Circle q is shown. secant l n and tangent p n intersect at point n outside of the circle. secant l n intersects the circle at point m. arc m p is y, arc l p is x, and arc m l is z.
which equation is correct regarding the measure of ∠mnp?

m∠mnp = one-half(x – y)
m∠mnp = one-half(x + y)
m∠mnp = one-half(z + y)
m∠mnp = one-half(z – y)

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