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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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Nonamiya [84]

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3 years ago

Each of the following situations describes a normally distributed population for which a statistical procedure should be used. M

densk [106]

Answer:

(a) Correct option (1).

(b) Correct option (3).

Step-by-step explanation:

A one-sample z-test for mean is used to determine whether the claimed value of mean is significant or not. To perform this test we can also use the t-distribution.

The t-test is used if the following conditions are given:

The population is normally distributed
The population standard deviation is not known
The sample selected is large enough.

Similarly the (1 - α)% confidence interval for population mean can be computed either using the z-interval or the t-interval.

The same conditions should be applied to use the t-interval.

(a)

In the first case, Gale wants to determine the likely range of weight of whole coffee beans from her trusty two-tablespoon scoop to create a reliable method of brewing the perfect cup of coffee.

She selects a sample of n = 15 scoops and perform the test.

Since the population standard deviation is not known and Gale wants to know the range of weight of whole coffee beans , she should use a one sample t-confidence interval for a mean.

The correct option is (1).

(b)

In the second case, Tanya wants to determine whether the mean IQ score is at least 112 or not.

She selects a a random sample n = 20 composers and compute the statistic to perform the one-sample test.

Since the population standard deviation is not known, Tanya should use one sample t-test for a mean.

The correct option is (3).

(c)

In the second case, Jason wants to estimate what the balance of his retirement account will be in one month.

He selects the data from 1950 to 2015 and calculates this index has had an average monthly return of 0.69% with a standard deviation of 4.15%.

Now, the sample selected is quite large. The Central limit theorem can be used to approximate the sampling distribution of sample mean.

Then, $\bar X\sim N(\mu_{\bar x}, \sigma_{\bar x})$

So, Jason can use the one sample z-test for a mean to determine the balance of his retirement account will be in one month.

The correct option is (2).

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4 years ago

HELP QUICK THIS IS MY LAST TRY I WILL GIVE YOU BRAINLIEST AND 5 STARS AND A THANKS JUST HELP PLEASE!!!!

Vladimir79 [104]

Answer:

Step-by-step explanation:

rectangular prism has a lateral face

cylinder has two bases

rectangular pyramid has a lateral face

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3 years ago

1/2 (2n + 6) simply the answer and show work

Evgesh-ka [11]

Answer:

The answer is n + 3.

Step-by-step explanation:

1) Simplify.

$\frac{2n + 6}{2}$

2) Factor out the common term 2.

$\frac{2( n+ 3)}{2}$

3) Cancle 2.

$n + 3$

Therefor, the answer is n + 3.

7 0

3 years ago

Paul is going to have the exterior of his home painted. Painting USA charges $75.00 to come out and evaluate the house plus $25.

Sladkaya [172]

Answer:

The most cost effective company will be Painting USA that charge $700 to paint Paul house .

As given

Paul is going to have the exterior of his home painted.

Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor.

If it takes 25 hours to paint Paul’s house.

Total amount charge by Painting USA = Painting USA charges for come out and evaluate the house + Cost of per hour of labor × Total hours take to paint Paul house .

Total amount charge by Painting USA = 75 + 25 × 25

= 75 + 625

= $ 700

As given

Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.

Total amount charge by Upscale Home Painting = Cost of per hour of labor × Total hours take to paint Paul house

= 40 × 25

= $ 1000

Therefore the most cost effective company will be Painting USA that charge $700 to paint Paul house .

Step-by-step explanation:

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3 years ago