Anew battery's voltage may be acceptable (a) or unacceptable (u). a certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. suppose that 93% of all batteries have acceptable voltages. let y denote the number of batteries that must be tested. (a) what is p(2), that is p(y = 2)? (round your answer to four decimal places.) p(2) = .8649 correct: your answer is correct. (b) what is p(3)? [hint: there are two different outcomes that result in y = 3.]. (round your answer to three decimal places.) p(3) = .121 correct: your answer is correct. (c) to have y = 5, what must be true of the fifth battery selected? the fifth battery must be an a. the fifth battery must be a u. correct: your answer is correct. list the four outcomes for which y = 5. (enter your answer in set notation.) determine p(5). (round your answer to five decimal places.) p(5) = (d) use the pattern in your answers for parts (a)–(c) to obtain a general formula for p(y). p(y) =

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.

i think the answer would be c

the result can be shown in both exact and decimal forms.

exact form; 76 · 75, 4911, 4935, 711, 735

decimal form: 5700, 4911, 4935, 711, 735