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FrozenT [24]
3 years ago
14

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the dri

nking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "yes" if they agree the drinking age should be lowered and "no" if not. Of the 100 people who phoned in, 70 answered "yes." The margin of error for a 90% confidence interval is:a) 0.045. b) 0.074. c) 0.089. d) 0.690.
Mathematics
1 answer:
vekshin13 years ago
8 0

Answer:

The margin of error for a 90% confidence interval is 0.075.

Step-by-step explanation:

We are given that he asks listeners to phone in and vote "yes" if they agree the drinking age should be lowered and "no" if not.

Of the 100 people who phoned in, 70 answered "yes."

Let \hat p = sample proportion of people who say yes

So,  \hat p=\frac{X}{n}  =  \frac{70}{100} = 0.70

where, X = Number of people who say yes = 70

            n = Number of people phoned in = 100

<u>Now, Margin of error formula for any confidence interval is given by;</u>

         Margin of error =  Z_(_\frac{\alpha}{2}_ ) \times \text{Standard of Error}

where, \alpha = level of significance = 10%

Standard of error =  \sqrt{\frac{\hat p(1-\hat p)}{n} }

Also, the critical value of x at 5% (\frac{\alpha}{2} =\frac{0.10}{2}) level of significance is 1.645.

SO,<em><u> Margin of Error</u></em> =  1.645 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }

                                =  1.645 \times \sqrt{\frac{0.70(1-0.70)}{100} }

                                =  0.075

Hence, the margin of error for a 90% confidence interval is 0.075.

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Xelga [282]

Answer:

The total amount due after five years is $57,000.

Step-by-step explanation:

Recall that simple interest is given by the formula:

\displaystyle A=P(1+rt)

Where <em>A</em> is the final amount, <em>P</em> is the principal amount, <em>r</em> is the rate, and <em>t</em> is the time (in years).

Since we are investing a principal amount of $38,000 at a rate of 10.0% for five years, <em>P</em> = 38000, <em>r</em> = 0.1, and <em>t</em> = 5. Substitute:

\displaystyle A=38000(1+(0.1)(5))

Evaluate. Hence:

\displaystyle A=\$ 57,000

The total amount due after five years is $57,000.

4 0
3 years ago
In ΔTUV, the measure of ∠V=90°, the measure of ∠U=70°, and UV = 9.6 feet. Find the length of TU to the nearest tenth of a foot.
Nutka1998 [239]

​

<u><em>28.1 feet</em></u>

<u><em></em></u>

<em><u>explaination</u></em>

<u><em>\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{9.6}{x}</em></u>

<u><em>cosU= </em></u>

<u><em>hypotenuse</em></u>

<u><em>adjacent</em></u>

<u><em>​ </em></u>

<u><em> = </em></u>

<u><em>x</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>\cos 70=\frac{9.6}{x}</em></u>

<u><em>cos70= </em></u>

<u><em>x</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>x\cos 70=9.6</em></u>

<u><em>xcos70=9.6</em></u>

<u><em>Cross multiply.</em></u>

<u><em>\frac{x\cos 70}{\cos 70}=\frac{9.6}{\cos 70}</em></u>

<u><em>cos70</em></u>

<u><em>xcos70</em></u>

<u><em>​ </em></u>

<u><em> = </em></u>

<u><em>cos70</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>Divide each side by cos 70.</em></u>

<u><em>x=\frac{9.6}{\cos 70}=28.0685\approx 28.1\text{ feet}</em></u>

<u><em>x= </em></u>

<u><em>cos70</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> =28.0685≈28.1 feet</em></u>

<u><em>Type into calculator and roundto the nearest tenth of a foot.</em></u>

8 0
2 years ago
Tanya's father travels every week for business. He has traveled around the
Nikitich [7]

The correct answer would be: 4.6 x 10^5

8 0
2 years ago
PLZ help <br><br> (5x10^2)+(4x10^3)
timurjin [86]
10 x 10 = 100
100 x 5 = 500
10 x 10 x 10 = 1,000
1,000 x 4 = 4,000
4,000 + 500 = 4,500
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3 years ago
Read 2 more answers
Don’t worry about number 7 just 5 and thank you
oksian1 [2.3K]
Subtract 15 from both sides

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3 years ago
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