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atroni [7]
3 years ago
11

3. Suppose that a positive integer is written in decimal notation as n = akak-1… a2a1a0 where 0 ai 9. Prove that n is divisible

by 9 if and only if the sum of its digits ak + ak–1 + … + a1 + a0 is divisible by 9.
Mathematics
1 answer:
ira [324]3 years ago
4 0

Answer:

Therefore n is divisible by 9 if and only if  a_k+a_{k-1}+.........+a_1+a_0 is also divisible by 9.

Step-by-step explanation:

Given number is

n= a_ka_{k-1}.....a_2a_1a_0

This means

n=a_k10^k +a_{k-1}10^{k-1}+.....+a_110^1+a_0

Here we need to prove

a_k+a_{k-1}+......+a_2+a_1+a_0 is divisible by 9.

We know that

10  ≡ 1 mod 9

It means if 10 divides by 9 the remainder = 1.

n=a_k10^k +a_{k-1}10^{k-1}+.....+a_110^1+a_0

\Rightarrow n \equiv a_k(1)^k+a_{k-1}(1)^{k-1}+.........+a_1(1)^1+a_0 mod 9

\Rightarrow n \equiv a_k+a_{k-1}+.........+a_1+a_0 mod 9

Therefore n is divisible by 9 if a_k+a_{k-1}+.........+a_1+a_0 is also divisible by 9.

And conversely is also true.

Therefore n is divisible by 9 if and only if  a_k+a_{k-1}+.........+a_1+a_0 is also divisible by 9.

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Answer:

B. Any integer greater than 0

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.   It is the set of all possible values of t which will make the function "work", and will give a result for the Air Pressure, P(t).

Since Time(t) is a continuous function, the domain could take on any positive real number. Since, we are looking for the best description of the domain, Option B (any integer greater than 0) would be suitable.

This is because choosing any real number in Option A will accept negative values and time cannot be negative.

6 0
2 years ago
Answer fast! Will mark brainliest-- Reflect quadrilateral SQRT over the y-axis. Then translate the new quadrilateral 3 units to
Usimov [2.4K]

Answer:

i think the answer for the new coordinates is C but it doesnt make sence

Step-by-step explanation:

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5 0
2 years ago
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Question 11 in my book. <br><br> y x 6 for y = 2/3<br><br> what is the answer
trapecia [35]
The answer is 4. I hope this helped.

8 0
2 years ago
What is 5 x 7 - 12 + 56 - 9 ?
-BARSIC- [3]

Answer: 70

Step-by-step explanation:

5 multiplied by 7 is 35.

35 - 12 is 23.

23 + 56 is 79.

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4 0
3 years ago
A stock can go​ up, go​ down, or stay unchanged. How many possibilities are there if you own 3 ​stocks?
Gala2k [10]

Answer:

There are 27 different possible outcomes.

Step-by-step explanation:

Assuming that you have 3 different stocks:

First, we need to find the number of events and the number of possible outcomes for each event.

Here we can assume that each one of the stocks is a event, and the number of possible outcomes for each one are:

Stock 1: 3 options (up, down, stay)

Stock 2: 3 options (up, down, stay)

Stock 3: 3 options (up, down, stay)

The total number of possible outcomes is equal to the product of the numbers of options for all the events.

Then the total number of possibilities is:

C = 3*3*3 = 27

4 0
2 years ago
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