Determine whether the events described below depict independent or dependent events A certain game spinner contains 8 dark or light colored sectors and a single value from 1 through 4 as shown below.​ Find the probability of spinning the spinner twice and getting a dark square and the four. Are the two spins independent or dependent justify your response.

These tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 9 to x = 10?

Describe how to translate the graph of y=/x to obtain the graph of y=/x+5

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