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2 years ago

12) A candy company used 8 gallons of syrup to make 4 batches of candy. What is the rate of syrup per batch?

Mathematics

1 answer:

Black_prince [1.1K]2 years ago

3 0

The answer is 2 gallons of syrup per batch.

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The art Club is having a fundraiser, and 198 people are attending. if 12 people can sit at each table, what is the least number

vitfil [10]

17 tables because you need to divide 198 and 12 and yu get 16.5 but you have to round it because you cant leave the 5 people out so it would be 17

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3 years ago

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What is the domain and range of y+3=2^x

Bad White [126]

Answer: y>-3 and x is all real numbers

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2 years ago

What equation can be used to find the length of AC

Leno4ka [110]

I'm pretty sure this is the answer:
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3 years ago

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

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

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3 years ago

What number is 30% of 150

mrs_skeptik [129]

Find 30% of 150. To do this, mult. 150 by 0.30. Result: 45.

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3 years ago

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