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.
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.
A temperature of F degrees Fahrenheit will be converted to C degrees Celsius. Given F = 9/5C + 32, which of the following expressions represents that temperature in degrees Celsius?
- A. 5/9(F-32)
- B. 5/9F-32
- C. 9/5(F-32)
- D. 9/5(F+32)
- E. 9/5F+32
Correct Answer & Rationale
Correct Answer: A
To convert Fahrenheit (F) to Celsius (C), the formula is rearranged from F = 9/5C + 32 to isolate C. Starting with F = 9/5C + 32, subtracting 32 from both sides gives F - 32 = 9/5C. Multiplying both sides by 5/9 yields C = 5/9(F - 32), which matches option A. Option B (5/9F - 32) incorrectly places 32 outside the parentheses, misrepresenting the conversion. Option C (9/5(F - 32)) incorrectly applies the conversion factor, while D (9/5(F + 32)) and E (9/5F + 32) misapply the formula entirely by not correctly isolating C.
To convert Fahrenheit (F) to Celsius (C), the formula is rearranged from F = 9/5C + 32 to isolate C. Starting with F = 9/5C + 32, subtracting 32 from both sides gives F - 32 = 9/5C. Multiplying both sides by 5/9 yields C = 5/9(F - 32), which matches option A. Option B (5/9F - 32) incorrectly places 32 outside the parentheses, misrepresenting the conversion. Option C (9/5(F - 32)) incorrectly applies the conversion factor, while D (9/5(F + 32)) and E (9/5F + 32) misapply the formula entirely by not correctly isolating C.
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.
Isabel earns $15.80 per hour for the first 8 hours she works each day. She earns 1.5 times her hourly rate for all time after the first 8 hours. How much does Isabel earn on a day when she works 8.5 hours?
- A. 126.4
- B. 138.25
- C. 189.6
- D. 201.45
- E. 237
Correct Answer & Rationale
Correct Answer: B
To determine Isabel's earnings for an 8.5-hour workday, first calculate her earnings for the first 8 hours at $15.80 per hour, which totals $126.40 (8 hours × $15.80/hour). For the additional 0.5 hours, she earns 1.5 times her hourly rate, which is $23.70 (1.5 × $15.80). Therefore, for the extra half hour, she earns $11.85 (0.5 hours × $23.70/hour). Adding these amounts together gives $138.25 ($126.40 + $11.85). Option A ($126.40) only accounts for the first 8 hours. Option C ($189.60) incorrectly assumes full-time pay without considering the overtime rate. Option D ($201.45) miscalculates the overtime pay, while Option E ($237) overestimates by not applying the correct hourly rates.
To determine Isabel's earnings for an 8.5-hour workday, first calculate her earnings for the first 8 hours at $15.80 per hour, which totals $126.40 (8 hours × $15.80/hour). For the additional 0.5 hours, she earns 1.5 times her hourly rate, which is $23.70 (1.5 × $15.80). Therefore, for the extra half hour, she earns $11.85 (0.5 hours × $23.70/hour). Adding these amounts together gives $138.25 ($126.40 + $11.85). Option A ($126.40) only accounts for the first 8 hours. Option C ($189.60) incorrectly assumes full-time pay without considering the overtime rate. Option D ($201.45) miscalculates the overtime pay, while Option E ($237) overestimates by not applying the correct hourly rates.