Answer:
There is no change.
Step-by-step explanation:
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.
First, do 16 x 3 to get 48. Then subtract 16 and youll get 32
Answer:

Step-by-step explanation:
=
The volume of a sphere is 


Yes. 6/16 simplifies to 3/8, which is the same amount of people singing.