Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Type your answer in the boxes. You may use numbers and/or a negative sign (-) in your answer.
A total of 42 runners dropped out before finishing the race. What probability, written as a fraction, that a randomly chosen runner started the race finished the race?
Correct Answer & Rationale
Correct Answer: 583/625
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
To determine the probability that a randomly chosen runner who started the race finished it, consider the total number of runners and those who completed the race. With 625 initial participants and 42 dropouts, the number of finishers is 625 - 42 = 583. Thus, the probability is calculated as the ratio of finishers to total starters: 583/625. Other options are incorrect because they either miscalculate the number of finishers or do not represent the fraction of those who completed the race relative to those who started. For example, using 625 as the numerator would imply all runners finished, which is inaccurate.
Other Related Questions
For an emergency service call, a plumbing company charges a flat fee of $60 plus $40 an hour. A customer remembers paying at least $200 for an emergency service. Which phrase describes the number of hours the plumbing company was at the service call?
- A. at most 2 hours
- B. at most 3.5 hours
- C. at least 3.5 hours
- D. at least 2 hours
Correct Answer & Rationale
Correct Answer: C
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 ÷ $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 ÷ $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
Which table shows a function?
- A. M-43A.png
- B. M-43B.png
- C. M-43C.png
- D. M-43D.png
Correct Answer & Rationale
Correct Answer: A
To determine which table represents a function, we look for a unique output for every input. Option A demonstrates this principle, as each input corresponds to a single output, confirming a functional relationship. In contrast, Option B features repeated inputs yielding different outputs, violating the definition of a function. Option C also presents multiple outputs for the same input, disqualifying it as a function. Lastly, Option D has inputs linked to multiple outputs as well, further indicating it does not represent a function. Thus, only Option A adheres to the criteria for a function.
To determine which table represents a function, we look for a unique output for every input. Option A demonstrates this principle, as each input corresponds to a single output, confirming a functional relationship. In contrast, Option B features repeated inputs yielding different outputs, violating the definition of a function. Option C also presents multiple outputs for the same input, disqualifying it as a function. Lastly, Option D has inputs linked to multiple outputs as well, further indicating it does not represent a function. Thus, only Option A adheres to the criteria for a function.
Which equation represents the graphed line?
- A. y = -1/3x +3
- B. y = 3x - 7
- C. y = 3x + 7
- D. y = 1/3x + 1
Correct Answer & Rationale
Correct Answer: D
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The equation y = 1/3x + 1 accurately represents the graphed line due to its positive slope of 1/3, indicating a gradual upward rise, consistent with the line’s direction. The y-intercept of 1 shows that the line crosses the y-axis at the point (0, 1), aligning perfectly with the graph. Option A, with a slope of -1/3, suggests a downward trend, which contradicts the graph’s upward slope. Option B has a much steeper slope of 3, leading to a different angle of rise. Option C also has a slope of 3 and a y-intercept of 7, which does not match the graph’s intercept. Thus, only D accurately reflects both the slope and intercept of the line shown.
The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
- A. 36
- B. 16
- C. 40
- D. 13
Correct Answer & Rationale
Correct Answer: A
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.