2. Solve the equation and check.

20 different comic books will be distributed to five kids. (a) How many ways are there to distribute the comic books if there ar

sveta [45]

Answer:

a) 21684

b) 15504

Step-by-step explanation:

a) Distribute the comic books as follows

only to 1 kid one way but we have five kids then 5

to two kids C₂₀,₂ = 20! /2! ( 20-2)! = 20*19 /2 = 190

To three C₂₀,₃ = 20! /3! ( 20 - 3)! = 20*19*18 /6 = 1140

To four C₂₀,₄ = 20 ! / 4! ( 20 - 4 )! = 20*19*18*17 /4*3*2 = 4845

To five C₂₀,₅ = 20! /5! (20 - 5 )! = 20*19*18*17*16/5*4*3*2*1

C₂₀,₅ = 15504

Then total ways of distribution are:

5 + 190 + 1140 + 4845 + 15504 = 21684

b) C₂₀,₅ we know from a that is equal to 15504

7 0

2 years ago

Find the volume. cylinder—r = 2 cm; h = 3 cm

Naddik [55]

Volume of a cylinder = πr^2 h = π x (2)^2 x 3 = π x 4 x 3 = 12π = 37.7 cm^3

5 0

2 years ago

FEE

frozen [14]

Answer:

The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

$3x - 4y = -4$

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the slope

b is the y-intercept

Given the line

3x - 4y = 7

writing in the slope-intercept form

4y = 3x - 7

dividing both sides by 4

4y/4 = 3/4x - 7/4

y = 3/4x - 7/4

Now, comparing with the slope-intercept form of the line equation

y = 3/4x - 7/4

The slope of the line m = 3/4

We know that parallel lines have the same slopes.

Therefore, the slope of the parallel line is: 3/4

now we have,

The point (-4, -2)

The slope m of parallel line = 3/4

Given the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting (-4, -2) and m = 3/4 in the point-slope form of line equation

$\:y-\left(-2\right)=\frac{3}{4}\left(x-\left(-4\right)\right)$

$y+2=\frac{3}{4}\left(x+4\right)$

Thus, the equation in the point-slope form of the line equation is:

$y+2=\frac{3}{4}\left(x+4\right)$

Simplifying the equation

$y+2=\frac{3}{4}\left(x+4\right)$

Subtract 3 from both sides

$y+2-2=\frac{3}{4}\left(x+4\right)-2$

$y=\frac{3}{4}x+1$

Multiplying the equation by 4

$4y = 3x + 4$

$3x - 4y = -4$

Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

$3x - 4y = -4$

7 0

2 years ago

F(x) = 2x^2 – 5x – 3<br> g(x) = 2x^2 + 5x + 2<br> Find: (f/g) (x)

GrogVix [38]

Answer:

Since this means f of g so I will get the function g(x) and replace it with X in the function of f (x)

5 0

2 years ago

What is 32 / 10 equal

kupik [55]

Answer:

3.2. The decimal point moves left once because there's only one 0

Step-by-step explanation:

8 0

2 years ago

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