Fred worked 39.5 hours last week. Alice worked 6.75 fewer hours than Fred. How many hours did Alice work?
- A. 33.75 HOURS
- B. 33.25 HOURS
- C. 33.35 HOURS
- D. 33.85 HOURS
Correct Answer & Rationale
Correct Answer: A
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
Other Related Questions
Which of the labeled points on the number line above has coordinate closest to
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: D
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
The coordinate of pointP on the number line above is x. The value of 10x is between
- A. 1 and 4
- B. 4 and 6
- C. 6 and 8
- D. 8 and 12
Correct Answer & Rationale
Correct Answer: B
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
What is the product of 2,2/3 and 3,3/8?
- A. 5,5/11
- B. 6,1/24
- C. 7
- D. 9
Correct Answer & Rationale
Correct Answer: D
To find the product of 2,2/3 and 3,3/8, first convert the mixed numbers to improper fractions. 2,2/3 becomes 8/3 and 3,3/8 becomes 27/8. Multiplying these fractions gives (8/3) * (27/8) = 216/24 = 9. Option A (5,5/11) and Option B (6,1/24) are incorrect as they do not represent the product of the two numbers. Option C (7) is also incorrect, as it is less than the calculated product. Thus, the only valid result from the multiplication is 9, confirming the correct answer.
To find the product of 2,2/3 and 3,3/8, first convert the mixed numbers to improper fractions. 2,2/3 becomes 8/3 and 3,3/8 becomes 27/8. Multiplying these fractions gives (8/3) * (27/8) = 216/24 = 9. Option A (5,5/11) and Option B (6,1/24) are incorrect as they do not represent the product of the two numbers. Option C (7) is also incorrect, as it is less than the calculated product. Thus, the only valid result from the multiplication is 9, confirming the correct answer.
Of the following, which is closest to 17/6 + 6/17 ?
- A. 1
- B. 2
- C. 3
- D. 23
Correct Answer & Rationale
Correct Answer: C
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.