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
Which of the following could be an equation of the line graphed in the xy-plane above?
- A. y=-x-3
- B. y=-x+3
- C. y=x-3
- D. y=x+3
Correct Answer & Rationale
Correct Answer: D
To determine the equation of the line, we analyze its slope and y-intercept. The line in the graph has a positive slope, indicating that as \(x\) increases, \(y\) also increases. Option D, \(y = x + 3\), has a positive slope of 1 and a y-intercept of 3, aligning with the graph's characteristics. Option A, \(y = -x - 3\), has a negative slope and would decrease as \(x\) increases, which contradicts the graph. Option B, \(y = -x + 3\), also has a negative slope, leading to a downward trend. Option C, \(y = x - 3\), has a positive slope but a y-intercept of -3, placing it below the graph. Thus, D is the only option that fits the observed line.
To determine the equation of the line, we analyze its slope and y-intercept. The line in the graph has a positive slope, indicating that as \(x\) increases, \(y\) also increases. Option D, \(y = x + 3\), has a positive slope of 1 and a y-intercept of 3, aligning with the graph's characteristics. Option A, \(y = -x - 3\), has a negative slope and would decrease as \(x\) increases, which contradicts the graph. Option B, \(y = -x + 3\), also has a negative slope, leading to a downward trend. Option C, \(y = x - 3\), has a positive slope but a y-intercept of -3, placing it below the graph. Thus, D is the only option that fits the observed line.
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.
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.
Square S has area 2√2 square units. What is the length of a side of square S?
- A. ∜128
- B. ∜32
- C. ∜8
- D. ∜2
Correct Answer & Rationale
Correct Answer: C
To find the length of a side of square S, we use the formula for the area of a square, which is \( \text{Area} = \text{side}^2 \). Given that the area is \( 2\sqrt{2} \), we set up the equation \( \text{side}^2 = 2\sqrt{2} \). Taking the square root gives us \( \text{side} = \sqrt{2\sqrt{2}} = \sqrt{2} \cdot \sqrt[4]{2} = \sqrt{2^2} = \sqrt{8} = 2\sqrt{2} \), which simplifies to \( \sqrt{8} \), leading to option C as the correct answer. Options A (\(\sqrt{128}\)), B (\(\sqrt{32}\)), and D (\(\sqrt{2}\)) are incorrect as they yield values greater than or less than the required side length. Specifically, \(\sqrt{128} = 8\sqrt{2}\) and \(\sqrt{32} = 4\sqrt{2}\) are both larger than \(2\sqrt{2}\), while \(\sqrt{2}\) is significantly smaller. Thus, option C accurately represents the side length of square S.
To find the length of a side of square S, we use the formula for the area of a square, which is \( \text{Area} = \text{side}^2 \). Given that the area is \( 2\sqrt{2} \), we set up the equation \( \text{side}^2 = 2\sqrt{2} \). Taking the square root gives us \( \text{side} = \sqrt{2\sqrt{2}} = \sqrt{2} \cdot \sqrt[4]{2} = \sqrt{2^2} = \sqrt{8} = 2\sqrt{2} \), which simplifies to \( \sqrt{8} \), leading to option C as the correct answer. Options A (\(\sqrt{128}\)), B (\(\sqrt{32}\)), and D (\(\sqrt{2}\)) are incorrect as they yield values greater than or less than the required side length. Specifically, \(\sqrt{128} = 8\sqrt{2}\) and \(\sqrt{32} = 4\sqrt{2}\) are both larger than \(2\sqrt{2}\), while \(\sqrt{2}\) is significantly smaller. Thus, option C accurately represents the side length of square S.