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. Which of the following is equivalent to 0.0009?

Correct answer: A

Rationale: The correct answer is A: 0.09%. To convert 0.0009 to a percentage, move the decimal point four places to the right and add a percentage sign. Therefore, 0.0009 is equal to 0.09%. Choice B (9%) is incorrect as it represents 0.09 without the decimal point adjustment. Choice C (0.01%) is incorrect as it represents 0.0009 with one less zero. Choice D (0.90%) is incorrect as it represents 0.9 not 0.0009.

3. Change 0.004 to a ratio.

Correct answer: A

Rationale: To convert 0.004 to a ratio, first express it as a fraction. 0.004 = 4/1000 = 1/250. Therefore, the ratio is 1:250. Choice A is the correct answer. Choices B, C, and D are incorrect ratios as they do not represent the equivalent fraction of 0.004.

4. A label states 1 mil contains 500 mg. How many mils are there if there are 1.5 grams?

Correct answer: C

Rationale: To calculate the number of mils, first, convert 1.5 grams to milligrams (1.5 grams = 1500 mg). Then, since 1 mil contains 500 mg, divide 1500 mg by 500 mg/mil, resulting in 3 mils required to contain 1.5 grams of substance. Choice A, 9, is incorrect because it miscalculates the conversion. Choice B, 2, is incorrect as it does not consider the correct conversion factor. Choice D, 5, is incorrect as it also miscalculates the conversion.

5. Add 7/8 + 9/10 + 6/5. Express the result as a mixed number.

Correct answer: A

Rationale: To add fractions, find a common denominator, which in this case is 40. Convert each fraction to have the common denominator: 7/8 = 35/40, 9/10 = 36/40, and 6/5 = 48/40. Add these fractions to get 119/40. Simplify this improper fraction to a mixed number, which is 3 & 39/40. Choice B and C are incorrect as they do not represent the sum of the fractions. Choice D is incorrect; the whole number part should be 3, not 2.

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