Answer:
175<=12.5x+40
Step-by-step explanation:
She starts with 40 points already so you add in those 40 then since she gets 12.5 points per visit that is your x, so you set that as greater than or equal to 175
Step-by-step explanation:
(a)
Using the definition given from the problem
![f(A) = \{x^2 \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2 \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4] = f(A \cap B)\\](https://tex.z-dn.net/?f=f%28A%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B0%2C2%5D%5C%7D%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B1%2C4%5D%5C%7D%20%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccap%20f%28B%29%20%3D%20%5B1%2C4%5D%20%20%3D%20f%28A%20%5Ccap%20B%29%5C%5C)
Therefore it is true for intersection. Now for union, we have that
![A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]](https://tex.z-dn.net/?f=A%20%5Ccup%20B%20%3D%20%5B0%2C4%5D%5C%5Cf%28A%5Ccup%20B%20%29%20%3D%20%5B0%2C16%5D%5C%5Cf%28A%29%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccup%20f%28B%29%20%3D%20%5B0%2C16%5D)
Therefore, for this case, it would be true that
.
(b)
1 is not a set.
(c)
To begin with
![A\cap B \subset A,B](https://tex.z-dn.net/?f=A%5Ccap%20B%20%5Csubset%20A%2CB)
Therefore
![g(A\cap B) \subset g(A) \cap g(B)](https://tex.z-dn.net/?f=g%28A%5Ccap%20B%29%20%5Csubset%20g%28A%29%20%5Ccap%20g%28B%29)
Now, given an element of
it will belong to both sets, therefore it also belongs to
, and you would have that
, therefore
.
(d)
To begin with
, therefore
![g(A) \cup g(b) \subset g(A\cup B)](https://tex.z-dn.net/?f=g%28A%29%20%5Ccup%20g%28b%29%20%5Csubset%20g%28A%5Ccup%20B%29)
The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.
<h3>How to explain the information?</h3>
A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.
Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.
We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.
Learn more about permutations and combination on:
brainly.com/question/4658834
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B.
You have to find how much blueberry muffins you could make with one pound of flour.