A cyclist can travel 17.6 feet per second. The cyclist would have a better understanding of her speed if it were measured in miles per hour. Which of these completes the expression used to convert the speed of the cyclist to miles per hour?
- A. 1 hour/60 seconds = 1 mile/5,280 feet
- B. 60 minutes/1 hour = 1 mile/5280 feet
- C. 60 minutes/1 hour = 5280 feet/1 mile
- D. 12 inches/1 foot = 60 minutes/1 hour
Correct Answer & Rationale
Correct Answer: C
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
Other Related Questions
What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
Which graph shows 3y - 2x = 6?
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A.
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B.
Correct Answer & Rationale
Correct Answer: B
To determine the graph of the equation \(3y - 2x = 6\), we can rearrange it into slope-intercept form \(y = mx + b\). This gives us \(y = \frac{2}{3}x + 2\), indicating a slope of \(\frac{2}{3}\) and a y-intercept of 2. Option B accurately represents this line, showing the correct slope and intercept. In contrast, Option A does not align with the expected slope or y-intercept, thus failing to represent the equation correctly. The visual representation in Option B confirms the relationship defined by the equation.
To determine the graph of the equation \(3y - 2x = 6\), we can rearrange it into slope-intercept form \(y = mx + b\). This gives us \(y = \frac{2}{3}x + 2\), indicating a slope of \(\frac{2}{3}\) and a y-intercept of 2. Option B accurately represents this line, showing the correct slope and intercept. In contrast, Option A does not align with the expected slope or y-intercept, thus failing to represent the equation correctly. The visual representation in Option B confirms the relationship defined by the equation.
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.
Dr. Evers is experimenting with light beams and prisms. He passes a beam of white light through a triangular prism which spreads the light out into its six rainbow colors. The bases of the prism are equilateral triangles. The surface area of this prism is 4,292 square millimeters. The area of each triangular face is 271 square millimeters. Which expression can be used to find h, the height, in millimeters, of the prism?
- A. 4,292/3(25)
- B. 4,292/271
- C. (4,292-271)/25
- D. (4,292-2(271))/3(25)
Correct Answer & Rationale
Correct Answer: D
To find the height \( h \) of the prism, we start with the total surface area of the prism, which includes the two triangular bases and three rectangular sides. The area of the two triangular bases is \( 2 \times 271 = 542 \) square millimeters. Subtracting this from the total surface area gives \( 4,292 - 542 = 3,750 \) square millimeters for the area of the rectangular sides. Since the height \( h \) is involved in the area of the rectangles, dividing this area by the perimeter of the base (which is \( 3 \times 25 = 75 \) mm) leads to \( h = \frac{3,750}{75} \) or \( \frac{4,292 - 542}{75} \), simplifying to option D. Options A and B incorrectly compute the height without accounting for the rectangular areas properly. Option C miscalculates the area of the triangular bases and does not consider the full surface area needed to find \( h \). Thus, only option D correctly utilizes the total surface area and the dimensions of the prism to derive the height.
To find the height \( h \) of the prism, we start with the total surface area of the prism, which includes the two triangular bases and three rectangular sides. The area of the two triangular bases is \( 2 \times 271 = 542 \) square millimeters. Subtracting this from the total surface area gives \( 4,292 - 542 = 3,750 \) square millimeters for the area of the rectangular sides. Since the height \( h \) is involved in the area of the rectangles, dividing this area by the perimeter of the base (which is \( 3 \times 25 = 75 \) mm) leads to \( h = \frac{3,750}{75} \) or \( \frac{4,292 - 542}{75} \), simplifying to option D. Options A and B incorrectly compute the height without accounting for the rectangular areas properly. Option C miscalculates the area of the triangular bases and does not consider the full surface area needed to find \( h \). Thus, only option D correctly utilizes the total surface area and the dimensions of the prism to derive the height.