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Gennadij [26K]
3 years ago
15

What is the cube root of 12? I have to show my work using common core.

Mathematics
1 answer:
eimsori [14]3 years ago
6 0
Analyze perfect cubes:

1^3 = 1
2^3 = 8
3^3 = 27

Since 12 is between 8 and 27, cube root of 12 is between 2 and 3.
You also know it is much closer to 2, since 12 is much closer to 8.

A good guess would be 2.25

(2.25)^3 = 11.39

This is close but slightly less than 12.

When you use your calculator you should get 2.2894.
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There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f
Ann [662]

Answer:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

The estimated population proportion for this case is:

\hat p = \frac{350}{500}=0.7

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0
3 years ago
When there is a positive trend (or positive correlation), do the y-values of the points on the scatter plot tend to increase or
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As the y-axes decreases the x-axes increases 

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3 years ago
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The sum of 3 times a number and 7 is equal to 2. Turn into an equation
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3x+7=2 is the equation
4 0
2 years ago
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. In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects thr
brilliants [131]

Answer:

0.18% probability that they are all women

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the senators are chosen is not important, so the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Desired outcomes:

3 women, from a set of 13. So

D = C_{13,3} = \frac{13!}{3!(13 - 3)!} = 286

Total outcomes:

3 senators, from a set of 100. So

T = C_{100,3} = \frac{100!}{3!(100 - 3)!} = 161700

Probability;

p = \frac{D}{T} = \frac{286}{161700} = 0.0018

0.18% probability that they are all women

5 0
3 years ago
CAN SOMEONE HELP ME PLS?
Mumz [18]

Answer:

√13

Step-by-step explanation:

1/33 is a fraction, meaning it is rational

1.6... has a repiton, meaning it is rational

-5.43 is a integer meaning it is rational

7 0
2 years ago
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