Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-15s + 38 + 3(5s - 10) = 0
Question 21 options:
A)
Conditional; {5}
B)
Identity; {all real numbers}
C)
Contradiction; ∅
D)
Conditional; {1}
To determine the solution set for the equation, let's simplify it:
-15s + 38 + 3(5s - 10) = 0
-15s + 38 + 15s - 30 = 0
38 - 30 = 0
8 = 0
Since 8 does not equal 0, this implies that there is no value of s that satisfies the equation. Therefore, the equation is a contradiction, and the solution set is the empty set (∅).
So, the correct answer is:
C)
Contradiction; ∅
Convert.
56 in. = underbar( ) ftunderbar( ) in.
Question 22 options:
A)
4 ft 7 in.
B)
4 ft 8 in.
C)
3 ft 20 in.
D)
8 ft 4 in.
To convert 56 inches to feet and inches, divide the total number of inches by 12.
56 inches ÷ 12 = 4 feet remainder 8 inches
So, 56 inches is equivalent to 4 feet and 8 inches.
The correct answer is:
B)
4 ft 8 in.
Solve.
The tree in the Morton's back yard is 7.8 m tall. Because it blocks too much light, they ask a tree trimmer to remove the top (1/3) of the tree. How tall will the tree be after being shortened?
Question 23 options:
A)
5.2 m
B)
5.1 m
C)
7.5 m
D)
2.6 m
To find the height of the tree after being shortened, we need to subtract 1/3 of the original height from the original height.
Original height of the tree = 7.8 m
1/3 of the original height = 1/3 * 7.8 = 2.6 m
Height of the tree after being shortened = 7.8 - 2.6 = 5.2 m
So, the tree will be 5.2 meters tall after being shortened.
The correct answer is:
A)
5.2 m
Solve the problem. Round to the nearest tenth if necessary.
Enrollment in a business seminar increased from 70 people to 94 people. What was the percent of increase?
Question 24 options:
A)
65.7%
B)
25.5%
C)
74.5%
D)
34.3%
To find the percent increase, we need to find the difference between the final enrollment and the initial enrollment, then divide that difference by the initial enrollment, and finally multiply by 100.
Initial enrollment = 70
Final enrollment = 94
Difference = Final enrollment - Initial enrollment = 94 - 70 = 24
Percent increase = (Difference / Initial enrollment) * 100 = (24 / 70) * 100 ≈ 34.3%
So, the percent of increase is approximately 34.3%.
The correct answer is:
D)
34.3%
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
4(24t + 16) = 16(2t - 4)
Question 25 options:
A)
Conditional; {-0}
B)
Conditional; {-2}
C)
Contradiction; ∅
D)
Identity; {all real numbers}
To determine the solution set for the equation, let's simplify it:
4(24t + 16) = 16(2t - 4)
96t + 64 = 32t - 64
96t - 32t = -64 - 64
64t = -128
t = -128/64
t = -2
So, the equation is conditional and the solution set is:
A)
Conditional; {-2}
Use dimensional analysis to convert the unit indicated.
6 m to ft
Question 26 options:
A)
6.7 ft
B)
19.7 ft
C)
5.4 ft
D)
1.8 ft