Given f(x)=3x + 2 and g(x) = x + 5, find (i.) f o g)(x)

(ii.)(g o f)(x)

is fg(x) = gf(x)?​

The measures of the angles in △abc are given by the expressions in the table. angle measure angle a 65° angle b (3x−10)° angle c (2x)∘ find the value of x. then find the m∠b and m∠c.

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

On her way to work, mrs. larsen gets a green light at a certain traffic light only 30% of the time. she wants to find the probability that she will get a green light at this traffic light all five mornings that she travels to work next week. use the following randomly generated list of 200 five-digit numbers to answer the questions and find the probability. select the digits you will use to represent a favorable outcome. how many favorable outcomes are on this list? what are they? given this simulation, what is the probability that mrs. larsen will get a green light at this traffic light all five mornings next week?