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saveliy_v [14]
3 years ago
6

Need help due tomorrow plz help!!

Mathematics
1 answer:
Sonbull [250]3 years ago
6 0
1.) B

because it says the person buys a ski for 350. He puts down $110 which means to subtract. Now he got a discount which also means to subtract. Then it told that he gave 1/2 them money to his mother. So that too means to subtract. 

2.) 2+5n

because it says 2 plus 5 times a number. So 2+5×n 
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Step-by-step explanation:multiply to find out the answer

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How might you solve a problem that has both a fraction and a decimal in it
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Well, one way is to convert one of the numbers to the other. For example, if I have 3/5 and 0.5, I could convert 3/5 to a decimal. So, I would have 0.6 (3/5 converted to a decimal), and 0.5. Next, I would just add the two together to get my answer of 1.1
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7 0
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}}

5 0
3 years ago
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