On a number line, what is the distance, in units, between 16 and -25
Correct Answer & Rationale
Correct Answer: 41 units
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
Other Related Questions
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.
At what point does the function stop decreasing and start increasing?
- A. (1, -4)
- B. (3, 0)
- C. (-4, 1)
- D. (0, -3)
Correct Answer & Rationale
Correct Answer: A
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
What is the slope of the line represented by the table?
- A. -4
- B. -2.5
- C. -2
- D. -0.5
Correct Answer & Rationale
Correct Answer: C
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.
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.