-1*$AE$12,AM8,IF(AL8=0,0,\"\"))","v":""},{"$f":"IF(AL8<=1*$AE$12,AM8,\"\")","v":5.9525324197758538E-3}]
[null,"Student 2",96,null,96,{"$f":"COUNTIF($C$8:$C$42,E9)","v":2},192,null,"Median",{"$f":"MEDIAN($C$8:$C$42)","v":72},null,null,null,null,null,null,null,0.2,7.9259709439102988E-2,8.3166163482442323E-2,8.7064422648214679E-2,9.0954115142005909E-2,9.4834871697795808E-2,9.8706325682923701E-2,0.10256811320176051,0.10641987319803947,0.11026124755579725,0.11409188119887737,null,null,null,null,null,null,null,null,null,-2.85,6.8727666906139712E-3,"",6.8727666906139712E-3]
[null,"Student 3",96,null,92,2,184,null,"Count, n",{"$f":"COUNT($C$8:$C$107)","v":32},null,null,null,null,null,null,null,0.3,0.11791142218895267,0.12171952182201928,0.12551583472332006,0.12930001894065346,0.13307173603602807,0.1368306511756191,0.14057643321799129,0.14430875480054683,0.14802729242416279,0.15173172653598244,null,"Enter Area:",{"$f":"D52","v":0},null,null,null,null,null,null,-2.8,7.9154515829799686E-3,"",7.9154515829799686E-3]
[null,"Student 4",92,null,{"$f":"E10-4","v":88},3,264,null,"Weighted Average ",{"$f":"AVERAGE($C$8:$C$107)","v":75},null,null,null,null,null,null,null,0.4,0.15542174161032429,0.15909702622767741,0.16275727315175059,0.16640217940454238,0.17003144633940637,0.17364477971208003,0.17724188974965227,0.1808224912174442,0.18438630348377749,0.18793305058260945,null,"Or:",{"$f":"1-AE10","v":1},null,"Each Side, nearest is:",{"$f":"NORMSDIST(AF12)-0.5","v":0.47500210485177952},{"$f":"AH11*100","v":47.500210485177952},{"$f":"LEFT(ROUND(AI11,2),5)","v":"47.5"},null,-2.75,9.0935625015910529E-3,"",9.0935625015910529E-3]
[null,"Student 5",92,null,{"$f":"E11-4","v":84},2,168,null,null,null,null,null,null,null,null,null,null,0.5,0.19146246127401312,0.19497426910248061,0.19846821245303381,0.20194403460512356,0.20540148378430201,0.20884031321165364,0.21226028115097295,0.21566115095367588,0.2190426911014357,0.22240467524653507,null,"From table, Z-Score:",{"$f":"I34","v":1.96},{"$f":"ROUND(AE12,2)","v":1.96},{"$f":"AF13&AG13","v":"1.96"},{"$f":"D52*100","v":0},{"$f":"AH12/2","v":0},null,null,-2.7,1.0420934814422592E-2,"",1.0420934814422592E-2]
[null,"Student 6",88,null,80,2,160,null,"*Standard Deviation, σ =",11,"(σ = 11 used for easier calcualtion)",null,null,null,null,null,null,0.6,0.22574688224992645,0.22906909621699434,0.232371106531017,0.23565270788432247,0.23891370030713843,0.24215388919413527,0.24537308532866386,0.24857110490468992,0.25174776954642952,0.25490290632569057,null,null,null,{"$f":"LEFT(AF12,3)","v":"1.9"},{"$f":"IF(AG7=3,0,RIGHT(AF12,1))","v":"6"},{"$f":"ROUND(J13,2)","v":11},null,null,null,-2.65,1.1912243607605179E-2,"",1.1912243607605179E-2]
[null,"Student 7",88,null,76,3,228,null,null,null,null,null,null,null,null,null,null,0.7,0.25803634777692697,0.26114793191001329,0.26423750222074882,0.26730490769910253,0.27035000283520938,0.27337264762313174,0.27637270756240062,0.27935005365735044,0.28230456241426682,0.28523611583636277,null,null,null,{"$f":"ROUND(J11,1)","v":75},null,null,null,null,null,-2.6,1.3582969233685613E-2,"",1.3582969233685613E-2]
[null,"Student 8",88,null,72,4,288,null,null,null,null,null,null,null,null,null,null,0.8,0.28814460141660336,0.29102991212839835,0.29389194641418692,0.29673060817193164,0.29954580673955034,0.30233745687730762,0.30510547874819172,0.30784979789630385,0.31057034522328786,0.31326705696282742,null,null,null,{"$f":"ROUND(B58,2)","v":{"$error":"#VALUE!"}},null,null,null,null,null,-2.5499999999999998,1.5449347134395174E-2,"",1.5449347134395174E-2]
[null,"Student 9",84,null,68,4,272,null,"Weighted Average:",null,null,null,null,null,null,null,null,0.9,0.31593987465324047,0.31858874510820279,0.32121362038562828,0.32381445775474216,0.32639121966137552,0.32894387369151823,0.33147239253316219,0.33397675393647042,0.33645694067230769,0.33891294048916909,null,null,null,{"$f":"ROUND(C59,2)","v":{"$error":"#VALUE!"}},null,null,null,null,null,-2.5,1.752830049356854E-2,"",1.752830049356854E-2]
[null,"Student 10",84,null,64,4,256,null,"  Average Using the weight of each grade",null,null,null,null,null,null,null,null,1,0.34134474606854304,0.34375235497874546,0.34613576962726511,0.34849499721165633,0.35083004966901865,0.35314094362410409,0.35542770033609039,0.35769034564406077,0.35992890991123094,0.3621434279679645,null,null,null,{"$f":"ROUND(J13,1)","v":11},null,null,null,null,null,-2.4500000000000002,1.9837354391795313E-2,"",1.9837354391795313E-2]
[null,"Student 11",80,null,60,2,120,null,"Simple, Straight Average: ",null,null,null,null,null,null,null,null,1.1000000000000001,0.36433393905361733,0.36650048675725277,0.36864311895726931,0.3707618877599822,0.37285684943720176,0.37492806436284987,0.37697559694865668,0.37899951557898182,0.38099989254479938,0.38297680397689127,null,null,null,{"$f":"(AF17*I34)+AF14","v":96.56},{"$f":"(AF17*-1*I34)+AF14","v":53.44},null,null,null,null,-2.4,2.2394530294842899E-2,"",2.2394530294842899E-2]
[null,"Student 12",80,null,56,3,168,null,"  Average without using the weight of each grade",null,null,null,null,null,null,null,null,1.2,0.38493032977829178,0.38686055355602278,0.38876756255216538,0.39065144757430814,0.39251230292541306,0.39435022633314476,0.39616531887869966,0.39795768492518091,0.39972743204555794,0.40147467095025213,null,null,null,{"$f":"ROUND(AF18,2)","v":96.56},{"$f":"ROUND(AG18,2)","v":53.44},null,null,null,null,-2.35,2.5218219915194382E-2,"",2.5218219915194382E-2]
[null,"Student 13",76,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.3,0.4031995154143897,0.40490208220476098,0.40658249100652821,0.40824086434971918,0.40987732753554751,0.41149200856259804,0.41308503805291497,0.41465654917803307,0.41620667758498575,0.41773556132233114,null,null,null,null,null,null,null,null,null,-2.2999999999999998,2.8327037741601186E-2,"",2.8327037741601186E-2]
[null,"Student 14",76,null,"Straight Avrage","N =","Total Points",null,"Weighted Average : ",null,null,null,null,null,null,null,null,1.4,0.41924334076622893,0.42073015854660756,0.42219615947345368,0.42364149046326083,0.42506630046567295,0.4264707403903516,0.42785496303410619,0.42921912300831444,0.43056337666666833,0.43188788203327455,null,null,null,null,null,null,null,null,null,-2.25,3.1739651835667418E-2,"",3.1739651835667418E-2]
[null,"Student 15",76,null,{"$f":"AVERAGE(E8:E19)","v":78},{"$f":"SUM(F8:F19)","v":32},{"$f":"SUM(G6:G19)","v":2400},null,{"$f":"\" = \"&G22&\" / \"&F22&\" = \"","v":" = 2400 / 32 = "},{"$f":"G22/F22","v":75},null,null,null,null,null,null,null,1.5,0.43319279873114191,0.43447828791108356,0.43574451218106425,0.43699163553602161,0.43821982328818809,0.43942924199794098,0.44062005940520699,0.44179244436144693,0.44294656676224586,0.44408259748053058,null,null,null,null,null,null,null,null,null,-2.2000000000000002,3.5474592846231424E-2,"",3.5474592846231424E-2]
[null,"Student 16",72,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6,0.44520070830044201,0.44630107185188028,0.44738386154574794,0.44844925150991066,0.44949741652589625,0.4505285319663519,0.45154277373327723,0.45254031819705265,0.45352134213628004,0.45448602267845017,null,null,null,null,null,null,null,null,null,-2.15,3.955004158937022E-2,"",3.955004158937022E-2]
[null,"Student 17",72,null,"Z-Score: How many standard \ndeviations is from the average ",null,null,null,null,null,null,null,null,null,null,null,null,1.7,0.45543453724145699,0.45636706347596812,0.45728377920867114,0.4581848623864051,0.45907049102119268,0.45994084313618289,0.46079609671251731,0.46163642963712881,0.46246201965148326,0.4632730443012737,null,null,null,null,null,null,null,null,null,-2.1,4.3983595980427191E-2,"",4.3983595980427191E-2]
[null,"Student 18",72,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8,0.46406968088707423,0.4648521064159612,0.46562049755411006,0.46637503058037166,0.46711588134083615,0.46784322520438626,0.46855723701924734,0.46925809107053407,0.46994596103880026,0.4706210199595906,null,null,null,null,null,null,null,null,null,-2.0499999999999998,4.8792018579182764E-2,"",4.8792018579182764E-2]
[null,"Student 19",72,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.9,0.47128344018399815,0.47193339334022744,0.4725710502961632,0.47319658112294505,0.47381015505954727,0.47441194047836144,0.47500210485177952,0.47558081471977742,0.47614823565849151,0.47670453224978815,null,null,null,null,null,null,null,null,null,-2,5.3990966513188063E-2,"",5.3990966513188063E-2]
[null,"Student 20",68,null,"Z-score = 0 represents a score  equal to the average, in the middle. (50% on each side)",null,null,null,null,null,null,null,null,null,null,null,null,2,0.47724986805182079,0.47778440557056856,0.47830830623235321,0.47882173035732778,0.47932483713392993,0.47981778459429558,0.48030072959062309,0.48077382777248268,0.48123723356506221,0.48169110014834104,null,null,null,null,null,null,null,null,null,-1.95,5.9594706068816075E-2,5.9594706068816075E-2,5.9594706068816075E-2]
[null,"Student 21",68,null,"Z-score = 1, -1 represent score that  is 1 standard deviation from the average (34.13% each side, 68.26% total)",null,null,null,null,null,null,null,null,null,null,null,null,2.1,0.48213557943718344,0.48257082206234292,0.48299697735236724,0.48341419331639501,0.48382261662783388,0.48422239260890954,0.48461366521607452,0.48499657702626775,0.48537126922401075,0.48573788158933118,null,null,null,null,null,null,null,null,null,-1.9,6.5615814774676595E-2,6.5615814774676595E-2,6.5615814774676595E-2]
[null,"Student 22",68,null,"Z-score = 2,-2, represent 2 standard deviations from the average (47.72% on each side, 95.44% total)",null,null,null,null,null,null,null,null,null,null,null,null,2.2000000000000002,0.48609655248650141,0.48644741885358,0.48679061619274377,0.48712627856139801,0.48745453856405341,0.48777552734495533,0.48808937458145296,0.48839620847809651,0.4886961557614472,0.48898934167558861,null,null,null,null,null,null,null,null,null,-1.85,7.2064874336217985E-2,7.2064874336217985E-2,7.2064874336217985E-2]
[null,"Student 23",68,null,"If Z-score ,  average and standard deviation are given, then:",null,null,null,null,null,null,null,null,null,null,null,null,2.2999999999999998,0.48927588997832416,0.48955592293804895,0.48982956133128031,0.49009692444083575,0.49035813005464168,0.49061329446516144,0.49086253246942735,0.49110595736966323,0.49134368097448344,0.49157581360065428,null,null,null,null,null,null,null,null,null,-1.8,7.8950158300894149E-2,7.8950158300894149E-2,7.8950158300894149E-2]
[null,"Student 24",64,null,null,null,null,null,null,null,"(isolate x in z-score formula)",null,null,null,null,null,null,2.4,0.49180246407540384,0.49202373973926627,0.49223974644944635,0.49245058858369084,0.49265636904465171,0.49285718926472855,0.49305314921137566,0.49324434739285938,0.49343088086445319,0.49361284523505677,null,null,null,null,null,null,null,null,null,-1.75,8.6277318826511532E-2,8.6277318826511532E-2,8.6277318826511532E-2]
