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Natasha2012 [34]

3 years ago

12

Sasha ordered a set of green and blue pins. She received 20 pins in all. 10 of the pins were green. What percentage of the pins

were green?

1 answer:

arlik [135]3 years ago

5 0

Answer:

50%

Step-by-step explanation:

10 of the pins were green

there are 20 pins in total

10/20 of the fries are green

10/20=1/2=50/100

50/100=50%

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Prove that if a is equivalent to 5 mod (8) and b is equivalent to 3 mod (8), then 8 divides ab+1

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Answer:

Explanation contains the proof.

Step-by-step explanation:

$a \equiv 5 (mod 8) \text{ means there is integer } k \text{ such that } a-5=8k$ .

$b \eqiv 3 (mod 8) \text{ means there is integer } m \text{ such that } b-3=8m$ .

We want to show that $8 \text{ divides } ab+1$ . So we are asked to show that there exist integer $n \text{ such that } 8n=ab+1 \text{ or 8n-1=ab$

So what is $ab$ ?

$a-5=8k \text{ gives us } a=8k+5$ .

$b-5=8m \text{ gives us } b=8m+5$ .

So back to $ab$ ....

$ab$

$=(8k+5)(8m+5)$

$=64km+40k+40m+25$ (I use foil to get this)

Factoring out 8 gives us:

$=8(8km+5k+5m)+25$

Now I could have factored some 8's out of 25. There are actually three 8's in 25 with a remainder of 1.

$=8(8km+5k+5m+3)+1$

We have shown that there is integer $n \text{ such that } ab=8n-1$ .

The integer I found that is n is 8km+5k+5m+3.

Therefore $8|(ab+1)$ .

//

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