Which of the following expressions represents the sum of three times a number and eight times a different number?
A: 3x + 8x
B: 3x + 8y
C: 8x - 3y
D: 3x - 8y
Correct Answer: B
Rationale: To represent the sum of three times a number and eight times a different number, you need to use the multiplication factors with the correct variables. Three times a number is 3x, and eight times a different number is 8y. Therefore, the correct expression is 3x + 8y, making choice B the correct answer.
Question 2:
The length of a rectangle is 3 units greater than its width. Which expression correctly represents the perimeter of the rectangle?
A: W(w+3)
B: 2w+2(w+3)
C: 2w+2(3w)
D: W+w+3
Correct Answer: B
Rationale: To find the perimeter of a rectangle, you add the lengths of all sides. In this case, the length is 3 units greater than the width. Therefore, the correct expression for the perimeter is 2w + 2(w+3), which simplifies to 4w + 6 or 2(2w + 3). This represents the sum of the two widths and two lengths of the rectangle.
Question 3:
A homeowner has hired two people to mow his lawn. If person A is able to mow the lawn in 2 hours by herself and person B is able to mow the lawn in 3 hours by himself, how long would it take both person A and person B to mow the lawn together?
A: 5 hours
B: 1 hour
C: 2.5 hours
D: 1.2 hours
Correct Answer: D
Rationale: To find the combined time it takes for both A and B to mow the lawn together, we use the formula: 1/(1/A + 1/B), where A and B are the individual times taken by each person. Substituting the values for A = 2 hours and B = 3 hours into the formula: 1/(1/2 + 1/3) = 1/(5/6) = 6/5 = 1.2 hours. Therefore, it would take both person A and person B 1.2 hours to mow the lawn together.
Question 4:
What is the metric equivalent of 7 inches in measurements used for appointments?
A: 3.2 cm
B: 17.8 cm
C: 15.4 cm
D: 2.8 cm
Correct Answer: B
Rationale: To convert inches to centimeters, you can use the conversion factor that 1 inch is equal to 2.54 centimeters. Therefore, 7 inches is equivalent to 7 * 2.54 = 17.78 cm, which is closest to 17.8 cm (Choice B). This conversion is commonly used in various fields to provide accurate measurements across different systems.
Question 5:
The table shows healthcare spending per capita in a group of African nations. Based on this information, which of the following countries had the greatest change in dollars spent per capita from 2013 to 2015?
A: Eritrea 2013 ($56), 2015 ($42)
B: Nigeria 2013 ($16), 2015 ($21)
C: Tanzania 2013 ($68), 2015 ($8)
D: Kenya 2013 ($81), 2015 ($88)
Correct Answer: C
Rationale: To find the country with the greatest change in healthcare spending per capita, we calculate the difference between the spending in 2015 and 2013 for each country. For Tanzania, the spending went down from $68 in 2013 to $8 in 2015, resulting in the largest decrease in dollars spent per capita among the options provided. Therefore, the correct answer is C, Tanzania.
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