Phone calls arrive at the rate of 48 per hour at the reservation desk for regional airways. A) Compute the probability of receiving three calls in a 10-minute interval of time?(to 4 decimals)
B) Compute the probability of receiving exactly 13 calls in 15 minutes. (To 4 decimals)
C) Suppose no calls are currently on hold. If an agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?
D) What is the probability that none will be waiting?
E) If no calls are being processed, what is the probability that the agent can take 5 minutes for a personal time without being interrupted by a call?

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.

x=0

step-by-step explanation: