Karen’s Kitty Korner offers cat sitting services for the pampered cats of Beverly Hills. During the week, she offers her cat sitting services $5 an hour along with an additional fee of $12. On the weekend, her fees change to $3 per hour and an additional fee of $18. After how many hours of cat sitting will her weekend rates be the same as her weekday rate? But can you give me the step by step like this
1 + 2x = 5 - 2x

1+2x = 5 + -2x
2x + 1 = -2x + 5
+2x +2x
4x + 1 = 5
-1 -1
4x = 4
4 4

X = 1

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