1) If N is the set of natural numbers that are factors of 18, represent this set in roster form.
2) Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set and A={1,4,5,9,10} What is A?
3) The wrestling team is holding a car wash. The teams goal is to raise at lease 252 and each car wash cost 5.25.
a) Write an inequality to represent this situation.
4) A student scored a 78 and 93 on his first two assignments respectively. He wants an average between 88 and 90.
a) Write a compound inequality representing the possible values for the a third assignment so his average is between 88 and 90.
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) Well, the factors of 18 are 1, 2, 3, 6, 9, and 18. So, in roster form, the set N would be {1, 2, 3, 6, 9, 18}. It's like having a group of numbers that all get along, cozy in a little roster.
2) Ah, the set A. It's like a party where only certain numbers are invited. In this case, A includes 1, 4, 5, 9, and 10. So, A = {1, 4, 5, 9, 10}. They're the cool kids that make up set A.
3) Ah, the wrestling team's car wash goal. Let's get creative with inequalities! We want to raise at least 252 dollars, and each car wash costs 5.25 dollars. So, the inequality would be 5.25c ≥ 252, where c represents the number of car washes. Let's hope they can wash their way to success!
4) Ah, the student who's aiming for the perfect average. To have an average between 88 and 90, the third assignment should also fall within that range. So, we can write the compound inequality as 88 ≤ (78 + 93 + a)/3 ≤ 90. Here, 'a' represents the score of the third assignment. Keep studying, student!
6) Oh, John and his car show adventure. The distance between John and the car can be represented by the equation d = |2.5 - 4.5t|. To find when the car is 0.5 miles away from John, we can set d = 0.5 and solve for t. So, 0.5 = |2.5 - 4.5t|. Solve for t, and you'll know when John and the car are having a close encounter!
1) To represent the set of natural numbers that are factors of 18 in roster form, we need to determine which numbers divide evenly into 18. The factors of 18 are {1, 2, 3, 6, 9, 18}.
2) In this question, A is a subset of the universal set U. The elements of A are {1, 4, 5, 9, 10}.
3) To write an inequality representing the situation of the wrestling team wanting to raise at least $252, with each car wash costing $5.25, we can use the inequality: 5.25x ≥ 252, where x represents the number of car washes required to reach the goal.
4) To find the third assignment score that would give the student an average between 88 and 90, we can write a compound inequality. Let's assume the third assignment score is represented by x. The average is calculated by (78 + 93 + x) / 3. Therefore, the compound inequality would be: 88 ≤ (78 + 93 + x) / 3 ≤ 90.
6) In this question, the equation given is d = |2.5 - 4.5t|. The distance between John and the car is represented by d. To find the times when the car is 0.5 miles from John, we need to solve the equation |2.5 - 4.5t| = 0.5. Solving this equation will result in specific values of t that correspond to when the distance is 0.5 miles.