Answers:
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Explanation:
7+6 = 13. Divide this over 5 to get 13/5 = 2 remainder 3. The quotient 2 is something we don't care about. <u>We only worry about the remainder</u>. Therefore 7+6 = 3 (mod 5)
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2+1 = 3 (mod 5) for similar reasoning as above. 3/5 = 0 remainder 3.
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20 = 9 (mod 11) since 20/11 = 1 remainder 9. Imagine you had 20 cookies and 11 friends. Each friend would get 1 whole cookie (quotient) and there could be 9 left over (remainder).
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35/11 = 3 remainder 2
Or you could use repeated subtraction like so to find the remainder
35-11 = 24
24-11 = 13
13-11 = 2
The last result (2) is smaller than 11, so we stop here and this is the remainder.
Therefore, 35 = 2 (mod 11)
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Here's another way to think of it. Consider you have $35 in your pocket. Let's say a store is selling trinkets for $11 each. We can pose these key questions:
- What is the most number of trinkets you can buy?
- If you buy that max amount, how much will you have left over?
The answer to the first question is 3 trinkets because 3*11 = 33 dollars is under the budget of $35. The amount left over is 35-33 = 2 dollars which is the remainder. It's not larger than 11, so we cannot buy any more trinkets at this point.
He will need to work 8 months
Answer:
5/51
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
<h2>Evaluating Composite Functions</h2><h3>
Answer:</h3>
<h3>
Step-by-step explanation:</h3>
We can write how 
will be defined but that's too much work and it's only useful when we are evaluating with many inputs.
First let's solve for 
first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
Solving for :
Now we can solve for 
, since 
, 
.
Given:
Solving for 
:
Now we are can solve for 
. By now you should get the idea why 
.
Given:
Solving for :
