The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 500 hours. Find the probability of a bulb lasting for between 480 and 526 hours.

If a • b*2 = 1.8 x 10*-7, and c•b/d = 7.2 x 10*-4, find the value of a•d*2/c*2

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

The radius of the sphere is 10 units .what is the approximate volume of the sphere use π=3.14