a bag contains 5 red marbles and 7 blue marbles if you draw a marble without looking what is the probability it will be red
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HESI A2

HESI A2 Math Portion

1. A bag contains 5 red marbles and 7 blue marbles. If you draw a marble without looking, what is the probability it will be red?

Correct answer: B

Rationale: The total number of marbles in the bag is 5 (red) + 7 (blue) = 12 marbles. The probability of drawing a red marble is the number of red marbles divided by the total number of marbles: 5/12. Simplifying 5/12 gives 1/3. Therefore, the correct probability of drawing a red marble is 1/3. Choice A (1/4) is incorrect because there are more red marbles than 1/4 of the total marbles. Choice C (1/2) is incorrect as it represents half of the total marbles. Choice D (2/3) is incorrect as it implies there are more red marbles than there actually are.

2. A newborn weighs 3,459 grams. There are 453.59 grams per pound. What is the infant's weight in pounds and ounces?

Correct answer: A

Rationale: To find the weight in pounds, divide the weight in grams by the conversion factor (453.59 grams per pound). 3,459 grams ÷ 453.59 = approximately 7 lbs 10 oz. Therefore, choice A (7 lbs 10 oz) is the correct answer. Choice B (10 lbs 7 oz) and Choice C (13 lbs 3 oz) are incorrect as they do not correspond to the correct conversion. Choice D (3 lbs 13 oz) is incorrect as it does not account for the additional pounds derived from dividing 3,459 grams by the conversion factor.

3. Out of a total of 50 homes, she sold 11. What percentage of the homes did she sell?

Correct answer: C

Rationale: To find the percentage of homes she sold, divide the number of homes she sold (11) by the total number of homes (50), then multiply by 100. (11 / 50) * 100 = 22%. Therefore, she sold 22% of the homes. Choice A (16%) is incorrect because it is less than the correct percentage. Choice B (18%) is also less than the correct percentage. Choice D (24%) is greater than the correct percentage of homes she sold.

4. How many grams are in 7 kilograms?

Correct answer: A

Rationale: To convert kilograms to grams, you need to multiply by 1,000 since there are 1,000 grams in a kilogram. Therefore, 7 kilograms is equal to 7 x 1,000 = 7,000 grams. The correct answer is 7000 grams. Choice B (70 grams) is incorrect as it represents the conversion of 7 kilograms to grams without considering the correct multiplier. Choice C (700 grams) is incorrect as it is a tenth of the correct conversion. Choice D (70,000 grams) is incorrect as it is ten times the correct conversion.

5. Express the ratio of 12:15 as a percentage.

Correct answer: C

Rationale: To express the ratio 12:15 as a percentage, you need to find the total parts in the ratio (12 + 15 = 27), then divide one part by the total (12 ÷ 27 = 0.4444). Finally, convert the decimal to a percentage by multiplying by 100 (0.4444 x 100 = 44.44%). Therefore, the ratio 12:15 is equivalent to 44.44% when rounded to two decimal places, which is closest to 75.25% among the answer choices. Choices A, B, and D are incorrect as they do not represent the correct percentage equivalent of the ratio 12:15.

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