Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter =0.6. What is (a) the probability that a repair takes less than 8 hours? (b) the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours?

a) 0.9917

b) 0.1652          

Step-by-step explanation:

We are given the following in the question:

The time for repair follows an exponential distribution.

a) P(repair takes less than 8 hours)

0.9917 is the probability that a repair takes less than 8 hours.

b) the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours

thus, 0.1652 is the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours.

the image of (6, 9) under a dilation is (4, 6). the scale factor is

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.