A hair salon has found that 25% of its new male customers and 40% of its new female customers become repeat customers. Today, it had six new customers:
Christine, Don, Esther, Gus, Melody, and Rowan. Don, Gus, and Rowan are
male, while Christine, Esther, and Melody are female.
To investigate the probability of two new female customers both becoming
repeat customers, the employees of the hair salon first put 20 scraps of paper
numbered from 1 to 20 in a hat. They then drew a scrap of paper, recorded the
number on it, put it back in the hat, and drew again. They let the numbers 13
through 20 represent new female customers who become repeat customers,
and they did five trials. The results are listed below:
Trial
1 2 3 4
5
Numbers 11, 2, 14, 9, 18,
Drawn 6 15 19 15 16
Using their trial as your reasoning, what percent would be returning
customers? Only type in the number.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

28

step-by-step explanation:

8+8+6+6