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3 years ago

(4, -3), (x, 1); slope -4

Mathematics

1 answer:

Alexandra [31]3 years ago

3 0

Answer:

x = 3

Step-by-step explanation:

$m = \frac{y \frac{}{2} - y \frac{}{1} }{x \frac{}{2} - x \frac{}{1} }$

m = slope

x, y = coordinates

$- 4 = \frac{1 - ( - 3)}{x - 4} \\ - 4(x - 4) = 1 + 3 \\ - 4x + 16 = 4 \\ - 4 x = 4 - 16 \\ - 4x = - 12 \\ x= \frac{ - 12}{ - 4} \\ x = 3$

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Caroline earns $54 for 6 hours of babysitting. What is Caroline's rate in dollars per hour?

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Answer:

Divided 54 divided by 6 = 9

Step-by-step explanation:

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3 years ago

Read 2 more answers

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.

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3 years ago

(05.05)On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2). What is the length of

Cerrena [4.2K]

Answer: 11 units

Step-by-step explanation:

Given: On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2).

To find : length of Side RT of the polygon.

Using distance formula to find distance between (a,b) and (c,d):

$d=\sqrt{(d-b)^2+(c-a)^2}$