Answer:
22
Step-by-step explanation:
Given:
An art teacher has the total number of buttons = 
1. In order to give each in the class 6 buttons, she will need 18 more buttons.
2. If she gives each child 5 buttons, she will have 4 left over.
Question asked:
How many children are in the class ?
Solution:
<u>Let total number of children in the class = </u>
<u><em>As given that, 18 more buttons will be needed to give 6 buttons to each.</em></u>
The equation will be:-

<em><u>Also given that, If she gives 5 buttons to each, she will have 4 left over.</u></em>
The equation will be:-

Subtraction equation 2 from 1

Hence, total number of children are 22.
I think its a rational number
"Volume(10) = 1,000" and "Volume(2) = 8" are the two statements among the following choices given in the question that is true. The correct options among all the options that are given in the question are option "B" and option "C". I hope that this is the answer that has actually come to your great help.
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.