Explanation
The symbol Σ (called sigma) means "sum up". So, in this case, the expression indicates the sum of the (xᵢ)², where i goes from 1 to 4, which is 1, 2, 3 and 4. Then, we have:
[tex]\sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2[/tex]
From the word problem, we know the value of each xᵢ.
[tex]\begin{gathered} x_1=5 \\ x_2=13 \\ x_3=19 \\ x_4=16 \end{gathered}[/tex]
Finally, we operate.
[tex]\begin{gathered} \sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=(5)^2+(13)^2+(19)^2+(16)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=25+169+361+256 \\ \sum_{i\mathop{=}1}^4(x_i)^2=811 \end{gathered}[/tex]Answer
The result of computing the given expression is 811.
