Two recreational volleyball teams, Cherryville and Mount Irving, wanted to compare the ages of their players. The ages of the Cherryville players are 16, 16, 17, 17, 17, 18, and 18. The mean age of the Cherryville players is 17. The ages of the Mount Irving players are 16, 17, 18, 18, 19, 19, and 19. The mean age of the Mount Irving players is 18. Which statement is true? Team Mount Irving's players ages vary the same amount as Team Cherryville's players ages.

Team Cherryville's players ages vary more than Team Mount Irving's players ages.
Team Mount Irving's players ages vary more than team Cherryville's Players ages.

The range of Cherryville's players ages is greater than the range of Mount Irving's players ages.

i would say true? if the unit was informational and it "refreshed your understanding", then true.

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.