[null,"Student 25",64,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5,0.49379033467422384,0.4939634419195873,0.49413225828466745,0.49429687366704933,0.49445737655691735,0.49461385404593328,0.49476639183644422,0.494915074251009,0.49505998424222941,0.49520120340287377,null,null,null,null,null,null,null,null,null,-1.7,9.4049077376886947E-2,9.4049077376886947E-2,9.4049077376886947E-2]
[null,"Student 26",64,null,"Example A: Using the data above of weighted average = 75, and the standard deviation = 11",null,null,null,null,null,null,null,null,null,null,null,null,2.6,0.49533881197628127,0.49547288886703267,0.49560351165187866,0.4957307565909107,0.49585469863896392,0.49597541145724167,0.49609296742514719,0.49620743765231456,0.49631889199082502,0.49642739904760025,null,null,null,null,null,null,null,null,null,-1.65,0.10226492456397804,0.10226492456397804,0.10226492456397804]
[null,"Student 27",64,null,null,null,null,"Enter a Z-score, to find the score and range:",1.96,{"$f":"\"( \"&AJ11&\"% on each side, or \"&AJ11*2&\"% total)\"","v":"( 47.5% on each side, or 95% total)"},null,null,null,null,null,null,null,2.7,0.49653302619695938,0.4966358395933308,0.49673590418410873,0.49683328372264224,0.49692804078134956,0.49702023676494544,0.49710993192377384,0.49719718536723501,0.49728205507729872,0.49736459792209509,null,null,null,null,null,null,null,null,null,-1.6,0.11092083467945554,0.11092083467945554,0.11092083467945554]
[null,"Student 28",60,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.8,0.49744486966957202,0.49752292500121409,0.4975988175258107,0.4976725997932685,0.49774432330845764,0.49781403854508677,0.49788179495959539,0.49794764100506028,0.49801162414510569,0.49807379086781212,null,null,null,null,null,null,null,null,null,-1.55000000000001,0.12000900069698374,0.12000900069698374,0.12000900069698374]
[null,"Student 29",60,null,null,{"$f":"\"Score on the left = (\"&AF17 &\" X \"&-1*I34 &\") + \"&AF14&\" =\"","v":"Score on the left = (11 X -1.96) + 75 ="},null,null,null,{"$f":"\"Score on the right = (\"&AF17 &\" X \"&I34 &\") + \"&AF14&\" =\"","v":"Score on the right = (11 X 1.96) + 75 ="},null,null,null,null,null,null,null,2.9,0.49813418669961596,0.49819285621919351,0.49824984307132392,0.49830518998072271,0.49835893876584303,0.49841113035263518,0.49846180478826196,0.49851100125476255,0.49855875808266004,0.4986051127645077,null,null,null,null,null,null,null,null,null,-1.50000000000001,0.1295175956658898,0.1295175956658898,0.1295175956658898]
[null,"Student 30",56,null,null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",AG19)","v":53.44},null,null,null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",AF19)","v":96.56},{"$f":"IF(J37>100,\"Beyond limit, Max = 100\",\"\")","v":""},null,null,null,null,null,null,3,0.4986501019683699,0.49869376155123057,0.49873612657232769,0.49877723130640772,0.4988171092568956,0.49885579316897732,0.49889331504259071,0.49892970614532106,0.49896499702519714,0.49899921752338594,null,null,null,null,null,null,null,null,null,-1.4500000000000099,0.13943056644535826,0.13943056644535826,0.13943056644535826]
[null,"Student 31",56,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.1,{"$f":"NORMSDIST(R38+$S$6)-0.5","v":0.49903239678678168},0.49906456328048587,0.49909574480017771,0.49912596848436841,0.49915526082654138,0.49918364768717138,0.49921115430562446,0.49923780531193274,0.4992636247384461,0.49928863603135465,null,null,null,null,null,null,null,null,null,-1.4000000000000099,0.1497274656357428,0.1497274656357428,0.1497274656357428]
[null,"Student 32",56,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.3500000000000101,0.1603833273419174,0.1603833273419174,0.1603833273419174]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.30000000000001,0.17136859204780513,0.17136859204780513,0.17136859204780513]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.25000000000001,0.18264908538901964,0.18264908538901964,0.18264908538901964]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(D52/2)*J11","v":0},{"$f":"ROUND(AD42,2)","v":0},null,{"$f":"J11*(1-D52/2)","v":75},{"$f":"ROUND(AG42,2)","v":75},null,null,null,-1.2000000000000099,0.19418605498321065,0.19418605498321065,0.19418605498321065]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.1500000000000099,0.20593626871997239,0.20593626871997239,0.20593626871997239]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(D52/2)*J11","v":0},{"$f":"ROUND(AD44,2)","v":0},null,{"$f":"J11*(1+D52/2)","v":75},{"$f":"ROUND(AG44,2)","v":75},null,null,null,-1.1000000000000101,0.21785217703254814,0.21785217703254814,0.21785217703254814]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.05000000000001,0.22988214068423063,0.22988214068423063,0.22988214068423063]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.00000000000001,0.24197072451914092,{"$f":"IF(AL46>=-1*$AE$12,AM46,IF(AL46=0,0,\"\"))","v":0.24197072451914092},0.24197072451914092]
[null,null,null,null,null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",AJ11*-1&\" %\")","v":"-47.5 %"},"<  Area on each side  < ",null,null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",AJ11&\" %\")","v":"47.5 %"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.95000000000000995,0.25405905646918658,{"$f":"IF(AL47>=-1*$AE$12,AM47,IF(AL47=0,0,\"\"))","v":0.25405905646918658},0.25405905646918658]
[null,null,null,null,null,"Lower Score",null,"Total Area:",null,"Upper Score",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.90000000000001001,0.26608524989875243,0.26608524989875243,0.26608524989875243]
[null,null,null,null,null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",F37)","v":53.44},null,{"$f":"AJ11*2&\" %\"","v":"95 %"},null,{"$f":"IF(OR(I34<0,I34>3.19),\"\",J37)","v":96.56},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.85000000000000997,0.27798488613099415,0.27798488613099415,0.27798488613099415]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.80000000000001004,0.2896915527614804,0.2896915527614804,0.2896915527614804]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.75000000000000999,0.30113743215480215,0.30113743215480215,0.30113743215480215]
[null,"Example B: Using the data above of weighted average = 75, and the standard deviation = 11",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.70000000000000995,0.31225393336675911,0.31225393336675911,0.31225393336675911]
[null,"    Case 1:  What is the Z-score for a test score x = 90?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.65000000000001001,0.32297235966791221,0.32297235966791221,0.32297235966791221]
[null,"Z-score = (90 - 75) / 11  = 1.36 ( positive, right side of the average)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.60000000000000997,0.33322460289179767,0.33322460289179767,0.33322460289179767]
[null,"From the table, the test is located at 0.4131, or 41.31% from the average",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.55000000000001004,0.34294385501938202,0.34294385501938202,0.34294385501938202]
[null,"  1) there are 91.31% score below 90, (Area for x <= 90)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.50000000000000999,0.35206532676429775,0.35206532676429775,0.35206532676429775]
[null,null,"= The left side of the average of 50% + the 41.31% on the right side",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.45000000000001,0.36052696246164634,0.36052696246164634,0.36052696246164634]
[null,"  2) there are 8.69 % above the score of 90 (Area for x >= 90)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.40000000000001001,0.36827014030332184,0.36827014030332184,0.36827014030332184]
[null,null,"the whole area under the curve is = 100%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.35000000000001003,0.37524034691693658,0.37524034691693658,0.37524034691693658]
[null,null,"100% - 50% - 41.31% = 8.69% above it ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.30000000000000998,0.38138781546052297,0.38138781546052297,0.38138781546052297]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.25000000000000999,0.38666811680284829,0.38666811680284829,0.38666811680284829]
[null,"    Case 2:  What is the Z-score for a test score x = 65?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.20000000000001,0.3910426939754551,0.3910426939754551,0.3910426939754551]
[null,"Z-score = (65 - 75) / 11  = -0.91 ( negative, left side of the average)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.15000000000000999,0.39447933090788834,0.39447933090788834,0.39447933090788834]
[null,"From the table, the test is located at 0.3186, or 31.86% from the average",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.10000000000001,0.39695254747701142,0.39695254747701142,0.39695254747701142]
[null,"  1) there are 18.31% below score of 65 ( Area for x <= 65)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-5.0000000000010002E-2,0.39844391409476382,{"$f":"IF(AL65>-1*$AE$12,AM65,\"\")","v":0.39844391409476382},0.39844391409476382]
[null,null,"= The left side of the average of 50% - the 31.86% ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0.3989422804014327,{"$f":"IF(AL66<=$AE$12,AM66,\"\")","v":0.3989422804014327},0.3989422804014327]
[null,"  2) there are 81.86 % above the score of 65 (Area for x > = 65)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.9999999999990101E-2,0.39844391409476421,0.39844391409476421,0.39844391409476421]
[null,null,"Left side = 31.863%  ;  right side = 50%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.9999999999989903E-2,0.3969525474770122,0.3969525474770122,0.3969525474770122]
