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3 years ago

The radius AND height of a cylinder are each doubled. What is the new volume?

Mathematics

1 answer:

Naya [18.7K]3 years ago

7 0

The volume of a cylinder is given by

$V = \pi hr^2$

Let $h\mapsto 2h$ and $r\mapsto 2r$

The new volume becomes

$V = \pi(2h)(2r)^2 = \pi\cdot 2h \cdot 4r^2 = 8\pi hr^2$

So, the new volume is 8 times the original volume. In fact, volume scales linearly with the height and quadratically with the radius.

You might be interested in

For a given IQ test, an individual is considered a genius if their score falls more than three standard deviations from the mean

ki77a [65]

Answer:

$P(Z>3) = 1-P(Z$

So then the probability that an individual present and IQ higher than 3 deviation from the mean is 0.00135

And if we find the number of individuals that can be considered as genius we got: 0.00135*1500=2.025

And we can say that the answer is a.2

Step-by-step explanation:

1) Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu=?,\sigma=?)$

We are interested on this probability

$P(X>X+3\mu)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

And we can find the following probablity:

$P(Z>3) = 1-P(Z$

So then the probability that an individual present and IQ higher than 3 deviation from the mean is 0.00135

And if we find the number of individuals that can be considered as genius we got: 0.00135*1500=2.025

And we can say that the answer is a/2.0

3 0

3 years ago

This is a polygon and I need help finding the missing angle ?

allsm [11]

First, you need to know that the total (degrees) of the interior angles is 360 because this is a quadrilateral.

The unnumbered angle is 109 degrees. We know this because the angle labeled 71 degrees and the unnumbered angle are supplementary. So you subtract 180 from 71 to get 109.
$180-71=109$

To solve for x, we need to realize the other numbers playing into the angles' values. To make solving this easier, I'm gonna assign letters to the angles.

(10x+6) is angle A.

(13x-2) is angle B.

(8x-1) is angle C.

and 109 (the one we solved) is angle D.

We know that the total of the interior angles is 360, so we can add the 2 from angle B and the 1 from angle C to 360. This is because these numbers are subtracted from the other values.
$360+2+1=363$

Now, we have to subtract the 6 from angle A from 363, because the 6 is added to the other values.
$363-6=357$

Now we have to subtract 109 from 357 because you want to get the x's by themselves. Since you're solving for x.
$357-109=248$

That leaves you with 248. Now you add all the x's up to get the total number of x's. You have 10x from angle A, 13x from angle B, and 8x from angle C.
$10x+13x+8x=31x$

You get 31x. To get what x is, you divide 248 by 31.
$\frac{248}{31} =8$

That equals 8. So now that you know that x equals 8, if you need to find the values of the angles, you just plug in the numbers into the formulas.

$(10(8))+6= 86$
$(13(8))-2=102$
$(8(8))-1=63$
$109$

Check your work by plugging your answers in and seeing if they add up to 360.
$86+102+63+109=360$

Which they should:)

So...
angle A= 86
angle B=102
angle C=63
angle D=109

and x=8

Hope this helped!!!

4 0

3 years ago

Pls help me it would be nice !!!

notsponge [240]

Answer:

y=−3x−10

That is the equation in slope intercept form.

5 0

3 years ago

This is a scale drawing of a field. The scale is 1 in.: 10 ft. What is the actual length of the

creativ13 [48]

Answer:7ft

Step-by-step explanation:

i got it right

4 0

3 years ago

Read 2 more answers

Find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one

ziro4ka [17]

The probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9% will be <u>0.000343311 %</u>

<h3>What is the probability?</h3>

Probability is synonymous with possibility. It is concerned with the occurrence of a random event.

Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.

No of failure,n = 7

No of trials,x≥6

A binomial probability is represented as;

$\rm P(x) = nC_x p^z(1-p)^{n-r}$

Substitute the given data;

$P(x \geq 6) = 7C_6 \times 9^6 \times 91-9)^{7-6} +7C_7 (9)^7+(1-9)^{(7-7)}$

$\rm P(x \geq 6) = 0.000000343311 \\\\ P(x \geq6)=0.000343311 \%$

Hence,the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9% will be <u>0.000343311 %</u>

To learn more about probability, refer to the link: brainly.com/question/795909.

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4 0

2 years ago