Each of the following is a solution to the equation x- 2y = 4 EXCEPT
- A. (-2,-3)
- B. (0,2)
- C. (4,0)
- D. (8,2)
Correct Answer & Rationale
Correct Answer: B
To determine which option is not a solution to the equation \(x - 2y = 4\), we can substitute each pair into the equation. - For A: \((-2, -3)\), substituting gives \(-2 - 2(-3) = -2 + 6 = 4\), which is correct. - For B: \((0, 2)\), substituting gives \(0 - 2(2) = 0 - 4 = -4\), which does not equal 4, making this option incorrect. - For C: \((4, 0)\), substituting gives \(4 - 2(0) = 4\), which is correct. - For D: \((8, 2)\), substituting gives \(8 - 2(2) = 8 - 4 = 4\), which is correct. Thus, option B is the only pair that does not satisfy the equation.
To determine which option is not a solution to the equation \(x - 2y = 4\), we can substitute each pair into the equation. - For A: \((-2, -3)\), substituting gives \(-2 - 2(-3) = -2 + 6 = 4\), which is correct. - For B: \((0, 2)\), substituting gives \(0 - 2(2) = 0 - 4 = -4\), which does not equal 4, making this option incorrect. - For C: \((4, 0)\), substituting gives \(4 - 2(0) = 4\), which is correct. - For D: \((8, 2)\), substituting gives \(8 - 2(2) = 8 - 4 = 4\), which is correct. Thus, option B is the only pair that does not satisfy the equation.
Other Related Questions
Malia collected information about whether the members of the 36 households on her block subscribed to cable television and home phone services. Her results are shown in the table below.\nIf a household on Malia's block is selected at random and does subscribe to cable television, what is the probability the members of the household also subscribe to home phone service?
- A. 14/18
- B. 14/26
- C. 18/36
- D. 14/36
Correct Answer & Rationale
Correct Answer: A
To determine the probability that a household subscribes to home phone service given that it subscribes to cable television, we focus on the relevant subset of households. Malia found 18 households that subscribe to cable, out of which 14 also subscribe to home phone service. Thus, the probability is calculated as the number of households with both services (14) divided by the total number of households with cable (18), resulting in 14/18. Option B (14/26) incorrectly uses the total number of households with home phone service instead of just those with cable. Option C (18/36) misinterprets the probability as a ratio of all households rather than those who subscribe to cable. Option D (14/36) inaccurately represents the total number of households instead of focusing on the cable subscribers.
To determine the probability that a household subscribes to home phone service given that it subscribes to cable television, we focus on the relevant subset of households. Malia found 18 households that subscribe to cable, out of which 14 also subscribe to home phone service. Thus, the probability is calculated as the number of households with both services (14) divided by the total number of households with cable (18), resulting in 14/18. Option B (14/26) incorrectly uses the total number of households with home phone service instead of just those with cable. Option C (18/36) misinterprets the probability as a ratio of all households rather than those who subscribe to cable. Option D (14/36) inaccurately represents the total number of households instead of focusing on the cable subscribers.
Fred, Norman, and Dave own a total of 128 comic books. If Dave owns 44 of them, what is the average (arithmetic mean) number of comic books owned by Fred and Norman?
- A. 42
- B. 44
- C. 46
- D. 48
Correct Answer & Rationale
Correct Answer: A
To find the average number of comic books owned by Fred and Norman, first determine how many comic books they collectively own. Since Dave has 44 comic books, subtract this from the total: 128 - 44 = 84. Fred and Norman together own 84 comic books. To find the average for the two, divide this number by 2: 84 ÷ 2 = 42. Option B (44) incorrectly assumes Fred and Norman have more than they actually do. Option C (46) miscalculates the average by not considering the correct total for Fred and Norman. Option D (48) similarly overestimates their combined ownership. Thus, the average is accurately calculated as 42.
To find the average number of comic books owned by Fred and Norman, first determine how many comic books they collectively own. Since Dave has 44 comic books, subtract this from the total: 128 - 44 = 84. Fred and Norman together own 84 comic books. To find the average for the two, divide this number by 2: 84 ÷ 2 = 42. Option B (44) incorrectly assumes Fred and Norman have more than they actually do. Option C (46) miscalculates the average by not considering the correct total for Fred and Norman. Option D (48) similarly overestimates their combined ownership. Thus, the average is accurately calculated as 42.
Point C is the center of the regular hexagon shown above. Which of the following expressions represents the area of this hexagon?
- A. 12xy
- B. 6xy
- C. 3xy
- D. xy
Correct Answer & Rationale
Correct Answer: B
The area of a regular hexagon can be calculated using the formula \( \frac{3\sqrt{3}}{2} s^2 \), where \( s \) is the length of a side. The expression \( 6xy \) aligns with this area formula when considering specific dimensions of the hexagon defined by \( x \) and \( y \). Option A, \( 12xy \), overestimates the area, suggesting a larger hexagon than the dimensions allow. Option C, \( 3xy \), and Option D, \( xy \), both underestimate the area, not accounting for the full extent of the hexagon's geometry. Thus, \( 6xy \) accurately represents the area based on the given variables.
The area of a regular hexagon can be calculated using the formula \( \frac{3\sqrt{3}}{2} s^2 \), where \( s \) is the length of a side. The expression \( 6xy \) aligns with this area formula when considering specific dimensions of the hexagon defined by \( x \) and \( y \). Option A, \( 12xy \), overestimates the area, suggesting a larger hexagon than the dimensions allow. Option C, \( 3xy \), and Option D, \( xy \), both underestimate the area, not accounting for the full extent of the hexagon's geometry. Thus, \( 6xy \) accurately represents the area based on the given variables.
The x-and y- coordinates of point P are each to be chosen at random from the set of integers 1 through 10. What is the probability that P will be in quadrant II?
- B. 01-Oct
- C. 01-Apr
- D. 01-Feb
Correct Answer & Rationale
Correct Answer: A
To determine the probability that point P is in quadrant II, we need to consider the coordinate system. In quadrant II, the x-coordinate must be negative, and the y-coordinate must be positive. However, since the x-coordinates are chosen from the integers 1 through 10, all possible x-values are positive. This means point P cannot be in quadrant II, making the probability 0. Option A correctly reflects this conclusion with a probability of 0. Options B, C, and D suggest specific dates, which are irrelevant to the question and do not address the coordinate conditions necessary for quadrant II. Thus, they are incorrect.
To determine the probability that point P is in quadrant II, we need to consider the coordinate system. In quadrant II, the x-coordinate must be negative, and the y-coordinate must be positive. However, since the x-coordinates are chosen from the integers 1 through 10, all possible x-values are positive. This means point P cannot be in quadrant II, making the probability 0. Option A correctly reflects this conclusion with a probability of 0. Options B, C, and D suggest specific dates, which are irrelevant to the question and do not address the coordinate conditions necessary for quadrant II. Thus, they are incorrect.