Quickly multiply 24x16?
- A. 20x20-4x4
- B. 20x20
- C. 20x10+4x6
- D. 25x10+4x15
Correct Answer & Rationale
Correct Answer: A
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Other Related Questions
Leslie descended 714 ft in 34 s, took 1 min 25 s to ground. Total distance?
- A. 1,270 feet
- B. 1,515 feet
- C. 1,785 feet
- D. 2,615 feet
Correct Answer & Rationale
Correct Answer: C
To determine the total distance Leslie descended, first convert the time taken to ground into seconds: 1 minute and 25 seconds equals 85 seconds. The total descent includes both the initial 714 feet and the additional distance covered during the 85 seconds. Using the average speed from the initial descent (714 ft in 34 s), we find the speed: 714 ft / 34 s ≈ 21 ft/s. Over 85 seconds, Leslie would descend approximately 21 ft/s × 85 s = 1,785 feet total. Option A (1,270 ft) underestimates the descent. Option B (1,515 ft) is also too low. Option D (2,615 ft) overestimates the total distance. Thus, C (1,785 ft) accurately reflects the total descent.
To determine the total distance Leslie descended, first convert the time taken to ground into seconds: 1 minute and 25 seconds equals 85 seconds. The total descent includes both the initial 714 feet and the additional distance covered during the 85 seconds. Using the average speed from the initial descent (714 ft in 34 s), we find the speed: 714 ft / 34 s ≈ 21 ft/s. Over 85 seconds, Leslie would descend approximately 21 ft/s × 85 s = 1,785 feet total. Option A (1,270 ft) underestimates the descent. Option B (1,515 ft) is also too low. Option D (2,615 ft) overestimates the total distance. Thus, C (1,785 ft) accurately reflects the total descent.
Graph for data over time?
- A. Bar
- B. Line
- C. Stem-and-leaf
- D. Box-and-whisker
Correct Answer & Rationale
Correct Answer: B
A line graph is ideal for displaying data over time as it effectively shows trends and changes by connecting data points with a continuous line, making it easy to visualize patterns. Option A, a bar graph, is better suited for comparing discrete categories rather than illustrating changes over time. Option C, a stem-and-leaf plot, is primarily used for displaying the distribution of numerical data and is not designed for time-series analysis. Option D, a box-and-whisker plot, summarizes data distribution and highlights outliers but does not convey trends over time effectively.
A line graph is ideal for displaying data over time as it effectively shows trends and changes by connecting data points with a continuous line, making it easy to visualize patterns. Option A, a bar graph, is better suited for comparing discrete categories rather than illustrating changes over time. Option C, a stem-and-leaf plot, is primarily used for displaying the distribution of numerical data and is not designed for time-series analysis. Option D, a box-and-whisker plot, summarizes data distribution and highlights outliers but does not convey trends over time effectively.
Greatest?
- A. 245 thousandths
- B. 24 hundredths
- C. 3 tenths
- D. 2 fifths
Correct Answer & Rationale
Correct Answer: D
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
p=5n, questions n, points p. True?
- A. Points dependent
- B. Questions dependent
- C. 5 points dependent
- D. 1/5 question dependent
Correct Answer & Rationale
Correct Answer: A
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.