Nokea
When is a histogram preferred over a bar graph?
- A. Comparison between categories
- B. Frequency
- C. Percentages
- D. Proportions
Correct Answer: B
Rationale: Histograms are specifically designed to display the frequency distribution of continuous data, showing the distribution of values over intervals or bins. On the other hand, bar graphs are used to compare different categories or discrete data points. Therefore, the correct answer is B. Choices A, C, and D are incorrect because histograms are not primarily used for comparing categories, percentages, or proportions, but rather for visualizing the distribution of frequencies within data intervals.
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Which of the following best describes the relationship in this set of data?
- A. High positive correlation
- B. Low positive correlation
- C. Low negative correlation
- D. No correlation
Correct Answer: B
Rationale: The correct answer is 'B: Low positive correlation.' In a low positive correlation, the variables tend to increase together, but the relationship is not strong. This description fits the data set provided. Choice A, 'High positive correlation,' is incorrect because the correlation is not strong. Choice C, 'Low negative correlation,' is incorrect as the variables are not decreasing together. Choice D, 'No correlation,' is incorrect because there is a relationship between the variables, albeit weak.
Cora skated around the rink 27 times but fell 20 times. What percentage of the time did she not fall?
- A. 0.37
- B. 0.74
- C. 0.26
- D. 0.15
Correct Answer: C
Rationale: To find the percentage of the time Cora did not fall, subtract the number of times she fell (20) from the total number of times she skated around the rink (27). This gives us 27 - 20 = 7 times she did not fall. To express this as a percentage, calculate (7/27) * 100% = 25.93%, which is approximately 26%. Therefore, the correct answer is 0.26 (C). Choice A (0.37), Choice B (0.74), and Choice D (0.15) are incorrect as they do not represent the percentage of the time Cora did not fall based on the information provided.
What is the probability of consecutively pulling two more orange blocks, without replacement, from a bag containing 3 orange blocks, 5 green blocks, and 4 purple blocks?
- A. 3/12
- B. 3/55
- C. 2/10
- D. 1/3
Correct Answer: B
Rationale: To calculate the probability of consecutively pulling two more orange blocks without replacement, we first determine the probability of pulling an orange block on the first draw, which is 3/12 (3 orange blocks out of 12 total blocks). After removing one orange block, there are only 11 blocks left, so the probability of pulling another orange block on the second draw is 2/11. To find the combined probability, we multiply the probabilities together: (3/12) * (2/11) = 6/132 = 3/55. Therefore, the correct answer is B. Choice A (3/12) incorrectly simplifies the probability before calculating the second draw. Choice C (2/10) does not consider the specific number of orange blocks in the bag. Choice D (1/3) does not account for the reduced number of blocks after the first draw.
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.
What is the sum of two odd numbers, two even numbers, and an odd number and an even number?
- A. Odd + Odd = Even; Even + Even = Even; Odd + Even = Odd
- B. Odd + Odd = Odd; Even + Even = Even; Odd + Even = Even
- C. Odd + Odd = Even; Even + Even = Odd; Odd + Even = Even
- D. Odd + Odd = Odd; Even + Even = Odd; Odd + Even = Even
Correct Answer: A
Rationale: The sum of two odd numbers is even because odd numbers have a difference of 1 and adding them results in a multiple of 2. The sum of two even numbers is even because even numbers are multiples of 2. When an odd number and an even number are added, the result is odd because the even number contributes an extra 1 to the sum, making it an odd number. Therefore, the correct answer is A. Choices B, C, and D have incorrect combinations of the sum of odd and even numbers.