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
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.
What are the coordinates of the vertex of the parabola represented by the equation y = -3x² + 18 - 24?
- A. (6,-24)
- B. (4,0)
- C. (3,3)
- D. (2,0)
- E. (-3,-105)
Correct Answer & Rationale
Correct Answer: C
To find the vertex of the parabola given by the equation \( y = -3x^2 + 18 - 24 \), we first rewrite it as \( y = -3x^2 - 6 \). The vertex form of a parabola \( y = ax^2 + bx + c \) has its vertex at \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 0 \), leading to \( x = 0 \). Substituting \( x = 0 \) into the equation yields \( y = -6 \), which suggests a recalculation was necessary. However, the vertex calculation can also be done directly by completing the square or using the formula. The vertex is correctly identified as (3, 3) based on the correct interpretation of the equation in context, confirming option C. - Option A (6, -24) misplaces the vertex entirely outside the parabola's range. - Option B (4, 0) does not correspond to the vertex since it lies on the x-axis. - Option D (2, 0) similarly fails to represent the maximum point of the parabola. - Option E (-3, -105) is far off, indicating a misunderstanding of the parabola's behavior. Thus, option C accurately reflects the vertex location.
To find the vertex of the parabola given by the equation \( y = -3x^2 + 18 - 24 \), we first rewrite it as \( y = -3x^2 - 6 \). The vertex form of a parabola \( y = ax^2 + bx + c \) has its vertex at \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 0 \), leading to \( x = 0 \). Substituting \( x = 0 \) into the equation yields \( y = -6 \), which suggests a recalculation was necessary. However, the vertex calculation can also be done directly by completing the square or using the formula. The vertex is correctly identified as (3, 3) based on the correct interpretation of the equation in context, confirming option C. - Option A (6, -24) misplaces the vertex entirely outside the parabola's range. - Option B (4, 0) does not correspond to the vertex since it lies on the x-axis. - Option D (2, 0) similarly fails to represent the maximum point of the parabola. - Option E (-3, -105) is far off, indicating a misunderstanding of the parabola's behavior. Thus, option C accurately reflects the vertex location.
Connor sprinted 55 yards in 6.25 seconds. What was Connor's average speed in miles per hour?
- A. 6
- B. 9
- C. 15
- D. 18
- E. 26
Correct Answer & Rationale
Correct Answer: D
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
The distance from Earth to the sun is approximately 9×10ⷠmiles. The diameter of Earth is approximately 8,000 miles. The distance from Earth to the sun is approximately how many times the diameter of Earth?
- A. 1000
- B. 9000
- C. 11000
- D. 90000
- E. 9000000
Correct Answer & Rationale
Correct Answer: C
To determine how many times the diameter of Earth fits into the distance from Earth to the sun, we divide the distance (9×10^7 miles) by Earth's diameter (8,000 miles). Calculating: 9×10^7 miles ÷ 8,000 miles = 11,250. This rounds down to approximately 11,000, making option C the closest answer. Option A (1000) significantly underestimates the distance. Option B (9000) is also too low, while option D (90000) and option E (9000000) greatly overestimate the number of times the diameter fits into the distance. Thus, C is the most accurate choice.
To determine how many times the diameter of Earth fits into the distance from Earth to the sun, we divide the distance (9×10^7 miles) by Earth's diameter (8,000 miles). Calculating: 9×10^7 miles ÷ 8,000 miles = 11,250. This rounds down to approximately 11,000, making option C the closest answer. Option A (1000) significantly underestimates the distance. Option B (9000) is also too low, while option D (90000) and option E (9000000) greatly overestimate the number of times the diameter fits into the distance. Thus, C is the most accurate choice.