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2 years ago

What is 39/12 in a mixed number in simplest form

Mathematics

2 answers:

valkas [14]2 years ago

8 0

39 dives by 12 is 3 with a remainder of 3.

3 / 12 simplifies to 1/4

Answer is 3 and 1/4

Lunna [17]2 years ago

7 0

39/12…
39/12=3.25
3.25=3 1/4

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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

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1 year ago

I make $40,000 per year. I have been offered a promotion and a $5,000 raise per year. My average federal income tax rate will go

Paha777 [63]

Answer:

Yes

Step-by-step explanation:

40000 x .10 is 4000 in tax. Total after tax would be 36,000

45,000 × .15 is 6750. Total after tax would be 38,250 which is more

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2 years ago

The ___ uses cash flows and the cost of raising capital as inputs to valuing a company's stock.

Vlad [161]

I think its camp. would be the answer

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3 years ago

Find the area of a circle with radius, r = 6.48m. Give your answer rounded to 2 DP.

Artyom0805 [142]

Answer:

Area = 131.9167322

Step-by-step explanation:

I'm not sure what 2 DP means so you will need to do that part.

area=pi*radius^2

area=3.14*42 (approx)

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2 years ago

THE PERSON WHO PAID $7.99 WAS EITHER THE PERSON WHO HAD THE ICED TEA OR THE PERSON WHO HAD THE WATER

Crazy boy [7]

Answer:

Iced Tea

Step-by-step explanation:

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3 years ago