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bearhunter [10]

2 years ago

5

If your percentile rank in a group of 500 students is 84, how many persons rank lower than you?

2 answers:

julsineya [31]2 years ago

5 0

If you do 84 x 5 then you have 420 people lower than you

NeX [460]2 years ago

5 0

First find 84% of 500
---> 0.84*500 = 420

If you are person 420, then 419 rank lower.

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

1 year ago

Is this multiplication? Can you also help me with the answer!?

vredina [299]

Answer:

84,375 m^2

Step-by-step explanation:

We need to find the surface area of the pyramid. The pyramid can be divided into 4 triangles and one square (the bottom).

Area of a triangle is 1/2*b*h where b is the base of the triangle and h is the height.

Area of a square is length times width.

Total area = $4\times(\frac{1}{2}\times 225 \times 75)+225\times225 = 84375 m^2$

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2 years ago

Find the perimeter of the figure:

Oksi-84 [34.3K]

Answer: idk but i could be

29 units

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3 years ago

Read 2 more answers

College bookstore charge $60 for a yearly membership. Books will then only cost $7.60 each, tax included. Right in equation to r

Yuri [45]

Equation - 7.60b+60=m

7.60b+60=100
You’d be able to buy 5 books

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3 years ago

What is the sum of (1.3 × 10-7) and (-3.8 × 10-3)?

SVETLANKA909090 [29]

b. -2.5 × 10-4 is the answer

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2 years ago