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.
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?
6) John is at a car show. Beginning 2.5 miles away, a car traveling at a constant 45 miles per hour approaches and then passes John. The distance between John and the car can be represented by the equation d=/2.5-4.5t/. at what times is the car 0.5 miles from john?
1) To represent all the different pets stores in the town, we can create a set which includes both pet stores. The first pet store has dogs, cats, and hamsters, while the second pet store has dogs, rabbits, and fish. Therefore, the set representing all the different pets in the town would be:
{dogs, cats, hamsters, rabbits, fish}
4) a) To write an inequality that describes the scenario, we need to express the condition that the number of cookies baked must be at least or greater than 120. Let's use variable "h" to represent the number of hours they must bake.
The inequality would be: 12h + 24h ≥ 120
b) To find out how many hours they must work to meet or surpass the goal, we need to solve the inequality.
12h + 24h ≥ 120 can be simplified as:
36h ≥ 120
Dividing both sides of the inequality by 36, we get:
h ≥ 120/36
Simplifying further, we get:
h ≥ 10/3
Therefore, they must work at least 10/3 (or 3.33) hours to meet or surpass the goal.
6) The equation d=(2.5-4.5t) represents the distance between John and the car, where "t" represents time (in hours). To find the times when the car is 0.5 miles from John, we need to set the equation equal to 0.5 and solve for "t".
Setting d = 0.5, we have:
0.5 = 2.5 - 4.5t
Rearranging the equation, we get:
4.5t = 2.5 - 0.5
Simplifying further, we have:
4.5t = 2
Dividing both sides by 4.5, we get:
t = 2/4.5
Simplifying the fraction, we have:
t ≈ 0.444
Therefore, the car is approximately 0.5 miles from John at around 0.444 hours (or 26.67 minutes) after it starts approaching John.