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3 years ago

What is m? 128° 173° 192° 256°

Mathematics

2 answers:

arsen [322]3 years ago

8 0

the question is

What is the measure of the arc PO?

we know that

The measure of the external angle is the semidifference of the arcs that it covers.

m∠MNO= $\frac{1}{2} *(arcPO-arcMO)$

$45=\frac{1}{2} *(arcPO-83)\\ 90+83=arcPO\\ arcPO=173\ degrees$

therefore

the answer is

the measure of the arc PO is equal to $173\ degrees$

Lesechka [4]3 years ago

3 0

The answer is 173 degrees

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storchak [24]

Answer:

The null hypothesis is $H_o: \mu = 4$ .

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Step-by-step explanation:

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

This means that the null hypothesis is that they are 4.00 cm long, that is:

$H_o: \mu = 4$

At the alternate hypothesis we test if it is different. So

$H_a: \mu \neq 4$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

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

4 is tested at the null hypothesis:

This means that $\mu = 4$

After sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14 cm.

This means that $n = 196, X = 4.14$

He knows that the population standard deviation is 0.83 cm.

This means that $\sigma = 0.83$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{4.14 - 4}{\frac{0.83}{\sqrt{196}}}$

$z = 2.36$

Pvalue of the test and decision:

The pvalue of the test is the probability that the sample mean is different by at least 4.14 - 4 = 0.14 from the target value, which is P(|z| > 2.36), which is 2 multiplied by the pvalue of z = -2.36.

Looking at the z-table, z = -2.36 has a pvalue of 0.0091

2*0.0091 = 0.0182

The pvalue of the test is 0.0182 < 0.05, which means that there is sufficient evidence to show that the manufacturer needs to recalibrate the machines.

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