The manager of a fast-food restaurant determines that the average time that her customers wait for service is 1.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

In this problem, we have that:

So

Find the probability that a customer has to wait more than 4 minutes.

Either the customer has to wait 4 minutes or less, or he has to wait more than 4 minutes. The sum of the probabilities of these events is decimal 1. So

We want P(X > 4). So

0.069 = 6.9% probability that a customer has to wait more than 4 minutes.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584