Answer:
A ∩ B = {1, 3, 5}
A - B = {2, 4}
Step-by-step explanation:
The given problem regards sets and set notation, a set can simply be defined as a collection of values. One is given the following information:
A = {1, 2, 3, 4, 5}
B = {1, 3, 5, 6, 9}
One is asked to find the following:
A ∩ B,
A - B
1. Solving problem 1
A ∩ B,
The symbol (∩) in set notation refers to the intersection between the two sets. It essentially asks one to find all of the terms that two sets have in common. The given sets (A) and (B) have the values ({1, 3, 5}) in common thus, the following statement can be made,
A ∩ B = {1, 3, 5}
2. Solving problem 2
A - B
Subtracting two sets is essentially taking one set, and removing the values that are shared in common with the other set. Sets (A) and (B) have the following values in common ({1, 3, 5}). Thus, when doing (A - B), one will omit the values ({1, 3, 5}) from set (A).
A - B = {2, 4}
Answer:
15
Step-by-step explanation:
To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula
In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.
Furthermore, we must round to the nearest whole number, as you cannot make part of an item.
Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:
Answer:
C. 55 inches
Step-by-step explanation:
a^2 = b^2 + c^2
a^2 = 47.5^2 + 27^2
a^2 = 2985.25
a = 54.637 = 55 inches
After one hour, the plane is 225 miles from its destination
Answer:
- 48
Step-by-step explanation:
If you want to learn more about this concept, it's called composition of functions.
First, you plug in g(x) as if it were x into f(x).
f(g(x))= -5 (1/2x + 4) + 2
= -5/2x - 20 + 2
= -5/2x - 18
Then, plug in the value given, as x.
= -5/2 (12) - 18
= -30 - 18
= - 48
I hope this helped!
