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
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.
Prime numbers? Select ALL.
- A. 21
- B. 23
- C. 25
- D. 27
- E. 29
Correct Answer & Rationale
Correct Answer: B,E
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.
Joe’s age 4 more than 3x Amy’s. Equation?
- A. A=J/3+4
- B. A=3J+4
- C. J=3A+4
- D. J=3(A+4)
Correct Answer & Rationale
Correct Answer: C
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
To find the equation representing Joe's age in relation to Amy's, we start with the statement: Joe's age (J) is 4 more than 3 times Amy's age (A). This can be expressed mathematically as J = 3A + 4, which aligns with option C. Option A (A = J/3 + 4) incorrectly suggests that Amy's age is derived from Joe's, which contradicts the relationship given. Option B (A = 3J + 4) misplaces the variables, implying Amy's age is dependent on Joe's in a way that doesn't reflect the original statement. Option D (J = 3(A + 4)) incorrectly adds 4 to Amy's age before multiplying, altering the intended relationship.
1.085/12 value?
- A. 90
- B. 90 * 5/1.085
- C. 90 * 5/12
- D. 90.5
Correct Answer & Rationale
Correct Answer: C
To find the value of 1.085/12, we need to simplify the expression. Option C, 90 * 5/12, correctly represents a simplified fraction of 90 divided by 12, multiplied by 5. This yields a value consistent with the original division. Option A (90) is incorrect as it does not involve the division by 12. Option B (90 * 5/1.085) incorrectly uses 1.085 as a divisor instead of 12, leading to an inaccurate calculation. Option D (90.5) is also incorrect as it does not relate to the division of 1.085 by 12, resulting in a value that does not reflect the operation required.
To find the value of 1.085/12, we need to simplify the expression. Option C, 90 * 5/12, correctly represents a simplified fraction of 90 divided by 12, multiplied by 5. This yields a value consistent with the original division. Option A (90) is incorrect as it does not involve the division by 12. Option B (90 * 5/1.085) incorrectly uses 1.085 as a divisor instead of 12, leading to an inaccurate calculation. Option D (90.5) is also incorrect as it does not relate to the division of 1.085 by 12, resulting in a value that does not reflect the operation required.