HESI A2 Math Practice

Correct Answer: A

Rationale: The correct answer is A: 16.67%. There is only one face of the die with a 5, out of a total of 6 faces. Therefore, the probability of rolling a 5 is 1/6, which is approximately 16.67%. Other choices are incorrect: B: 20% - This is the probability if there were 5 faces with a 5. C: 50% - This would be the probability if there were only two faces on the die. D: 83.33% - This would be the probability if there were 5 faces with a 5.

Correct Answer: C

Rationale: To find the total surface area, we calculate the area of the rectangular base (20*15=300 sq cm). Then, we find the surface area of the hemispherical top, which is half the surface area of a sphere with radius 10cm (diameter is the same as the base). So, the surface area of the hemispherical top is 2πr^2 = 2*π*(10)^2 = 200π sq cm. Adding the two areas together (300+200π), we get 300+200π ≈ 300+628.32 ≈ 928.32 sq cm. The correct answer is 1325 sq cm (Option C), which is the total surface area of the box excluding the base. Option A, B, and D are incorrect as they do not represent the accurate total surface area of the box.

Correct Answer: A

Rationale: The correct answer is A: 1/6. There is only one face showing a 5 on a six-sided die, so the favorable outcome is 1. The total number of possible outcomes when rolling a six-sided die is 6. Therefore, the probability of rolling a 5 is 1/6. Choice B (1/4) is incorrect because there is only one face showing a 5 out of 6 possible outcomes, not 4. Choice C (1/2) is incorrect as it represents the probability of rolling an even number on a six-sided die, not specifically a 5. Choice D (1/3) is incorrect as it does not accurately represent the probability of rolling a 5 on a six-sided die.

Correct Answer: D

Rationale: The correct answer is D (50%). To determine the probability of getting an even number when rolling a dice, we first need to identify the total possible outcomes, which is 6 (numbers 1 to 6 on a dice). Out of these 6 outcomes, 3 are even numbers (2, 4, 6). Therefore, the probability of getting an even number is calculated as the number of favorable outcomes (even numbers) divided by the total possible outcomes, which is 3/6 = 1/2 = 50%. Choice A (16%) is incorrect because it represents the probability of rolling a specific number (1 out of 6) rather than the probability of rolling an even number. Choice B (33%) and Choice C (66%) are also incorrect as they do not accurately represent the probability of rolling an even number based on the total number of outcomes.

Correct Answer: D

Rationale: The correct answer is D: 7/9. To convert the repeating decimal 0.7777... to a fraction, let x = 0.7777... Multiplying both sides by 10 to shift the decimal point gives 10x = 7.7777... Subtracting the original equation from the shifted one eliminates the repeating decimal, giving 9x = 7. Solving for x, we get x = 7/9, hence 0.7777... = 7/9. Choice A, 77/1000, does not represent the repeating nature of the decimal. Choice B, 70/99, is close but not equivalent to 0.7777... Choice C, 777/900, can be simplified to 7/9, making it the correct answer.