Nokea
What is the volume of a cube with a side length of 3 cm?
- A. 9 cm³
- B. 27 cm³
- C. 18 cm³
- D. 12 cm³
Correct Answer: B
Rationale: To find the volume of a cube, you cube the length of one side. In this case, the side length is 3 cm, so the volume is calculated as 3 cm * 3 cm * 3 cm = 27 cm³. Therefore, the correct answer is 27 cm³. Choice A (9 cm³), Choice C (18 cm³), and Choice D (12 cm³) are incorrect as they do not correctly calculate the volume of a cube with a side length of 3 cm.
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What is the mode of the set of numbers {4, 4, 5, 7, 8}?
- A. 4
- B. 5
- C. 7
- D. 8
Correct Answer: A
Rationale: The mode of a set of numbers is the value that appears most frequently. In the given set {4, 4, 5, 7, 8}, the number 4 appears twice, which is more frequent than any other number. Therefore, the mode of this set is 4. Choice B, 5, is incorrect as it only appears once in the set. Choices C and D, 7 and 8 respectively, also appear only once each, making them less frequent than the number 4.
How is the number -4 classified?
- A. Real, rational, integer, whole, natural
- B. Real, rational, integer, natural
- C. Real, rational, integer
- D. Real, irrational
Correct Answer: C
Rationale: The number -4 is classified as a real number because it exists on the number line. It is also a rational number since it can be expressed as -4/1. Additionally, -4 is an integer because it is a whole number that can be positive, negative, or zero. However, -4 is not a whole number because whole numbers are non-negative integers starting from zero. Similarly, -4 is not a natural number since natural numbers are positive integers starting from one. Therefore, the correct classification for the number -4 is real, rational, and integer, making option C the correct answer.
When rounding 245.2678 to the nearest thousandth, which place value would be used to decide whether to round up or round down?
- A. Ten-thousandths
- B. Thousandths
- C. Hundredths
- D. Thousand
Correct Answer: A
Rationale: When rounding a number to the nearest thousandth, you look at the digit in the ten-thousandths place to determine whether to round up or down the digit in the thousandths place. In this case, rounding 245.2678 to the nearest thousandth, the digit in the ten-thousandths place is 6, which is greater than or equal to 5, so you would round up the digit in the thousandths place. Therefore, the correct answer is the ten-thousandths place. Choices B, C, and D are incorrect because they do not directly influence the rounding of the thousandths place in this scenario.
Divide 52 by 27 and 51 by 27 and simplify.
- A. 52/27
- B. 51/27
- C. 52/29
- D. 51/29
Correct Answer: A
Rationale: To divide 52 by 27 and 51 by 27, you get 52/27 and 51/27, respectively. When simplified, 52/27 is the correct answer. The other choices, 51/27, 52/29, and 51/29, are incorrect because they do not reflect the correct result of dividing the given numbers.
Express 3 5/7 as an improper fraction.
- A. 26/7
- B. 21/7
- C. 22/7
- D. 26/5
Correct Answer: A
Rationale: To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. In this case, 3 * 7 + 5 = 21 + 5 = 26. So, 3 5/7 as an improper fraction is 26/7. Choice B (21/7) is incorrect because it represents the original fraction 3 5/7. Choice C (22/7) is incorrect and represents a different fraction. Choice D (26/5) is incorrect and does not reflect the proper conversion of the mixed number to an improper fraction.