Members of a softball team raised $1513.50 to go to a tournament. They rented a bus for $961.50 and budgeted $46 per player for
1 answer:
Answer: 1513.50=961.50+46x
The number of players the team can bring to the tournament = 12.
Step-by-step explanation:
Let x= the number of players the team can bring to the tournament.
Total money raised = Rent of bus + (Cost per player) (Number of players)
Hence, the number of players the team can bring to the tournament = 12.
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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
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.