) The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). a. Find the probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) b. What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.09? (Round your answer to two decimal places.)

a) 0.3012 = 30.12% probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

b) 240.79 cfs.

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:

The probability of finding a value higher than x is:

In this problem, we have that:

a. Find the probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

This is

0.3012 = 30.12% probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

b. What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.09?

We want x for which

So

So 240.79 cfs.

answer: 370

step-by-step explanation:

remember use pemdas! there are no parentheses or exponents so lets move onto the first part of the equation: multiplication and division. first, lets break the first part of the equation up into something easier using the distributive property. 28 * 12= (20 *12) + (8*12) you know that 20*12 is 240 and 8*12 is 96. add them and you get 336. then, lets solve the last part of the equation (the last part of pemdas is addition and subtraction). 336 plus 34 is 370. hope this !

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a