[null,null,"     Then Total = 31.86% + 50% = 81.86%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.14999999999999,0.3944793309078895,0.3944793309078895,0.3944793309078895]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19999999999998999,0.39104269397545666,0.39104269397545666,0.39104269397545666]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.24999999999999001,{"$f":"_xlfn.NORM.S.DIST(AL71,FALSE)","v":0.38666811680285018},0.38666811680285018,0.38666811680285018]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.39999999999998997,0.36827014030332483,0.36827014030332483,0.36827014030332483]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.44999999999999002,0.36052696246164961,0.36052696246164961,0.36052696246164961]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.49999999999999001,0.35206532676430125,0.35206532676430125,0.35206532676430125]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.54999999999999005,0.34294385501938579,0.34294385501938579,0.34294385501938579]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.59999999999998999,0.33322460289180167,0.33322460289180167,0.33322460289180167]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.64999999999999003,0.32297235966791638,0.32297235966791638,0.32297235966791638]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.69999999999998996,0.31225393336676349,0.31225393336676349,0.31225393336676349]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.74999999999999001,0.30113743215480671,0.30113743215480671,0.30113743215480671]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.79999999999999005,0.28969155276148506,0.28969155276148506,0.28969155276148506]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.84999999999998999,0.27798488613099881,0.27798488613099881,0.27798488613099881]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.89999999999999003,0.2660852498987572,0.2660852498987572,0.2660852498987572]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.94999999999998996,0.25405905646919141,0.25405905646919141,0.25405905646919141]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.99999999999999001,0.24197072451914581,0.24197072451914581,0.24197072451914581]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.0499999999999901,0.22988214068423543,0.22988214068423543,0.22988214068423543]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.0999999999999901,0.21785217703255294,0.21785217703255294,0.21785217703255294]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.1499999999999899,0.20593626871997714,0.20593626871997714,0.20593626871997714]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.19999999999999,0.19418605498321528,0.19418605498321528,0.19418605498321528]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.44999999999998,0.13943056644536433,0.13943056644536433,0.13943056644536433]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.69999999999998,9.4049077376890139E-2,9.4049077376890139E-2,9.4049077376890139E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.74999999999998,8.6277318826514543E-2,8.6277318826514543E-2,8.6277318826514543E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.7999999999999801,7.8950158300896994E-2,7.8950158300896994E-2,7.8950158300896994E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8499999999999801,7.206487433622065E-2,7.206487433622065E-2,7.206487433622065E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8999999999999799,6.5615814774679093E-2,6.5615814774679093E-2,6.5615814774679093E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.94999999999998,5.95947060688184E-2,5.95947060688184E-2,5.95947060688184E-2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.99999999999998,5.3990966513190221E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0499999999999798,4.8792018579184783E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0999999999999801,4.398359598042903E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1499999999999799,3.9550041589371927E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1999999999999802,3.5474592846232986E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.24999999999998,3.173965183566884E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2999999999999798,2.8327037741602484E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.3499999999999801,2.5218219915195565E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.3999999999999799,2.2394530294843975E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4499999999999802,1.9837354391796288E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.49999999999998,1.7528300493569411E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5499999999999798,1.5449347134395964E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5999999999999801,1.3582969233686319E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.6499999999999799,1.1912243607605814E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.6999999999999802,1.042093481442315E-2,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.74999999999998,9.0935625015915542E-3,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7999999999999798,7.9154515829804109E-3,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.8499999999999801,6.8727666906143615E-3,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.8999999999999799,5.9525324197762025E-3,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.9499999999999802,5.1426409230542402E-3,"",""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.99999999999998,4.4318484119382755E-3]

{"sheet":"Example 2","index":31,"n_rows":126,"n_cols":38,"rows_kept":126,"cut":false,"hidden":false,"merged":[[23,4,24,5],[23,6,24,6],[23,7,24,10],[3,15,4,17],[4,8,5,9],[10,8,11,8],[10,9,11,9],[12,8,13,8],[12,9,13,9],[14,8,16,10],[1,22,1,23],[3,24,3,25],[4,24,4,25],[5,1,6,1],[5,2,6,2],[5,4,6,4],[5,5,6,5],[5,6,6,6]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Area Under the Curve from Left","Z = ",{"$f":"G28","v":"1.96"},"Area =",{"$f":"NORMSDIST(U2)","v":0.97500210485177952}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Round","Left","last"]
[null,null,null,null,"The following are 14 different prices for one item in 100 projects:",null,null,null,null,null,null,null,null,null,null,"Used :Area Under The Curve From the Center",null,null,null,"Range Selected",{"$f":"G24","v":0.95},null,null,"Nearest Area in the Table:",{"$f":"G27","v":0.47500210485177952},null,null,null,null,null,null,null,null,null,null,{"$f":"ROUND(AC12,2)","v":1.96},{"$f":"LEFT(AJ4,3)*1","v":1.9},{"$f":"AE13/100","v":0.06}]
[null,"Detailed Data",null,null,"Data Summarized",null,null,null,"Data Summary",null,null,null,null,null,null,null,null,null,null,"Area on Each Side",{"$f":"G24/2","v":0.47499999999999998},null,null,"Z-Score:",{"$f":"AE12","v":"1.96"},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(AJ6>=-1*$AC$12,AK6,\"\")","v":""}]
[null,"Projects","Price",null,"Price","Frequency, # Of Occurrence","Total",null,null,null,null,null,null,null,null,"Z",0,0.01,0.02,0.03,0.04,0.05,0.06,7.0000000000000007E-2,0.08,0.09,null,null,null,null,null,null,null,null,null,-3,{"$f":"_xlfn.NORM.S.DIST(AJ6,FALSE)","v":4.4318484119380075E-3}]
[null,null,null,null,null,null,null,null,"Minimum",{"$f":"MIN($C$8:$C$107)","v":1},null,null,null,null,null,0,{"$f":"NORMSDIST(P7+$Q$6)-0.5","v":0},{"$f":"NORMSDIST(P7+$R$6)-0.5","v":3.989356314631598E-3},{"$f":"NORMSDIST(P7+$S$6)-0.5","v":7.9783137169020524E-3},{"$f":"NORMSDIST(P7+$T$6)-0.5","v":1.1966473414112722E-2},{"$f":"NORMSDIST(P7+$U$6)-0.5","v":1.5953436852830682E-2},{"$f":"NORMSDIST(P7+$V$6)-0.5","v":1.9938805838372486E-2},{"$f":"NORMSDIST(P7+$W$6)-0.5","v":2.3922182654106838E-2},{"$f":"NORMSDIST(P7+$X$6)-0.5","v":2.7903170180521131E-2},{"$f":"NORMSDIST(P7+$Y$6)-0.5","v":3.1881372013987441E-2},{"$f":"NORMSDIST(P7+$Z$6)-0.5","v":3.5856392585172037E-2},null,null,null,null,{"$f":"LEN(AD12)","v":4},null,null,null,null,-2.95,{"$f":"_xlfn.NORM.S.DIST(AJ7,FALSE)","v":5.1426409230539392E-3},{"$f":"IF(AJ7>=-1*$AC$12,AK7,\"\")","v":""}]
[null,"Project 1",2,null,1,{"$f":"COUNTIF($C$8:$C$107,E8)","v":14},{"$f":"E8*F8","v":14},null,"Maximum",{"$f":"MAX($C$8:$C$107)","v":22},null,null,null,null,null,0.1,3.9827837277028988E-2,4.3795312542316722E-2,4.7758426020583888E-2,5.1716786654561142E-2,5.5670004805906448E-2,5.9617692370242503E-2,6.3559462891432883E-2,6.7494931675038394E-2,7.1423715900900797E-2,7.5345434734795491E-2,null,null,null,null,null,null,null,null,null,-2.9,5.9525324197758538E-3,""]
[null,"Project 2",3,null,2,{"$f":"COUNTIF($C$8:$C$107,E9)","v":17},34,null,"Median",{"$f":"MEDIAN($C$8:$C$107)","v":4},null,null,null,null,null,0.2,7.9259709439102988E-2,8.3166163482442323E-2,8.7064422648214679E-2,9.0954115142005909E-2,9.4834871697795808E-2,9.8706325682923701E-2,0.10256811320176051,0.10641987319803947,0.11026124755579725,0.11409188119887737,null,null,null,null,null,null,null,null,null,-2.85,6.8727666906139712E-3,""]
[null,"Project 3",8,null,3,18,54,null,"Count, n",{"$f":"COUNT($C$8:$C$107)","v":100},null,null,null,null,null,0.3,0.11791142218895267,0.12171952182201928,0.12551583472332006,0.12930001894065346,0.13307173603602807,0.1368306511756191,0.14057643321799129,0.14430875480054683,0.14802729242416279,0.15173172653598244,null,"Enter Area:",{"$f":"G24","v":0.95},null,null,null,null,null,null,-2.8,7.9154515829799686E-3,""]
[null,"Project 4",6,null,4,16,64,null,"Weighted Average ",{"$f":"AVERAGE($C$8:$C$107)","v":4.53},null,null,null,null,null,0.4,0.15542174161032429,0.15909702622767741,0.16275727315175059,0.16640217940454238,0.17003144633940637,0.17364477971208003,0.17724188974965227,0.1808224912174442,0.18438630348377749,0.18793305058260945,null,"Or:",{"$f":"AC10/2","v":0.47499999999999998},null,"Each Side, nearest is:",{"$f":"NORMSDIST(AD12)-0.5","v":0.47500210485177952},{"$f":"AF11*100","v":47.500210485177952},{"$f":"LEFT(ROUND(AG11,2),5)","v":"47.5"},null,-2.75,9.0935625015910529E-3,""]
[null,"Project 5",4,null,5,9,45,null,null,null,null,null,null,null,null,0.5,0.19146246127401312,0.19497426910248061,0.19846821245303381,0.20194403460512356,0.20540148378430201,0.20884031321165364,0.21226028115097295,0.21566115095367588,0.2190426911014357,0.22240467524653507,null,"From table, Z-Score:",{"$f":"IF(AC11=0.5,3.19,IF(OR(AC10>1,AC10<0),\"Not Appl.\",-1*NORMSINV(0.5-AC11)))","v":1.9599639845400536},{"$f":"ROUND(AC12,2)","v":1.96},{"$f":"IF(AE7=1,LEFT(AD12,1),AD13&AE13)","v":"1.96"},{"$f":"G24*100","v":95},{"$f":"AF12/2","v":47.5},null,null,-2.7,1.0420934814422592E-2,""]
[null,"Project 6",4,null,6,9,54,null,"Standard Deviation σ",{"$f":"_xlfn.STDEV.S($C$8:$C$107)","v":3.6775458439485744},null,null,null,null,null,0.6,0.22574688224992645,0.22906909621699434,0.232371106531017,0.23565270788432247,0.23891370030713843,0.24215388919413527,0.24537308532866386,0.24857110490468992,0.25174776954642952,0.25490290632569057,null,null,null,{"$f":"LEFT(AD12,3)","v":"1.9"},{"$f":"IF(AE7=3,0,RIGHT(AD12,1))","v":"6"},{"$f":"ROUND(J13,2)","v":3.68},null,null,null,-2.65,1.1912243607605179E-2,""]
[null,"Project 7",6,null,7,1,7,null,null,null,null,null,null,null,null,0.7,0.25803634777692697,0.26114793191001329,0.26423750222074882,0.26730490769910253,0.27035000283520938,0.27337264762313174,0.27637270756240062,0.27935005365735044,0.28230456241426682,0.28523611583636277,null,null,null,null,null,null,null,null,null,-2.6,1.3582969233685613E-2,""]
[null,"Project 8",4,null,8,2,16,null,"Straight Average for the 14 prices:\n($1+$2+$3+$4+$5+$6+$7+$8+$9+$10+$11+$14+$17+$22) / 14 =  $9",null,null,null,null,null,null,0.8,0.28814460141660336,0.29102991212839835,0.29389194641418692,0.29673060817193164,0.29954580673955034,0.30233745687730762,0.30510547874819172,0.30784979789630385,0.31057034522328786,0.31326705696282742,null,null,null,{"$f":"ROUND(G31,2)","v":3.81},null,null,null,null,null,-2.5499999999999998,1.5449347134395174E-2,""]
[null,"Project 9",2,null,9,6,54,null,null,null,null,null,null,null,null,0.9,0.31593987465324047,0.31858874510820279,0.32121362038562828,0.32381445775474216,0.32639121966137552,0.32894387369151823,0.33147239253316219,0.33397675393647042,0.33645694067230769,0.33891294048916909,null,null,null,{"$f":"ROUND(G34,2)","v":5.25},null,null,null,null,null,-2.5,1.752830049356854E-2,""]
