((2.76-4.11)^2+(3.72-4.11)^2+(1.5-4.11)^2+(3.37-4.11)^2+(9.25-4.11)^2+(4.08-4.11)^2)/(6-1)

asked by guest
on Nov 17, 2024 at 6:32 am



You asked:

Evaluate the expression: (2.76−4.11)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1\frac{{\left( 2.76 - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}

MathBot Answer:

(2.76−4.11)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=8938712500=7.15096\frac{{\left( 2.76 - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1} = \frac{89387}{12500} = 7.15096

(2.76−4.11)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=(6925−4.11)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=(6925−411100)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=(−2720)2+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=729400+(3.72−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=729400+(9325−4.11)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=729400+(9325−411100)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=729400+(−39100)2+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=729400+152110000+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=98735000+(1.5−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=98735000+(32−4.11)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=98735000+(32−411100)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=98735000+(−261100)2+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=98735000+6812110000+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=8786710000+(3.37−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=8786710000+(337100−4.11)2+(9.25−4.11)2+(4.08−4.11)26−1=8786710000+(337100−411100)2+(9.25−4.11)2+(4.08−4.11)26−1=8786710000+(−3750)2+(9.25−4.11)2+(4.08−4.11)26−1=8786710000+13692500+(9.25−4.11)2+(4.08−4.11)26−1=9334310000+(9.25−4.11)2+(4.08−4.11)26−1=9334310000+(374−4.11)2+(4.08−4.11)26−1=9334310000+(374−411100)2+(4.08−4.11)26−1=9334310000+(25750)2+(4.08−4.11)26−1=9334310000+660492500+(4.08−4.11)26−1=35753910000+(4.08−4.11)26−1=35753910000+(10225−4.11)26−1=35753910000+(10225−411100)26−1=35753910000+(−3100)26−1=35753910000+9100006−1=8938725006−1=8938725005=8938712500\begin{aligned}\frac{{\left( 2.76 - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}&=\frac{{\left( \frac{69}{25} - 4.11 \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{{\left( \frac{69}{25} - \frac{411}{100} \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{{\left( \frac{-27}{20} \right)}^{2} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{729}{400} + {\left( 3.72 - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{729}{400} + {\left( \frac{93}{25} - 4.11 \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{729}{400} + {\left( \frac{93}{25} - \frac{411}{100} \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{729}{400} + {\left( \frac{-39}{100} \right)}^{2} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{729}{400} + \frac{1521}{10000} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{9873}{5000} + {\left( 1.5 - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{9873}{5000} + {\left( \frac{3}{2} - 4.11 \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{9873}{5000} + {\left( \frac{3}{2} - \frac{411}{100} \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{9873}{5000} + {\left( \frac{-261}{100} \right)}^{2} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{9873}{5000} + \frac{68121}{10000} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{87867}{10000} + {\left( 3.37 - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{87867}{10000} + {\left( \frac{337}{100} - 4.11 \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{87867}{10000} + {\left( \frac{337}{100} - \frac{411}{100} \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{87867}{10000} + {\left( \frac{-37}{50} \right)}^{2} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{87867}{10000} + \frac{1369}{2500} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{93343}{10000} + {\left( 9.25 - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{93343}{10000} + {\left( \frac{37}{4} - 4.11 \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{93343}{10000} + {\left( \frac{37}{4} - \frac{411}{100} \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{93343}{10000} + {\left( \frac{257}{50} \right)}^{2} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{93343}{10000} + \frac{66049}{2500} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{357539}{10000} + {\left( 4.08 - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{357539}{10000} + {\left( \frac{102}{25} - 4.11 \right)}^{2}}{6 - 1}\\&=\frac{\frac{357539}{10000} + {\left( \frac{102}{25} - \frac{411}{100} \right)}^{2}}{6 - 1}\\&=\frac{\frac{357539}{10000} + {\left( \frac{-3}{100} \right)}^{2}}{6 - 1}\\&=\frac{\frac{357539}{10000} + \frac{9}{10000}}{6 - 1}\\&=\frac{\frac{89387}{2500}}{6 - 1}\\&=\frac{\frac{89387}{2500}}{5}\\&=\frac{89387}{12500}\end{aligned}

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