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3 years ago

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

1 answer:

3 0

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!
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:

$A_{2}=25^{2}$

$A_{2}=625yd^{2}$

- From Eq.2:

$A_{3}=10*25$

$A_{3}=250yd^{2}$

3 0

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

8 0

3 years ago

Whats 9 + 10 fr fr ong fr on fr fr

Fed [463]

Answer:

19.

21 sometimes though.

5 0

2 years ago

Read 2 more answers

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:

The complete question is

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

Perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$