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3 years ago

13

A bookcase has 4 shelves. The bottom shelf has 10 books. Each of the other shelves has 5 more books than the shelf below it. How

many books are in the bookcase.

2 answers:

Pani-rosa [81]3 years ago

7 0

Answer:

70

Step-by-step explanation:

Leto [7]3 years ago

5 0

It would have a total of 70 books.

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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

The box plot suggests that Olga served fewer than what number of aces during about 75% of tennis matches

mariarad [96]

Answer:

d) 10

Step-by-step explanation:

6 0

3 years ago

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Last week, a store sold laptops worth a total of $3,885.Each laptop cost $555.how many laptops did the store sell last week

mojhsa [17]

The store sold 7 laptops. 3,885/555 = 7

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2 years ago

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1.2983 rounded to nearest hundredth

exis [7]

Answer:

1.3000

Step-by-step explanation:

The 9 makes the 2 move to 3. Hope this helps.

3 0

3 years ago

Y=35+x how I do solve for x

Mazyrski [523]

Try to put x on one side.

Do y = 35+X

-35 -35

Now you have Y-35=x

Hope this helped

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3 years ago