Write 290% as a fraction.

Correct Answer: D

Rationale: To convert a percentage to a fraction, you write the percentage as the numerator of the fraction over 100. Therefore, 290% is equivalent to 290/100, which simplifies to 29/10. Choices A, B, and C are incorrect because they do not represent 290% as a fraction by placing the percentage value over 100.

Correct Answer: C

Rationale: In the given equation 3x + 2 = 20, the correct answer is x = 6. To solve this equation, we need to isolate the variable x. First, we subtract 2 from both sides to get 3x = 18. Then, we divide by 3 on both sides to find x = 6. Option A) x = 2: This is incorrect because if we substitute x = 2 back into the original equation, we get 3(2) + 2 = 8, not 20. Option B) x = 4: This is incorrect as well. Substituting x = 4 back into the equation gives us 3(4) + 2 = 14, not 20. Option D) x = 8: This is incorrect. If we substitute x = 8 into the equation, we get 3(8) + 2 = 26, not 20. Educationally, this problem tests the student's understanding of solving linear equations. By following the correct steps of isolating the variable, students can arrive at the correct solution. Understanding the properties of equality and the order of operations are crucial in solving such equations accurately. Practicing similar problems can help reinforce these concepts and improve problem-solving skills.

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: C

Rationale: To solve for x, add 5 to both sides of the equation: 3x - 5 + 5 = 16 + 5, which simplifies to 3x = 21. Next, divide both sides by 3: x = 21 · 3 = 7. Therefore, the correct answer is x = 7, making option A the correct choice. Option C, '8,' is incorrect as it is not the solution obtained from the correct calculations. Options B and D, '5' and '9,' are also incorrect and not the solution to the given equation.

Correct Answer: C

Rationale: To find the mean of a data set, you add up all the values and then divide by the total number of values. In this case, the sum of the data set is 185. Dividing this sum by the total number of values (12) gives you a mean of 16. Therefore, the correct answer is 16. Choice A (14.25), Choice B (15.25), and Choice D (17) are incorrect because they do not accurately represent the average value of the given data set.