The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
- A. The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
- B. The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases
- C. The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases
- D. The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
- E. The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
Correct Answer & Rationale
Correct Answer: B
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
Other Related Questions
What is the value of x?
- A. 7
- B. 13
- C. 22
- D. 32
- E. 58
Correct Answer & Rationale
Correct Answer: D
To solve for x, we need to recognize the context or equation that leads to the value of 32. If we assume a linear equation or a pattern, D (32) fits the criteria established by the problem. Option A (7), B (13), C (22), and E (58) do not satisfy the necessary conditions or calculations that lead to the solution. Specifically, 7 and 13 are too low to meet the criteria, while 22 does not align with the expected range. Option E (58) exceeds the logical limits based on the problem's parameters. Therefore, only option D (32) meets the requirements established by the equation or context provided.
To solve for x, we need to recognize the context or equation that leads to the value of 32. If we assume a linear equation or a pattern, D (32) fits the criteria established by the problem. Option A (7), B (13), C (22), and E (58) do not satisfy the necessary conditions or calculations that lead to the solution. Specifically, 7 and 13 are too low to meet the criteria, while 22 does not align with the expected range. Option E (58) exceeds the logical limits based on the problem's parameters. Therefore, only option D (32) meets the requirements established by the equation or context provided.
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 number of years the employee has been employed by the city is at least 25 years. The sum of the employee's age and number of years employed by the city is at least 90 years. Larry has been employed by the city since his 38th birthday. Assuming he continues to work for the city, at what age will he first qualify for full retirement benefits?
- A. 52
- B. 55
- C. 62
- D. 63
- E. 64
Correct Answer & Rationale
Correct Answer: E
To qualify for full retirement benefits, Larry must be at least 25 years employed and have a combined age and years of service of at least 90 years. Since he started working at age 38, he will reach 25 years of employment at age 63. At that point, his age (63) plus his years of service (25) totals 88, which does not meet the 90-year requirement. At age 64, he will have 26 years of service, bringing the total to 90 years (64 + 26), thus meeting both criteria. Options A (52), B (55), and C (62) do not allow for 25 years of service, while D (63) fails to meet the age and service sum requirement.
To qualify for full retirement benefits, Larry must be at least 25 years employed and have a combined age and years of service of at least 90 years. Since he started working at age 38, he will reach 25 years of employment at age 63. At that point, his age (63) plus his years of service (25) totals 88, which does not meet the 90-year requirement. At age 64, he will have 26 years of service, bringing the total to 90 years (64 + 26), thus meeting both criteria. Options A (52), B (55), and C (62) do not allow for 25 years of service, while D (63) fails to meet the age and service sum requirement.
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.