A large stockpile of used pumps contains 20% that are currently unusable and need to be repaired. A repairman is sent to the stockpile with three repair kits. He selects pumps at random and tests them one at a time. If a pump works, he goes on to the next one. If a pump doesn't work, he uses one of his repair kits on it. Suppose that it takes 10 minutes to test whether a pump works, and 20 minutes to repair a pump that does not work. The expected value and variance of the total time it takes the repairman to use up his three kits are, respectively:.

Expected value = 190

Variance = 4000

Step-by-step explanation:

Let X be the number of the trials until the third success of the bad pump.

This implies that X is a negative binomial distribution having θ = 20% = 0.2.

Now, if for example it will take X trials to use up the three pumps, then the total time is 10 min/trials + extra 10 minutes for the 3 bad pumps

This means the total time is written as;

T = 10X + (10 + 10 + 20)

T = 10X + 40

Mean which is also expected value of X is;

μ_x = 3/0.2 = 15

Variance of X is; σ²_x = 40

Thus;

Mean of T will be;

μ_T = 10μ_x + 40

μ_T = 10(15) + 40

μ_T = 190

Also, variance of T will be;

σ²_T = 10²•σ²_x

σ²_T = 100 × 40

σ²_T = 4000

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1