Trevani bought a book. She paid a total of $13.50, including 8% sales tax. How much tax did Trevani pay on the book?
- A. $0.96
- B. $1.00
- C. $1.04
- D. $1.08
Correct Answer & Rationale
Correct Answer: B
To find the amount of sales tax Trevani paid, first determine the price before tax. The total amount paid, $13.50, includes an 8% tax. To find the pre-tax amount, divide the total by 1.08 (which accounts for the original price plus tax): $13.50 ÷ 1.08 = $12.50. Next, calculate the sales tax by subtracting the pre-tax amount from the total: $13.50 - $12.50 = $1.00. This confirms that Trevani paid $1.00 in tax. - Option A ($0.96) is incorrect as it underestimates the tax. - Option C ($1.04) slightly overestimates the tax. - Option D ($1.08) incorrectly assumes the total is all tax without accounting for the book's price.
To find the amount of sales tax Trevani paid, first determine the price before tax. The total amount paid, $13.50, includes an 8% tax. To find the pre-tax amount, divide the total by 1.08 (which accounts for the original price plus tax): $13.50 ÷ 1.08 = $12.50. Next, calculate the sales tax by subtracting the pre-tax amount from the total: $13.50 - $12.50 = $1.00. This confirms that Trevani paid $1.00 in tax. - Option A ($0.96) is incorrect as it underestimates the tax. - Option C ($1.04) slightly overestimates the tax. - Option D ($1.08) incorrectly assumes the total is all tax without accounting for the book's price.
Other Related Questions
Valentina attends several meetings each day, as shown in the table below. Which of the following describes this pattern?
- A. The number of meetings increases by the same amount each day.
- B. The number of meetings decreases by the same amount each day.
- C. Each day, the number of meetings increases by the same percent over the previous day's number of meetings.
- D. Each day, the number of meetings decreases by the same percent over the previous day's number of meetings.
Correct Answer & Rationale
Correct Answer: C
The pattern of Valentina's meetings indicates that the number of meetings increases by a consistent percentage each day, reflecting exponential growth. This is evident when comparing the daily totals, which show a proportional rise rather than a fixed increase. Option A is incorrect because it suggests a linear growth, where the same number of meetings is added daily, which is not observed. Option B implies a consistent decrease, which contradicts the observed increase in meetings. Option D also misrepresents the data by suggesting a percentage decrease, which does not align with the trend of increasing meetings.
The pattern of Valentina's meetings indicates that the number of meetings increases by a consistent percentage each day, reflecting exponential growth. This is evident when comparing the daily totals, which show a proportional rise rather than a fixed increase. Option A is incorrect because it suggests a linear growth, where the same number of meetings is added daily, which is not observed. Option B implies a consistent decrease, which contradicts the observed increase in meetings. Option D also misrepresents the data by suggesting a percentage decrease, which does not align with the trend of increasing meetings.
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.
In the xy-plane above, the circle has center (0, 0) and AB is a diameter of the circle. What is the equation of the line passing through points A and B?
- A. y=-2/3 x
- B. y=2/3 x
- C. y=3/2 x
- D. y=4x
Correct Answer & Rationale
Correct Answer: B
The line passing through points A and B, which are endpoints of a diameter of the circle centered at (0, 0), must be a straight line that passes through the origin. Option B, \(y = \frac{2}{3}x\), represents a line with a positive slope, indicating that as x increases, y also increases, which is consistent with the properties of a diameter. Option A, \(y = -\frac{2}{3}x\), has a negative slope, suggesting a downward trend, which does not align with the upward direction of a diameter in the first quadrant. Option C, \(y = \frac{3}{2}x\), has a steeper slope than option B, which may not accurately represent the diameter's angle unless specified. Option D, \(y = 4x\), has an even steeper slope, making it unlikely to be the diameter unless A and B are positioned at extreme angles, which is not given in the problem.
The line passing through points A and B, which are endpoints of a diameter of the circle centered at (0, 0), must be a straight line that passes through the origin. Option B, \(y = \frac{2}{3}x\), represents a line with a positive slope, indicating that as x increases, y also increases, which is consistent with the properties of a diameter. Option A, \(y = -\frac{2}{3}x\), has a negative slope, suggesting a downward trend, which does not align with the upward direction of a diameter in the first quadrant. Option C, \(y = \frac{3}{2}x\), has a steeper slope than option B, which may not accurately represent the diameter's angle unless specified. Option D, \(y = 4x\), has an even steeper slope, making it unlikely to be the diameter unless A and B are positioned at extreme angles, which is not given in the problem.
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.