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Kay [80]
3 years ago
13

In ΔLMN, the measure of ∠N=90°, the measure of ∠M=17°, and MN = 20 feet. Find the length of LM to the nearest tenth of a foot.

Mathematics
2 answers:
astra-53 [7]3 years ago
4 0

Answer:

Step-by-step explanation:

70

andrey2020 [161]3 years ago
3 0
20.9 ft
This is a right triangle trigonometry question because N is 90 degrees. MN is adjacent to M and LM is the hypotenuse. Adjacent any hypotenuse use the cosine function. 
cos \theta = \frac{adj}{hyp}
plug in known values
cos(17) = \frac{20}{x}
switch cos(20) and x using the products property
x = \frac{20}{cos(17)}
plug into calculator to get 20.9 ft

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According to a polling​ organization, 24% of adults in a large region consider themselves to be liberal. A survey asked 200 resp
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Now we can calculate the p value based on the alternative hypothesis with this probability:

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Step-by-step explanation:

Information given

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\hat p=\frac{75}{200}=0.375 estimated proportion of people liberal

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z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to verify if the true proportion of adults liberal is higher than 0.24:

Null hypothesis:p \leq 0.24  

Alternative hypothesis:p > 0.24  

The statistic is given by:

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

Replacing the info given we got:

z=\frac{0.375 -0.24}{\sqrt{\frac{0.24(1-0.24)}{200}}}=4.47  

Now we can calculate the p value based on the alternative hypothesis with this probability:

p_v =P(z>4.47)=0.00000391  

The p value is very low compared to the significance level of \alpha=0.05 then we can reject the null hypothesis and we can conclude that the true proportion of people liberal is higher than 0.24

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