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blagie [28]
2 years ago
14

What is the length of GH¯¯¯¯¯¯, to the nearest tenth of a meter? 7.3 m 13.7 m 14.1 m 19.4 m A scalene triangle G H J. The base s

ide is J H. Side G J is labeled as 10 meters. Angle J is labeled as 45 degrees. Angle H is labeled as 31 degrees.

Mathematics
2 answers:
nlexa [21]2 years ago
8 0
By applying the law of sines.

\frac{GH}{sin \ J} =  \frac{GJ}{sin \ H}

Given:
<span>GJ = 10 , ∠J =45° , ∠H = 31°

∴ </span><span>\frac{GH}{sin \ 45} =  \frac{10}{sin \ 31}

∴ GH = 10 * sin 45° / sin 31° ≈ 13.7 m
</span>
attashe74 [19]2 years ago
7 0

Answer:

13.7 m

Proof in Pic:

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We conclude that there is difference in the proportion of deaths between the 2 groups.

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We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let p_1 = <u><em>proportion of deaths when drivers were not wearing seat belts.</em></u>

p_2 = <u><em>proportion of deaths when drivers were wearing seat belts.</em></u>

So, Null Hypothesis, H_0 : p_1=p_2      {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, H_A : p_1\neq p_2     {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here <u>Two-sample z test for proportions;</u>

                          T.S. =  \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }  ~ N(0,1)

where, \hat p_1 = sample proportion of deaths when drivers were not wearing seat belts = \frac{31}{2823} = 0.011

\hat p_2 = sample proportion of deaths when drivers were wearing seat belts = \frac{16}{7765} = 0.002

n_1 = sample of drivers not wearing seat belts = 2823

n_2 = sample of drivers wearing seat belts = 7765

So, <u><em>the test statistics</em></u>  =  \frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }

                                       =  4.438

The value of z test statistics is 4.438.

<u>Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</u>

Since our test statistic doesn't lie within the range of critical values of z, 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 there is difference in the proportion of deaths between the 2 groups.

Also, <u>Margin of error</u> (E) =  1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }

                                        =  1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }

                                        =  <u>0.00397</u>

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