Ryan's motorcycle is now worth $2500. It

Mathematics

1 answer:

Ann [662]3 years ago

5 0

52% of 4807.6923 is 2500 so 48% of 4807.6923 would be 2019.230766 rounding it to the nearest dollar is $2019.23

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I'm getting dressed in the dark, and I have 6 pairs of white socks and 6 pairs of black socks, but they're all mixed up in my so

saul85 [17]

Answer:

<em>We'll need to pull out 11 pairs of socks to be sure to get five pairs of white socks.</em>

Step-by-step explanation:

Combinations

We have 6 pairs of white socks and 6 pairs of black socks. If we wanted to pull out five pairs of white socks, there are to extreme scenarios:

The most favorable event is to take the five pairs in the first five takes. But that won't be for sure.

The worst case would be to take all the black socks first, and then take the five white socks. It would be a sure event and we must assume it as a possibility. Thus:

We'll need to pull out 11 pairs of socks to be sure to get five pairs of white socks

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3 years ago

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Ilya [14]

Answer:

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Step-by-step explanation:

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Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$