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Ne4ueva [31]
3 years ago
8

Find the area of the yellow region. Round to the nearest tenth. 7.53 cm Area = [?] cm^2​

Mathematics
1 answer:
cestrela7 [59]3 years ago
5 0
I’m guessing it’s 8.00
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What is Permutations and Combinations?
marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0
2 years ago
Leo multiplied all numbers from 1 to 11 and wrote the answer on the board. During the break three digits were erased 39,9...6,8.
Pavlova-9 [17]
11! = 39,916,800

The erased digits are 1, 0, 0.
6 0
3 years ago
ASAP The team plowed 36 rows in 5 hours. The rain slowed their rate by one-half. How many rows could they now plow in 18 hours?
Vlad [161]

Answer:

Its A just explan the work like 129.6/64.8x98

8 0
3 years ago
Could i get some help 14m+2n-5(m-4n)-6n
frosja888 [35]

Answer:

9m + 16n

Step-by-step explanation:

14m+2n-5m+20m-6n

9m+2n+20n-6n

add like variable

9m + 16n

3 0
2 years ago
If y varies directly as x and y = 3 when x = - 9, then find x when y = 5.
Rus_ich [418]

Answer:

d. - 15

Step-by-step explanation:

The equation for direct variation is

y = kx

We know y =3 when x = -9

3 = k(-9)

Divide by -9

3/-9 = -9k/-9

-1/3 = k

The equation is then

y = -1/3 x

We know y = 5

5 = -1/3 x

Multiply each side by -3

-3*5 = -3*-1/3x

-15 = x

3 0
3 years ago
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