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2 years ago

Help!!! multiple choice!

Mathematics

1 answer:

Talja [164]2 years ago

4 0

5.C

6.A

Hope this helps and is correct

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Deepak randomly chooses two marbles from the bag,

Alika [10]

Green 5/15
red 2/15
that should be your answer

3 0

2 years ago

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The greatest comen factor of 24 and 30

Alja [10]

Answer:

Step-by-step explanation:

Write the prime factorizations:

24 = 2³ × 3

30 = 2 × 3 × 5

The greatest common factor is the product of the common factors at their lowest exponents.

GCF = 2 × 3

GCF = 6

7 0

3 years ago

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What is the ratio

storchak [24]

9;9
Explanation:
You divide 18 by 2 to get 9 and divide 27 by 3 to get 9.

Hope that helps!

3 0

2 years ago

Simplify each expression. Use positive exponents. <br> A^4b^-3<br> ab^-2

choli [55]

$\dfrac{a^4b^{-3}}{ab^{-2}}$

$= {a^{4-1}b^{-3+2}}$

$= {a^{3}b^{-1}}$

$= \dfrac{a^3}{b}$

6 0

2 years ago

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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