[null,"Project 10",5,null,10,3,30,null,null,null,null,null,null,null,null,1,0.34134474606854304,0.34375235497874546,0.34613576962726511,0.34849499721165633,0.35083004966901865,0.35314094362410409,0.35542770033609039,0.35769034564406077,0.35992890991123094,0.3621434279679645,null,null,null,null,null,null,null,null,null,-2.4500000000000002,1.9837354391795313E-2,""]
[null,"Project 11",8,null,11,1,11,null,"Weighted Average (Default) : ",null,null,null,null,null,null,1.1000000000000001,0.36433393905361733,0.36650048675725277,0.36864311895726931,0.3707618877599822,0.37285684943720176,0.37492806436284987,0.37697559694865668,0.37899951557898182,0.38099989254479938,0.38297680397689127,null,null,null,null,null,null,null,null,null,-2.4,2.2394530294842899E-2,""]
[null,"Project 12",10,null,14,1,14,null,{"$f":"\" = $\"&G22&\" / \"&F22&\" = $\" &J11","v":" = $453 / 100 = $4.53"},null,null,null,null,null,null,1.2,0.38493032977829178,0.38686055355602278,0.38876756255216538,0.39065144757430814,0.39251230292541306,0.39435022633314476,0.39616531887869966,0.39795768492518091,0.39972743204555794,0.40147467095025213,null,null,null,null,null,null,null,null,null,-2.35,2.5218219915194382E-2,""]
[null,"Project 13",4,null,17,2,34,null,null,null,null,null,null,null,null,1.3,0.4031995154143897,0.40490208220476098,0.40658249100652821,0.40824086434971918,0.40987732753554751,0.41149200856259804,0.41308503805291497,0.41465654917803307,0.41620667758498575,0.41773556132233114,null,null,null,null,null,null,null,null,null,-2.2999999999999998,2.8327037741601186E-2,""]
[null,"Project 14",4,null,22,1,22,null,null,null,null,null,null,null,null,1.4,0.41924334076622893,0.42073015854660756,0.42219615947345368,0.42364149046326083,0.42506630046567295,0.4264707403903516,0.42785496303410619,0.42921912300831444,0.43056337666666833,0.43188788203327455,null,null,null,null,null,null,null,null,null,-2.25,3.1739651835667418E-2,""]
[null,"Project 15",4,null,null,{"$f":"SUM(F8:F21)","v":100},{"$f":"SUM(G8:G21)","v":453},null,null,null,null,null,null,null,null,1.5,0.43319279873114191,0.43447828791108356,0.43574451218106425,0.43699163553602161,0.43821982328818809,0.43942924199794098,0.44062005940520699,0.44179244436144693,0.44294656676224586,0.44408259748053058,null,null,null,null,null,null,null,null,null,-2.2000000000000002,3.5474592846231424E-2,""]
[null,"Project 16",2,null,null,null,null,null,null,null,null,null,null,null,null,1.6,0.44520070830044201,0.44630107185188028,0.44738386154574794,0.44844925150991066,0.44949741652589625,0.4505285319663519,0.45154277373327723,0.45254031819705265,0.45352134213628004,0.45448602267845017,null,null,null,null,null,null,null,null,null,-2.15,3.955004158937022E-2,""]
[null,"Project 17",1,null,"Enter Interval Range:",null,0.95,{"$f":"\"( Or  \"&AG12&\"% on each side of the average)\"","v":"( Or  47.5% on each side of the average)"},null,null,null,null,null,null,null,1.7,0.45543453724145699,0.45636706347596812,0.45728377920867114,0.4581848623864051,0.45907049102119268,0.45994084313618289,0.46079609671251731,0.46163642963712881,0.46246201965148326,0.4632730443012737,null,null,null,null,null,null,null,null,null,-2.1,4.3983595980427191E-2,""]
[null,"Project 18",3,null,null,null,null,null,null,null,null,null,null,null,null,1.8,0.46406968088707423,0.4648521064159612,0.46562049755411006,0.46637503058037166,0.46711588134083615,0.46784322520438626,0.46855723701924734,0.46925809107053407,0.46994596103880026,0.4706210199595906,null,null,null,null,null,null,null,null,null,-2.0499999999999998,4.8792018579182764E-2,""]
[null,"Project 19",2,null,null,null,null,null,null,null,null,null,null,null,null,1.9,0.47128344018399815,0.47193339334022744,0.4725710502961632,0.47319658112294505,0.47381015505954727,0.47441194047836144,0.47500210485177952,0.47558081471977742,0.47614823565849151,0.47670453224978815,null,null,null,null,null,null,null,null,null,-2,5.3990966513188063E-2,""]
[null,"Project 20",10,null,null,{"$f":"\"Nearest value to \"&AG12&\"% is:\"","v":"Nearest value to 47.5% is:"},{"$f":"AF11","v":0.47500210485177952},"or ",{"$f":"AH11&\" % from Table\"","v":"47.5 % from Table"},null,null,null,null,null,null,2,0.47724986805182079,0.47778440557056856,0.47830830623235321,0.47882173035732778,0.47932483713392993,0.47981778459429558,0.48030072959062309,0.48077382777248268,0.48123723356506221,0.48169110014834104,null,null,null,null,null,null,null,null,null,-1.95,5.9594706068816075E-2,5.9594706068816075E-2]
[null,"Project 21",1,null,null,"Z- Score=",{"$f":"AE12","v":"1.96"},{"$f":"\"    (Row of \"&AK4&\", Column of \"&AL4&\")\"","v":"    (Row of 1.9, Column of 0.06)"},null,null,null,null,null,null,null,2.1,0.48213557943718344,0.48257082206234292,0.48299697735236724,0.48341419331639501,0.48382261662783388,0.48422239260890954,0.48461366521607452,0.48499657702626775,0.48537126922401075,0.48573788158933118,null,null,null,null,null,null,null,null,null,-1.9,6.5615814774676595E-2,6.5615814774676595E-2]
[null,"Project 22",3,null,null,"Lower Price in the Range =","Average - Z * (Standard Deviation / Square Root of n)",null,null,null,null,null,null,null,null,2.2000000000000002,0.48609655248650141,0.48644741885358,0.48679061619274377,0.48712627856139801,0.48745453856405341,0.48777552734495533,0.48808937458145296,0.48839620847809651,0.4886961557614472,0.48898934167558861,null,null,null,null,null,null,null,null,null,-1.85,7.2064874336217985E-2,7.2064874336217985E-2]
[null,"Project 23",2,null,null,"=",{"$f":"J11&\" - \"&AE12&\" * (\"&AF13&\" / Square Root of \"&J10&\")\"","v":"4.53 - 1.96 * (3.68 / Square Root of 100)"},null,null,null,null,null,null,null,null,2.2999999999999998,0.48927588997832416,0.48955592293804895,0.48982956133128031,0.49009692444083575,0.49035813005464168,0.49061329446516144,0.49086253246942735,0.49110595736966323,0.49134368097448344,0.49157581360065428,null,null,null,null,null,null,null,null,null,-1.8,7.8950158300894149E-2,7.8950158300894149E-2]
[null,"Project 24",3,null,null,"=",{"$f":"J11-AC12*(J13/SQRT(J10))","v":3.8092142594365841},null,null,null,null,null,null,null,null,2.4,0.49180246407540384,0.49202373973926627,0.49223974644944635,0.49245058858369084,0.49265636904465171,0.49285718926472855,0.49305314921137566,0.49324434739285938,0.49343088086445319,0.49361284523505677,null,null,null,null,null,null,null,null,null,-1.75,8.6277318826511532E-2,8.6277318826511532E-2]
[null,"Project 25",4,null,null,"Upper Price in the Range =","Average + Z * (Standard Deviation / Square Root of n)",null,null,null,null,null,null,null,null,2.5,0.49379033467422384,0.4939634419195873,0.49413225828466745,0.49429687366704933,0.49445737655691735,0.49461385404593328,0.49476639183644422,0.494915074251009,0.49505998424222941,0.49520120340287377,null,null,null,null,null,null,null,null,null,-1.7,9.4049077376886947E-2,9.4049077376886947E-2]
[null,"Project 26",3,null,null,"=",{"$f":"J11&\" + \"&AE12&\" * (\"&AF13&\" / Square Root of \"&J10&\")\"","v":"4.53 + 1.96 * (3.68 / Square Root of 100)"},null,null,null,null,null,null,null,null,2.6,0.49533881197628127,0.49547288886703267,0.49560351165187866,0.4957307565909107,0.49585469863896392,0.49597541145724167,0.49609296742514719,0.49620743765231456,0.49631889199082502,0.49642739904760025,null,null,null,null,null,null,null,null,null,-1.65,0.10226492456397804,0.10226492456397804]
[null,"Project 27",5,null,null,"=",{"$f":"J11+AC12*(J13/SQRT(J10))","v":5.2507857405634164},null,null,null,null,null,null,null,null,2.7,0.49653302619695938,0.4966358395933308,0.49673590418410873,0.49683328372264224,0.49692804078134956,0.49702023676494544,0.49710993192377384,0.49719718536723501,0.49728205507729872,0.49736459792209509,null,null,null,null,null,null,null,null,null,-1.6,0.11092083467945554,0.11092083467945554]
[null,"Project 28",2,null,null,null,null,null,null,null,null,null,null,null,null,2.8,0.49744486966957202,0.49752292500121409,0.4975988175258107,0.4976725997932685,0.49774432330845764,0.49781403854508677,0.49788179495959539,0.49794764100506028,0.49801162414510569,0.49807379086781212,null,null,null,null,null,null,null,null,null,-1.55000000000001,0.12000900069698374,0.12000900069698374]
[null,"Project 29",4,null,null,null,null,null,null,null,null,null,null,null,null,2.9,0.49813418669961596,0.49819285621919351,0.49824984307132392,0.49830518998072271,0.49835893876584303,0.49841113035263518,0.49846180478826196,0.49851100125476255,0.49855875808266004,0.4986051127645077,null,null,null,null,null,null,null,null,null,-1.50000000000001,0.1295175956658898,0.1295175956658898]
[null,"Project 30",1,null,null,null,null,null,null,null,null,null,null,null,null,3,0.4986501019683699,0.49869376155123057,0.49873612657232769,0.49877723130640772,0.4988171092568956,0.49885579316897732,0.49889331504259071,0.49892970614532106,0.49896499702519714,0.49899921752338594,null,null,null,null,null,null,null,null,null,-1.4500000000000099,0.13943056644535826,0.13943056644535826]
[null,"Project 31",2,null,null,null,null,null,null,null,null,null,null,null,null,3.1,0.49903239678678168,0.49906456328048587,0.49909574480017771,0.49912596848436841,0.49915526082654138,0.49918364768717138,0.49921115430562446,0.49923780531193274,0.4992636247384461,0.49928863603135465,null,null,null,null,null,null,null,null,null,-1.4000000000000099,0.1497274656357428,0.1497274656357428]
[null,"Project 32",9,null,null,"Left Area:",null,null,null,"Right Area:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.3500000000000101,0.1603833273419174,0.1603833273419174]
[null,"Project 33",1,null,null,{"$f":"I27","v":"47.5 % from Table"},null,null,null,{"$f":"I27","v":"47.5 % from Table"},null,null,"Right Area:",null,null,null,"Common Error:   If using Straight calculation instead of Area ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.30000000000001,0.17136859204780513,0.17136859204780513]
[null,"Project 34",7,null,null,null,null,null,null,null,null,null,{"$f":"#REF!&\" %\"","v":{"$error":"#REF!"}},null,null,null,null,null,{"$f":"\"With \"&AF12&\"%, or  \"&AG12&\"% on each side; \"","v":"With 95%, or  47.5% on each side; "},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.25000000000001,0.18264908538901964,0.18264908538901964]
[null,"Project 35",17,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Wrong Lower Price = ",{"$f":"\"Average - \"&AG12&\" %  = $\"&J11&\" - \"&\"$\"&AC42&\" = $\"&AF42","v":"Average - 47.5 %  = $4.53 - $2.15 = $2.38"},null,null,null,null,{"$f":"\"   (Compared to $ \"&AD15&\" )\"","v":"   (Compared to $ 3.81 )"},null,null,null,{"$f":"(G24/2)*J11","v":2.1517499999999998},{"$f":"ROUND(AB42,2)","v":2.15},null,{"$f":"J11*(1-G24/2)","v":2.3782500000000004},{"$f":"ROUND(AE42,2)","v":2.38},null,null,null,-1.2000000000000099,0.19418605498321065,0.19418605498321065]
[null,"Project 36",9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.1500000000000099,0.20593626871997239,0.20593626871997239]
