1. Of 350 males athletes at a high school, some play only basketball, some play only baseball, and some do both. if 250 of males play basketball, and 120 play both sports how many of the males play baseball?
A. 100
B. 220**
C. 130
D. 120
2. Suppose T = ( -8, -4, 0, 4, 8, 12, 16, 20 ) and K = ( -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 ) What is T n k (Then an upside down u) looks like a hill almost)
A. ( -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 )
B. ( -8, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 8, 12, 16, 20)***
C. ( -8, -4, 8, 12, 16, 20)
D ( 0, 4 )
3. What are all of the subsets of the set?
( -8, 4)
A. 0, (-8), (4)
B.(-8), (4), (-8, 4)
C, (-8), (4)
D. 0, (-8), (4), (-8, 4)**
4. Your class hopes to collect at least 325 cans of food for the annual food drive. There were 132 cans donated the first week and 146 more the second week. a. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. b. How many cans are needed to meet or surpass your goal?
I think:
c+135+89>325
c>325-89-135
1 and 2 are correct I think
a. The inequality is c + 132 + 146 ≥ 325.
b. To meet or surpass the goal, the class needs at least 325 cans.
1. To find the number of males who play baseball, we can use the principle of inclusion-exclusion. The total number of males who play basketball is given as 250, and the number of males who play both sports is given as 120.
Let's assume the number of males who play only baseball is x. Then, the number of males who play only basketball would be 250 - 120 = 130.
Now, the total number of males who play either basketball or baseball is x + 130 + 120 = x + 250.
Since there are 350 males in total, we can set up the equation:
x + 250 = 350
Simplifying the equation, we get:
x = 350 - 250
x = 100
Therefore, 100 of the males play baseball. So, the answer is option A.
2. The symbol T ∩ K represents the intersection of sets T and K. In other words, it gives us the elements that are common to both sets.
Looking at the given sets T and K, we can see that the only common elements are -3, -2, -1, 0, 1, 2, 3, 4, 5, and 6.
Therefore, T ∩ K = (-3, -2, -1, 0, 1, 2, 3, 4, 5, 6).
So, the correct answer is option A.
3. To find all the subsets of the set { -8, 4 }, we can use the concept of powerset. The powerset of a set is a set that contains all the possible subsets of that set.
For the given set { -8, 4 }, the powerset would be:
{ ∅, (-8), (4), (-8, 4) }
So, the answer is option D.
4. a. To write an inequality for the number of cans of food that must be collected by the end of the third week, we can let 'c' represent the number of cans needed.
The total number of cans collected at the end of the first week is 132, and 146 more were collected in the second week. So, the total number of cans collected by the end of the second week is 132 + 146.
To meet or surpass the goal of 325 cans, the total number of cans collected by the end of the third week (c) should be greater than or equal to 325.
Therefore, the inequality is:
c + 132 + 146 ≥ 325
b. To find out how many cans are needed to meet or surpass the goal, we can solve the inequality:
c + 278 ≥ 325
Subtracting 278 from both sides of the inequality, we get:
c ≥ 325 - 278
c ≥ 47
Therefore, at least 47 cans of food are needed to meet or surpass the goal.
So, the correct answer is 47 cans.