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.
Other Related Questions
Favorite food via survey numbers. Best measure?
- A. Mean
- B. Median
- C. Mode
- D. Mean+median
Correct Answer & Rationale
Correct Answer: C
When analyzing survey data on favorite foods, the mode is the best measure since it identifies the most frequently chosen option, reflecting the popular preference among respondents. The mean can be skewed by outliers, making it less reliable in this context. The median, while useful for understanding the middle value, does not capture the most popular choice effectively. Combining mean and median (option D) does not address the core goal of identifying the favorite food, which is best represented by the mode. Thus, the mode provides a clear insight into the most favored food item.
When analyzing survey data on favorite foods, the mode is the best measure since it identifies the most frequently chosen option, reflecting the popular preference among respondents. The mean can be skewed by outliers, making it less reliable in this context. The median, while useful for understanding the middle value, does not capture the most popular choice effectively. Combining mean and median (option D) does not address the core goal of identifying the favorite food, which is best represented by the mode. Thus, the mode provides a clear insight into the most favored food item.
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.
(2x+3y-7)-(2x-3y-8)?
- A. 1
- B. -15
- C. 6y+1
- D. 6y-15
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
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.