[null,"Project 37",9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Wrong Upper Price =",{"$f":"\"Average + \"&AG12&\" %  = $\"&J11&\" + \"&\"$\"&AC44&\" = $\"&AF44","v":"Average + 47.5 %  = $4.53 + $2.15 = $6.68"},null,null,null,null,{"$f":"\"    (Compared to $ \"&AD16&\" )\"","v":"    (Compared to $ 5.25 )"},null,null,null,{"$f":"(G24/2)*J11","v":2.1517499999999998},{"$f":"ROUND(AB44,2)","v":2.15},null,{"$f":"J11*(1+G24/2)","v":6.681750000000001},{"$f":"ROUND(AE44,2)","v":6.68},null,null,null,-1.1000000000000101,0.21785217703254814,0.21785217703254814]
[null,"Project 38",9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.05000000000001,0.22988214068423063,0.22988214068423063]
[null,"Project 39",4,null,null,{"$f":"IF(AC12>1.4,\"Lower Price:\",\"\")","v":"Lower Price:"},{"$f":"IF(AC12<=1.4,\"Lower Price:\",\"\")","v":""},null,{"$f":"IF(AC12<=1.4,\"Upper Price:\",\"\")","v":""},{"$f":"IF(AC12>1.4,\"Upper Price:\",\"\")","v":"Upper Price:"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-1.00000000000001,0.24197072451914092,0.24197072451914092]
[null,"Project 40",4,null,null,{"$f":"IF(AC12>1.4,\"$ \"&AD15,\"\")","v":"$ 3.81"},{"$f":"IF(AC12<=1.4,\"$ \"&AD15,\"\")","v":""},null,{"$f":"IF(AC12<=1.4,\"$ \"&AD16,\"\")","v":""},{"$f":"IF(AC12>1.4,\"$ \"&AD16,\"\")","v":"$ 5.25"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.95000000000000995,0.25405905646918658,0.25405905646918658]
[null,"Project 41",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.90000000000001001,0.26608524989875243,0.26608524989875243]
[null,"Project 42",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.85000000000000997,0.27798488613099415,0.27798488613099415]
[null,"Project 43",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.80000000000001004,0.2896915527614804,0.2896915527614804]
[null,"Project 44",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.75000000000000999,0.30113743215480215,0.30113743215480215]
[null,"Project 45",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.70000000000000995,0.31225393336675911,0.31225393336675911]
[null,"Project 46",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.65000000000001001,0.32297235966791221,0.32297235966791221]
[null,"Project 47",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.60000000000000997,0.33322460289179767,0.33322460289179767]
[null,"Project 48",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.55000000000001004,0.34294385501938202,0.34294385501938202]
[null,"Project 49",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.50000000000000999,0.35206532676429775,0.35206532676429775]
[null,"Project 50",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.45000000000001,0.36052696246164634,0.36052696246164634]
[null,"Project 51",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.40000000000001001,0.36827014030332184,0.36827014030332184]
[null,"Project 52",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.35000000000001003,0.37524034691693658,0.37524034691693658]
[null,"Project 53",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.30000000000000998,0.38138781546052297,0.38138781546052297]
[null,"Project 54",14,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.25000000000000999,0.38666811680284829,0.38666811680284829]
[null,"Project 55",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.20000000000001,0.3910426939754551,0.3910426939754551]
[null,"Project 56",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.15000000000000999,0.39447933090788834,0.39447933090788834]
[null,"Project 57",9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.10000000000001,0.39695254747701142,0.39695254747701142]
[null,"Project 58",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-5.0000000000010002E-2,0.39844391409476382,0.39844391409476382]
[null,"Project 59",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0.3989422804014327,0.3989422804014327]
[null,"Project 60",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.9999999999990101E-2,0.39844391409476421,{"$f":"IF(AJ67<=$AC$12,AK67,\"\")","v":0.39844391409476421}]
[null,"Project 61",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,9.9999999999989903E-2,0.3969525474770122,0.3969525474770122]
[null,"Project 62",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.14999999999999,0.3944793309078895,0.3944793309078895]
[null,"Project 63",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19999999999998999,0.39104269397545666,0.39104269397545666]
[null,"Project 64",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.24999999999999001,{"$f":"_xlfn.NORM.S.DIST(AJ71,FALSE)","v":0.38666811680285018},0.38666811680285018]
[null,"Project 65",11,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.29999999999999,0.38138781546052525,0.38138781546052525]
[null,"Project 66",22,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.34999999999998999,0.37524034691693919,0.37524034691693919]
[null,"Project 67",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.39999999999998997,0.36827014030332483,0.36827014030332483]
[null,"Project 68",9,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.44999999999999002,0.36052696246164961,0.36052696246164961]
[null,"Project 69",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.49999999999999001,0.35206532676430125,0.35206532676430125]
[null,"Project 70",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.54999999999999005,0.34294385501938579,0.34294385501938579]
[null,"Project 71",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.59999999999998999,0.33322460289180167,0.33322460289180167]
[null,"Project 72",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.64999999999999003,0.32297235966791638,0.32297235966791638]
[null,"Project 73",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.69999999999998996,0.31225393336676349,0.31225393336676349]
[null,"Project 74",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.74999999999999001,0.30113743215480671,0.30113743215480671]
[null,"Project 75",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.79999999999999005,0.28969155276148506,0.28969155276148506]
[null,"Project 76",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.84999999999998999,0.27798488613099881,0.27798488613099881]
[null,"Project 77",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.89999999999999003,0.2660852498987572,0.2660852498987572]
[null,"Project 78",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.94999999999998996,0.25405905646919141,0.25405905646919141]
[null,"Project 79",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.99999999999999001,0.24197072451914581,0.24197072451914581]
[null,"Project 80",6,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.0499999999999901,0.22988214068423543,0.22988214068423543]
[null,"Project 81",17,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.0999999999999901,0.21785217703255294,0.21785217703255294]
[null,"Project 82",1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.1499999999999899,0.20593626871997714,0.20593626871997714]
[null,"Project 83",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.19999999999999,0.19418605498321528,0.19418605498321528]
[null,"Project 84",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.24999999999998,0.18264908538902649,0.18264908538902649]
[null,"Project 85",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.2999999999999801,0.1713685920478118,0.1713685920478118]
[null,"Project 86",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.3499999999999801,0.1603833273419239,0.1603833273419239]
[null,"Project 87",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.3999999999999799,0.14972746563574907,0.14972746563574907]
[null,"Project 88",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.44999999999998,0.13943056644536433,0.13943056644536433]
[null,"Project 89",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.49999999999998,0.1295175956658956,0.1295175956658956]
[null,"Project 90",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.5499999999999801,0.12000900069698932,0.12000900069698932]
[null,"Project 91",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.5999999999999801,0.11092083467945908,0.11092083467945908]
[null,"Project 92",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.6499999999999799,0.10226492456398137,0.10226492456398137]
[null,"Project 93",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.69999999999998,9.4049077376890139E-2,9.4049077376890139E-2]
[null,"Project 94",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.74999999999998,8.6277318826514543E-2,8.6277318826514543E-2]
[null,"Project 95",3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.7999999999999801,7.8950158300896994E-2,7.8950158300896994E-2]
[null,"Project 96",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8499999999999801,7.206487433622065E-2,7.206487433622065E-2]
[null,"Project 97",10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.8999999999999799,6.5615814774679093E-2,6.5615814774679093E-2]
[null,"Project 98",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.94999999999998,5.95947060688184E-2,5.95947060688184E-2]
[null,"Project 99",4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.99999999999998,5.3990966513190221E-2,""]
[null,"Project 100",2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0499999999999798,4.8792018579184783E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.0999999999999801,4.398359598042903E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1499999999999799,3.9550041589371927E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1999999999999802,3.5474592846232986E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.24999999999998,3.173965183566884E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.2999999999999798,2.8327037741602484E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.3499999999999801,2.5218219915195565E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.3999999999999799,2.2394530294843975E-2,""]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4499999999999802,1.9837354391796288E-2,""]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.5499999999999798,1.5449347134395964E-2,""]
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{"sheet":"Background","index":32,"n_rows":57,"n_cols":23,"rows_kept":57,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,"Hint 1:","Straight Average VS Weighted Average:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The Variance: \n",null,null," Standard Seviation"]
[null,null,null,"  Weighted Average =  average where each value has a specific weight or frequency "]
[null,null,null,"       Example: The following were 5 different Unit Prices in 11 projects distubuted as:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"  They are measures of how  spread out a distribution is."]
