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3 years ago

Nine more than 3 times a number is the same as 6 less than twice the number

Mathematics

1 answer:

Ludmilka [50]3 years ago

7 0

Answer:

Step-by-step explanation:

Let the number = x

3x + 9 = 2x - 6 Looks like you are going to get something negative here.

Subtract 2x from both sides.

3x - 2x + 9 = 2x - 2x - 6

x + 9 = -6

Subtract 9 from both sides.

x + 9 - 9 = - 6 - 9

Combine

x = - 15

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One number is 4 more than another. The difference between their squares is 56. What are the numbers?

kompoz [17]

The answer is 7 and 11 :)

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3 years ago

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Rudiy27

Answer: 15) 1 16) 30

Step-by-step explanation:

15 ) Since 15 you are shown that the larger has 30 & 5 so, if it has shrunk until now that 30 has turned into 6 that means it has shrunk by 5 times the original bigger triangle has (30 divided by 6 = 5). 5 can go into 5 1 time so you get 1

16) We have an isosceles triangle so all the sides will be equal. So If one side is 30 then the rest will be 30. This is also shown with the smaller triangle, with both sides equaling 6.

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3 years ago

Choose 3 values that would make this inequality true. 8n + 4 ≤ 28

Lilit [14]

Answer:

-1, 0, 2

Step-by-step explanation:

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4 0

3 years ago

According to the U.S. Bureau of Labor Statistics, 20% of all people 16 years of age or older do volunteer work. In this age grou

Murljashka [212]

Answer:

1. P(X≥35) = 0.0183

2. P(X≤21) = 0.0183

3. P(0.18<p<0.25) = 0.7915

Step-by-step explanation:

We have the proportion for women: pw=0.22, and the proportion for men: pm=0.19.

1. We have a sample of 140 woman and we have to calculate the probability of getting 35 or more who do volunteer work.

This is equivalent to a proportion of

$p=X/n=35/140=0.25$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.22*0.78}{300}}\\\\\\ \sigma_p=\sqrt{0.0006}=0.0239$

We calculate the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.25-0.22}{0.0239}=\dfrac{0.03}{0.0239}=0.8198$

Then, the probability of having 35 women or more who do volunteer work in this sample of 140 women is:

$P(X>35)=P(p>0.25)=P(z>2.0906)=0.0183$

2. We have to calculate the probability of having 21 or fewer women in the group who do volunteer work.

The proportion is now:

$p=X/n=21/140=0.15$

We can calculate then the z-score as:

$z=\dfrac{p-p_w}{\sigma_p}=\dfrac{0.15-0.2}{0.0239}=\dfrac{-0.05}{0.0239}=-2.0906$

Then, the probability of having 21 women or less who do volunteer work in this sample of 140 women is:

$P(X$

3. For the sample with men and women, we use the proportion for both, which is π=0.2.

The sample size is n=300.

Then, the standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.2*0.8}{300}}\\\\\\ \sigma_p=\sqrt{0.0005}=0.0231$

We can calculate the z-scores for p1=0.18 and p2=0.25:

$z_1=\dfrac{p_1-\pi}{\sigma_p}=\dfrac{0.18-0.2}{0.0231}=\dfrac{-0.02}{0.0231}=-0.8660\\\\\\z_2=\dfrac{p_2-\pi}{\sigma_p}=\dfrac{0.25-0.2}{0.0231}=\dfrac{0.05}{0.0231}=2.1651$