Solve (-10-5/6)^2*1/4+(0-5/6)^2*1/6+(5-frac{5}{6})^2*frac{1}{2}+(10-frac{5}{6})^2*frac{1}{12}

$$( - 10 - \frac { 5 } { 6 } ) ^ { 2 } \cdot \frac { 1 } { 4 } + ( 0 - \frac { 5 } { 6 } ) ^ { 2 } \cdot \frac { 1 } { 6 } + ( 5 - \frac { 5 } { 6 } ) ^ { 2 } \cdot \frac { 1 } { 2 } + ( 10 - \frac { 5 } { 6 } ) ^ { 2 } \cdot \frac { 1 } { 12 }$$

Evaluate

$$\frac{1625}{36}\approx 45.138888889$$

Solution Steps

Subtract \frac{5}{6} from -10 to get -\frac{65}{6}.

$$\left(-\frac{65}{6}\right)^{2}\times \frac{1}{4}+\left(0-\frac{5}{6}\right)^{2}\times \frac{1}{6}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Calculate -\frac{65}{6} to the power of 2 and get \frac{4225}{36}.

$$\frac{4225}{36}\times \frac{1}{4}+\left(0-\frac{5}{6}\right)^{2}\times \frac{1}{6}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Multiply \frac{4225}{36} and \frac{1}{4} to get \frac{4225}{144}.

$$\frac{4225}{144}+\left(0-\frac{5}{6}\right)^{2}\times \frac{1}{6}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Subtract \frac{5}{6} from 0 to get -\frac{5}{6}.

$$\frac{4225}{144}+\left(-\frac{5}{6}\right)^{2}\times \frac{1}{6}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Calculate -\frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{4225}{144}+\frac{25}{36}\times \frac{1}{6}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Multiply \frac{25}{36} and \frac{1}{6} to get \frac{25}{216}.

$$\frac{4225}{144}+\frac{25}{216}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Add \frac{4225}{144} and \frac{25}{216} to get \frac{12725}{432}.

$$\frac{12725}{432}+\left(5-\frac{5}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Subtract \frac{5}{6} from 5 to get \frac{25}{6}.

$$\frac{12725}{432}+\left(\frac{25}{6}\right)^{2}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Calculate \frac{25}{6} to the power of 2 and get \frac{625}{36}.

$$\frac{12725}{432}+\frac{625}{36}\times \frac{1}{2}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Multiply \frac{625}{36} and \frac{1}{2} to get \frac{625}{72}.

$$\frac{12725}{432}+\frac{625}{72}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Add \frac{12725}{432} and \frac{625}{72} to get \frac{16475}{432}.

$$\frac{16475}{432}+\left(10-\frac{5}{6}\right)^{2}\times \frac{1}{12}$$

Subtract \frac{5}{6} from 10 to get \frac{55}{6}.

$$\frac{16475}{432}+\left(\frac{55}{6}\right)^{2}\times \frac{1}{12}$$

Calculate \frac{55}{6} to the power of 2 and get \frac{3025}{36}.

$$\frac{16475}{432}+\frac{3025}{36}\times \frac{1}{12}$$

Multiply \frac{3025}{36} and \frac{1}{12} to get \frac{3025}{432}.

$$\frac{16475}{432}+\frac{3025}{432}$$

Add \frac{16475}{432} and \frac{3025}{432} to get \frac{1625}{36}.

$$\frac{1625}{36}$$

Factor

$$\frac{5 ^ {3} \cdot 13}{2 ^ {2} \cdot 3 ^ {2}} = 45\frac{5}{36} = 45.138888888888886$$