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3 years ago

Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened

Mathematics

1 answer:

Aleksandr [31]3 years ago

6 0

Answer:

92087,14873

Step-by-step explanation:

Given that Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened in 1990, the population of Marymount increased by about 20% each year for the first ten years and then increased by 5% each year after that

Let P0 be the population in 1990

Then we have in 2000 the population is

$P(2000) = P_0(1.2)^{10}$

with this initial population for next growth we have in 2010 the population would be

$P(1.05)^{10}$ , where P = population is 2000

a) Given that $P(1.05)^{10) = 150000\\P = 150000(1.05)^{-10} =92.086.99\\=92087$

b) we use the exponential equation and solve for initial population in 2000.

c) we have

$P_0(1.2)^{10} =92087\\P_0 = 92087((1.2)^{-10})\\=14872.56\\=14873$

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An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed wi

Elza [17]

Answer:

$P(X$

And we can find this probability using the normal standard distribution table and we got:

$P(z$

And the percentage faster than 13.28 seconds would be 91.9%

Step-by-step explanation:

Let X the random variable that represent the runtimes of a population, and for this case we know the distribution for X is given by:

$X \sim N(13,0.2)$

Where $\mu=13$ and $\sigma=0.2$

We want to find this probability:

$P(X$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we have:

$P(X$

And we can find this probability using the normal standard distribution table and we got:

$P(z$

And the percentage faster than 13.28 seconds would be 91.9%

8 0

2 years ago

The lcm of 2 numbers is 60 and one of the numbers is 7 less than the other number

brilliants [131]

The two numbers are 5 and 12.

6 0

3 years ago

The heights of adult males in the United States are approximately normally distributed. The mean height is 70 inches (5 feet 10

steposvetlana [31]

Using the normal distribution, it is found that the probability is 0.16.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are given by, respectively, $\mu = 70, \sigma = 3$ .

The proportion of students between 45 and 67 inches is the p-value of Z when <u>X = 67 subtracted by the p-value of Z when X = 45</u>, hence:

X = 67:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{67 - 70}{3}$

Z = -1

Z = -1 has a p-value of 0.16.

X = 45:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{45 - 70}{3}$

Z = -8.3

Z = -8.3 has a p-value of 0.

0.16 - 0 = 0.16

The probability is 0.16.

More can be learned about the normal distribution at brainly.com/question/24663213

3 0

2 years ago

X2 +10x + 21<br> I need to factor the

Ber [7]

Answer:

(x + 7)(x + 3).

Step-by-step explanation:

x^2 +10x + 21

21 = 7 * 3 and 10 = 7 +3

so the factors are

(x + 7)(x + 3).

4 0

3 years ago

Solve the system of equations.<br><br> 5x + y = 9<br> 3x + 2y = 4

tiny-mole [99]

Y=-5x+9

3x+2(-5x+9)=4
3x-10x+18=4
-7x=4-18
-7x=-14
x=2

5(2)+y=9
10+y=9
y=9-10
y=-1

The answer is (2,-1) :)

5 0

3 years ago

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