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1 year ago

Find the length of each arc. Round your answers to the nearest tenth. r = 40 =24use 3.14 for π

Mathematics

1 answer:

liraira [26]1 year ago

6 0

Answer:

1.7 units

Explanation:

The length of an arc is calculated using the formula below:

$l=\frac{\theta}{360\degree}\times2\pi r$

Substitute the given values of θ and r:

$\begin{gathered} l=\frac{24\degree}{360\degree}\times2\times3.14\times4 \\ =1.674 \\ \approx1.7\text{ units (to the nearest tenth)} \end{gathered}$

The length of the arc is 1.7 units.

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mixas84 [53]

Answer:

A sample of at least 545 adults is needed.

Step-by-step explanation:

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.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = 0.15$

The margin of error is:

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

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

If he wishes to be 95% confident that his estimate contains the population proportion, how large a sample will be necessary?

We need a sample of at least n.

n is found when M = 0.03. So

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

$0.03 = 1.96\sqrt{\frac{0.15*0.85}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.15*0.85}$

$\sqrt{n} = \frac{1.96\sqrt{0.15*0.85}}{0.03}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.15*0.85}}{0.03})^{2}$

$n = 544.23$

Rounding up

A sample of at least 545 adults is needed.

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