Consider an espresso stand with a single barista. customers arrive at the rate of 25 per hour according to a poisson distribution. service times are exponentially distributed with a mean service time of 1.5 minutes per customer. a. what is the service rate per hour for the expresso stand? b. what is the probability that the server is busy? c. what is the probability that the server is idle? d. what is the average number of customers waiting in line? e. what is the average time in minutes a customer spends waiting in line for service?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).