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3 years ago

Triangle ABC is shown the measure of the interior angle at point A is 40 and the exterior angle point C is 102

Mathematics

1 answer:

mixas84 [53]3 years ago

4 0

Answer:

∠C (Interior) =78°

∠B (Interior) = 62°

Step-by-step explanation:

Given:

∠A (Interior) = 40°

∠C (exterior) = 102°

Computation:

∠C (Interior) = 180° - 102°

∠C (Interior) =78°

∠B (Interior) = 180° - ∠A (Interior) - ∠C (Interior)

∠B (Interior) = 180° - 78° - 40°

∠B (Interior) = 180° - 118°

∠B (Interior) = 62°

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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4 years ago

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Answer:

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Step-by-step explanation:

Simplify the following:

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Hint: | Add like terms in 11 x^2 + 11 x^2.

11 x^2 + 11 x^2 = 22 x^2:

Answer: 22 x^2

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Answer:

Step-by-step explanation:

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vladimir2022 [97]

Answer:

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Answer:

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