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2 years ago

Question 2 (Essay Worth 10 points)

Mathematics

1 answer:

icang [17]2 years ago

7 0

Answer:

Part A: 1 solution

Part B:

3(2x-7)=3

6x-21=3

+21 +21

6x=24

/6 /6

x=4

Step-by-step explanation:

First you distribute 3(2x-7)=3 to 6x-21=3. Next you do inverse operations by adding 21 to both sides of the equation to get 6x=24. Finally you divide both sides by 6 to get x=4

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One environmental group did a study of recycling habits in a California community. It found that 75% of the aluminum cans sold i

AysviL [449]

Answer:

$P( \^ p > 0.775 ) = 0.12798$

$P( 0.6718 < p < 0.775 ) =0.87183$

Step-by-step explanation:

From the question we are told that

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The sample size is $n = 387$

Generally the standard deviation of this sampling distribution is

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=> $\sigma = \sqrt{ \frac{0.75(1 - 0.75)}{ 387 } }$

=> $\sigma = 0.022$

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Generally the probability that 300 or more will be recycled is mathematically represented as

$P( \^ p > 0.775 ) = P( \frac{\^ p - p }{ \sigma } > \frac{0.775 - 0.75 }{ 0.022} )$

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$P( \^ p > 0.775 ) = P( Z > 1.136 )$

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$P( Z > 1.136) = 0.12798$

=> $P( \^ p > 0.775 ) = 0.12798$

Considering question b

Generally the lower limit of sample proportion of cans that are recycled is

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=> $\^ p_1 = 0.6718$

Generally the upper limit of sample proportion of cans that are recycled is

$\^ p_2 = \frac{ 300}{387 }$

=> $\^ p_2 = 0.775$

Generally probability that between 260 and 300 will be recycled is mathematically represented as

$P( 0.6718 < p < 0.775 ) = P( \frac{0.6718 - 0.75 }{ 0.022}< \frac{\^ p - p }{ \sigma }$

=> $P( 0.6718 < p < 0.775 ) = P( -3.55 < Z < 1.136 )$

=> $P( 0.6718 < p < 0.775 ) = P(Z < 1.136 ) - P( Z < -3.55 )$

From the z table the area under the normal curve to the left corresponding to 1.136 and -3.55 is

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and

$P(Z < 1.136 ) = 0.87202$

$P( 0.6718 < p < 0.775 ) = 0.87202- 0.00019262$

=> $P( 0.6718 < p < 0.775 ) =0.87183$

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