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tester [92]
3 years ago
12

A right triangle has side lengths of 0.6 meter and 0.8 meter. What is the length of the hypotenuse? Round to the nearest tenth.

Mathematics
1 answer:
Sonja [21]3 years ago
4 0

Use the Pythagorean theorem since you are working with a right triangle:

a^2+b^2=c^2a2+b2=c2

The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:

0.8^2+0.6^2=c^20.82+0.62=c2

Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):

0.64+0.36=c^20.64+0.36=c2

Add:

1=c^21=c2

Isolate c. Find the square root of both sides:

\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c

Simplify \sqrt{1}1 . Any root of 1 is 1:

c=c= ±11 *

c=1,-1c=1,−1

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construct a 90% confidence interval of the population proportion using the giver information x=74 n=150
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The 90% confidence interval of the population proportion is (0.43, 0.56).

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The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

<em>X</em> = 74

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Compute the value of sample proportion as follows:

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Compute the critical value of <em>z</em> for 90% confidence level as follows:

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*Use a <em>z</em>-table.

Compute the 90% confidence interval of the population proportion as follows:

CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}

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Thus, the 90% confidence interval of the population proportion is (0.43, 0.56).

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Which equation represents a proportional relationship?
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