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2 years ago

If you arrange a group of numbeers in order of size, the middle number is called the ____________.

Mathematics

1 answer:

ArbitrLikvidat [17]2 years ago

4 0

Its called the median

hope this helps you

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

Simplify using exponents: B12/B5

stiks02 [169]

I think what you mean is:
$\frac{b^{12}}{b^{5}}$

Then using our rules of exponents, this is the same as
$b^{12-5}=b^{7}$

8 0

2 years ago

What is 36kg in the ratio 7:2

babymother [125]

Answer:

28 Kg : 8 Kg

Step-by-step explanation:

Sum the parts of the ratio, 7 + 2 = 9 parts

Divide 36 Kg by 9 to find the value of one part of the ratio.

36 Kg ÷ 9 = 4 Kg ← value of 1 part of the ratio, thus

7 parts = 7 × 4 Kg = 28 Kg

2 parts = 2 × 4Kg = 8 Kg

36 Kg in the ratio 7 : 2 = 28 Kg : 8 Kg

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2 years ago

The bookstore sells 6 books for $13.50 How much will it cost to purchase 2 books?

Neporo4naja [7]

It would cost $4.50 to purchase 2 books.

5 0

3 years ago

Read 2 more answers

Factor the given polynomial<br> 3х2 + 5х – 12

Juliette [100K]

The answer is (3x - 4) (x + 3)

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3 years ago