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4 years ago

ACION

Mathematics

1 answer:

max2010maxim [7]4 years ago

7 0

Answer:Yes

Step-by-step explanation:

Given

Suppose side length of cube is a

If we dilate the cube using a scale factor of 2

Side length becomes 2a

and the surface area becomes $=6(\text{side length})^2$

Surface area $=6(2a)^2$

Surface area $=4\times 6(a)^2$

Thus surface area multiplied by a factor of 4

Now for volume

$V=(\text{side length })^3$

$V=(2a)^3$

$V=8(a^3)$

Therefore volume is multiplied by a factor of 8

Therefore the above statements make sense

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Nimfa-mama [501]

Step-by-step explanation:

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3 years ago

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What is the area of a square with a 80 ft. Perimeter

slega [8]

Answer:

400 sq. ft.

Step-by-step explanation:

We gotta find the length of a side:

First, we divide 80 by 4, because the perimeter of a square is (4 x side):

80 ft. / 4 = 20 ft.

Second, we doing the normal area of a square equation:

$20^{2}$ = 400 square ft.

Which leads to out answer of 400 sq. ft.

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3 years ago

Translate the<br> following phase<br> into an inequality<br> -3 times r is at least 57

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Answer:

Step-by-step explanation:

at least means it can be 57 or higher

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3 years ago

Simplify 3 times x plus 3 times 4

IgorLugansk [536]

Hey,

~ 3x + 3x4

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3 years ago

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You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confide

Gelneren [198K]

Answer:

The 90% confidence interval would be given by (110.168;117.832)

The 95% confidence interval would be given by (119.393;118.607)

Step-by-step explanation:

Assuming this info:" A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% and 95 confidence interval for the population mean".

1) 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".

$\bar X=114$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=15.30 represent the sample standard deviation

n=45 represent the sample size

2) 90% confidence interval

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

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

The degrees of freedom are given by:

$df=n-1=45-1=44$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,44)".And we see that $t_{\alpha/2}=1.68$

Now we have everything in order to replace into formula (1):

$114-1.68\frac{15.30}{\sqrt{45}}=110.168$

$114+1.68\frac{15.30}{\sqrt{45}}=117.832$

So on this case the 90% confidence interval would be given by (110.168;117.832)

3) 95% confidence interval

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: "=-T.INV(0.025,44)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$114-2.02\frac{15.30}{\sqrt{45}}=119.393$

$114+2.02\frac{15.30}{\sqrt{45}}=118.607$

So on this case the 95% confidence interval would be given by (119.393;118.607)

6 0

3 years ago