The Krasnapolski is a top-of-the-line hotel in Amsterdam, the Netherlands. Among their many services, they rent bicycles to guests. The bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. On average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. Guests keep bicycles for four days on average, with a standard deviation of two days. How long does a guest on average have to wait for a bike? a. Approximately 24 hours
b. Approximately 0.033 hours
c. Approximately 4 days
d. Approximately 47 minutes

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.