You measure the lifetime of a random sample of 64 tires of a certain brand. the sample mean is x¯=50 months. suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown mean µ and standard deviation σ=5 months, then a 99% confidence interval for µ is:

Astandard deck of cards contains 52 cards. one card is selected from the deck. (a) compute the probability of randomly selecting a diamond or heart. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability of randomly selecting a diamond or heart or club. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability of randomly selecting queen or club. (type an integer or a decimal rounded to three decimal places as needed.)

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

Asalesperson has january sales of $20,000(1,$20,000) and april sales of $80,000 (4,$80,000). what is the rate of change?