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Sergio [31]
3 years ago
5

What is the value of x ?enter your answer as a decimal in the box

Mathematics
1 answer:
maksim [4K]3 years ago
4 0

Answer:

x=67.5\ ft

Step-by-step explanation:

we know that

Triangles MNP and MAB are similar by AAA theorem

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{MB}{MP}=\frac{MA}{MN}

substitute the values

\frac{x}{97.5}=\frac{71.5-22}{71.5}

\frac{x}{97.5}=\frac{49.5}{71.5}

x=97.5*\frac{49.5}{71.5}=67.5\ ft

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) The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupa
asambeis [7]

Answer:

We conclude that there is a difference in seat belt use.

Step-by-step explanation:

We are given that of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did.

<u><em>Let </em></u>p_1<u><em> = population proportion of drivers 16-24 years old who buckle up .</em></u>

<u><em /></u>p_2<u><em> = population proportion of drivers 25-69 years old who buckle up .</em></u>

So, Null Hypothesis, H_0 : p_1-p_2 = 0      {means that there is no significant difference in seat belt use}

Alternate Hypothesis, H_A : p_1-p_2\neq 0      {means that there is a difference in seat belt use}

The test statistics that would be used here <u>Two-sample z proportion statistics;</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 drivers 16-24 years old who buckle up = 79%

\hat p_2 = sample proportion of drivers 25-69 years old who buckle up = \frac{924}{1100} = 84%

n_1 = sample of 16-24 years old drivers = 1000

n_2 = sample of 25-69 years old drivers = 1100

So, <u><em>test statistics</em></u>  =  \frac{(0.79-0.84)-(0)}{\sqrt{\frac{0.79(1-0.79)}{1000}+\frac{0.84(1-0.84)}{1100} } }  

                              =  -2.946

The value of z test statistics is -2.946.

Since, in the question we are not given with the level of significance so we assume it to be 5%. <u><em>Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</em></u><em> </em>

<em>Since our test statistics 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 </em><em><u>we reject our null hypothesis</u></em><em>.</em>

Therefore, we conclude that there is a difference in seat belt use.

4 0
3 years ago
Evaluate the determinant for the following matrix: 1 4 4 5 2 2 1 5 5
Elina [12.6K]
A Laplace expansion along the first row gives

\begin{vmatrix}1&4&4\\5&2&1\\1&5&5\end{vmatrix}=1\begin{vmatrix}2&1\\5&5\end{vmatrix}-4\begin{vmatrix}5&1\\1&5\end{vmatrix}+4\begin{vmatrix}5&2\\1&5\end{vmatrix}
=1(10-5)-4(25-1)+4(25-2)
=1
7 0
3 years ago
The volume of a sphere is 972 PI ft3. What is the radius of the sphere? Use the formula V = 4/3 PI r3 to find your answer. Enter
Kryger [21]
972=4/3πr^3
729=πr^3
232.16~ r^3
r~ 6 feet, so the radius is about 6 feet. Hope it help!
7 0
3 years ago
Read 2 more answers
2(4-8x)+6=-1 interpreting experiessions
Anestetic [448]

Answer:

X = \frac{13}{16}

Step-by-step explanation:

2 (4-8x) + 6 = 1

Multiply parentheses by 2

8 - 16x + 6 = 1

add (8 + 6)

14 - 16x = 1

Move constant to right and change its sign

-16x = 1 -14

Calcualte te difference

-16x = -13

divide bot sides by -16

x = \frac{13}{16}

8 0
3 years ago
An item is regularly priced at $94. It is now priced at a discount of 30% off the regular price.
Vedmedyk [2.9K]
30% off an item would make that item valued at 70% of its original price

94 times 0.7 = 65.8

$65.80
4 0
3 years ago
Read 2 more answers
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