Jenny makes food for her hummingbird feeders. the food is made up of 1 part sugar and 4 parts water. she uses 3434 cup of sugar to make the hummingbird food. how much water should jenny use?

Evaluate this using ! 0.25^2 x 2.4 + 0.25 x 2.4^2 − 0.25 x 2.4 x 0.65

Three students each examine the system of linear equations shown. 8x + 4y = 16 8x + 2y = 8 caleb says there is exactly one solution. jeremy says there is no solution. kim says there are infinitely many solutions. which student is correct? provide mathematical reasoning to support your answer. answer in complete sentences. : d

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