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What is the sixth number in the sequence 5, 6, 7, 8, 9?
- A. 8
- B. 10
- C. 11
- D. 12
Correct Answer: C
Rationale: In the given sequence 5, 6, 7, 8, 9, the sixth number would come after 9, not after the fifth number in the sequence. To find the sixth number, we need to continue the pattern after 9. The next number after 9 would be 10, making it the sixth number in the sequence. Therefore, the correct answer is not listed among the choices provided. Choice A, 8, is the fifth number in the sequence. Choice B, 10, is the number right after the sixth number. Choice D, 12, is not in the sequence at all, making it incorrect. Thus, the correct answer is 11.
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You measure the width of your door to be 36 inches. The true width of the door is 75 inches. What is the relative error in your measurement?
- A. 0.52%
- B. 0.01%
- C. 0.99%
- D. 0.10%
Correct Answer: A
Rationale: The relative error is calculated using the formula: (|Measured Value - True Value| / True Value) * 100%. Substituting the values given, we have (|36 - 75| / 75) * 100% = (39 / 75) * 100% ≈ 0.52 * 100% = 0.52%. Therefore, the relative error in measurement is approximately 0.52%. Choice A is correct because it reflects this calculation. Choice B is incorrect as it represents a lower relative error than the actual value obtained. Choice C is incorrect as it overestimates the relative error. Choice D is incorrect as it underestimates the relative error.
When rounding 2678 to the nearest thousandth, which place value would be used to decide whether to round up or round down?
- A. Ten-thousandth
- B. Thousandth
- C. Hundredth
- D. Thousand
Correct Answer: B
Rationale: When rounding 2678 to the nearest thousandth, you would look at the digit in the thousandth place, which is 7. To decide whether to round up or down, you consider the digit to the immediate right of the place you are rounding to. Since 7 is equal to or greater than 5, you round up. Choice A, ten-thousandth, is incorrect as we are rounding to the thousandth place. Choice C, hundredth, is not relevant as we are not rounding to that place value. Choice D, thousand, is incorrect as it is the original number being rounded, not the place value used for rounding.
A quantity increases from 40 to 60. Express this increase as a percentage.
- A. 26%
- B. 50%
- C. 35%
- D. 12%
Correct Answer: B
Rationale: To calculate the percentage increase, use the formula:
Percentage Increase = ((New Value - Original Value) / Original Value) x 100
Substitute the values:
((60 - 40) / 40) x 100 = (20 / 40) x 100 = 0.5 x 100 = 50%
Therefore, the correct answer is 50%.
Choice A (26%) is incorrect as the percentage increase is not 26%. Choice C (35%) is incorrect as the percentage increase is not 35%. Choice D (12%) is incorrect as the percentage increase is not 12%.
Calculate the sum of the numbers from 1 to 6:
- A. 30
- B. 21
- C. 15
- D. 13
Correct Answer: B
Rationale: To find the sum of numbers from 1 to 6, we add them together: 1 + 2 + 3 + 4 + 5 + 6 = 21. Therefore, the correct answer is 21. Choice A (30) is incorrect because it is not the sum of the numbers 1 to 6. Choice C (15) is incorrect as it is the sum of numbers 1 to 5. Choice D (13) is incorrect as it is the sum of numbers 1 to 4, not 1 to 6.
Which measure for the center of a small sample set would be most affected by outliers?
- A. Mean
- B. Median
- C. Mode
- D. None of the above
Correct Answer: A
Rationale: The mean is calculated by summing all values in a dataset and then dividing by the total number of values. Outliers, which are data points significantly different from the other values, can greatly impact the mean because they affect the sum. The mean is sensitive to extreme values, making it the measure for the center of a small sample set most affected by outliers. The median, on the other hand, is not influenced by outliers as it represents the middle value when the data points are ordered. The mode is the value that appears most frequently in the dataset and is not directly influenced by outliers. Therefore, the correct answer is the mean, as it is highly influenced by outliers in a small sample set.