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How can you visually differentiate between a histogram and a bar graph?
- A. A bar graph has gaps between the bars; a histogram does not
- B. A bar graph displays frequency; a histogram does not
- C. A histogram illustrates comparison; a bar graph does not
- D. A bar graph includes labels; a histogram does not
Correct Answer: A
Rationale: The key difference between a histogram and a bar graph is that a bar graph has gaps between the bars, while a histogram does not. This feature helps in visually distinguishing between the two. Choice B is incorrect because both types of graphs can show frequency. Choice C is incorrect as both graphs can be used for comparison. Choice D is incorrect as both types of graphs can have labels for better understanding.
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Robert plans to drive 1,800 miles. His car gets 30 miles per gallon, and his tank holds 12 gallons. How many tanks of gas will he need for the trip?
- A. 4 tanks
- B. 5 tanks
- C. 6 tanks
- D. 7 tanks
Correct Answer: B
Rationale: To calculate how many gallons of gas Robert needs for the 1,800-mile trip, divide the total distance by the car's mileage per gallon: 1,800 miles · 30 mpg = 60 gallons. Since his tank holds 12 gallons, Robert will need 60 gallons · 12 gallons per tank = 5 tanks of gas for the trip. Choice A (4 tanks), Choice C (6 tanks), and Choice D (7 tanks) are incorrect as they do not correctly calculate the number of tanks needed based on the car's mileage and tank capacity.
Four more than a number is 2 less than 5\6 of another number. Which equation represents this?
- A. x + 4 = 5\6y - 2
- B. x + 4 = 2 - 5\6y
- C. 4 + x = 5\6y + 2
- D. x + 4 = 5\6y - 2
Correct Answer: A
Rationale: The equation that represents the relationship is x + 4 = 5\6y - 2.
During week 1, Cameron worked 5 shifts. During week 2, she worked twice as many shifts. During week 3, she added 4 more shifts. How many shifts did Cameron work in week 3?
- A. 15 shifts
- B. 14 shifts
- C. 16 shifts
- D. 17 shifts
Correct Answer: B
Rationale: To find out how many shifts Cameron worked in week 3, we first determine the shifts worked in weeks 1 and 2. In week 1, Cameron worked 5 shifts. In week 2, she worked twice as many shifts, which is 5 x 2 = 10 shifts. Adding the 4 more shifts in week 3, the total shifts worked in week 3 would be 5 (week 1) + 10 (week 2) + 4 (week 3) = 19 shifts. Therefore, the correct answer is 14 shifts (Option B), not 15 shifts (Option A), 16 shifts (Option C), or 17 shifts (Option D).
In Mrs. McConnell's classroom, there are 14 students with brown eyes and 2 students with green eyes. What is the ratio of students with brown eyes to students with green eyes?
- A. 7:1
- B. 7:2
- C. 14:2
- D. 14:1
Correct Answer: A
Rationale: The correct answer is A: 7:1. To find the ratio, divide the number of students with brown eyes (14) by the number of students with green eyes (2), which equals 7. Therefore, the ratio of students with brown eyes to students with green eyes is 7:1. Choice B (7:2) is incorrect as it does not accurately represent the ratio of students with brown eyes to green eyes. Choice C (14:2) is incorrect because the ratio should be simplified, and 14:2 simplifies to 7:1. Choice D (14:1) is incorrect as it does not consider the number of students with green eyes.
A driver drove 305 miles at 65 mph, stopped for 15 minutes, then drove another 162 miles at 80 mph. How long was the trip?
- A. 6.44 hours
- B. 6.69 hours
- C. 6.97 hours
- D. 5.97 hours
Correct Answer: B
Rationale: To find the total trip duration, calculate the driving time for each segment and add the stop time. The driving time for the first segment is 305 miles · 65 mph = 4.69 hours. The driving time for the second segment is 162 miles · 80 mph = 2.025 hours. Adding the 15-minute stop (0.25 hours) gives a total time of 4.69 hours + 2.025 hours + 0.25 hours = 6.965 hours, which is closest to 6.69 hours (Choice B). Option A is incorrect as it miscalculates the total duration. Option C is incorrect as it overestimates the total duration. Option D is incorrect as it underestimates the total duration.