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2 years ago

A farmer owns a total of 8 4/5 acres of land. The land is separated into 4

Mathematics

1 answer:

Stells [14]2 years ago

8 0

<h3>Answer: 2 & 1/5 acres</h3>

Explanation:

The mixed number 8 & 4/5 consists of the whole part 8 and the fractional part 4/5.

Divide the whole part 8 into 4 equal pieces

8/4 = 2

This means 2 is part of the final answer.

Also, divide the 4/5 into 4 equal pieces as well. This is the same as multiplying by 1/4

(1/4)*(4/5) = 1/5

Overall, the size of each section is 2 & 1/5 acres

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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.

Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

$= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} } \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du } \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}] \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\$

$= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C$

substitute u = 1-2x⁵ into the result

$= \dfrac{1}{40(1-2x^5)^4} +C$

Hence $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ $= \dfrac{1}{40(1-2x^5)^4} +C$

5 0

2 years ago

Eight less than 7.2 times a number is -29.6 wrote out in numbers

enot [183]

7.2x - 8 = -29.6 that is your answer wrote out in numbers.

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3 years ago

If Joan reads 75 pages in 4 hours how long will it take her to read 250 pages?

uysha [10]

Answer:10 hours to read all 250 pages

Step-by-step explanation:

4 0

3 years ago

What is x please help

NeTakaya

Your x will be -60 because you subtract 9x from 8x that equal-1 and you divide it by 60 because if you add 42+18 it will be 60 so you divide 60 by -1 and the answer will be -60

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3 years ago

A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the fl

ankoles [38]

Answer:

The null hypothesis is $H_0: \mu = 4$

The alternate hypothesis is $H_1: \mu > 4$

The p-value of the test is of 0.0045.

The p-value of the test is low(< 0.01), which means that there is enough evidence that the flow rate is more than 4 gallons per minute (gpm) and thus, the pump should be put into service.

Step-by-step explanation:

A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 4 gallons per minute (gpm).

At the null hypothesis, we test that the mean is 4, so:

$H_0: \mu = 4$

At the alternate hypothesis, we test that the mean is more than 4, that is:

$H_1: \mu > 4$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

4 is tested at the null hypothesis:

This means that $\mu = 4$

In an initial study, eight runs were made. The average flow rate was 6.4 gpm and the standard deviation was 1.9 gpm.

This means that $n = 8, X = 6.4, s = 1.9$

Test statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{6.4 - 4}{\frac{1.9}{\sqrt{8}}}$

$t = 3.57$

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 6.4, which is a right-tailed test with t = 3.57 and 8 - 1 = 7 degrees of freedom.

With the help of a calculator, the p-value of the test is of 0.0045.

3. Should the pump be put into service?

The p-value of the test is low(< 0.01), which means that there is enough evidence that the flow rate is more than 4 gallons per minute (gpm) and thus, the pump should be put into service.

6 0

2 years ago