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3 years ago

There are 10 students in a class: 6 boys and 4 girls.

Mathematics

2 answers:

Evgesh-ka [11]3 years ago

6 0

Answer:

1/6

Step-by-step explanation:

Think of drawing 1 student at a time without replacement.

First drawing:

p(boy) = 6/10

Second drawing:

p(boy) = 5/9

Third drawing:

p(boy) = 4/8

p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6

Answer: 1/6

horsena [70]3 years ago

4 0

Answer:

1/ 6

Step-by-step explanation:

Therefore, the required probability is 1/6.

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Step-by-step explanation:

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3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

Using the volume formula of a cylinder

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

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