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2 years ago

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Find one solution for the equation. Assume that all angles involved are acute angles. tangent (3 Upper B minus 32 degrees )equal

s cotangent (5 Upper B plus 10 degrees )

1 answer:

raketka [301]2 years ago

5 0

Answer:

Step-by-step explanation:

Equation given

tan(3B-32 ) = cot ( 5B +10 ) = tan [ 90 - ( 5B + 10 ) ]

tan(3B-32 ) = tan (90 - 5B - 10 )

(3B-32 ) = (90 - 5B - 10 )

8B = 32 + 80

B = 14° .

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia

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Answer:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

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So the answer for this case would be n=791 rounded up to the nearest integer

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n 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 0.99 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 $z_{\alpha/2}=2.58$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =+5 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (3)

$n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791$

So the answer for this case would be n=791 rounded up to the nearest integer

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