A manufacturer of flea collars for animals that weigh less than 5 kilograms injects the collars
with 15 milligrams of a biocide that only acts on fleas. The manufacturer will release a collar that
has no less than 14 milligrams and no more than 16 milligrams of insecticide. The following list
shows the result of sampling 36 collars from an actual production run of 720 collars.
17, 14, 14, 16, 14, 15, 15, 15, 16, 14, 16, 14, 15, 15, 15, 16, 13, 13, 13, 13, 13, 14, 14, 13, 17, 14,
15, 13, 14, 15, 16, 17, 14, 17, 14, 15, 4.
7. How many flea collars out of a production run of 720 collars would be acceptable to ship
according to this sample? Explain your reasoning.

it would be a on edgenuit y

the diagram below is your final answer

divide the numbers

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.