Compare 3 in 123,456 to others.
436,521 315,624 126,354 642,135
- A. 100x_____
- B. 10x_____
- C. 0.1x_____
- D. 0.01x_____
Correct Answer & Rationale
Correct Answer: B,A,C,D
To determine the appropriate multiplier for each number, we analyze their values: - **B: 10x_____** is valid as multiplying by 10 shifts the decimal point one place to the right, increasing the value significantly, making it suitable for larger numbers like 436,521 and 315,624. - **A: 100x_____** is also applicable, as multiplying by 100 shifts the decimal two places, further increasing the value. However, it is not the most fitting choice for the context of smaller increments. - **C: 0.1x_____** indicates a decrease in value, which applies to smaller numbers but is less relevant for the context of significant values like 126,354. - **D: 0.01x_____** further diminishes the number, making it the least appropriate option for the given values, as it reduces the numbers excessively. In conclusion, B is the best fit for maintaining relevance to the larger values, while A, C, and D serve progressively less appropriate roles.
To determine the appropriate multiplier for each number, we analyze their values: - **B: 10x_____** is valid as multiplying by 10 shifts the decimal point one place to the right, increasing the value significantly, making it suitable for larger numbers like 436,521 and 315,624. - **A: 100x_____** is also applicable, as multiplying by 100 shifts the decimal two places, further increasing the value. However, it is not the most fitting choice for the context of smaller increments. - **C: 0.1x_____** indicates a decrease in value, which applies to smaller numbers but is less relevant for the context of significant values like 126,354. - **D: 0.01x_____** further diminishes the number, making it the least appropriate option for the given values, as it reduces the numbers excessively. In conclusion, B is the best fit for maintaining relevance to the larger values, while A, C, and D serve progressively less appropriate roles.
Other Related Questions
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.
d=rt, triple d, same t, new rate?
- A. 3dt
- B. (3d)/t
- C. t/(3d)
- D. d/(3t)
Correct Answer & Rationale
Correct Answer: B
In the equation d = rt, if distance (d) is tripled while time (t) remains constant, the new distance becomes 3d. To find the new rate (r'), we can rearrange the formula to r' = d/t. Substituting the new distance gives r' = (3d)/t, which is option B. Option A (3dt) incorrectly suggests multiplying distance by time, which does not represent rate. Option C (t/(3d)) misplaces the variables, implying time is divided by distance, which does not align with the rate formula. Option D (d/(3t)) incorrectly divides distance by three times the time, again misrepresenting the relationship between distance, rate, and time.
In the equation d = rt, if distance (d) is tripled while time (t) remains constant, the new distance becomes 3d. To find the new rate (r'), we can rearrange the formula to r' = d/t. Substituting the new distance gives r' = (3d)/t, which is option B. Option A (3dt) incorrectly suggests multiplying distance by time, which does not represent rate. Option C (t/(3d)) misplaces the variables, implying time is divided by distance, which does not align with the rate formula. Option D (d/(3t)) incorrectly divides distance by three times the time, again misrepresenting the relationship between distance, rate, and time.
Order 0.68, 1/12, 1(1/5), 3/5 least to greatest?
- A. 1(1/5), 0.68, 3/5, 1/12
- B. 1/12, 3/5, 0.68, 1(1/5)
- C. 1/12, 0.68, 3/5, 1(1/5)
- D. 0.68, 1/12, 3/5, 1(1/5)
Correct Answer & Rationale
Correct Answer: B
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.
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.