a bookshelf has triangular shelves with a base of 40cm and a height of 30cm the depth of the shelf is 25cm what is the volume of each shelf

HESI A2

Practice HESI A2 Math Test

1. A bookshelf has triangular shelves with a base of 40cm and a height of 30cm. The depth of the shelf is 25cm. What is the volume of each shelf?

A. 3000 cu cm
B. 3750 cu cm
C. 5000 cu cm
D. 7500 cu cm

Correct answer: B

Rationale: To find the volume of the triangular shelf, first calculate the area of the triangle (1/2 * base * height) which is (1/2 * 40 * 30) = 600 sq cm. Then, multiply this area by the depth of the shelf (600 * 25) = 15000 cu cm. Therefore, the volume of each shelf is 3750 cu cm. Choice A, C, and D are incorrect as they do not correctly calculate the volume based on the dimensions provided.

2. Convert this military time to regular time: 2120 hours.

A. 9:20 A.M.
B. 9:20 P.M.
C. 2:12 A.M.
D. 2:12 P.M.

Correct answer: B

Rationale: To convert military time to regular time, subtract 12 from the hours if the time is in the afternoon or evening. In this case, 21 - 12 = 9, so 2120 hours is equivalent to 9:20 P.M. Therefore, the correct answer is option B, 9:20 P.M. Choices A, C, and D are incorrect because they do not correctly adjust the military time to regular time format. Choice A shows 9:20 A.M., which is incorrect as the time is in the evening. Choices C and D show times that are not derived from the given military time, making them incorrect as well.

3. Which of the following numbers is a perfect square?

A. 10
B. 12
C. 15
D. 16

Correct answer: D

Rationale: A perfect square is a number obtained by squaring an integer. In this case, 16 is a perfect square because it is the result of squaring 4 (4 x 4 = 16). The other answer choices, 10, 12, and 15, are not the product of squaring any whole number, making them incorrect. Therefore, the correct answer is 16, as it is a perfect square.

4. 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?

A. 1/4
B. 1/3
C. 1/2
D. 2/3

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.

5. What is the opposite of -3?

A. -6
B. 3
C. 0
D. 6

Correct answer: B

Rationale: The opposite of a number is the number that, when added to it, results in zero. In this case, the opposite of -3 is a number that, when added to -3, gives 0. Therefore, the opposite of -3 is 3, as -3 + 3 = 0. Choice A, -6, is incorrect because -3 + (-6) = -9, not zero. Choice C, 0, is the additive inverse of 0, not -3. Choice D, 6, is also incorrect as -3 + 6 = 3, not zero.