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ss7ja [257]
3 years ago
11

Triangle abc is a right traingle if side ac=7 and side bc= 10 what is the measure of ab?

Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0
<span>Use the Pythagorean theorem for the right triangle ABC, where

AB is the hypotenuse of the triangle;

AC and BC are the other two sides.


So,

(AC)^{2}+(BC)^{2}=(AB)^{2}\\\\ 7^{2}+10^{2}=(AB)^{2}\\\\ (AB)^{2}=49+100\\\\ (AB)^{2}=149\\\\ AB=\sqrt{149}

</span>
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We conclude that the mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.

In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

Let \mu = <u><em>mean commute time in the U.S..</em></u>

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Alternate Hypothesis, H_A : \mu < 30 minutes     {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;

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            n = sample of people from the 2000 U.S. Census = 500

So, <u><em>the test statistics</em></u>  =  \frac{27.6 -30}{\frac{19.6}{\sqrt{500} } }  ~ t_4_9_9

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The value of t test statistic is -2.738.

Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.</u>

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis.</u>

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

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