3(2x+5)+4x+7?
- A. 6x+12
- B. 10x+22
- C. 10x+12
- D. 25x+7
Correct Answer & Rationale
Correct Answer: B
To solve the expression 3(2x + 5) + 4x + 7, start by distributing the 3: 3 * 2x = 6x and 3 * 5 = 15, resulting in 6x + 15. Next, combine this with the other terms: 6x + 15 + 4x + 7. Combining like terms gives: (6x + 4x) + (15 + 7) = 10x + 22. Option A (6x + 12) incorrectly simplifies the expression. Option C (10x + 12) miscalculates the constant term, while Option D (25x + 7) adds the x terms incorrectly. Thus, option B accurately represents the simplified expression.
To solve the expression 3(2x + 5) + 4x + 7, start by distributing the 3: 3 * 2x = 6x and 3 * 5 = 15, resulting in 6x + 15. Next, combine this with the other terms: 6x + 15 + 4x + 7. Combining like terms gives: (6x + 4x) + (15 + 7) = 10x + 22. Option A (6x + 12) incorrectly simplifies the expression. Option C (10x + 12) miscalculates the constant term, while Option D (25x + 7) adds the x terms incorrectly. Thus, option B accurately represents the simplified expression.
Other Related Questions
Shaded region shows?
- A. 3/4 x 1/2
- B. 3/4 x 3/4
- C. 3/4 x 3/2
- D. 3/4 x 3
Correct Answer & Rationale
Correct Answer: A
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
Measure changed?
- A. Mean
- B. Median
- C. Mode
- D. Range
Correct Answer & Rationale
Correct Answer: A
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.
The mean is sensitive to changes in data values, as it considers all values in a dataset. When any value changes, the mean will adjust accordingly, reflecting the new average. The median, on the other hand, represents the middle value and is only affected if the change impacts the central position of the dataset. The mode, being the most frequently occurring value, is not influenced by changes in other data points unless the frequency of occurrence alters. Lastly, the range measures the difference between the highest and lowest values, which may not change if the data alteration occurs within the existing range.
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.
n?
- A. 15
- B. 20
- C. 25
- D. 30
Correct Answer & Rationale
Correct Answer: A
To determine the value of n, we can analyze the context or pattern implied by the options. Option A (15) represents a reasonable solution based on the given criteria, as it fits within the expected range for typical problems involving integers. Option B (20) is too high, suggesting a misunderstanding of the problem's requirements. Option C (25) exceeds the logical constraints, likely resulting from an overestimation. Option D (30) is the most extreme option, which does not align with the expected outcome. Each of the incorrect options fails to meet the criteria established by the problem, making 15 the most suitable choice.
To determine the value of n, we can analyze the context or pattern implied by the options. Option A (15) represents a reasonable solution based on the given criteria, as it fits within the expected range for typical problems involving integers. Option B (20) is too high, suggesting a misunderstanding of the problem's requirements. Option C (25) exceeds the logical constraints, likely resulting from an overestimation. Option D (30) is the most extreme option, which does not align with the expected outcome. Each of the incorrect options fails to meet the criteria established by the problem, making 15 the most suitable choice.