X Katelyn incorrectly simplified an expression using the steps shown below.
(3 x 10^) (9 x 10) + 0.0002
(27 x 10-2) + 0.0002
= (27 x 10-2) + (2 x 10-4)
= (0.27 x 10 4) + (2 x 10-4)
= 2.27 x 10-8
Which of the following equations from Katelyn's steps are false?
Select all that apply.
Х
(3 x 104) (9 x 10²) + 0.0002 = (27 x 10-2) + 0.0002
(27 x 10-2) + 0.0002 = (27 x 10-2) + (2 x 10-4)
(27 x 10-2) + (2 x 10-4) = (0.27 x 10-4) + (2 x 10-4)
(0.27 x 10-4) + (2 x 10-) = 2.27 x 10-8

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