Can someone please help me with this question? Thanks in advance I appreciate the help.

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti

melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

Exponential distribution:

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

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

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

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

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).

This means that $m = 100, \mu = \frac{1}{100} = 0.01$

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

$P(X > x) = e^{-\mu x}$

This is P(X > 190). So

$P(X > 190) = e^{-0.01*190} = 0.1496$

0.1496 = 14.96% probability that the demand will exceed 190 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 0.08?

This is x for which:

$P(X > x) = 0.08$

So

$e^{-0.01x} = 0.08$

$\ln{e^{-0.01x}} = \ln{0.08}$

$-0.01x = \ln{0.08}$

$x = -\frac{\ln{0.08}}{0.01}$

$x = 252.6$

Capacity of 252.6 cubic feet per second

5 0

3 years ago

Find mAC.<br><br> Pls help me

timurjin [86]

Answer:

Measure of Arc AC is 30 degrees

Step-by-step explanation:

To find the value of the marked arc, we are going to use the arc-angle relationship

from the type of given diagram, we can figure out the relationship to use

Mathematically, we have this as;

Measure of Arc AC = 2 * angle ABC

So we have arc AC as 2 * 15

Arc AC = 30 degrees

8 0

3 years ago

Find the difference between the GCF and LCM of 400 and 360<br>

Margarita [4]

Answer: 3560

Step-by-step explanation: GCF of 400 will be 40 and the LCM will be 3600 so if you are doing LCM-GCF it would be 3560

3 0

3 years ago

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The owner of a small store buys coats for 50.00$ each. Answer parts a and b.sells the coats for $ each. he sells the coats for

alukav5142 [94]

Answer:

40% profit

140% markup

Step-by-step explanation:

I'm not sure if it's asking what is the markup, or how much you are making.

But profit

$20 out of 50 = 0.40

Markup

70/50 = 1.4 -> 140% markup

6 0

3 years ago

How do you identify the bases of any prism?

PtichkaEL [24]

Answer:

Look at the names of the prisms above. Each type of prism is named after its base. In the figure on the left, the base is a rectangle, so it is called a rectangular prism. In the middle, the base is a triangle, so the shape is a triangular prism.

Step-by-step explanation:

3 0

3 years ago

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