Caterpillar 1 ft in 7.5 min. 18 min?
- A. 2.4
- B. 8
- C. 11.5
- D. 25.5
Correct Answer & Rationale
Correct Answer: A
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
Other Related Questions
x?
- A. -11
- B. -3
- C. 3
- D. 11
Correct Answer & Rationale
Correct Answer: B
To determine the value of \( x \), consider the context of the problem. Option B, -3, is the only value that fits the criteria established by the equation or conditions provided. Option A, -11, is too far from the expected range and does not satisfy the requirements. Option C, 3, is positive and contradicts the need for a negative solution. Option D, 11, is also positive and therefore incorrect. Each of the other options fails to meet the necessary conditions outlined in the problem, making -3 the only viable solution.
To determine the value of \( x \), consider the context of the problem. Option B, -3, is the only value that fits the criteria established by the equation or conditions provided. Option A, -11, is too far from the expected range and does not satisfy the requirements. Option C, 3, is positive and contradicts the need for a negative solution. Option D, 11, is also positive and therefore incorrect. Each of the other options fails to meet the necessary conditions outlined in the problem, making -3 the only viable solution.
178-degree angle?
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Correct Answer & Rationale
Correct Answer: B
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
50 acres, 23 apple. Percent left?
- A. 27%
- B. 46%
- C. 54%
- D. 77%
Correct Answer & Rationale
Correct Answer: C
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
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.