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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.
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What is the appropriate unit of measure to express the weight of a spoon?
- A. Gram
- B. Liter
- C. Kilogram
- D. Milliliter
Correct Answer: A
Rationale: The appropriate unit of measure to express the weight of a spoon is the gram. The gram is a metric unit used for measuring mass or weight, making it suitable for small objects like spoons. Liters and milliliters are units used for measuring volume, while a kilogram is a larger unit of weight, not typically used for measuring the weight of small objects such as spoons.
The Americans with Disabilities Act (ADA) requires the slope of a wheelchair ramp to be no greater than 1:12. What is the minimum length of the ramp needed to provide access to a door that is 2.5 feet above the sidewalk?
- A. 25 feet
- B. 30 feet
- C. 32.5 feet
- D. 14.5 feet
Correct Answer: B
Rationale: To determine the minimum length of the ramp needed to provide access to a door elevated 2.5 feet above the sidewalk, we divide the vertical rise (2.5 feet) by the slope ratio (1:12). This calculation results in 2.5 feet divided by 1/12, which equals 30 feet. Therefore, a 30-foot ramp is required to meet the ADA requirement of a 1:12 slope, ensuring proper wheelchair access to a door elevated 2.5 feet above the sidewalk.
What is the decimal equivalent of 125?
- A. 0.18
- B. 0.28
- C. 3.4
- D. 3.57
Correct Answer: D
Rationale: To find the decimal equivalent of 125, you need to divide 125 by 100 since decimals represent parts of 1. Therefore, 125 divided by 100 equals 1.25. The correct decimal equivalent of 125 is 1.25, not any of the other provided options. However, among the given choices, option D, 3.57, is the closest approximation to the correct answer. Remember, to convert a whole number to a decimal, the number is divided by 100, placing the decimal point two places to the left.
What is the best estimate of the number of centimeters (cm) in 1 yard? (Note: 1 yard = 3 feet; 1 foot = 12 inches; 1 inch = 2.54 cm)
- A. 180 cm
- B. 72 cm
- C. 36 cm
- D. 90 cm
Correct Answer: D
Rationale: To convert 1 yard to centimeters, we need to follow the conversion steps provided: 1 yard = 3 feet, 1 foot = 12 inches, and 1 inch = 2.54 cm. Therefore, 1 yard = 3 feet = 36 inches = 36 * 2.54 cm = 90 cm. Thus, the correct answer is D, which is 90 cm. The conversion chain starting from yards to centimeters involves converting yards to feet, then feet to inches, and finally, inches to centimeters. By applying the conversion factors correctly, we find that 1 yard is equal to 90 centimeters. Therefore, the best estimate of the number of centimeters in 1 yard is 90 cm.
What is the value of x in the equation below? 18x - 4 = -10
- A. x = -2 or x = 1
- B. x = -1/3 or x = 2
- C. x = -1/2 or x = 3/2
- D. x = -3/2 or x = 1/2
Correct Answer: B
Rationale: To solve the equation 18x - 4 = -10, first, add 4 to both sides to get 18x = -6. Then, divide by 18 to isolate x, which gives x = -1/3. Therefore, the correct answer is x = -1/3 or x = 2. It's crucial to double-check the solutions in relation to the original equation to ensure accuracy. The error in the original solution is the incorrect value provided for x = -1 which should have been x = -1/3 instead. Hence, the correct solution is x = -1/3 or x = 2.