Answer:

Step-by-step explanation:
In order to find the slope of a line, we need to find the rise over the run.
Basically - the change in y divided by the change in x.

We can compare the two points and find both.
We go from (0, 2) to (3, 1).
From 0 to 3 (x) is 3 units.
From 2 to 1 (y) is -1 units.
Therefore we can divide the x by the y.


Hope this helped!
Answer:
B
Step-by-step explanation:
f(0) - f(-3) = area under f'(x) from x=0 to x=3.
We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.
A = 1/2 b h
A = 1/2 (3) (3)
A = 4.5
f(0) - f(-3) = 4.5
Since f(0) = 7:
7 - f(-3) = 4.5
f(-3) = 7 - 4.5
f(-3) = 2.5
The question has no domain restriction therefor the answer is C. All real numbers.
Answer:
C
Step-by-step explanation:
The line on the left has equation y = x - 2
The start of the line has an open circle at x = 3 meaning that x ≠ 3
The line is defined as y = x - 2 for x < 3
The line on the right has equation y = x - 1
The start of the line has a closed circle at x = 3 meaning that x can equal 3
The line is defined as y = x - 1 for x ≥ 3
Thus the definition of the function is C
Answer:

Step-by-step explanation:
We can find the total amount of ways at least a woman receives a coupon by calculating the total amount of possibilities ot distribute the coupon and substract it to the total amount of possibilities to distribute 10 coupons to the 15 men (this is the complementary case that at least a woman receives a cupon).
- The total amount of possibilities to distribute the coupons among the 20 shoppers is equivalent to the total amount of ways to pick a subset of 10 elements from a set of 20. This is the combinatiorial number of 20 with 10, in other words, 
- To calculate the total amount of possibilities to distribute the coupons among the 15 men, we need to make the same computation we made above but with a set of 15 elements instead of 20. This gives us
possibilities.
Therefore, we have
possibilities to distribute the coupons so that at least one woman receives a coupon.
I hope that works for you!