[null,null,null,null," =","100, 90, 90, 85, 80, 80, 75, 75, 75, 75, 75",null,null,null,null,null,null,null,null,null,null,null,null,"   In other words, they are measures of variability."]
[null,null,null,null," =",11]
[null,null,null,"              Straight (normal) Average:  (100 + 90 + 85 + 80 + 75)/ 5 = 86",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ : Population standard deviation (n > 30) "]
[null,null,null,"              Weighted Average:  (100x1 + 90 x2 + 85x1 + 80x2 + 75x5) / 11 = 81.82"]
[]
[null,null,null," Median: is the middle point , in which half the numbers are above the median and half are below."]
[null,null,null,"              Median of the prices above is = 80 (5 above and 5 below)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Weighted Average  of a population"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The population Number "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Formula to find σ     =STDEV.P"]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"s: Sample standard deviation  (n < 30)"]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Weighted Average of a sample"]
[null,null,null,null,null,"Left, negatively skewed ",null,null,null,"Symmetric",null,null,"Right, positively skewed ",null,null,null,null,null,null,null,"The population Number "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Formula to find s     =STDEV.S"]
[]
[]
[null,null,"Hint 2:","Limit: Confidence Interval",null,null,null,null,null,null,null,"Formulas Used"]
[null,null,null,"Common level of confidence Interval = 95%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Normal Distribution, Z- table"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Number of record, n > 30 ",null,null,null,null,null,null,"For  Prob = 47.5% (covering 95% total),    Z-score is = 1.96"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Using the Z table."]
[null,null,null,null,null,null,null,null,null,null,"Standard Normal Distribution"]
[null,null,null,null,null,null,null,null,null,null," σ: Population standard deviation. "]
[]
[null,null,null,"Example:",null,null,null,null,null,null,"Example 1: For 95% Confidence interval:"]
[null,null,null,"If the weighted average is $70, and the 95% confidence level = $68 -  $74",null,null,null,null,null,null,null,"Prob =  47.5% on each side, Borders:  2.5%"]
[null,null,null,"Then, 95% of prices should be within that limit or between $68 and $74",null,null,null,null,null,null,null,"Or: Z = 1.96 for 0.4750, 47.5% from table"]
[null,null,null,"   (47.5% below and 47.5% above the weighted average)"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"* Excel uses the border values in the formula"]
[null,null,null,null,null,null,null,null,null,null,"Example 2: For 30% Confidence interval:",null,null,null,null,null,null,null,null,"      For 95%, then the borders are (1-0.95)/2 = 0.025"]
[null,null,null,null,null,null,null,null,null,null,null,"Prob =  15% on each side, Borders: 35%",null,null,null,null,null,null,null,"      The other border is (1 - 0.025) = 0.9750"]
[null,null,null,null,null,null,null,null,null,null,null,"Or: Z = approx. 0.385 from table",null,null,null,null,null,null,null,null,"=NORMSINV(0.025)= -1.95996 = -1.96"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"=NORMSINV(0.975) = 1.95996 = 1.96"]
[null,null,null,null,null,null,null,null,null,null,"* Excel Formula to find Z for 95%:     =NORMSINV(0.025)"]
[null,null,null,"Optional: By selecting any range such as 30%",null,null,null,null,null,null,null,null,"Number of record, n < 30 "]
[null,null,null,"If the prices are: $69 - $72 within the 30% range,  then:"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Using the t table with Degrees of Freedom  df = n - 1."]
[null,null,null,null,null,null,null,null,null,null,"t distribution (Student's distribution)"]
[null,null,null,null,null,null,null,null,null,null,"s: Sample standard deviation."]
[null,null,null,null,null,null,null,null,null,null,"For 95% Confidence interval, Prob = 0.05 for 2 tailed (used)"]
[null,null,null,null,null,null,null,null,null,null,"For 95% Confidence interval, Prob = 0.025 for 1 tailed"]
[null,null,null,"                     (15% below and 15% above the weighted average)",null,null,null,null,null,null,"Excel Formula to find t for 95%:   = TINV(0.05, df)"]

{"sheet":"Macros","index":33,"n_rows":18,"n_cols":12,"rows_kept":18,"cut":false,"hidden":false,"merged":[[17,8,17,14],[1,8,1,14]]}
[]
[null,"1) To Enable Macros in your Excel, follow the steps in this video:",null,null,null,null,null,null,"https://www.youtube.com/watch?v=NdsndEtaG98"]
[]
[]
[null,"2) When you download the file, you might get this message"]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Click on:    Enable Editing"]
[]
[null,"3) If you get this message regarding Security Risk:"]
[]
[]
[]
[]
[]
[null,"Then follow these steps below, or watch this video in Youtube",null,null,null,null,null,null,"https://www.youtube.com/watch?v=d7yqilosNBE"]

{"sheet":"Z Tables","index":34,"n_rows":38,"n_cols":56,"rows_kept":38,"cut":false,"hidden":false,"merged":[[20,28,22,39],[5,35,5,36],[1,28,1,32],[1,3,1,4],[1,17,1,18],[2,17,3,18],[2,3,3,4],[4,35,4,36]]}
[]
[null,null,null,"Enter Neg Z",null,null,null,"Row: First two digits ",{"$f":"IF(OR(D3<-3.99,D3>0),\"\",LEFT(D3,4))","v":"-2.6"},"Answer:",{"$f":"IF(OR(D3<-3.99,D3>0),\"\",NORMSDIST(D3))","v":4.0245885427583044E-3},null,null,null,null,null,null,"Enter Pos Z",null,null,null,"Row: First two digits ",{"$f":"IF(OR(R3>3.99,R3<0),\"\",LEFT(R3,3))","v":"2"},"Answer:",{"$f":"IF(OR(R3>3.99,R3<0),\"\",NORMSDIST(R3))","v":0.97724986805182079},null,null,null,"Reverse:  If Probability is given, Nearest Z-score",null,null,null,null,null,"Example: To find  Z-score for Top %:",null,null,null,null,null,null,null,{"$f":"AF3*100","v":8500},{"$f":"IF(AF3=\"\",\"\",AF3/100)","v":0.85},null,{"$f":"NORMSDIST(AR6)","v":0.85083004966901865},null,{"$f":"AW7*100","v":8500},{"$f":"IF(AW7=\"\",\"\",AW7/100)","v":0.85},null,{"$f":"NORMSDIST(AW6)","v":0.85083004966901865}]
[null,null,"For Z - Score ",-2.65,null,null,null,"Column: Third digit ",{"$f":"IF(OR(D3<-3.99,D3>0),\"\",IF(LEN(D3)=2,0,IF(LEN(D3)=4,0,\"00\"& RIGHT(D3,1))))","v":"005"},null,{"$f":"K2","v":4.0245885427583044E-3},null,null,null,null,null,"For Z - Score ",2,null,null,null,"Column: Third digit ",{"$f":"IF(OR(R3>3.99,R3<0),\"\",IF(LEN(R3)=1,0,IF(R3=0,0,IF(LEN(R3)=3,0,IF(LEN(R3)=4,\"00\"&RIGHT(R3,1))))))","v":0},null,{"$f":"Y2","v":0.97724986805182079},null,null,null,"Enter Probability  (0 - 100%) = ",null,null,85,"%",null,"If Top  is",15,"%,  left area is:",{"$f":"AW7&\"%\"","v":"85%"},null,null,null,null,null,{"$f":"IF(AF3=\"\",\"\",IF(OR(AR2>0.97,AR2<0.05,AR2=19),NORMSINV(AR2+0.0001),IF(AR2<>0,NORMSINV(AR2+0.001),NORMSINV(AR2+0.0007))))","v":1.040731886467543},{"$f":"IF(AR6<0,LEFT(AR6,4),LEFT(AR6,3))","v":"1.0"},{"$f":"IF(AND(AR6>=0,AT5=3),0,IF(AND(AR6<0,AT5=5),0,IF(AND(AR6>=0,AT5=1),0,IF(AND(AR6<0,AT5=3),0,RIGHT(AR6,1)))))","v":"4"},{"$f":"RIGHT(AF3,1)","v":"5"},null,{"$f":"IF(AW7=\"\",\"\",IF(OR(AW2>0.97,AW2<0.05,AW2=19),NORMSINV(AW2+0.0001),IF(AW2<>0,NORMSINV(AW2+0.001),NORMSINV(AW2+0.0007))))","v":1.040731886467543},{"$f":"IF(AW6<0,LEFT(AW6,4),LEFT(AW6,3))","v":"1.0"},{"$f":"IF(AND(AW6>=0,AY5=3),0,IF(AND(AW6<0,AY5=5),0,IF(AND(AW6>=0,AY5=1),0,IF(AND(AW6<0,AY5=3),0,RIGHT(AW6,1)))))","v":"4"},{"$f":"RIGHT(AK5,1)","v":""}]
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[null,null,{"$f":"IF(D3>0,\"Negative Values only\",\"\")","v":""},null,"Area Under The Standard Normal Curve (Z < 0)",null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(R3<0,\"Positive Values only\",\"\")","v":""},null,"Area Under The Standard Normal Curve (Z > 0)",null,null,null,null,null,null,null,null,null,{"$f":"\" Covering >=  \"&AR4& \"%, the nearest P: \"","v":" Covering >=  85%, the nearest P: "},null,null,{"$f":"ROUND(NORMSDIST(AR6),4)","v":0.8508}," blue value\n in table",null,{"$f":"\" for \"&AW7& \"%\"","v":" for 85%"},"The nearest P:",null,{"$f":"AY2","v":0.85083004966901865},null,null,null,null,null,{"$f":"ROUND(AR4,2)","v":85},null,{"$f":"IF(AR6<0,LEN(AR6)+1,LEN(AR6))","v":4},{"$f":"IFERROR(VLOOKUP(AF3,AS7:AS23,1,FALSE),0)","v":0},null,{"$f":"ROUND(AW4,2)","v":85},null,{"$f":"IF(AW6<0,LEN(AW6)+1,LEN(AW6))","v":4},{"$f":"IFERROR(VLOOKUP(AK5,AX7:AX23,1,FALSE),0)","v":0}]
