Problem 21 :
A sidewalk in the shape of two triangles, a rectangle, and a square was built around the edge of a building as shown.
What is the area of the sidewalk in square feet?
A. 108 ft^{2 }B. 162 ft^{2 }C. 144 ft^{2 }D. 180 ft^{2}
Solution:
The area of the bottom square A = S^{2}
A = 6²
A = 36 ft²
So, the area of the sidewalk = 144 + 36
= 180 ft²
So, option (D) is correct.
Problem 22 :
The price of a computer is $899.00. The sales tax rate is 7%. What is the sales tax on this computer in dollars and cents?
Solution:
Given, price = $899
Tax rate = 7% = 0.07
Sales tax = 899 × 0.07
= $62.93
Hence, the sales tax on this computer in 62 dollars and 93 cents.
Problem 23 :
An online game increases in number of users at a rate of 500 users each day. Which graph best represents the relationship between y, the number of users and x, the number of days?
Solution:
In option D,
2 days = 1000 users
4 days = 2000 users
1 day = 2000/4
1 day = 500 users
So, option D is correct.
Problem 24 :
The radius of circle S is half the radius of circle L. The radius of circle L is 8 millimeters.
Which measurement is closest to the area of circle S in square millimeters?
A. 50.24 mm^{2 }B. 25.12 mm^{2 }C. 200.96 mm^{2}
D.12.56 mm^{2}
Solution:
The radius of circle S is 4 mm.
Area of circle = πr^{2}
= 3.14 × 4 × 4
= 50.24 mm²
So, option (A) is correct.
Problem 25 :
Which situation is best represented by the following equation?
68.50x + 127.95 = 675.95
A. An office manager paid $675.95 to build a web site. The office manager bought a software package for $68.50 and paid an employee $127.95 for each hour she worked on the website. What is x, the number of hours the employee worked on the website?
B. An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is x, the number of hard drives the office manager bought?
C. A sales manager paid $675.95 for advertising. The sales manager paid $127.95 per hour for consulting and received a $68.50 discount. What is x, the number of hours the manager paid for consulting?
D. A business owner paid a total of $675.95 for two employees to work the same number of days. The business owner paid one employee $68.50. The business paid a second employee $127.95 per day. What is x, the number of days the employees worked?
Solution :
Option B is correct.
Problem 26 :
Regina has three number cubes. The faces of each number cube are numbered from 1 to 6. Regina will roll each number cube one time.
What is the probability that all three number cubes will land on an odd number?
Solution:
Number of cubes = 3
Sections on each cube = 6
Odd sections on each cube = 3
For the three cubes, we have
P(All odd) = P(odd)^Number of cubes
Hence, the probability is 1/8.
So, option (D) is correct.
Problem 27 :
What is the solution set for this inequality?
Solution:
So, option (A) is correct.
Problem 28 :
The net of a triangular prism and its approximate dimensions are shown in the diagram.
Which measurement is closest to the total surface area of the triangular prism in square inches?
A. 268.8 in^{2 }B. 432 in^{2 }C. 288 in^{2 }D. 393.6 in^{2}
Solution:
Given that, sides of triangular base
b_{1} = 12 in, b_{2} = 12 in, b_{3} = 12 in
Height = 10.4 in, Base = 12 in, Length = 4 in
Total surface area of triangular prism SA = bh + (b_{1} + b_{2} + b_{3})
SA = 12 × 10.4 + (12 + 12 + 12) × 4
SA = 124.8 + 144
SA = 268.8 in^{2}
So, option (A) is correct.
Problem 29 :
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table.
What percentage of these customers put chocolate creamer in their coffee during this hour?
A. 30% B. 14% C. 70% D. 75%
Solution:
Total number of customers = 2 + 4 + 6 + 8 = 20
Number of customers who put chocolate creamer
= 6 + 8 = 14
So, option (C) is correct.
Problem 30 :
An engineer created a scale drawing of a building using a scale in which 0.25 inch represents 2 feet. The length of the actual building is 250 feet.
What is the length in inches of the building in the scale drawing?
Solution:
If 0.25 inches = 2 feet
Then x inches = 250 feet
Cross multiply,
x × 2 = 0.25 × 2500
2x = 62.5
x = 62.5/2
x = 31.25 inches
Thus, the length of the building in the scale drawing is 31.25 inches.
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