Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.

Correct Answer: D

Rationale: The formula for the area of a circle is: Area = π x (radius²). Given: Diameter = 16 cm, so Radius = Diameter / 2 = 16 / 2 = 8 cm. Now, calculate the area using π = 3.14: Area = 3.14 x (8²) = 3.14 x 64 = 200.96 cm². The correct answer is D (200.96 cm²) as it correctly calculates the area of the circle. Choices A, B, and C are incorrect as they do not represent the accurate area of the circle based on the given diameter and π value.

Correct Answer: B

Rationale: The formula for the area of a full circle is calculated as Area = π (radius²). When finding the area of half a circle, we multiply by 0.5. Thus, the formula becomes Area = 0.5 π (radius²). Given that the radius of the circular garden is 11.5 feet, the calculation using π = 3.14 is as follows: Area = 0.5 3.14 (11.5²) = 0.5 3.14 132.25 = 0.5 415.27 = 207.64 square feet. Therefore, the correct answer is B. Choices A, C, and D are incorrect because they do not reflect the correct calculation for finding the area of half a circular garden with a radius of 11.5 feet.

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: A

Rationale: When solving an inequality, the direction of the inequality sign changes depending on the operation performed. In this case, if the given inequality simplifies to x > 5, it means that the unknown value x must be greater than 5 for the inequality to hold true. Therefore, x > 5 is the correct solution. Option A is correct. Choices B, C, and D are incorrect because they do not correctly represent the relationship between x and 5 based on the given inequality.

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.