Afish tank contains 18 goldfish and 22 guppies. if you randomly select 2 fish, what is the probability that they are both goldfish?
a. 1/20
b. 51/260
c. 1/22
d. 1/36

The probability is the number of positive events divided by the number of total possible events. The probability searched will be the probability that the first fish selected is a goldfish times the probability that the second fish selected is also a goldfish. The probability that the first fish selected is a goldfish is the number of goldfish in the tank divided by the total number of fish, i.e. 18 / 40. The probality that the second fish selected is a goldfish is 17 / 39 (because there is one goldfish less in the thank). Then, the joint probability is (18/40)*(17/39) = 306/1560 =102/ 520 = 51/260. Then, the answer is the option b. 51/260

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

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.

The answer would be c