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What is an appropriate unit of measure to express the length of a dollar bill?
- A. Meters
- B. Decimeters
- C. Kilometers
- D. Centimeters
Correct Answer: D
Rationale: Dollar bills are relatively small items, so their length is commonly measured in centimeters. Meters, decimeters, and kilometers are much larger units of length, making centimeters the most suitable unit to accurately express the length of a dollar bill. Centimeters provide a more precise and practical measurement for the size of a dollar bill compared to the other options, which are more suitable for larger distances or objects.
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When a person increases cycling speed, the rate of calories burned, distance traveled, and energy expended also increase. Which of the following is the independent variable?
- A. Speed
- B. Energy
- C. Distance
- D. Calories
Correct Answer: A
Rationale: In the context of this scenario, the independent variable is the factor that is deliberately altered or controlled to observe its impact on other variables. When a person adjusts their cycling speed, it directly influences the rate of calories burned, distance traveled, and energy expended. Speed is the independent variable because it is manipulated to study its effects on the dependent variables - calories burned, distance traveled, and energy expended. Therefore, the correct answer is 'Speed.'
A student performs the following estimations: 24 + 190 = 210, 151 + 319 = 470, 974 + 1022 = 1990. Based on these estimations, what is the student's estimate of 452 + 5017?
- A. 5430
- B. 5470
- C. 5500
- D. 5400
Correct Answer: B
Rationale: The student's pattern involves rounding numbers to the nearest tens or hundreds to simplify calculations. By analyzing the given examples, it is evident that the student tends to round numbers up or down, leading to slight variations from the exact sum. Applying the same strategy to 452 and 5017, we can estimate 450 + 5020 = 5470. Therefore, choice B is the correct estimate for the sum of 452 + 5017.
A circle has an area of 49π square inches. What is the circumference of the circle in terms of π?
- A. 7Ï€ in
- B. 14Ï€ in
- C. 28Ï€ in
- D. 3.5Ï€ in
Correct Answer: B
Rationale: To find the circumference of a circle in terms of π, we first determine the radius using the formula for the area of a circle, A = πr^2. Given that the area is 49π square inches, we have 49π = πr^2, which simplifies to r = 7. The circumference of a circle is calculated using the formula C = 2πr. Substituting r = 7, we get C = 2π(7) = 14π. Therefore, the circumference of the circle is 14π inches.
A recipe calls for 2.5 teaspoons, which equals approximately 4.93 ml. What is the correct amount of vanilla in ml?
- A. 7.43 ml
- B. 0.507 ml
- C. 5.33 ml
- D. 12.325 ml
Correct Answer: D
Rationale: To find the correct amount of vanilla in ml, you need to multiply the required teaspoons by the conversion factor. 2.5 teaspoons * 4.93 ml = 12.325 ml. Therefore, the correct amount of vanilla required is 12.325 ml.
A bucket containing 2 4/5 gallons of water is 1/3 full. How many gallons of water are in one fully filled bucket?
- A. 14/15
- B. 8 2/5
- C. 6 4/5
- D. 2 7/15
Correct Answer: C
Rationale: To determine the amount of water in a fully filled bucket, we need to find out how much 1/3 represents in gallons. If 2 4/5 gallons represent 1/3 of the bucket, then the total amount in the bucket can be calculated by multiplying 2 4/5 by 3 (since 1/3 is multiplied by 3 to get the whole). 2 4/5 * 3 = 8 2/5 gallons, which is the capacity of the bucket when completely filled. Therefore, one fully filled bucket contains 8 2/5 gallons of water.