1. Which number is a solution of the inequality?
10.6<b
A)-18
B)-9
C)7
D)14***
2. Which number is a solution of the inequality?
y+2>8
A)-5
B)-6
C)6***
D)7
3. Which number is a solution of the inequality?
12 < y ( 8 - y )
A. 0
B. 1
C. 2
D. 3***
4. If N is the set of natural numbers that are factors of 24, choose the selection below that correctly shows this set in roster form.
A. {1,2,4,8,16,20,24}
B. {2,4,6,8,10,12,14,16,18,20,22,24}
C. {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}
D. {1,2,3,4,6,8,12,24}***
5. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set, and P = {2, 4, 6, 8, 10}. What is p'?
A. ( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
B. ( 3, 5, 7, 9)
C. ( 1, 3, 5, 7, 9)**
D. ( 2, 4, 8)
I believe your answers are right.
1. D) 14 is a solution of the inequality 10.6 < b.
2. C) 6 is a solution of the inequality y + 2 > 8.
3. D) 3 is a solution of the inequality 12 < y (8 - y).
4. D) {1,2,3,4,6,8,12,24} is the set of natural numbers that are factors of 24 in roster form.
5. C) (1, 3, 5, 7, 9) is the complement of set P in the universal set U.
1. To find the solution to the inequality 10.6 < b, we need to compare each answer choice to the inequality.
A) -18: 10.6 < -18 is not true.
B) -9: 10.6 < -9 is not true.
C) 7: 10.6 < 7 is not true.
D) 14: 10.6 < 14 is true.
Therefore, the correct answer is D) 14.
2. To find the solution to the inequality y + 2 > 8, we need to compare each answer choice to the inequality.
A) -5: -5 + 2 > 8 is not true.
B) -6: -6 + 2 > 8 is not true.
C) 6: 6 + 2 > 8 is true.
D) 7: 7 + 2 > 8 is true.
Therefore, the correct answer is C) 6.
3. To find the solution to the inequality 12 < y(8 - y), we can start by expanding the product on the right side of the inequality:
12 < 8y - y^2.
Next, we can rearrange the inequality to have a quadratic expression equal to zero:
y^2 - 8y + 12 > 0.
Now, we can solve this quadratic inequality by factoring or using the quadratic formula. The factors of 12 that add up to -8 are -2 and -6, so the inequality can be factored as:
(y - 2)(y - 6) > 0.
To determine the solution, we need to analyze the signs within the intervals defined by the zeros of the factored expression:
Intervals: (-∞, 2), (2, 6), (6, ∞).
Testing a value within each interval will allow us to determine the sign of the expression:
For example, for the interval (2, 6), we can test y = 4:
(4 - 2)(4 - 6) > 0, which simplifies to 2(-2) > 0, which is true.
Based on this analysis, we can conclude that the values that satisfy the inequality are in the intervals (2, 6).
Among the answer choices:
A) 0: 12 < 0 is not true.
B) 1: 12 < 1(8 - 1) simplifies to 12 < 7, which is not true.
C) 2: 12 < 2(8 - 2) simplifies to 12 < 12, which is not true.
D) 3: 12 < 3(8 - 3) simplifies to 12 < 15, which is not true.
Therefore, the correct answer is D) 3.
4. To find the set of natural numbers that are factors of 24, we need to identify all the numbers that divide 24 without leaving a remainder.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
Among the answer choices:
A) {1,2,4,8,16,20,24}: This set includes numbers that are not factors of 24, such as 16 and 20.
B) {2,4,6,8,10,12,14,16,18,20,22,24}: This set includes numbers that are not factors of 24, such as 6, 10, 14, 16, 18, 20, and 22.
C) {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}: This set includes numbers that are not factors of 24, such as 3, 5, 7, 11, 13, 15, 17, 19, 21, 23.
D) {1,2,3,4,6,8,12,24}: This set includes all the factors of 24.
Therefore, the correct answer is D) {1,2,3,4,6,8,12,24}.
5. To find p', which represents the complement of set P, we need to find all the elements in the universal set U that are not in P.
The universal set U is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set P is {2, 4, 6, 8, 10}.
To find p', we simply list all the elements in U that are not in P: {1, 3, 5, 7, 9}.
Therefore, the correct answer is C) {1, 3, 5, 7, 9}.