What is the slope of the line shown on the graph
- A. -0.333333333
- B. -3
- C. 3
- D. 1\3
Correct Answer & Rationale
Correct Answer: D
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
Other Related Questions
The mass of an amoeba is approximately 4.0 × 10^(-6) grams. Approximately how many amoebas are present in a sample that weighs 1 gram?
- A. 2.5 × 10^5
- B. 4.0 × 10^7
- C. 4.0 × 10^5
- D. 2.5 × 10^7
Correct Answer & Rationale
Correct Answer: A
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
What is the value of 0.6 - (0.7)(1.4)?
- A. -0.38
- B. -0.14
- C. -0.42
- D. -1.5
Correct Answer & Rationale
Correct Answer: A
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
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.
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.