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[null,-3.1,{"$f":"NORMSDIST(B7-$C$6)","v":9.676032132183561E-4},{"$f":"NORMSDIST(B7-+$D$6)","v":9.3543671951410031E-4},{"$f":"NORMSDIST(B7-$E$6)","v":9.0425519982233952E-4},{"$f":"NORMSDIST(B7-$F$6)","v":8.7403151563156744E-4},{"$f":"NORMSDIST(B7-$G$6)","v":8.4473917345862643E-4},{"$f":"NORMSDIST(B7-$H$6)","v":8.1635231282856167E-4},{"$f":"NORMSDIST(B7-$I$6)","v":7.8884569437557184E-4},{"$f":"NORMSDIST(B7-$J$6)","v":7.6219468806723459E-4},{"$f":"NORMSDIST(B7-$K$6)","v":7.3637526155392961E-4},{"$f":"NORMSDIST(B7-$L$6)","v":7.1136396864536315E-4},null,null,null,0,{"$f":"NORMSDIST(P7+$Q$6)","v":0.5},{"$f":"NORMSDIST(P7+$R$6)","v":0.5039893563146316},{"$f":"NORMSDIST(P7+$S$6)","v":0.50797831371690205},{"$f":"NORMSDIST(P7+$T$6)","v":0.51196647341411272},{"$f":"NORMSDIST(P7+$U$6)","v":0.51595343685283068},{"$f":"NORMSDIST(P7+$V$6)","v":0.51993880583837249},{"$f":"NORMSDIST(P7+$W$6)","v":0.52392218265410684},{"$f":"NORMSDIST(P7+$X$6)","v":0.52790317018052113},{"$f":"NORMSDIST(P7+$Y$6)","v":0.53188137201398744},{"$f":"NORMSDIST(P7+$Z$6)","v":0.53585639258517204},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,19,null,null,null,{"$f":"100-AJ3","v":85}]
[null,-3,{"$f":"NORMSDIST(B8-$C$6)","v":1.3498980316300933E-3},1.3062384487694675E-3,1.2638734276722969E-3,1.2227686935922593E-3,1.1828907431044044E-3,1.1442068310226975E-3,1.1066849574092469E-3,1.0702938546789222E-3,1.0350029748028415E-3,1.0007824766140115E-3,null,null,null,0.1,{"$f":"NORMSDIST(P8+$Q$6)","v":0.53982783727702899},{"$f":"NORMSDIST(P8+$R$6)","v":0.54379531254231672},{"$f":"NORMSDIST(P8+$S$6)","v":0.54775842602058389},{"$f":"NORMSDIST(P8+$T$6)","v":0.55171678665456114},{"$f":"NORMSDIST(P8+$U$6)","v":0.55567000480590645},{"$f":"NORMSDIST(P8+$V$6)","v":0.5596176923702425},{"$f":"NORMSDIST(P8+$W$6)","v":0.56355946289143288},{"$f":"NORMSDIST(P8+$X$6)","v":0.56749493167503839},{"$f":"NORMSDIST(P8+$Y$6)","v":0.5714237159009008},{"$f":"NORMSDIST(P8+$Z$6)","v":0.57534543473479549},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,23]
[null,-2.9,1.8658133003840378E-3,1.807143780806431E-3,1.7501569286760988E-3,1.6948100192772627E-3,1.6410612341569962E-3,1.5888696473648693E-3,1.538195211738057E-3,1.4889987452374655E-3,1.4412419173400134E-3,1.3948872354922507E-3,null,null,null,0.2,0.57925970943910299,0.58316616348244232,0.58706442264821468,0.59095411514200591,0.59483487169779581,0.5987063256829237,0.60256811320176051,0.60641987319803947,0.61026124755579725,0.61409188119887737,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,32]
[null,-2.8,2.5551303304279312E-3,2.4770749987858636E-3,2.4011824741892529E-3,2.3274002067315554E-3,2.2556766915423207E-3,2.1859614549132396E-3,2.1182050404046204E-3,2.0523589949397532E-3,1.9883758548943252E-3,1.9262091321878626E-3,null,null,null,0.3,0.61791142218895267,0.62171952182201928,0.62551583472332006,0.62930001894065346,0.63307173603602807,0.6368306511756191,0.64057643321799129,0.64430875480054683,0.64802729242416279,0.65173172653598244,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,36]
[null,-2.7,3.4669738030406643E-3,3.3641604066691941E-3,3.2640958158913066E-3,3.1667162773577947E-3,3.071959218650487E-3,2.9797632350545551E-3,2.8900680762261443E-3,2.8028146327650242E-3,2.7179449227012539E-3,2.6354020779049505E-3,null,null,null,0.4,0.65542174161032429,0.65909702622767741,0.66275727315175059,0.66640217940454238,0.67003144633940637,0.67364477971208003,0.67724188974965227,0.6808224912174442,0.68438630348377749,0.68793305058260945,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,39]
[null,-2.6,4.6611880237187476E-3,4.5271111329673241E-3,4.3964883481213092E-3,4.2692434090893508E-3,4.1453013610360367E-3,4.0245885427583044E-3,3.9070325748527717E-3,3.7925623476854869E-3,3.6811080091749787E-3,3.5726009523997363E-3,null,null,null,0.5,0.69146246127401312,0.69497426910248061,0.69846821245303381,0.70194403460512356,0.70540148378430201,0.70884031321165364,0.71226028115097295,0.71566115095367588,0.7190426911014357,0.72240467524653507,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,41]
[null,-2.5,6.2096653257761331E-3,6.0365580804126653E-3,5.8677417153325615E-3,5.7031263329506993E-3,5.5426234430825993E-3,5.3861459540666869E-3,5.2336081635557816E-3,5.0849257489910355E-3,4.9400157577706438E-3,4.7987965971261785E-3,null,null,null,0.6,0.72574688224992645,0.72906909621699434,0.732371106531017,0.73565270788432247,0.73891370030713843,0.74215388919413527,0.74537308532866386,0.74857110490468992,0.75174776954642952,0.75490290632569057,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,52]
[null,-2.4,8.1975359245961311E-3,7.9762602607337287E-3,7.7602535505536425E-3,7.5494114163092126E-3,7.3436309553483459E-3,7.1428107352714204E-3,6.9468507886243092E-3,6.7556526071406503E-3,6.569119135546763E-3,6.3871547649431782E-3,null,null,null,0.7,0.75803634777692697,0.76114793191001329,0.76423750222074882,0.76730490769910253,0.77035000283520938,0.77337264762313174,0.77637270756240062,0.77935005365735044,0.78230456241426682,0.78523611583636277,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,54]
[null,-2.2999999999999998,1.0724110021675811E-2,1.044407706195109E-2,1.0170438668719676E-2,9.9030755591642573E-3,9.6418699453583289E-3,9.3867055348385835E-3,9.1374675305726672E-3,8.8940426303367806E-3,8.6563190255165429E-3,8.4241863993456938E-3,null,null,null,0.8,0.78814460141660336,0.79102991212839835,0.79389194641418692,0.79673060817193164,0.79954580673955034,0.80233745687730762,0.80510547874819172,0.80784979789630385,0.81057034522328786,0.81326705696282742,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,56]
[null,-2.2000000000000002,1.3903447513498597E-2,1.3552581146419981E-2,1.3209383807256267E-2,1.287372143860201E-2,1.2545461435946561E-2,1.2224472655044696E-2,1.1910625418547057E-2,1.1603791521903535E-2,1.1303844238552777E-2,1.1010658324411384E-2,null,null,null,0.9,0.81593987465324047,0.81858874510820279,0.82121362038562828,0.82381445775474216,0.82639121966137552,0.82894387369151823,0.83147239253316219,0.83397675393647042,0.83645694067230769,0.83891294048916909,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,58]
[null,-2.1,1.7864420562816546E-2,1.7429177937657091E-2,1.7003022647632787E-2,1.6585806683605007E-2,1.6177383372166076E-2,1.5777607391090503E-2,1.538633478392545E-2,1.5003422973732208E-2,1.4628730775989252E-2,1.4262118410668875E-2,null,null,null,1,0.84134474606854304,0.84375235497874546,0.84613576962726511,0.84849499721165633,0.85083004966901865,0.85314094362410409,0.85542770033609039,0.85769034564406077,0.85992890991123094,0.8621434279679645,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,66]
[null,-2,2.2750131948179191E-2,2.2215594429431475E-2,2.1691693767646781E-2,2.1178269642672266E-2,2.0675162866070039E-2,2.0182215405704397E-2,1.9699270409376895E-2,1.9226172227517276E-2,1.8762766434937749E-2,1.8308899851658973E-2,null,null,null,1.1000000000000001,0.86433393905361733,0.86650048675725277,0.86864311895726931,0.8707618877599822,0.87285684943720176,0.87492806436284987,0.87697559694865668,0.87899951557898182,0.88099989254479938,0.88297680397689127,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,72]
[null,-1.9,2.87165598160018E-2,2.8066606659772512E-2,2.7428949703836809E-2,2.6803418877054948E-2,2.6189844940452685E-2,2.5588059521638607E-2,2.4997895148220432E-2,2.441918528022255E-2,2.3851764341508513E-2,2.329546775021182E-2,null,null,null,1.2,0.88493032977829178,0.88686055355602278,0.88876756255216538,0.89065144757430814,0.89251230292541306,0.89435022633314476,0.89616531887869966,0.89795768492518091,0.89972743204555794,0.90147467095025213,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,73]
