a playground fence has a rectangular section 5m by 3m attached to a semicircular section with a radius of 2m what is the total perimeter
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HESI A2

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1. What is the total perimeter of a playground fence that has a rectangular section (5m by 3m) attached to a semicircular section with a radius of 2m?

Correct answer: D

Rationale: To find the total perimeter, we first calculate the perimeter of the semicircle, which is half of a full circle, so the formula is π * radius. For the semicircle with a radius of 2m, the perimeter is approximately 3.14 * 2m = 6.28m. Next, we calculate the perimeter of the rectangular section by adding twice the length and twice the width (2 * length + 2 * width). For the rectangle with dimensions 5m by 3m, the perimeter is 2 * 5m + 2 * 3m = 10m + 6m = 16m. Finally, we sum the perimeters of the semicircle and the rectangle to get the total perimeter: 6.28m + 16m = 22.28m. Rounding to the nearest meter, the total perimeter is approximately 22m. Therefore, the correct answer is 22m. Choices A, B, and C are incorrect as they do not accurately calculate the total perimeter of the playground fence.

2. How many liters are there in 500 milliliters?

Correct answer: A

Rationale: The correct answer is A: 0.5 liters. To convert milliliters to liters, you need to divide by 1000 since there are 1000 milliliters in 1 liter. Therefore, 500 milliliters is equal to 0.5 liters. Choice B, 5 liters, is incorrect because it would be the equivalent of 5000 milliliters. Choice C, 50 liters, is incorrect as it is ten times the converted value. Choice D, 500,000 liters, is way off as it is a thousand times more than the correct conversion.

3. What is the result of adding 6 3/4 + 8 1/6?

Correct answer: A

Rationale: To add mixed numbers, first convert them to improper fractions. 6 3/4 = 27/4 and 8 1/6 = 49/6. Finding a common denominator, we get 27/4 + 49/6 = 81/12 + 98/12 = 179/12 = 14 & 11/12. Therefore, the correct answer is A. Choice B is incorrect as it does not simplify to the correct result. Choice C is in fraction form and not in mixed number form, making it incorrect. Choice D is not the correct sum of the given mixed numbers, so it is also incorrect.

4. What is 15% of 95?

Correct answer: A

Rationale: To find 15% of 95, you multiply 95 by 0.15 (which represents 15% as a decimal). Therefore, 95 * 0.15 = 14.25. The correct answer is A. Choice B, 18.5, is incorrect as it does not represent 15% of 95. Choices C and D, 24.25 and 28.5, are also incorrect calculations for 15% of 95.

5. How many inches are in 1.5 yards?

Correct answer: A

Rationale: To convert yards to inches, you multiply the number of yards by 36 (since there are 36 inches in a yard). So, 1.5 yards × 36 inches/yard = 54 inches. Therefore, the correct answer is A. Choice B, C, and D are incorrect as they do not correctly convert yards to inches.

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