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?
S = {a,b}
89+45 = 134
So, the extra 14 students must play both games
1) To find the set that represents all the different pets stores in the town, we need to consider the types of pets available at each store.
Let's call the first pet store "Pet Store 1" and the second pet store "Pet Store 2".
The types of pets at Pet Store 1 are dogs, cats, and hamsters. We can represent this set as {dogs, cats, hamsters}.
The types of pets at Pet Store 2 are dogs, rabbits, and fish. We can represent this set as {dogs, rabbits, fish}.
To find the set that represents all the different pet stores in the town, we combine the sets of pets from both stores. So, the set representing all the different pet stores in the town would be {dogs, cats, hamsters, rabbits, fish}.
2) To find the number of students who play checkers, we need to subtract the number of students who play chess from the total number of students who play both checkers and chess.
Given:
Total number of students = 125
Number of students who play checkers and chess = 45
To find the number of students who play checkers, we subtract 45 from the total number of students:
Number of students who play checkers = Total number of students - Number of students who play checkers and chess
Number of students who play checkers = 125 - 45
Number of students who play checkers = 80
Therefore, 80 students in the school play checkers.
3) When identifying all the subsets of a set, we need to consider all possible combinations of the elements in the set.
Given set: {2, 9}
The subsets of a set include the empty set as well as subsets that contain one or both elements of the original set.
Possible subsets of the given set {2, 9} are:
- Empty set: {}
- Subsets with one element: {2}, {9}
- Subsets with both elements: {2, 9}
Therefore, the subsets of {2, 9} are: {}, {2}, {9}, {2, 9}.
4a) To write an inequality that describes the scenario of the cheerleading squad needing to bake at least 120 cookies, we can use the variable "h" to represent the number of hours they must bake.
Given:
Number of cookies made in the first hour = 12
Number of cookies made in the second hour = 24
Total number of cookies needed = 120 (or more)
We can write the inequality as:
12h + 24h ≥ 120
This inequality states that the total number of cookies made in the first hour (12h) combined with the total number of cookies made in the second hour (24h) must be greater than or equal to 120.
4b) To find how many hours the cheerleading squad must work to meet or surpass the goal of baking at least 120 cookies, we solve the inequality from part (a).
12h + 24h ≥ 120
Combine like terms:
36h ≥ 120
Divide both sides by 36:
h ≥ 120/36
Simplify:
h ≥ 10/3
Since we cannot have a fraction of an hour, we round up to the nearest whole number.
Therefore, the cheerleading squad must work at least 4 hours to meet or surpass the goal of baking at least 120 cookies.