Answer:
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
<span>(x - 2)(x - 3) = 2
x^2 - 2x - 3x + 6 - 2 = 0
x^2 - 5x + 4 = 0
(x -4)(x - 1) = 0
x - 4 = 0; x = 4
x - 1 = 0; x =1
{1,4}
answer
</span><span>{1, 4}</span>
Answer:(0,4)
Step-by-step explanation:
First you find the vertex of x squared = 12 y, then slightly move it
Add 8π to both sides of the equation to get:


We have found that x = 9π. Remember that in solving problems like these with pi that it can often be helpful to treat pi as a variable.