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 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

Answers

Answer 1

Answer:

Answer:

The probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day is $P(Y>190)=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

Step-by-step explanation:

Let Y be the water demand in the early afternoon.

If the random variable Y has density function f (y) and a < b, then the probability that Y falls in the interval [a, b] is

$P(a\leq Y \leq b)=\int\limits^a_b {f(y)} \, dy$

A random variable Y is said to have an exponential distribution with parameter $\beta > 0$ if and only if the density function of Y is

$f(y)=\left \{ {{(1)/(\beta)e^{-(y)/(\beta) }, \quad{0\:\leq \:y \:\leq \:\infty} } \atop {0}, \quad elsewhere} \right.$

If Y is an exponential random variable with parameter β, then

mean = β

To find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day, you must:

We are given the mean = β = 100 cubic feet per second

$P(Y>190)=\int\limits^(\infty)_(190) {(1)/(100)e^(-y/100) } \, dy$

Compute the indefinite integral $\int (1)/(100)e^{-(y)/(100)}dy$

$(1)/(100)\cdot \int \:e^{-(y)/(100)}dy\n\n\mathrm{Apply\:u \:substitution}\:u=-(y)/(100)\n\n(1)/(100)\cdot \int \:-100e^udu\n\n(1)/(100)\left(-100\cdot \int \:e^udu\right)\n\n(1)/(100)\left(-100e^u\right)\n\n\mathrm{Substitute\:back}\:u=-(y)/(100)\n\n(1)/(100)\left(-100e^{-(y)/(100)}\right)\n\n-e^{-(y)/(100)}$

Compute the boundaries

$\int _(190)^(\infty \:)(1)/(100)e^{-(y)/(100)}dy=0-\left(-\frac{1}{e^{(19)/(10)}}\right)$

$\int _(190)^(\infty \:)(1)/(100)e^{-(y)/(100)}dy=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

The probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day is $P(Y>190)=\frac{1}{e^{(19)/(10)}}\approx 0.1496$

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James has $20.00 in his checking account. He goes to the bank and withdraws $20.00. How much money does James have in his account immediately after withdrawing the $20.00?

Answers

Answer:

$0.00

Step-by-step explanation:

$20.00-$20.00=$0.00

Could someone help me out?

Answers

Answer:

Step-by-step explanation:

Answer:

The value of x is 28cm.

Step-by-step explanation:

Area of a trapezium = ½h(a + b)

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Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (–5, –5), (4, 6) L2 : (–9, 8), (–18, –3)

Answers

Answer: The lines L1 and L2 are parallel.

Step-by-step explanation: We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :

L1 : (–5, –5), (4, 6),

L2 : (–9, 8), (–18, –3).

We know that a pair of lines are

(i) PARALLEL if the slopes of both the lines are equal.

(II) PERPENDICULAR if the product of the slopes of the lines is -1.

The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by

$m=(d-b)/(c-a).$

So, the slope of line L1 is

$m_1=(6-(-5))/(4-(-5))=(6+5)/(4+5)=(11)/(9)$

and

the slope of line L2 is

$m_2=(-3-8)/(-18-(-9))=(-11)/(-9)=(11)/(9).$

Therefore, we get

$m_1=m_2\n\n\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.$

Hence, the lines L1 and L2 are parallel.

Answer:

Parallel

Step-by-step explanation:

IN 2013 The number of students in a small school is 284. it is estimated that the student population will increase by 4% every year. write formula for student population and estimate student population in 2020

Answers

Answer:

Amount = Initial value × (1 + rate of interest)^years and 374

Step-by-step explanation:

The formula to determine the student population and the estimated student population is given below:

As we know that

Amount = Initial value × (1 + rate of interest)^years

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Answers

Answer:

121.857

Step-by-step explanation:

6×7r = 5118

42r = 5118

r = 121.857

Answer:

121.8571428571429

Step-by-step explanation:

r= 5118/42

What integer multiplied by 8 equals -96?

Answers

Answer:

-12

Step-by-step explanation:

Let "integer" = x

When x is multiplied by 8, it equals -96:

8x = -96

Isolate the variable x. Note the equal sign, what you do to one side, you do to the other. Divide 8 from both sides

(8x)/8 = (-96)/8

x = -96/8

x = -12

-12 is your answer

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