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Aleksandr [31]
3 years ago
14

Cindy has 6 identical pink candies and 8 identical green candies. Find the number of ways that Cindy can line up her candies in

a row, so that there are exactly four places where a pink candy is next to a green candy. One example is $PPGGGPPPGGGGGP.$
Mathematics
1 answer:
Daniel [21]3 years ago
4 0

Answer:

175 ways

Step-by-step explanation:

Form a partition into 2 or 3 parts and the number of ways.

Pink candies

[1,5](2) , [2,4](2) , [3,3](1) , [1,4](3), [1,2,3](6) , [2,2,2](1)

Green candies

[1,7](2) , [2,6](2) , [3,5](2) , [4,4](1) , [1,1,6](3) , [1,2,5](6) , [1,3,4](6) , ,[2,2,4](3) , [2,3,3](3)

Number of ways will be:

(2+2+1) (2+6+6+3+3) + (3+6+1)(2+2+2+1)

Number of ways =( 5×21) + (10×7) = 175ways

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The value of x is D. 5
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2 years ago
Use the ladder method to find the factored version of this expression. (3x-18)
Vera_Pavlovna [14]

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Step-by-step explanation:

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6 0
3 years ago
Consider these functions
Evgen [1.6K]
<h3>Answer:  D) 31</h3>

==========================================================

Explanation:

The expression g(f(2)) has f(2) as the inner function.

Let's compute f(2)

This means we plug x = 2 into the f(x) function

f(x) = 4x^3 - 10

f(x) = 4(x)^3 - 10

f(2) = 4(2)^3-10

f(2) = 4*8-10

f(2) = 32-10

f(2) = 22

Now we'll plug this into the g(x) function

This is because g(f(2)) = g(22). I've replaced f(2) with 22

So,

g(x) = (3x-4)/2

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g(22) = (66-4)/2

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7 0
3 years ago
Nine more than the quotient of a number and 5 is -22
rusak2 [61]

Answer:

number is -155

Step-by-step explanation:

let the number equal 'x'

quotient means divide

nine more means plus 9

quotient of a number and 5 means x divided by 5

9+ x/5 = -22

now to solve for x

x/5 = -31

x = -155

5 0
2 years ago
30. What is the solution to the system of equations? (1 point)
sesenic [268]

Answer:

Option B) (-1,7,5) is correct.

The solution to the given system of equation is (-1,7,5)

Step-by-step explanation:

Given system of equations are

-7x-2y+z=-2\hfill (1)

6x-y-z=-18\hfill (2)

5x+4y-z=18\hfill (3)

To find the solution of the given system of equations by using Elimination method:

Now adding equations (1) and (2)

-7x-2y+z=-2

6x-y-z=-18

_________________

-x-3y=-20

________________

-x-3y=-20

-(x+3y)=-20

x+3y=20\hfill (4)  (since "-" getting cancelled)

Now adding equations (1) and (3)

-7x-2y+z=-2

5x+4y-z=18

_________________

-2x+2y=16

________________

-2x+2y=16

2(-x+y)=16

-x+y=8\hfill (5)

Now adding equations (4) and (5)

x+3y=20

-x+y=8

_________________

4y=28

________________

y=\frac{28}{4}

Therefore y=7

Substituting y=7 in equation (4)

x+3y=20

x+3(7)=20

x+21=20

x=20-21

Therefore x=-1

Now substituting the values x=-1 and y=7 in equation (1) we get

-7x-2y+z=-2

-7(-1)-2(7)+z=-2

7-14+z=-2

z=-2+7

Therefore z=5

Therefore the solution to the given system of equation is (-1,7,5)

Therefore Option B) (-1,7,5) is correct.

8 0
3 years ago
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