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romanna [79]
3 years ago
14

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch radius A = sq. in.

Mathematics
1 answer:
katovenus [111]3 years ago
8 0
\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad 
\begin{cases}
s=length~of\\
\qquad a~side\\
-------\\
s=6
\end{cases}\implies A=\cfrac{6^2\sqrt{3}}{4}\implies A=\cfrac{36\sqrt{3}}{4}
\\\\\\
A=9\sqrt{3}
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<u>Testing the hypothesis</u>, it is found that since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.

At the null hypothesis, it is tested if the <u>proportion is of 0.5</u>, that is:

H_0: p = 0.5

At the alternative hypothesis, it is tested if the <u>proportion is different of 0.5</u>, that is:

H_1: p \neq 0.5

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}

In which:

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  • p is the value tested at the null hypothesis.
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In this problem, the parameters are given by:

p = 0.5, n = 483 + 398 = 881, \overline{p} = \frac{483}{881} = 0.5482

The value of the test statistic is:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}

z = \frac{0.5482 - 0.5}{\sqrt{\frac{0.5(0.5)}{881}}}

z = 2.86

Since we have a <u>two-tailed test</u>(test if the proportion is different of a value), the p-value of the test is P(|z| > 2.86), which is 2 multiplied by the p-value of z = -2.86.

Looking at the z-table, z = -2.86 has a p-value of 0.0021.

2(0.0021) = 0.0042

Since the <u>p-value of the test is 0.0042 < 0.01</u>, it can be concluded that the proportion of subjects who respond in favor is different of 0.5.

A similar problem is given at brainly.com/question/24330815

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