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.
Scale factor is a ratio. The correct option is C.
<h3>How are
scale drawings formed?</h3>
For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
The length of AB can be written as,
AB = √[(1-4)²+ (1-1)²]
AB = 3
Since the length A'B' is 6 units, therefore, the scale factor will be,
Scale factor = (Length after transformation)/(Length before transformation)
Scale factor = 6 /3 = 2
Hence, the correct option is C.
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The inequality that represents the number of each type of fabric that Naomi has is:

Let the number of short-sleeved shirts she made be x
Let the number of long-sleeved shirts she made be y
Length of clothes used to make a short-sleeved shirt = 9 yards
Length of clothes used to make a long-sleeved shirt = 16 yards
Length of short-sleeved shirts made = 9x
Length of long-sleeved shirts made = 16y
Total length of fabric used = 53 yards
The inequality that represents the number of each type of fabric that Naomi has is:

Learn more on inequality here: brainly.com/question/15269537
Answer:

Step-by-step explanation:
We need to find which statements are true.
Solution to find the same we will solve each statement and will conclude the same.
1. 
Now On solving we get;


So we can see that 0.70 > 0.66
Hence The given statement is False.
2. 
Now On solving we get;


So we can see that 0.5625 > 0.5
Hence The given statement is True.
3. 
Now On solving we get;


So we can see that 1.33 > 1.2
Hence The given statement is False.
4. 
Now On solving we get;


So we can see that 0.82 > 0.66
Hence The given statement is False.
Answer:
A: 22
Step-by-step explanation:
2The interquartile range begins at 45 and ends at 67. All you need to do is subtract 45 drom 67, and you get 22.