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3 years ago

What is the measure of angle 3

Mathematics

2 answers:

ValentinkaMS [17]3 years ago

8 0

Answer:

<3=31

Step-by-step explanation:

since opposite angle are equal angle 3 and the angle on the left side of 118 have to be equal. And since there are 180 degrees in a triangle,180-118=62, 62/2= 31 so angle 3 is 31

hope this helps

kiruha [24]3 years ago

7 0

ANSWER

$\angle3 = 31\degree$

EXPLANATION

The adjacent angles of a parallelogram are supplementary.

The angle adjacent to 118° is

$180 \degree - 118 = 62 \degree$

Since the diagonals bisect corner angles,

we divide the adjacent angle into two to obtain;

$\angle3 = \frac{62 \degree}{2} = 31\degree$

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a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

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So on this case the 99% confidence interval would be given by (13.83;28.17)

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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3 years ago