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2 years ago

Which of the following demonstrates how the 20 is calculated using the combination pattern

Mathematics

1 answer:

UNO [17]2 years ago

5 0

The combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3

<h3>Permutation and Combination</h3>

While combination has to do with selection, permutation has to do with arrangement.

According to the combination rule

nCr = n!/(n-r)!r!

The expression that gives the result of 20 is expressed below;

6C3 = 6!/(6-3)!3!

6C3 = 6!/3!3!

6C3 = 6!/6*6
6C3 = 720/36
6C3 =20

Hence the combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3

Learn more on combination here: brainly.com/question/4658834

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Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

Can someone please help me with this problem

Nadusha1986 [10]

X= 2/3

6x/x-6 - 4/x - 24 / x^2 - 6x = 0

6x^2 -4 (x-6)-24 / x(x-6) = 0

6x^2 -4x+ 24 -24/x(x-6) = 0

X(6x-4) / x(x-6)

6x-4/x-5 = 0

6x-4= 0

6x = 4 divide both sides by 6
X= 2/3

5 0

3 years ago

The length of a rectangle is 8 inches more than twice its width. The area of the rectangle is 120 square inches. How many inches

Irina-Kira [14]

Answer:

L = 20 inches

Step-by-step explanation:

w = width

L = length

area = 120

W x L = 120

L - 8 = 2W then L = 2W + 8

substitute for L:

W x (2W + 8) = 120

2W² + 8W -120 = 0

(2W - 12)(W + 10) = 0

2W-12 = 0

2W = 12

W = 6

L = 20

7 0

3 years ago

Which polynomial represents the sum below? (4x5 + 6x3 + 3) + (3x3 + x + 9)

umka21 [38]

Answer:

i think

4x^5+9x^3+x+12

Step-by-step explanation:

7 0

3 years ago

Give a recursive definition of each of these sets of ordered pairs of positive integers. [Hint: Plot the points in the set in th

konstantin123 [22]

Answer:

(2,1), (1,2) is your base step

if (a,b) is in the set (a+1,b+1) will be in the set

if (a,b) is in the set (a+2,b) will be in the set

if (a,b) is in the set (a,b+2) will be in the set.

Step-by-step explanation:

Think about how to solve this problem in general. How can you assure that the sum a+b is odd ?

Think about this, what happens when you sum two even numbers ? The result is even or odd ?

2+6 = 8 (even )

10+12 = 22 (even)

And what happens when you sum two odd numbers ? The result will be even or odd ? Look

3+7 = 10 (even)

5+11 = 16 (even)

Therefore to assure that a+b is odd, one of them has to be odd and one of them has to be even, that is why

(2,1), (1,2) is your base step

if (a,b) is in the set (a+1,b+1) will be in the set

if (a,b) is in the set (a+2,b) will be in the set

if (a,b) is in the set (a,b+2) will be in the set.

3 0

3 years ago

Which of the following demonstrates how the 20 is calculated using the combination pattern​

Which of the following demonstrates how the 20 is calculated using the combination pattern