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.
Other Related Questions
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.
3/4 as sum of unit fractions?
- A. 1/8 + 1/8 + 1/8 + 1/4 + 1/4
- B. 2/8 + 1/4 + 4/16
- C. 5/8 + 2/16
- D. 1/2 + 1/4
Correct Answer & Rationale
Correct Answer: D
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
(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.
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.