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3 years ago

Need help please please

Mathematics

2 answers:

Leona [35]3 years ago

5 0

Answer:

$176.7 in^{2}$

Step-by-step explanation:

The area of a circle is defined as:

$A = \pi r^{2}$

Where r is the radius and A is the area. We're given the diameter, 15 inches. The radius is half of the diameter, so the radius is therefore 7.5 inches. Now let's take this value back into the formula above:

$A = \pi r^{2} =\pi (7.5)^{2} = 56.25\pi = 176.7 in^{2}$

So the circle has an area of $176.7 in^{2}$

Hope this helps!

alina1380 [7]3 years ago

3 0

Answer:

D or 176.71 inches squared.

Step-by-step explanation:

the radius is 7.5. put it in a calculator and you get D.

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In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$