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Answer :
Sure! Let's go through each option to determine which scales are equivalent to the given scale of 3 cm to 4 km.
First, let's consider the given scale:
- 3 cm to 4 km means 3 cm on the map represents 400,000 cm in reality (since 4 km = 4,000,000 cm). This simplifies to a ratio of 3/400,000 or approximately 7.5e-06 per cm.
Now, let's evaluate each option:
Option A: 0.75 cm to 1 km
- 1 km = 100,000 cm. The scale becomes 0.75 cm to 100,000 cm.
- The ratio is 0.75/100,000, which equals 7.5e-06 per cm.
Option B: 1 cm to 12 km
- 12 km = 1,200,000 cm. The scale becomes 1 cm to 1,200,000 cm.
- The ratio is 1/1,200,000, which equals approximately 8.33e-07 per cm.
Option C: 6 mm to 2 km
- Convert 6 mm to cm: 6 mm = 0.6 cm.
- 2 km = 200,000 cm. The scale becomes 0.6 cm to 200,000 cm.
- The ratio is 0.6/200,000, which equals 3e-06 per cm.
Option D: 0.3 mm to 40 m
- Convert 0.3 mm to cm: 0.3 mm = 0.03 cm.
- 40 m = 4,000 cm. The scale becomes 0.03 cm to 4,000 cm.
- The ratio is 0.03/4,000, which equals 7.5e-06 per cm.
Option E: 1 inch to 7.62 km
- Convert 1 inch to cm: 1 inch = 2.54 cm.
- 7.62 km = 762,000 cm. The scale becomes 2.54 cm to 762,000 cm.
- The ratio is 2.54/762,000, which equals approximately 3.33e-06 per cm.
Finally, we compare the ratios:
- The original ratio was approximately 7.5e-06.
- Options A and D have equivalent ratios to the original scale.
Therefore, the scales that are equivalent to the given scale of 3 cm to 4 km are options A and D.
First, let's consider the given scale:
- 3 cm to 4 km means 3 cm on the map represents 400,000 cm in reality (since 4 km = 4,000,000 cm). This simplifies to a ratio of 3/400,000 or approximately 7.5e-06 per cm.
Now, let's evaluate each option:
Option A: 0.75 cm to 1 km
- 1 km = 100,000 cm. The scale becomes 0.75 cm to 100,000 cm.
- The ratio is 0.75/100,000, which equals 7.5e-06 per cm.
Option B: 1 cm to 12 km
- 12 km = 1,200,000 cm. The scale becomes 1 cm to 1,200,000 cm.
- The ratio is 1/1,200,000, which equals approximately 8.33e-07 per cm.
Option C: 6 mm to 2 km
- Convert 6 mm to cm: 6 mm = 0.6 cm.
- 2 km = 200,000 cm. The scale becomes 0.6 cm to 200,000 cm.
- The ratio is 0.6/200,000, which equals 3e-06 per cm.
Option D: 0.3 mm to 40 m
- Convert 0.3 mm to cm: 0.3 mm = 0.03 cm.
- 40 m = 4,000 cm. The scale becomes 0.03 cm to 4,000 cm.
- The ratio is 0.03/4,000, which equals 7.5e-06 per cm.
Option E: 1 inch to 7.62 km
- Convert 1 inch to cm: 1 inch = 2.54 cm.
- 7.62 km = 762,000 cm. The scale becomes 2.54 cm to 762,000 cm.
- The ratio is 2.54/762,000, which equals approximately 3.33e-06 per cm.
Finally, we compare the ratios:
- The original ratio was approximately 7.5e-06.
- Options A and D have equivalent ratios to the original scale.
Therefore, the scales that are equivalent to the given scale of 3 cm to 4 km are options A and D.
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