What is the median of the data set: 3, 5, 7, 9, 11?

Correct Answer: B

Rationale: To find the median of a set of numbers, you arrange them in ascending order and then find the middle value. Given the data set 3, 5, 7, 9, 11, when arranged in ascending order, becomes 3, 5, 7, 9, 11. The middle value in this set is 7, making it the median. Choice A (3) is the smallest value, not the middle value. Choice C (9) and Choice D (5) are not the middle values of the set either. Therefore, the correct answer is B (7).

Correct Answer: C

Rationale: The mode of a data set is the value that appears most frequently. In this data set (2, 3, 3, 4, 4, 4, 5), the number 4 appears three times, which is more frequent than any other number in the set. Therefore, the correct answer is 4. Choice A (2), B (3), and D (5) do not appear as frequently as 4 in the data set, so they are not the mode.

Correct Answer: B

Rationale: From Equation 1: 2x + y = 0. Solve for y: y = -2x. Substitute y = -2x into Equation 2: x - 2(-2x) = 8. Simplify to x + 4x = 8, then 5x = 8, and x = 8 · 5 = 1.6. Substitute x = 1.6 back into y = -2x to find y = -3.2. Therefore, one solution is (1.6, -3.2). To find the second solution, use -1.6 for x to get (-1.6, 3.2). Thus, the correct answer is B, representing the solutions (1.8, -3.6) and (-1.8, 3.6). Choices A, C, and D contain incorrect values that do not match the solutions derived from solving the system of equations.

Correct Answer: A

Rationale: To multiply fractions, you multiply the numerators to get the new numerator and multiply the denominators to get the new denominator. Therefore, multiplying 2/3 by 3/4 results in (2*3) / (3*4) = 6/12. Simplifying 6/12 by dividing both the numerator and denominator by 6 gives 1. Hence, the correct answer is 1. Choices B, C, and D are incorrect as they do not represent the correct product of multiplying 2/3 by 3/4.

Correct Answer: C

Rationale: To determine the smallest decimal, we look at the digits after the decimal point. In this case, 2.002 is the smallest because it has the least value in the thousandths place. Choice A, 2.22, has a higher value in the hundredths place making it larger. Choice B, 2.02, has a higher value in the hundredths place compared to 2.002. Choice D, 2.2, is larger than 2.002 as it has a higher value in the tenths place.

Correct Answer: A

Rationale: To simplify the expression 2x + 3x - 5, follow these steps: Identify and combine like terms. The terms 2x and 3x are both 'like terms' because they both contain the variable x. Add the coefficients of the like terms: 2x + 3x = 5x. Simplify the expression. After combining the like terms, the expression becomes 5x - 5, which includes the simplified term 5x and the constant -5. Thus, the fully simplified expression is 5x - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

Correct Answer: A

Rationale: To convert fluid ounces to gallons, you need to divide the number of fluid ounces by the number of fluid ounces in a gallon. Since there are 128 fluid ounces in a gallon, to find out how many gallons are in 1,000 fluid ounces, you divide 1,000 by 128. The correct calculation is 1,000 / 128 = 7.8125 gallons. Therefore, the correct answer is A. Choices B, C, and D are incorrect as they do not accurately represent the conversion from fluid ounces to gallons.

Correct Answer: B

Rationale: The correct answer is B: 'Positive number.' When you subtract one negative number from another negative number, the result can be a positive number. For example, the difference between -5 and -3 is 2, which is a positive number. Choice A, 'Negative number,' is incorrect because the result of subtracting two negative numbers can be positive. Choice C, 'Zero,' is incorrect because the difference between two negative numbers is not always zero. Choice D, 'Not enough information,' is incorrect because there is enough information to determine that the difference between two negative numbers can be a positive number.

Correct Answer: B

Rationale: The correct answer is B: 30. To find the sum, you need to add 4 + 5 + 12 + 9, which equals 30, not 40 as stated in the original rationale. Choice A (20) is incorrect because it does not account for the correct addition of the numbers provided. Choice C (40) is incorrect as it represents the sum of the numbers incorrectly. Choice D (50) is also incorrect as it is not the sum of the given numbers.