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3 years ago

How many different ways can the letters of " accommodate" be arranged?

Mathematics

2 answers:

Mariulka [41]3 years ago

8 0

Here is your answer.....

pychu [463]3 years ago

8 0

Answer:

2,494,800

Step-by-step explanation:

"Accommodate" has n = 11 letters.

Without repeated letters the answer would be 11! = 39,916,800.

But there are 4 letters repeated twice, these are: (a, c, o, m).

Then the solution is to divide 11! by 2! multiplied 4 times to compensate for duplications, that is:

11! 39,916,800 39,916,800

X = -------------- = -------------------- = ------------------- = 2,494,800

2! 2! 2! 2! 2 . 2 . 2 . 2 16

Then, the letters of "accommodate" can be arranged of 2,494,800 different ways

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Please help!!! i'll give brainliest and offering 20 pts each!!!

Aleks04 [339]

Answer:

5(x +1.5)^2
10(x +1)^2
1/4(x +2)^2
3(x +5/6)^2

Step-by-step explanation:

When your desired form is expanded, it becomes ...

a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2

This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.

a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2

b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2

c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2

d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2

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<em>Additional comment</em>

If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.

8 0

3 years ago

Your building plan for your restaurant includes one men's and women's restroom. The city inspector lets you kno that you must ha

Ivanshal [37]

Answer: 3200 ft^2

Step-by-step explanation:

You have a total area of 4,000 ft^2.

In your plan, you will make two bathrooms (one men's restroom and one women's restroom)

We know that each one of them needs 400ft^2, then the total area needed is two times 400ft^2, or:

2*400ft^2 = 800ft^2

If we subtract this to the total area, we get:

4000ft^2 - 800ft^2 = 3200 ft^2

That is the square feet left for the development of other nonbathroom areas.

6 0

3 years ago

Please need help from math experts!!!! Struggling so hard…

Alenkinab [10]

Answer:

Step-by-step explanation:

A(10,10) B(b,10b)

ax-2y=30

$a)\\a(10)-2(10)=30\\10a-20=30\\10a-20+20=30+20\\10a=50$

Divide both parts of the equation by 10:

a=5

Hence,

5x-2y=30

5(b)-2(10b)=30

5b-20b=30

-15b=30

Divide both parts of the equation by -15:

b=-2

Thus,

a=5 b=-2

$b)\\A(10,10)\ \ \ \ \ \ B(-2,-20)\\ \displaystyle\\C(x_C,y_C)=(\frac{10+(-2)}{2} ,\frac{10+(-20)}{2} )\\\\C(x_C,y_C)=(\frac{10-2}{2},\frac{10-20}{2} )\\\\C(x_C,y_C)=(\frac{8}{2} ,\frac{-10}{2})\\\\C(x_C,y_C)=(4,-5)\\Hence,\ C(4,-5)$