Find the average value of the function f \left( x, y, z \right) = x^{2} + y^{2} + z^{2} over the rectangular prism 0 \leq x \leq 5, \ \ 0 \leq y \leq 4, \ \ 0 \leq z \leq 2.

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?