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Setler79 [48]
3 years ago
12

PLEASE HELP!!! Will give brainliest!

Mathematics
1 answer:
pychu [463]3 years ago
8 0

Answer:

x=11\°

m∠N=59\°

m∠O=121\°

Step-by-step explanation:

we know that

In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary

so

In this problem

m∠M=m∠O

m∠L=m∠N

m∠M+m∠N=180\° -------> by supplementary angles

substitute the values and solve for x

11x+(6x-7)=180\°

17x=(180+7)\°

x=11\°

so

Statements

<u>case A)</u> x=11\°

The statement is true ------> see the procedure

<u>case B)</u> m∠L=22\°

The statement is False

we know that

opposite angles are congruent

so

m∠L=m∠N

m∠L=6x-7=6(11)-7=59\°

<u>case C)</u> m∠M=111\°

The statement is False

we know that

m∠M=11x=11(11)=121\°

<u>case D)</u> m∠N=59\°

The statement is True

we know that

m∠N=6x-7=6(11)-7=59\°

<u>case E)</u> m∠O=121\°

The statement is True

we know that

opposite angles are congruent

so

m∠O=m∠M

m∠O=11x=11(11)=121\°

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<span>2nd: 7x − 3 = x – 3</span>

7x – x = 3 – 3

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<span>3rd: 7x + 3 = x − 3</span>

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<span>7x + 3 = x − 3</span>

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Answer:

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The alternate hypothesis is H_a: \mu \neq 4

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.

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

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

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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

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Answer:

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Step-by-step explanation:

Solution

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