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ELEN [110]
3 years ago
10

Six pyramids are shown inside of a cube. The height of the cube is h units. Six identical square pyramids can fill the same volu

me as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid? The height of each pyramid is One-halfh units. The height of each pyramid is One-thirdh units. The height of each pyramid is One-sixthh units. The height of each pyramid is h units.
Mathematics
2 answers:
MAXImum [283]3 years ago
5 0

Answer:

(A)The height of each pyramid is One-half h units.

Step-by-step explanation:

Height of the Cube = h units

Volume of the Cube =h^3 $ cubic units

If Base of the cube =Base of the square pyramid

Base of the square pyramid = h units

\text{Volume of a Pyramid}=\dfrac{1}{3}*Base Area*Height

\text{Volume of One Pyramid}=\dfrac{1}{3}*h^2*Height

\text{Volume of Six Pyramids}=6*\dfrac{1}{3}*h^2*Height\\=(2h^2*Height)\:cubic\:units

Since Volume of the Cube = Volume of Six Square Pyramids

Then:

2h^2*Height=h^3\\Height=\dfrac{h^3}{2h^2} \\$Height of each pyramid =\dfrac{1}{2}h \:Units

aalyn [17]3 years ago
3 0

Answer:

A= the Height is 1/2

Step-by-step explanation:

Just took the test on edge 2020

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Answer:

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So the answer for this case would be n=791 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.

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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 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

The margin of error is given by this formula:

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

And on this case we have that ME =+5 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (3)

n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791

So the answer for this case would be n=791 rounded up to the nearest integer

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