1) There are two pet stores in zacharys town. There are dogs, cats, and hamsters at the first pet store. The second store has dogs, rabbits, and fish. Write a set that represents all of the different pets stores in the town.
2) of the 125 students in an elementary school, 89 students play checkers and 45 students play checkers and chess. How many students in the school play checkers?
3) Identify all the subsets of {2,9}
4) The cheerleading squad is having a bake sale. They want to bake at least 120 cookies. They made 12 cookies the first hour and 24 cookies the second hour.
a)Write an inequality that describes the scenario. Let Variable h represent the number of hours that must bake to meet or surpass the goal.
B) How many hours must they work to meet or surpass the goal?
1) To find the set representing all the different pets stores in the town, we need to list all the pets available in each store and combine them into a single set.
First Pet Store: {dogs, cats, hamsters}
Second Pet Store: {dogs, rabbits, fish}
Combining the two sets, we have:
All Pet Stores: {dogs, cats, hamsters, rabbits, fish}
2) To find the number of students who play checkers in the school, we need to use set theory and the principle of inclusion-exclusion.
Given:
Total number of students in the school = 125
Number of students who play checkers and chess = 45
Number of students who play checkers only = ?
We can represent the different sets as follows:
A = Set of students who play checkers
B = Set of students who play chess
Using the principle of inclusion-exclusion, we can write the equation:
n(A U B) = n(A) + n(B) - n(A ∩ B)
Substituting the given values:
125 = n(A) + 45 - 45
Solving for n(A):
n(A) = 125 - 45
n(A) = 80
Therefore, there are 80 students who play checkers in the school.
3) To identify all the subsets of {2, 9}, we need to list all the possible combinations of elements, including the empty set and the set itself.
Given: Set = {2, 9}
Subsets:
{}, {2}, {9}, {2, 9}
So the subsets of {2, 9} are: {}, {2}, {9}, {2, 9}
4a) To write an inequality that describes the scenario, we need to express the total number of cookies baked in terms of the number of hours worked.
Let h represent the number of hours the cheerleading squad must bake to meet or surpass the goal.
The number of cookies baked in the first hour is 12, and the number of cookies baked in the second hour is 24. To find the total number of cookies baked in h hours, we can use the equation:
Total number of cookies baked = 12 + 24h
To meet or surpass the goal, the total number of cookies baked must be at least 120. So the inequality is:
12 + 24h ≥ 120
4b) To find how many hours the cheerleading squad must work to meet or surpass the goal, we can solve the inequality:
12 + 24h ≥ 120
Subtracting 12 from both sides:
24h ≥ 108
Dividing both sides by 24:
h ≥ 4.5
Therefore, the cheerleading squad must work at least 4.5 hours to meet or surpass the goal of baking at least 120 cookies.