The recommended dosage of a medicine is 4 milligrams per kilogram of body weight. What is the recommended dosage, in milligrams, for a person who weighs 84 kilograms?
- A. 21
- B. 88
- C. 324
- D. 336
- E. 2100
Correct Answer & Rationale
Correct Answer: D
To determine the recommended dosage for a person weighing 84 kilograms, multiply their weight by the dosage per kilogram: 4 mg/kg × 84 kg = 336 mg. Option A (21 mg) is incorrect as it significantly underestimates the dosage based on the weight. Option B (88 mg) also miscalculates the dosage, failing to apply the correct multiplication. Option C (324 mg) is close but still incorrect, as it does not reflect the accurate calculation. Option E (2100 mg) is far too high, indicating a misunderstanding of the dosage per kilogram. Thus, 336 mg is the correct dosage for the individual.
To determine the recommended dosage for a person weighing 84 kilograms, multiply their weight by the dosage per kilogram: 4 mg/kg × 84 kg = 336 mg. Option A (21 mg) is incorrect as it significantly underestimates the dosage based on the weight. Option B (88 mg) also miscalculates the dosage, failing to apply the correct multiplication. Option C (324 mg) is close but still incorrect, as it does not reflect the accurate calculation. Option E (2100 mg) is far too high, indicating a misunderstanding of the dosage per kilogram. Thus, 336 mg is the correct dosage for the individual.
Other Related Questions
The volume of 1 cup of water is 14.4 cubic inches. The diameter of an empty cylindrical can is 3.0 inches. The can holds 2.0 cups of water. What is the height of the can, to the nearest 0.1 inch?
- A. 1
- B. 2
- C. 3.1
- D. 4.1
- E. 6.2
Correct Answer & Rationale
Correct Answer: D
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
Which of the following equations does not represent y as a function of x in the standard (x, y) coordinate plane?
- A. y = x
- B. y = x + 2
- C. y = x² + 2
- D. x = y + 2
- E. x = y² + 2
Correct Answer & Rationale
Correct Answer: E
Option E, \( x = y^2 + 2 \), does not represent \( y \) as a function of \( x \) because it can yield multiple \( y \) values for a single \( x \) value. For example, when \( x = 6 \), \( y \) can be either 2 or -2, violating the definition of a function. In contrast, options A, B, and C express \( y \) explicitly in terms of \( x \), allowing only one output for each input. Option D, while rearranging the equation, can also be transformed into a function of \( y \) in terms of \( x \) (i.e., \( y = x - 2 \)). Thus, options A, B, C, and D all represent \( y \) as a function of \( x \).
Option E, \( x = y^2 + 2 \), does not represent \( y \) as a function of \( x \) because it can yield multiple \( y \) values for a single \( x \) value. For example, when \( x = 6 \), \( y \) can be either 2 or -2, violating the definition of a function. In contrast, options A, B, and C express \( y \) explicitly in terms of \( x \), allowing only one output for each input. Option D, while rearranging the equation, can also be transformed into a function of \( y \) in terms of \( x \) (i.e., \( y = x - 2 \)). Thus, options A, B, C, and D all represent \( y \) as a function of \( x \).
One online movie-streaming service costs $8 per month and charges $1.50 per movie. A second service costs $2 per month and charges $2 per movie. For what number of movies per month is the monthly cost of both services the same?
- A. 3
- B. 6
- C. 5
- D. 12
- E. 20
Correct Answer & Rationale
Correct Answer: D
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
To determine when the costs of both services are equal, we can set up equations based on the monthly fees and per-movie charges. For the first service: Cost = $8 + $1.50 * number of movies (m) Cost = $8 + 1.5m For the second service: Cost = $2 + $2 * number of movies (m) Cost = $2 + 2m Setting the two equations equal gives us: $8 + 1.5m = $2 + 2m Rearranging leads to: $6 = 0.5m m = 12 Thus, when 12 movies are rented, the costs are equal. Options A (3), B (6), and C (5) yield different costs, as they do not satisfy the equation. Option E (20) results in a higher cost for the second service, confirming that 12 is the only solution where both services cost the same.
Jasmine’s pace for a 3-mile race is 1 minute per mile faster than her pace for a 13-mile race. She ran the 3-mile race in 21 minutes. How many minutes will it take her to run the 13-mile race?
- A. 34
- B. 78
- C. 92
- D. 101
- E. 104
Correct Answer & Rationale
Correct Answer: E
Jasmine completed the 3-mile race in 21 minutes, which gives her a pace of 7 minutes per mile (21 minutes ÷ 3 miles). Since her pace for the 13-mile race is 1 minute slower, her pace for that race is 8 minutes per mile. To find the time for the 13-mile race, multiply her 13-mile pace by the distance: 8 minutes/mile × 13 miles = 104 minutes. Options A (34), B (78), C (92), and D (101) all reflect incorrect calculations or misunderstandings of her pacing difference and distance, leading to values that do not align with the established pace of 8 minutes per mile.
Jasmine completed the 3-mile race in 21 minutes, which gives her a pace of 7 minutes per mile (21 minutes ÷ 3 miles). Since her pace for the 13-mile race is 1 minute slower, her pace for that race is 8 minutes per mile. To find the time for the 13-mile race, multiply her 13-mile pace by the distance: 8 minutes/mile × 13 miles = 104 minutes. Options A (34), B (78), C (92), and D (101) all reflect incorrect calculations or misunderstandings of her pacing difference and distance, leading to values that do not align with the established pace of 8 minutes per mile.