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. 18 = 1*18 = 1*2*9 = 1*2*3*3.
Factors: N = {1,2,3,9,18}.
3a. 5.25x => 252
4a. Inequality: 88 < (78+93+x)/3 < 90
264 < 171 + x < 270
93 < X < 99
The inequality says: (78+93+x)/3 is
greater than 88 but less than 90.
1) To find the set of natural numbers that are factors of 18, we need to list all the numbers that divide 18 evenly. The factors of 18 are 1, 2, 3, 6, 9, and 18. Therefore, we can represent this set in roster form as N = {1, 2, 3, 6, 9, 18}.
2) In this question, we are given a universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and a set A = {1, 4, 5, 9, 10}. Set A consists of the elements from the universal set U that are also present in A. Therefore, A = {1, 4, 5, 9, 10}.
3) To represent the situation of the wrestling team trying to raise at least 252 dollars with each car wash costing 5.25 dollars, we can use an inequality. Let's assume the number of car washes conducted is represented by x. Since each car wash costs 5.25 dollars, the total amount raised can be calculated as 5.25x. And we want this amount to be at least 252. Therefore, the inequality representing this situation is 5.25x ≥ 252.
4) In this question, the student has scored 78 and 93 on his first two assignments respectively. To find the possible values for the third assignment so that his average is between 88 and 90, we need to find the average of the three assignments and represent it as a compound inequality. Let's assume the score for the third assignment is represented by x. The average between 88 and 90 is (88+90)/2 = 89. To find the average of the three assignments, we calculate (78+93+x)/3. Therefore, the compound inequality representing the possible values for the third assignment is (78+93+x)/3 ≥ 88 and (78+93+x)/3 ≤ 90.
5) To determine the time at which the car is 0.5 miles from John, we can use the given equation d = |2.5-4.5t|. Here, d represents the distance between John and the car, and t represents time. We need to find the values of t when d is equal to 0.5 miles. Therefore, we can set up the equation |2.5-4.5t| = 0.5 and solve for t. By solving this equation, you can find the times at which the car is 0.5 miles from John.