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svet-max [94.6K]

3 years ago

6

three cones have a volume of 192π cm³.Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm. fin

d the height of each one

1 answer:

andrew11 [14]3 years ago

8 0

9514 1404 393

Answer:

A: 144 cm

B: 64 cm

C: 36 cm

Step-by-step explanation:

The volume of a cone is given by ...

V = (1/3)πr²h

Solving for h, we get ...

3V/(πr²) = h

Filling in the given values, we get ...

3(192π)/(πr²) = h

576/r² = h

Then the heights of the different cones are ...

A: r = 2, h = 576/4 = 144 . . . cm

B: r = 3, h = 576/9 = 64 . . . cm

C: r = 4, h = 576/16 = 36 . . . cm

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Answer:

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Step-by-step explanation:

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3 years ago

Divide £250 in the ratio 3:6:1

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Answer:

Step-by-step explanation:

The numbers in the ratio add up to 10. So divide 250 by 10. One part is £25. Multiply by the given numbers: 3x25=75. 6x25=150. 1x25=25. So you have £75:£150:£25.

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3 years ago

4. A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean

Ede4ka [16]

Adding 2 to each value of the random variable $X$ makes a new random variable $X+2$ . Its mean would be

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since expectation is linear, and the expected value of a constant is that constant. $E[X]$ is the mean of $X$ , so the new mean would be

$E[X+2]=10+2=12$

The variance of a random variable $X$ is

$V[X]=E[X^2]-E[X]^2$

so the variance of $X+2$ would be

$V[X+2]=E[(X+2)^2]-E[X+2]^2$

We already know $E[X+2]=12$ , so simplifying above, we get

$V[X+2]=E[X^2+4X+4]-12^2$

$V[X+2]=E[X^2]+4E[X]+4-12^2$

$V[X+2]=(V[X]+E[X]^2)+4E[X]-140$

Standard deviation is the square root of variance, so $V[X]=3^2=9$ .

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so the standard deviation remains unchanged at 3.

NB: More generally, the variance of $aX+b$ for $a,b\in\mathbb R$ is

$V[aX+b]=a^2V[X]+b^2V[1]$

but the variance of a constant is 0. In this case, $a=1$ , so we're left with $V[X+2]=V[X]$ , as expected.

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3 years ago

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allochka39001 [22]

Answer:

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Step-by-step explanation:

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3 years ago

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Svetlanka [38]

Answer:

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Step-by-step explanation:

The distance formula that gives the distance between two points is given as:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plugging in our given points, we get:

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3 years ago