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3 years ago

How will the volume of the pyramid change if each side is multiplied by a factor of 1/2?

Mathematics

2 answers:

slamgirl [31]3 years ago

4 0

D,The volume will be 1/8 times the volume.

kakasveta [241]3 years ago

4 0

Answer:

D. The volume will be 1/8 times the volume.

Step-by-step explanation:

We have been asked to find the affect on the volume of a pyramid if each side is multiplied by factor of 1/2.

Let x and y be the sides of base of pyramid and z be the height of original pyramid.

$\text{Volume of pyramid}=\text{Base area*Height}$

$\text{Volume of pyramid}=x*y*z$

Now each side of our pyramid is multiplied by a factor of 1/2, so sides of new pyramid will be:

$x*\frac{1}{2}=\frac{x}{2}$ ,

$y*\frac{1}{2}=\frac{y}{2}$ ,

$z*\frac{1}{2}=\frac{z}{2}$

Let us substitute sides of new pyramid in volume formula to figure out volume of new pyramid.

$\text{Volume of new pyramid}=\frac{x}{2}*\frac{y}{2}*\frac{z}{2}$

$\text{Volume of new pyramid}=\frac{x*y*z}{2*2*2}$

$\text{Volume of new pyramid}=\frac{x*y*z}{8}$

$\text{Volume of new pyramid}=\frac{1}{8}*(x*y*z)$

We can see that volume of new pyramid is 1/8 times the volume of original pyramid, therefore, option D is the correct choice.

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Yanka [14]

Answer:

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Step-by-step explanation:

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3 years ago

When grading an exam, 90% of a professor's 50 students passed. If the professor randomly selected 10 exams, what is the probabil

Damm [24]

Using the binomial distribution, it is found that there is a:

a) 0.9298 = 92.98% probability that at least 8 of them passed.

b) 0.0001 = 0.01% probability that fewer than 5 passed.

For each student, there are only two possible outcomes, either they passed, or they did not pass. The probability of a student passing is independent of any other student, hence, the binomial distribution is used to solve this question.

<h3>What is the binomial probability distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

90% of the students passed, hence $p = 0.9$ .

The professor randomly selected 10 exams, hence $n = 10$ .

Item a:

The probability is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.9)^{8}.(0.1)^{2} = 0.1937$

$P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874$

$P(X = 10) = C_{10,10}.(0.9)^{10}.(0.1)^{0} = 0.3487$

Then:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1937 + 0.3874 + 0.3487 = 0.9298$

0.9298 = 92.98% probability that at least 8 of them passed.

Item b:

The probability is:

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Using the binomial formula, as in item a, to find each probability, then adding them, it is found that:

$P(X < 5) = 0.0001$

Hence:

0.0001 = 0.01% probability that fewer than 5 passed.

You can learn more about the the binomial distribution at brainly.com/question/24863377

3 0

2 years ago

Which shows the terms of the series? 4 12 48 192 4 12 36 3 12 48 192 3 12 48

Stells [14]

The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

<h3>What is summation?</h3>

In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.

Now we have a given term

$\sum_{n=1}^{4} 3(4)^{n-1}$

By solving the above term;

$\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}$

$\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3$

$\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192$

Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

To know more about Summation follow

brainly.com/question/2767605

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2 years ago

Select the correct answer.<br> Over which interval of the domain is function h decreasing?<br> 25?

zmey [24]

Answer:

the function is only increasing.

Step-by-step explanation:

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2 years ago

Is 660 10 times as much as 600

mr Goodwill [35]

No,
660 is 1.1 times as much;

to find how many times 660 goes into 600, you must divide 660 by 600

660÷600 = 1.1

∴660 is 1.1 times as much as 600

6 0

3 years ago