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Which of the following numbers is the largest?
- A. 0.45
- B. 0.096
- C. 0.3
- D. 0.313
Correct Answer: A
Rationale: Among the provided options, 0.45 is the largest number. To determine the largest number, compare the decimal values directly. 0.45 is greater than 0.313, 0.3, and 0.096. Therefore, 0.45 is the correct answer. Choice B (0.096) is the smallest as it has the lowest decimal value. Choice C (0.3) is greater than 0.096 but smaller than both 0.313 and 0.45. Choice D (0.313) is greater than 0.3 and 0.096 but smaller than 0.45, making it incorrect.
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John's Gym charges its members according to the equation y = 40x, where x is the number of months and y represents the total cost to each customer after x months. Ralph's Recreation Room charges its members according to the equation y = 45x. What relationship can be determined about the monthly cost to the members of each company?
- A. John's monthly membership fee is equal to Ralph's monthly membership fee.
- B. John's monthly membership fee is more than Ralph's monthly membership fee.
- C. John's monthly membership fee is less than Ralph's monthly membership fee.
- D. No relationship can be determined between the monthly membership fees.
Correct Answer: C
Rationale: The equation y = 40x represents John's Gym charging $40 per month, while the equation y = 45x represents Ralph's Recreation Room charging $45 per month. Since $40 is less than $45, it can be concluded that John's Gym offers a lower monthly membership fee compared to Ralph's Recreation Room. Therefore, the correct answer is that John's monthly membership fee is less than Ralph's monthly membership fee. Choices A and B are incorrect because John's fee is not equal to or greater than Ralph's fee. Choice D is incorrect as there is a clear relationship indicating that John's monthly membership fee is less than Ralph's monthly membership fee.
How will the number 89632 be written if rounded to the nearest hundred?
- A. 847.9
- B. 900
- C. 847.89
- D. 847.896
Correct Answer: B
Rationale: Rounding the number 89632 to the nearest hundred means keeping only two digits before the decimal point. The digit in the hundredth place is the digit in the thousands place of the original number, which is 6. Since 6 is equal to or greater than 5, the digit in the hundredth place, which is 3, gets rounded up. Thus, the number 89632 rounded to the nearest hundred is 900. Choice A, 847.9, rounds the number to the nearest tenth, not hundredth. Choice C, 847.89, adds an extra decimal place which is not correct for rounding to the nearest hundred. Choice D, 847.896, adds more decimal places than necessary for rounding to the nearest hundred.
A student gets an 85% on a test with 20 questions. How many answers did the student solve correctly?
- A. 15
- B. 16
- C. 17
- D. 18
Correct Answer: C
Rationale: To determine the number of questions the student solved correctly, we need to calculate 85% of the total number of questions. This can be done by multiplying the total number of questions by 85%, which is 20 questions x 85% = 20 x 0.85 = 17 questions. Therefore, the student solved 17 questions correctly. Choice A, 15, is incorrect as it does not reflect the correct percentage of questions solved. Choice B, 16, and Choice D, 18, are also incorrect as they do not match the calculation based on the given percentage.
What is the solution to 4 x 7 + (25 - 21)²?
- A. 512
- B. 36
- C. 44
- D. 22
Correct Answer: C
Rationale: To find the solution, first solve the expression inside the parentheses: 25 - 21 = 4. Then, square the result from the parentheses: 4² = 16. Next, perform the multiplication: 4 x 7 = 28. Finally, add the results: 28 + 16 = 44. Therefore, the correct answer is 44. Choice A (512), Choice B (36), and Choice D (22) are incorrect as they do not follow the correct order of operations for solving the given mathematical expression.
When rounding 2678 to the nearest thousandth, which place value would be used to decide whether to round up or round down?
- A. Ten-thousandth
- B. Thousandth
- C. Hundredth
- D. Thousand
Correct Answer: B
Rationale: When rounding 2678 to the nearest thousandth, you would look at the digit in the thousandth place, which is 7. To decide whether to round up or down, you consider the digit to the immediate right of the place you are rounding to. Since 7 is equal to or greater than 5, you round up. Choice A, ten-thousandth, is incorrect as we are rounding to the thousandth place. Choice C, hundredth, is not relevant as we are not rounding to that place value. Choice D, thousand, is incorrect as it is the original number being rounded, not the place value used for rounding.