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3 years ago

Each of the dimensions of a pyramid are doubled. What is true about the volume of the new pyramid?

Mathematics

1 answer:

VladimirAG [237]3 years ago

6 0

Answer:

The new pyramid has a volume that is 8 times the volume of the original pyramid

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor and the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ----> the scale factor

V_1 -----> volume of the original pyramid

V_2 -----> volume of the new pyramid

$z^{3}=\frac{V_2}{V_1}$

In this problem we have that each of the dimensions of the original pyramid are doubled

$z=2$

substitute

$2^{3}=\frac{V_2}{V_1}$

$8=\frac{V_2}{V_1}$

$V_2=8V_1$

therefore

The volume of the new pyramid is 8 times the volume of the original pyramid

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schepotkina [342]

Answer:

7.64% probability that they spend less than $160 on back-to-college electronics

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

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Probability that they spend less than $160 on back-to-college electronics

This is the pvalue of Z when X = 160. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{160 - 237}{54}$

$Z = -1.43$

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7.64% probability that they spend less than $160 on back-to-college electronics

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