The U.S. Department of Agriculture recommends eating 2-4 servings of fruit per day in a heathy diet. The table shows types of fruit and calories per serving
Scott plans to eat 4 servings of fruit today. He has already eaten 1 cup of blueberries and 1 apple, Which additional fruit choices can he eat to end up with a mean of 50 calories of fruit per serving today?
- A. 1 plum and 1 tangerine
- B. 1 banana and 1 mandarin orange
- C. 1 cup of blueberries and 1 banana
- D. 1 apple and 1 plum
Correct Answer & Rationale
Correct Answer: A
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
Other Related Questions
The distance, d, in feet, it takes to come to a complete stop when driving a car r miles per hour can be found using the equation d = 1/20(r^2)+ r. If it takes a car 240 feet to come to a complete stop, what was the speed of the car, in miles per hour, when the driver began to stop it?
- A. 40
- B. 30
- C. 60
- D. 80
Correct Answer & Rationale
Correct Answer: A
To find the speed of the car when it takes 240 feet to stop, substitute d = 240 into the equation d = 1/20(r^2) + r. This leads to the equation 240 = 1/20(r^2) + r. Multiplying through by 20 simplifies to 4800 = r^2 + 20r, which rearranges to r^2 + 20r - 4800 = 0. Solving this quadratic equation yields r = 40 or r = -120. Since speed cannot be negative, the valid solution is 40 mph. Option B (30) does not satisfy the equation, leading to a shorter stopping distance. Option C (60) results in a stopping distance of 480 feet, which exceeds 240 feet. Option D (80) produces a stopping distance of 800 feet, also incorrect. Thus, only 40 mph meets the criteria.
To find the speed of the car when it takes 240 feet to stop, substitute d = 240 into the equation d = 1/20(r^2) + r. This leads to the equation 240 = 1/20(r^2) + r. Multiplying through by 20 simplifies to 4800 = r^2 + 20r, which rearranges to r^2 + 20r - 4800 = 0. Solving this quadratic equation yields r = 40 or r = -120. Since speed cannot be negative, the valid solution is 40 mph. Option B (30) does not satisfy the equation, leading to a shorter stopping distance. Option C (60) results in a stopping distance of 480 feet, which exceeds 240 feet. Option D (80) produces a stopping distance of 800 feet, also incorrect. Thus, only 40 mph meets the criteria.
A scale drawing of a truck has a length of 3 inches (in.), as shown below. The actual truck has a length of 18 feet (ft). What scale was used for the drawing?
- A. 6 in. = 1 ft
- B. 1 in. = 15 ft
- C. 1 in. = 6 ft
- D. 15 in. = 1 ft
Correct Answer & Rationale
Correct Answer: C
To determine the scale used for the drawing, we first convert the actual truck length from feet to inches. Since 1 foot equals 12 inches, an 18-foot truck is 216 inches long (18 ft x 12 in/ft). The scale drawing shows a length of 3 inches. To find the scale, we set up the ratio of the drawing length to the actual length: 3 in. (drawing) to 216 in. (actual). Simplifying this gives us a scale of 1 in. = 72 in., which translates to 1 in. = 6 ft (since 72 in. ÷ 12 in/ft = 6 ft). Option A (6 in. = 1 ft) is incorrect; it implies a much larger drawing. Option B (1 in. = 15 ft) underestimates the actual size. Option D (15 in. = 1 ft) greatly exaggerates the scale, making the drawing too small.
To determine the scale used for the drawing, we first convert the actual truck length from feet to inches. Since 1 foot equals 12 inches, an 18-foot truck is 216 inches long (18 ft x 12 in/ft). The scale drawing shows a length of 3 inches. To find the scale, we set up the ratio of the drawing length to the actual length: 3 in. (drawing) to 216 in. (actual). Simplifying this gives us a scale of 1 in. = 72 in., which translates to 1 in. = 6 ft (since 72 in. ÷ 12 in/ft = 6 ft). Option A (6 in. = 1 ft) is incorrect; it implies a much larger drawing. Option B (1 in. = 15 ft) underestimates the actual size. Option D (15 in. = 1 ft) greatly exaggerates the scale, making the drawing too small.
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Based on the scatter plot, what is the range of ages of the top 10 runners?
- A. 9
- B. 1
- C. 16
- D. 40
Correct Answer & Rationale
Correct Answer: C
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.
The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
- A. 36
- B. 16
- C. 40
- D. 13
Correct Answer & Rationale
Correct Answer: A
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.