3 in 321,745 vs 4,631?
- A. 100
- B. 1000
- C. 10000
- D. 100000
Correct Answer & Rationale
Correct Answer: C
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.
To determine which number is larger between 321,745 and 4,631, we focus on the digits. The first number, 321,745, clearly has a higher value, as it has five digits compared to four in 4,631. Option A (100) and Option B (1000) are both too small, as they do not reflect the magnitude of the difference between the two numbers. Option D (100,000) is also incorrect, as it exceeds the value of 321,745. Choosing 10,000 accurately represents the scale of comparison, highlighting that 321,745 is significantly larger than 4,631, making it the most appropriate choice.
Other Related Questions
Point (-3,-6) quadrant?
- A. I
- B. II
- C. III
- D. IV
Correct Answer & Rationale
Correct Answer: C
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
Equivalent to 2(4f+2g)? Select ALL.
- A. 4*(2f+g)
- B. 4(2f+2g)
- C. 2f(4+2g)
- D. 16f+4g
- E. 8f+2g
Correct Answer & Rationale
Correct Answer: A,F
To determine which expressions are equivalent to \( 2(4f + 2g) \), we first simplify it: \[ 2(4f + 2g) = 8f + 4g \] Now, let's analyze each option: **A: \( 4(2f + g) \)** This expands to \( 8f + 4g \), matching our simplified expression. **B: \( 4(2f + 2g) \)** This simplifies to \( 8f + 8g \), which does not match \( 8f + 4g \). **C: \( 2f(4 + 2g) \)** This expands to \( 8f + 4fg \), introducing an extra term \( 4fg \) that makes it unequal. **D: \( 16f + 4g \)** This expression has \( 16f \), which is double the \( 8f \) we expect, thus it is not equivalent. **E: \( 8f + 2g \)** Here, while \( 8f \) matches, \( 2g \) does not equal \( 4g \), making it non-equivalent. **F: \( 8f + 4g \)** This matches our simplified expression exactly, confirming its equivalence. In summary, options A and F correctly represent the original expression, while B, C, D, and E do not.
To determine which expressions are equivalent to \( 2(4f + 2g) \), we first simplify it: \[ 2(4f + 2g) = 8f + 4g \] Now, let's analyze each option: **A: \( 4(2f + g) \)** This expands to \( 8f + 4g \), matching our simplified expression. **B: \( 4(2f + 2g) \)** This simplifies to \( 8f + 8g \), which does not match \( 8f + 4g \). **C: \( 2f(4 + 2g) \)** This expands to \( 8f + 4fg \), introducing an extra term \( 4fg \) that makes it unequal. **D: \( 16f + 4g \)** This expression has \( 16f \), which is double the \( 8f \) we expect, thus it is not equivalent. **E: \( 8f + 2g \)** Here, while \( 8f \) matches, \( 2g \) does not equal \( 4g \), making it non-equivalent. **F: \( 8f + 4g \)** This matches our simplified expression exactly, confirming its equivalence. In summary, options A and F correctly represent the original expression, while B, C, D, and E do not.
Eraser 20g in mg?
- A. 1.002
- B. 0.02
- C. 2,000
- D. 20
Correct Answer & Rationale
Correct Answer: D
To convert grams to milligrams, one must remember that 1 gram equals 1,000 milligrams. Therefore, 20 grams can be calculated as follows: 20 g x 1,000 mg/g = 20,000 mg. Option A (1.002 mg) is incorrect as it significantly underestimates the conversion. Option B (0.02 mg) is also wrong; it suggests a conversion error by not accounting for the unit scale correctly. Option C (2,000 mg) miscalculates the conversion by a factor of ten. Option D correctly represents 20 grams as 20,000 milligrams, aligning with the proper conversion calculation.
To convert grams to milligrams, one must remember that 1 gram equals 1,000 milligrams. Therefore, 20 grams can be calculated as follows: 20 g x 1,000 mg/g = 20,000 mg. Option A (1.002 mg) is incorrect as it significantly underestimates the conversion. Option B (0.02 mg) is also wrong; it suggests a conversion error by not accounting for the unit scale correctly. Option C (2,000 mg) miscalculates the conversion by a factor of ten. Option D correctly represents 20 grams as 20,000 milligrams, aligning with the proper conversion calculation.
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.