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3 years ago

Find the smallest non-zero whole number n such that 756n is a perfect cube.

Mathematics

1 answer:

Kitty [74]3 years ago

5 0

Step-by-step explanation:

756 = 2² * 3³ * 7.

For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.

How to get from 2² to 2³: Multiply by 2.

3³ has already a power that is a multiple of 3.

How to get from 7 to 7³: Multiply by 7².

Hence n = 2 * 7² = 98.

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A researcher, interested in estimating a population mean wants to be 95% certain that the length of the confidence interval does

djyliett [7]

Answer:

$n=(\frac{1.96(20)}{5})^2 =61.47 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

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".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =L/2 =5/2 =2.5, since the margin of error is the half of the length for the confidence interval, we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ from part a, replacing into formula (2) we got:

$n=(\frac{1.96(20)}{5})^2 =61.47 \approx 62$

So the answer for this case would be n=62 rounded up to the nearest integer

3 0

3 years ago

4(a^2+5a-6)-3(2a^3+4a-5)

Kazeer [188]

Answer: -6a exp3 + 4a exp2 + 8a - 9

Step-by-step explanation:

5 0

3 years ago

NEED HELP PLEASE I need number 3 and 4 please if anybody can help

zepelin [54]

Answer:

top bar on 3. 120 dollars for strawberry milk per month

bottom bar on 3. 100 dollars chocolate milk per month

#4. bars help an individual know information visually and may help an individual understand better.

6 0

2 years ago

A camera store offers a discount of 5% off the cost of photo paper. The discount is applied before tax. A customer buys photo pa

cestrela7 [59]

Answer:

$12.86

Step-by-step explanation:

multiply 13.50 by 0.05 and subtract the answer from 13.50

7 0

3 years ago

On a number line, point D is at -3, and point E is at 6. The point F lies on DE. The ratio of DF to FE is 2:3. Where does point

expeople1 [14]

Answer: point F is at <u> 0.6 </u> on the number line

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Explanation:

The ratio 2:3 scales up to 2x:3x for some positive real number x.

This means the distance from D to F is 2x units, and the distance from F to E is 3x units. Combine those two smaller distances to get 2x+3x = 5x to represent the full distance from D to E.

D is at -3 and E is at 6. This is a distance of 9 units since |-3-6| = |-9| = 9

Set this equal to the 5x from earlier and solve

5x = 9

x = 9/5

x = 1.8

This leads to 2x = 2*1.8 = 3.6

Therefore, we'll move 3.6 units from -3 to -3+3.6 = 0.6 which is the location of point F on the number line.

Notice that from 0.6 to 6 is 5.4 units and that 3x = 3*1.8 = 5.4 matches up to help confirm the answer.

5 0

3 years ago