Answer:
CHEESE
Step-by-step explanation:
CHEESE IS ALWAYS THE ANSWER!!!
... <span>exactly one output for each input
This is an important concept; be certain that you understand it.
</span>
Step 1. Set up long division
_______
7| 1 9 8 6
Step 2. <span>Calculate 19 ÷ 7, which is 2 with a remainder of 5.
2
</span> _______
7| 1 9 8 6
1 4
_________
5
Step 3. Bring down 8, so that 58 is large enough to be divided by 7.
2
_______
7| 1 9 8 6
1 4
_________
5 8
Step 4. <span>Calculate 58 ÷ 7, which is 8 with a remainder of 2.
</span> 2 8
_______
7| 1 9 8 6
1 4
_________
5 8
5 6
_________
2
Step 5. <span>Bring down 6, so that 26 is large enough to be divided by 7.
</span> 2 8
_______
7| 1 9 8 6
1 4
_________
5 8
5 6
_______
2 6
Step 6. Calculate 26 ÷ 7, which is 3 with a remainder of 5.
2 8 3
_______
7| 1 9 8 6
1 4
_________
5 8
5 6
_______
2 6
2 1
______
5
Step 7. <span>Therefore, 1986 ÷ 7 = 283 with a remainder of 5.
823 With a remainder of 5
Done!
</span><span>Decimal Form If Needed: 283.714286</span>
Answer:
a. closed under addition and multiplication
b. not closed under addition but closed under multiplication.
c. not closed under addition and multiplication
d. closed under addition and multiplication
e. not closed under addition but closed under multiplication
Step-by-step explanation:
a.
Let A be a set of all integers divisible by 5.
Let
∈A such that 
Find 

So,
is divisible by 5.

So,
is divisible by 5.
Therefore, A is closed under addition and multiplication.
b.
Let A = { 2n +1 | n ∈ Z}
Let
∈A such that
where m, n ∈ Z.
Find 

So,
∉ A

So,
∈ A
Therefore, A is not closed under addition but A is closed under multiplication.
c.

Let
but
∉A
Also,
∉A
Therefore, A is not closed under addition and multiplication.
d.
Let A = { 17n: n∈Z}
Let
∈ A such that 
Find x + y and xy


So,
∈ A
Therefore, A is closed under addition and multiplication.
e.
Let A be the set of nonzero real numbers.
Let
∈ A such that 
Find x + y

So,
∈ A
Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.
Therefore, A is not closed under addition but A is closed under multiplication.