In how many ways can the letters of the word CHROMATIC be arrangeda. without any restrictions
b. if the position of the vowels can’t change
c. find the probability that the string of letters begins with the letter M

Answers

Answer 1

Answer: a. without any restrictions
since there 9 letters in the word CHROMATIC, then the number of ways it can be arrange is
P = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x1
P = 362880 ways can the word CHROMATIC be arranged with no restirction

B. if the position of the vowels can’t change
since there are 6 consonant letters in the word CHROMATIC, then the number of ways it can be arrange without changing the vowel is:
P = 6 x 5 x 4 x 3 x2 x 1
P = 720 ways

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What is 2y+x=-6 and y=-2x+0 using substitution method?

Answers

2y + x = -6
y = -2x + 0

We can substitute the second equation into the first one.

2y + x = -6
2(-2x + 0) + x = -6
-4x + x = -6
-3x = -6

Divide -3 on both sides.

x = 2

Now, plug x = 2 into any equation and solve for y.

y = -2x + 0
y = -2(2) + 0
y = -4

The solution to the system of equations is (2,-4).

Suppose v varies directly as g, and v=36 when g=4. Find v when g =11

Answers

36v.......4g

x...........11g

Cross multiply

4x= 36*11

4x= 396

x= 396/4

x= 99

When g=11 V will equal 99

I hope that's help !

you can also doing it another way

4*9= 36v

11*9= 99

If you have questions please ask !

how do you solve the system of elimination method.

x-6y=-30

-2x-5y=-25

Answers

x-6y=-30...equatn 1
-2x-5y=-25....equatn 2
multiply eqn 1 and 2 with 5 and 6 respectively
5x-30y=-150
-12x-30y=-150
subtract to eliminate y
17x=0
x=0
substitute x=0 into any of the equations
0-6y=-30
-6y=-30
y=-30/-6
y=5
x=0;y=5

x - 6y = -30 / * 2
-2x - 5y = -25

2x - 12y = -60
-2x - 5y = -25
--------------------
+
2x - 2x - 12y - 5y = -60 - 25
-17y = -85 / : (-17)
y = 85/17
y = 5

y = 5
x - 6y = -30

y = 5
x - 6 * 5 = -30

y = 5
x - 30 = -30

y = 5
x = 30 - 30

y = 5
x = 0

answer:
x = 0
y = 5

Can Miguel use 3/4 inch strips to make a line that is exactly 5 inches long.Explain

Answers

No:
0.75+0.75=1.5
1.5+0.75=2.25
2.25+0.75=3.00
3.00+0.75=3.75
3.75+0.75=4.50
4.50+0.75=5.25

Karen bakes cookies. She has observed that the number of cookies that turn out well in each batch varies with the size of the batch and is given by the function f(x) = 2x – 23, where x is the size of the batch (number of cookies in each batch). She never bakes fewer than 12 cookies in a batch. If the size of five batches is {20, 25, 26, 27, 34}, how many cookies turn out well in each batch?Answers Choices
{17, 27, 29, 31, 45}
{18, 24, 26, 30, 46}
{14, 23, 25, 31, 42}
{20, 24, 25, 26, 44

Answers

Substitute the values of the size of the 5 batches to the model.

For example

@x = 20

f(20) = 2*20 – 23 = 17

f(25) = 2*25 – 23 = 27

f(26) =29

f(27) = 31

f(34) = 45

Therefore the answer is the first choice (17, 27, 29, 31, 42)

A 12 ft long ladder is leaning against a wall and makes an 80 degree angle with the ground. How high up the wall does the ladder reach, and how far is the rest of the ladder from the base of the wall? Round to the nearest inch.