A coin collection contains d dimes and q quarters worth a total of $50. Which equation models this information?

d + q = 50

10d + 25q = 50

0.1d + 0.25q = 50

0.01d + 0.25q = 50

An octagonal prism has jow many lateral faces?

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

Abarge can safely haul no more than 400 tons across the river. the barge has an empty weight of 24 tons. the average weight of the railroad cars is 4 tons each.bhow many railroad cars can the barge haul?