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GarryVolchara [31]
3 years ago
5

How many distinguishable 7 letter​ "words" can be formed using the letters in alabamaalabama​?

Mathematics
1 answer:
otez555 [7]3 years ago
3 0
<span>You are given the word alabama and you are asked to find how many distinguishable 7 letter​ "words" can be formed from it.

ALABAMA has seven letters so we will start at 7! 
Counting the number of A's in the word we have 4 A's and so we will divide it by 4!
</span>Counting the number of L's in the word we have 1 L and so we will divide it by 1!
Counting the number of B's in the word we have 1 B and so we will divide it by 1!
Counting the number of M's in the word we have 1 M and so we will divide it by 1!

And so the number of ways is 7! / (4! x 1! x 1! x 1!) = 210 words.

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This question has three parts. Answer the parts in order.
nalin [4]

Answer:

The area of the smallest section is A_{1}=100yd^{2}

The area of the largest section is A_{2}=625yd^{2}

The area of the remaining section is A_{3}=250yd^{2}

Step-by-step explanation:

Please see the picture below.

1. First we are going to name the side of the larger square as x.

As the third section shares a side with the larger square and the four sides of a square are equal, we have the following:

- Area of the first section:

A_{1}=10yd*10yd

A_{1}=100yd^{2}

- Area of the second section:

A_{2}=x^{2} (Eq.1)

- Area of the third section:

A_{3}=width*length

A_{3}=10yd*x (Eq.2)

2. The problem says that the total area of the enclosed field is 975 square yards, and looking at the picture below, we have:

A_{1}+A_{2}+A_{3}=975yd^{2}

Replacing values:

100+x^{2}+10x=975

Solving for x:

x^{2}+10x-875=0

x=\frac{-10+\sqrt{100+(4*875)}}{2}

x=\frac{-10+\sqrt{3600}}{2}

x=\frac{-10+60}{2}

x=25

3. Replacing the value of x in Eq.1 and Eq.2:

- From Eq.1:

A_{2}=25^{2}

A_{2}=625yd^{2}

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A_{3}=10*25

A_{3}=250yd^{2}

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2 years ago
Help please math ..??
astraxan [27]

Answer:

(3, - 1)

Step-by-step explanation:

5x - 4y = -11

2x + 3y = -9

Multiply the top equation by 2 and the bottom equation by - 5 to cancel out the x's.

10x - 8y = - 22

- 10x - 15y = 45

Cancel out x's.

-8y = - 22

- 15y = 45

Add like terms.

- 23y = 23

Can't have a negative variable to flip them.

-23 = 23y

Divide.

y = - 1

Input y into one of the equations and solve for x.

2x + 3(-1) = -9

Simplify.

2x -3 = -9

Cancel out -3 by adding 3.

2x = -6

Divide.

x - -3

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Whats 9 + 10 fr fr ong fr on fr fr
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Answer:

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2 years ago
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Find each difference. Write in simplest form 7/8-5/8=
Ivanshal [37]
7/8-5/8= 2/8 and if you reduce 2/8 by 2 it becomes 1/4. So 1/4 is your answer. Hope This Helps :D
5 0
3 years ago
The perimeter of the rectangle is 22 meters, and the perimeter of the triangle is 12 meters. Find the dimensions of the rectangl
lianna [129]

Answer:

Length:8 m

Width:3 m

Step-by-step explanation:

<u><em>The complete question is</em></u>

If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.

step 1

<em>Perimeter of rectangle</em>

we know that

The perimeter of rectangle is equal to

P=2(L+W)

we have

P=22\ m

so

22=2(L+W)

Simplify

11=L+W -----> equation A

step 2

Perimeter of triangle

The perimeter of triangle is equal to

P=\frac{L}{2}+W+5

P=12\ m

so

12=\frac{L}{2}+W+5

Multiply by 2 both sides

24=L+2W+10

L+2W=14 ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (8,3)

see the attached figure

therefore

The dimensions of the rectangle are

Length:8 m

Width:3 m

3 0
3 years ago
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