Find a formula for the sum of the first n even positive integers. b. prove the formula that you conjectured in part (a)

Which property is illustrated by the following statement? if hxa rgi, then rgi hxa.

Hillel is juggling flaming torches to raise money for charity. his initial appearance raises $500\$500 $500 , and he raises $15\$15 $15 for each minute of juggling performance. the amount rr r of money hillel raises is a function of tt t , the length of his performance in minutes. write the function's formula.

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