Write a function that models the variation. x = 1/3, y = 1/5, and r = 3 when z = 1/2. z varies directly with x and inversely with the product of r^2 and y.

Asmall business produces and sells balls. the fixed costs are $20 and each ball costs $4.32 to produce. each ball sells for $8.32. write the equations for the total cost, c, and the revenue, r, then use the graphing method to determine how many balls must be sold to break even.

Helena lost her marbles. but then she found them and put them in 44 bags with mm marbles in each bag. she had 33 marbles left over that didn't fit in the bags.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.