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3 years ago

If ANYONE could help ASAP Pls

Mathematics

1 answer:

Goryan [66]3 years ago

7 0

ANSWER

The correct answer is C

EXPLANATION

This is the composition the two functions

We have

$a(x) = 3x + 1$

and

$b(x) = \sqrt{x - 4}$

$(b \circ \: a)(x) = b(a(x))$

$(b \circ \: a)(x) = b(3x + 1)$

We substitute to obtain,

$(b \circ \: a)(x) = \sqrt{(3x + 1) - 4}$

$(b \circ \: a)(x) = \sqrt{3x - 3}$

The domain of this function can be found by solving,

$3x - 3 \geqslant 0$

This implies that

$3x \geqslant 3$

Or

$x \geqslant 1$

In interval notation, we have,

$[1, \infty )$

The correct answer is option C

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2 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:

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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 $n = 8, X = 6.4, s = 1.9$

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

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

$t = 3.57$

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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