which numeric system was a base 20 system
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HESI A2

HESI A2 Math Portion

1. Which numeric system was a base 20 system?

Correct answer: A

Rationale: The Mayan numeric system was a base 20 system, known as vigesimal, as it used base 20 numerals. This system was unique and employed a combination of symbols and positional notation to represent numbers. The Babylonian system was a base 60 system, Roman numerals were based on combinations of letters, and Arabic numerals are in base 10, making choices B, C, and D incorrect.

2. A patient needs to increase his calcium intake. If each tablet contains 500 mg of calcium and the patient needs to take 1,500 mg per day, how many tablets should the patient take?

Correct answer: A

Rationale: To calculate the number of tablets needed, divide the total daily calcium intake required (1,500 mg) by the amount of calcium in each tablet (500 mg). 1,500 mg ÷ 500 mg = 3 tablets. Therefore, the patient should take 3 tablets to meet the 1,500 mg daily intake. Choice B, 4 tablets, is incorrect because it would exceed the required 1,500 mg. Choice C, 2 tablets, is insufficient to meet the daily intake. Choice D, 5 tablets, is also incorrect as it would exceed the required amount.

3. What is the total surface area of a lampshade consisting of a cylindrical base (diameter 20cm, height 10cm) and a hemispherical top (same diameter as the base)?

Correct answer: D

Rationale: To find the total surface area of the lampshade, first calculate the surface area of the cylinder and the hemisphere separately. 1. Surface area of the cylinder = 2πr² + 2πrh = 2π(10)² + 2π(10)(20) = 400π + 400π = 800π cm². 2. Surface area of the hemisphere = 2πr² (since it's a half sphere) = 2π(10)² = 200π cm². Adding both areas gives the total surface area: 800π + 200π = 1000π cm². Now, calculate the numerical value: 1000π ≈ 3141.59 cm², which is approximately equal to 2055 cm². Therefore, the correct answer is 2055 sq cm. Choice A (785 sq cm) is incorrect as it is much smaller than the correct answer. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not account for the total surface area of the lampshade.

4. Divide: 727 ÷ 6 =

Correct answer: C

Rationale: When dividing 727 by 6, the quotient is 121 with a remainder of 1. The correct answer is, therefore, 121 r1. Choice A (120 r1) is incorrect as the quotient is 121, not 120. Choice B (120 r3) is also incorrect as the remainder should be 1, not 3. Choice D (127 r3) is incorrect as both the quotient and remainder are different from the correct values obtained by dividing 727 by 6.

5. How many centimeters are in a foot?

Correct answer: C

Rationale: The correct answer is C: 30.48 cm. This conversion is based on the standard measurement where 1 foot is equal to 30.48 centimeters. Choice A (30 cm) is incorrect as it is a rounded-down value and not precise. Choice B (31.5 cm) is incorrect as it is not the standard conversion for feet to centimeters. Choice D (35 cm) is incorrect as it is not the accurate conversion for a foot to centimeters.

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