[null,-1.8,3.5930319112925789E-2,3.5147893584038796E-2,3.4379502445889977E-2,3.3624969419628316E-2,3.2884118659163887E-2,3.2156774795613713E-2,3.1442762980752693E-2,3.074190892946595E-2,3.0054038961199774E-2,2.9378980040409414E-2,null,null,null,1.3,0.9031995154143897,0.90490208220476098,0.90658249100652821,0.90824086434971918,0.90987732753554751,0.91149200856259804,0.91308503805291497,0.91465654917803307,0.91620667758498575,0.91773556132233114,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,78]
[null,-1.7,4.4565462758543041E-2,4.3632936524031884E-2,4.2716220791328911E-2,4.181513761359492E-2,4.0929508978807365E-2,4.00591568638171E-2,3.9203903287482647E-2,3.8363570362871233E-2,3.7537980348516783E-2,3.6726955698726291E-2,null,null,null,1.4,0.91924334076622893,0.92073015854660756,0.92219615947345368,0.92364149046326083,0.92506630046567295,0.9264707403903516,0.92785496303410619,0.92921912300831444,0.93056337666666833,0.93188788203327455,null,null,"\nExample: Class exam has an average (mean) score μ of 70 and a standard deviation σ of 10.\n If the top 15% get an A,  what is the cut-off Z-score  and the corresponding cut-off score for A ?",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,80]
[null,-1.6,5.4799291699557967E-2,5.3698928148119669E-2,5.2616138454252052E-2,5.1550748490089351E-2,5.0502583474103704E-2,4.9471468033648082E-2,4.845722626672281E-2,4.7459681802947302E-2,4.6478657863720019E-2,4.551397732154977E-2,null,null,null,1.5,0.93319279873114191,0.93447828791108356,0.93574451218106425,0.93699163553602161,0.93821982328818809,0.93942924199794098,0.94062005940520699,0.94179244436144693,0.94294656676224586,0.94408259748053058,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,86]
[null,-1.5,6.6807201268858057E-2,6.5521712088916481E-2,6.4255487818935766E-2,6.3008364463978436E-2,6.1780176711811879E-2,6.057075800205898E-2,5.9379940594793013E-2,5.8207555638553017E-2,5.7053433237754192E-2,5.5917402519469417E-2,null,null,null,1.6,0.94520070830044201,0.94630107185188028,0.94738386154574794,0.94844925150991066,0.94949741652589625,0.9505285319663519,0.95154277373327723,0.95254031819705265,0.95352134213628004,0.95448602267845017,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,63]
[null,-1.4,8.0756659233771053E-2,7.9269841453392401E-2,7.7803840526546347E-2,7.6358509536739116E-2,7.4933699534327061E-2,7.3529259609648373E-2,7.2145036965893777E-2,7.0780876991685518E-2,6.9436623333331698E-2,6.8112117966725436E-2,null,null,null,1.7,0.95543453724145699,0.95636706347596812,0.95728377920867114,0.9581848623864051,0.95907049102119268,0.95994084313618289,0.96079609671251731,0.96163642963712881,0.96246201965148326,0.9632730443012737]
[null,-1.3,9.6800484585610316E-2,9.5097917795239018E-2,9.3417508993471773E-2,9.1759135650280807E-2,9.0122672464452463E-2,8.8507991437401998E-2,8.6914961947084993E-2,8.534345082196694E-2,8.3793322415014249E-2,8.2264438677668902E-2,null,null,null,1.8,0.96406968088707423,0.9648521064159612,0.96562049755411006,0.96637503058037166,0.96711588134083615,0.96784322520438626,0.96855723701924734,0.96925809107053407,0.96994596103880026,0.9706210199595906]
[null,-1.2,0.11506967022170828,0.11313944644397728,0.11123243744783459,0.1093485524256919,0.1074876970745869,0.10564977366685525,0.10383468112130037,0.1020423150748191,0.10027256795444205,9.8525329049747812E-2,null,null,null,1.9,0.97128344018399815,0.97193339334022744,0.9725710502961632,0.97319658112294505,0.97381015505954727,0.97441194047836144,0.97500210485177952,0.97558081471977742,0.97614823565849151,0.97670453224978815]
[null,-1.1000000000000001,0.13566606094638264,0.1334995132427472,0.13135688104273069,0.12923811224001777,0.12714315056279821,0.12507193563715019,0.12302440305134332,0.12100048442101816,0.11900010745520065,0.11702319602310868,null,null,null,2,0.97724986805182079,0.97778440557056856,0.97830830623235321,0.97882173035732778,0.97932483713392993,0.97981778459429558,0.98030072959062309,0.98077382777248268,0.98123723356506221,0.98169110014834104]
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[null,-0.9,0.1840601253467595,0.18141125489179724,0.17878637961437172,0.1761855422452579,0.17360878033862448,0.17105612630848177,0.16852760746683779,0.16602324606352964,0.16354305932769236,0.16108705951083091,null,null,null,2.2000000000000002,0.98609655248650141,0.98644741885358,0.98679061619274377,0.98712627856139801,0.98745453856405341,0.98777552734495533,0.98808937458145296,0.98839620847809651,0.9886961557614472,0.98898934167558861]
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[null,-0.7,0.24196365222307298,0.23885206808998671,0.23576249777925118,0.23269509230089741,0.22964999716479059,0.22662735237686821,0.22362729243759941,0.22064994634264959,0.21769543758573318,0.21476388416363718,null,null,null,2.4,0.99180246407540384,0.99202373973926627,0.99223974644944635,0.99245058858369084,0.99265636904465171,0.99285718926472855,0.99305314921137566,0.99324434739285938,0.99343088086445319,0.99361284523505677]
[null,-0.6,0.27425311775007355,0.27093090378300566,0.267628893468983,0.26434729211567748,0.26108629969286151,0.25784611080586467,0.25462691467133614,0.25142889509531008,0.24825223045357048,0.24509709367430943,null,null,null,2.5,0.99379033467422384,0.9939634419195873,0.99413225828466745,0.99429687366704933,0.99445737655691735,0.99461385404593328,0.99476639183644422,0.994915074251009,0.99505998424222941,0.99520120340287377]
[null,-0.5,0.30853753872598688,0.30502573089751939,0.30153178754696619,0.29805596539487639,0.29459851621569799,0.29115968678834636,0.28773971884902705,0.28433884904632412,0.2809573088985643,0.27759532475346493,null,null,null,2.6,0.99533881197628127,0.99547288886703267,0.99560351165187866,0.9957307565909107,0.99585469863896392,0.99597541145724167,0.99609296742514719,0.99620743765231456,0.99631889199082502,0.99642739904760025]
[null,-0.4,0.34457825838967576,0.34090297377232259,0.33724272684824946,0.33359782059545762,0.32996855366059363,0.32635522028791997,0.32275811025034773,0.3191775087825558,0.31561369651622251,0.31206694941739055,null,null,null,2.7,0.99653302619695938,0.9966358395933308,0.99673590418410873,0.99683328372264224,0.99692804078134956,0.99702023676494544,0.99710993192377384,0.99719718536723501,0.99728205507729872,0.99736459792209509,null,null,null,"For area of 85%, the nearest probability from the table is: 0.8508, or Z = 1.04"]
[null,-0.3,0.38208857781104733,0.37828047817798072,0.37448416527667994,0.37069998105934648,0.36692826396397193,0.3631693488243809,0.35942356678200876,0.35569124519945322,0.35197270757583721,0.34826827346401756,null,null,null,2.8,0.99744486966957202,0.99752292500121409,0.9975988175258107,0.9976725997932685,0.99774432330845764,0.99781403854508677,0.99788179495959539,0.99794764100506028,0.99801162414510569,0.99807379086781212]
[null,-0.2,0.42074029056089696,0.41683383651755768,0.41293557735178538,0.40904588485799409,0.40516512830220414,0.4012936743170763,0.39743188679823949,0.39358012680196047,0.38973875244420275,0.38590811880112263,null,null,null,2.9,0.99813418669961596,0.99819285621919351,0.99824984307132392,0.99830518998072271,0.99835893876584303,0.99841113035263518,0.99846180478826196,0.99851100125476255,0.99855875808266004,0.9986051127645077,null,null,null,null,"The Z-Score formula is: ",null,"or: ",null,1.04," = (x - 70 ) / 10"]
[null,-0.1,0.46017216272297101,0.45620468745768322,0.45224157397941611,0.44828321334543886,0.44432999519409355,0.44038230762975744,0.43644053710856717,0.43250506832496155,0.42857628409909926,0.42465456526520451,null,null,null,3,0.9986501019683699,0.99869376155123057,0.99873612657232769,0.99877723130640772,0.9988171092568956,0.99885579316897732,0.99889331504259071,0.99892970614532106,0.99896499702519714,0.99899921752338594]
[null,0,0.5,0.4960106436853684,0.492021686283098,0.48803352658588733,0.48404656314716926,0.48006119416162751,0.47607781734589316,0.47209682981947887,0.46811862798601261,0.46414360741482791,null,null,null,3.1,0.99903239678678168,0.99906456328048587,0.99909574480017771,0.99912596848436841,0.99915526082654138,0.99918364768717138,0.99921115430562446,0.99923780531193274,0.9992636247384461,0.99928863603135465,null,null,null,null,null,null,"Solve for  x = ",null,80.400000000000006,"Min Score to get an A"]

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