Nokea
Given a double bar graph, which statement is true about the distributions of Group A and Group B?
- A. Group A is negatively skewed, Group B is normal.
- B. Group A is positively skewed, Group B is normal.
- C. Group A is positively skewed, Group B is neutral.
- D. Group A is normal, Group B is negatively skewed.
Correct Answer: B
Rationale: The correct answer is B. In statistical terms, a positively skewed distribution means that the tail on the right side of the distribution is longer or fatter than the left side, indicating more high values. Therefore, Group A is positively skewed. Conversely, an approximately normal distribution, also known as a bell curve, is symmetrical with no skewness. Hence, Group B is normal. Choices A, C, and D are incorrect because they do not accurately describe the skewness of Group A and the normal distribution of Group B as depicted in a double bar graph.
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How do you find the radius of a circle when given the diameter? How do you find the radius of a circle when given the circumference?
- A. Radius = Diameter · 2; Radius = Circumference · 2π
- B. Radius = Diameter · 3; Radius = Circumference · π
- C. Radius = Diameter 2; Radius = Circumference 2π
- D. Radius = Diameter · 4; Radius = Circumference · π
Correct Answer: A
Rationale: The correct way to find the radius of a circle when given the diameter is by dividing the diameter by 2 to get the radius (Radius = Diameter · 2). When given the circumference, you need to divide the circumference by 2π to find the radius (Radius = Circumference · 2π). Choice A provides the accurate formulas for finding the radius in both scenarios. Choices B, C, and D present incorrect formulas that do not align with the correct calculations for determining the radius of a circle based on the given information.
How many ounces are in a pound?
- A. 8 ounces
- B. 16 ounces
- C. 32 ounces
- D. 12 ounces
Correct Answer: B
Rationale: The correct answer is B: 16 ounces. There are 16 ounces in a pound. This conversion is a common measure of weight in the imperial system. Choices A, C, and D are incorrect because they do not reflect the correct conversion of ounces in a pound.
What is the formula for the area of a circle?
- A. A = πr²
- B. A = 2πr
- C. A = πd
- D. A = 2πd
Correct Answer: A
Rationale: The correct formula for the area of a circle is A = πr², where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle. Choice B, A = 2πr, represents the circumference of a circle, not the area. Choice C, A = πd, incorrectly uses the diameter (d) instead of the radius in the formula for area. Choice D, A = 2πd, is also related to the circumference of the circle, not the area. Therefore, option A is the only correct formula for calculating the area of a circle.
What is a direct proportion? What is an inverse proportion?
- A. Direct: Both quantities increase or decrease together; Inverse: When one quantity increases, the other decreases by the same factor
- B. Direct: Both quantities decrease together; Inverse: When one quantity increases, the other increases
- C. Direct: One quantity stays the same while the other increases; Inverse: Both quantities increase together
- D. Direct: One quantity increases while the other decreases; Inverse: Both quantities decrease together
Correct Answer: A
Rationale: In a direct proportion, both quantities increase or decrease together. This means that as one quantity goes up, the other also goes up, and vice versa. On the other hand, in an inverse proportion, when one quantity increases, the other decreases by the same factor. Therefore, choice A is correct as it accurately defines direct and inverse proportions. Choices B, C, and D are incorrect because they do not accurately describe the relationship between quantities in direct and inverse proportions.
Erma has her eye on two sweaters, one for $50 and one for $44. With a sale of 25% off the cheaper item, what will she spend?
- A. 79
- B. 81
- C. 83
- D. 85
Correct Answer: A
Rationale: Erma pays full price for the $50 sweater and gets 25% off the $44 sweater. 25% of $44 is $11, so she pays $33 for the second sweater. Therefore, the total amount Erma spends is $50 (first sweater) + $33 (second sweater) = $79. Choices B, C, and D are incorrect as they do not correctly calculate the total amount Erma would spend on both sweaters.