The ratio in the table for red balls to blue balls is constant in each column. Number of Red Balls
7
14
r
35
42
Number of Blue Balls
4.
8
16
20
24
Let r = number of red balls corresponding to 16 blue balls
Which table shows the correct value for r?
Number of Red Balls
7
14
OA)
21
35
42
Number of Red Balls
Number of Blue Balls
7
14
4
14
8
B)
16
20
24
Number of Blue Balls
4
8
16
14
4

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0