What is the value of 0.6 - (0.7)(1.4)?
- A. -0.38
- B. -0.14
- C. -0.42
- D. -1.5
Correct Answer & Rationale
Correct Answer: A
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
Other Related Questions
At a local bank, certificates of deposit (CDs) mature every 9 months. At another bank, CDs mature every 12 months. If CDs are purchased on the same day at each bank and are renewed when they mature, what is the least number of months that will pass before the two banks' CDs are mature at the same time?
- A. 72
- B. 36
- C. 108
- D. 3
Correct Answer & Rationale
Correct Answer: B
To find when the CDs from both banks mature simultaneously, we need to determine the least common multiple (LCM) of their maturity periods: 9 months and 12 months. Calculating the LCM, we see that the multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, and 81. The multiples of 12 are 12, 24, 36, 48, 60, 72, and 84. The smallest common multiple is 36 months. Option A (72) is incorrect as it’s not the smallest shared maturity. Option C (108) is also incorrect; it exceeds the LCM. Option D (3) is far too short, as it does not accommodate either maturity period. Thus, 36 months is the earliest point both CDs will mature together.
To find when the CDs from both banks mature simultaneously, we need to determine the least common multiple (LCM) of their maturity periods: 9 months and 12 months. Calculating the LCM, we see that the multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, and 81. The multiples of 12 are 12, 24, 36, 48, 60, 72, and 84. The smallest common multiple is 36 months. Option A (72) is incorrect as it’s not the smallest shared maturity. Option C (108) is also incorrect; it exceeds the LCM. Option D (3) is far too short, as it does not accommodate either maturity period. Thus, 36 months is the earliest point both CDs will mature together.
Two men are employed at a local supermarket. The table shows James's earnings, and the graph shows Eric's earnings.
Based on the information above, who earns the greater amount per hour, and how much does he earn for a 7-hour shift?
- A. James earns the greater amount per hour and earns $73.50 for a 7-hour shift.
- B. James earns the greater amount per hour and earns $70.00 for a 7-hour shift.
- C. Eric earns the greater amount per hour and earns $70.00 for a 7-hour shift.
- D. Eric earns the greater amount per hour and earns $73.50 for a 7-hour shift.
Correct Answer & Rationale
Correct Answer: D
To determine who earns more per hour, one must compare the hourly rates of James and Eric. If Eric's hourly rate is higher, he earns more for a 7-hour shift, calculated as his hourly rate multiplied by 7. Option A incorrectly states James earns more and miscalculates his earnings. Option B also claims James earns more but provides the wrong total for a 7-hour shift. Option C correctly identifies Eric as the higher earner but misstates his total earnings for a 7-hour shift. Option D accurately identifies Eric as the higher earner and correctly calculates his earnings for a 7-hour shift at $73.50.
To determine who earns more per hour, one must compare the hourly rates of James and Eric. If Eric's hourly rate is higher, he earns more for a 7-hour shift, calculated as his hourly rate multiplied by 7. Option A incorrectly states James earns more and miscalculates his earnings. Option B also claims James earns more but provides the wrong total for a 7-hour shift. Option C correctly identifies Eric as the higher earner but misstates his total earnings for a 7-hour shift. Option D accurately identifies Eric as the higher earner and correctly calculates his earnings for a 7-hour shift at $73.50.
On a number line, what is the distance, in units, between 16 and -25
Correct Answer & Rationale
Correct Answer: 41 units
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
Type your answer in the box. You may use numbers, a decimal point (•), and/or a negative sign (-) in your answer.
The table shows the costs of items Anna purchased at an art supply store for her art class.
What was the total cost of the items that Anna purchased?
Correct Answer & Rationale
Correct Answer: 128.65
To find the total cost of Anna's purchases, add the individual prices of each item she bought. Summing these values accurately gives a total of 128.65. Other options are incorrect because they result from either miscalculating the addition or omitting an item from the total. For instance, if an item was not included, the total would be lower than 128.65. Conversely, adding extra costs or misreading the prices could lead to an inflated total. Therefore, precise addition of all listed costs is essential to arrive at the correct total.
To find the total cost of Anna's purchases, add the individual prices of each item she bought. Summing these values accurately gives a total of 128.65. Other options are incorrect because they result from either miscalculating the addition or omitting an item from the total. For instance, if an item was not included, the total would be lower than 128.65. Conversely, adding extra costs or misreading the prices could lead to an inflated total. Therefore, precise addition of all listed costs is essential to arrive at the correct total.