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Which of the following translates the phrase '5 less than 2 times a number' into a mathematical expression?
- A. 5 - 2x
- B. 5x - 2
- C. 2x - 5
- D. 2 - 5x
Correct Answer: C
Rationale: To translate the phrase '5 less than 2 times a number' into a mathematical expression, you first express '2 times a number' as 2x. Then, '5 less than' indicates subtracting 5 from the result, leading to 2x - 5. Therefore, choice C, 2x - 5, correctly represents the given phrase in a mathematical expression.
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A child has a bottle full of pennies, nickels, dimes, and quarters. There are twice as many quarters as pennies, four times as many nickels as pennies, and five times as many dimes as nickels. How many more dimes does the child have than quarters?
- A. 10 times as many
- B. 4 times as many
- C. 5 times as many
- D. 29 times as many
Correct Answer: D
Rationale: Let's assign a value to the number of pennies. If we say there is 1 penny, then there are 2 quarters (twice as many as pennies), 4 nickels (four times as many as pennies), and 20 dimes (five times as many as nickels). The number of dimes is 20, and the number of quarters is 2. The difference between the number of dimes and quarters is 20 - 2 = 18. Therefore, the child has 18 more dimes than quarters, which is 18 times as many, not 29 times as many as stated in the original answer choice.
Simplify the expression [2(3 + 5 × 3)] / (12 ÷ 2)
- A. 12
- B. 1
- C. 8
- D. 6
Correct Answer: D
Rationale: To simplify: Calculate 5 × 3 = 15; then 3 + 15 = 18. So, 2 × 18 = 36. Then, 12 ÷ 2 = 6. Finally, 36 ÷ 6 = 6.
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.
In a study of the average weight of babies at different time intervals of birth, the babies' measured weight is which of the following types of variable?
- A. Independent
- B. Constant
- C. Dependent
- D. Control
Correct Answer: C
Rationale: The correct answer is C: Dependent. The babies' measured weight in this study would be considered a dependent variable. In research, a dependent variable is the outcome that is being measured and studied based on changes in other factors, known as independent variables. In this context, the babies' weight is the variable that is dependent on the time intervals of birth, making it the dependent variable in the study. Therefore, the measured weight of the babies is influenced by the time intervals of birth, indicating a dependency relationship between the variables.
A sweater that normally sells for $87 is marked 25% off. Which of the following estimates the sale price of the sweater?
- A. $36
- B. $65
- C. $51
- D. $22
Correct Answer: B
Rationale: To calculate the sale price after a 25% discount, you need to find 25% of the original price and subtract it from the original price. 25% of $87 is $21.75 ($87 x 0.25 = $21.75). Subtracting this from the original price gives you $87 - $21.75 = $65, which is the estimated sale price of the sweater.