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17) A scale is \( 1 \mathrm{~cm}: 20 \mathrm{mh} \). Which descritess the erroy in finding the actual distancec that corresponds to 5 centimeters? N \( \frac{1 e m}{20 m}=\frac{x m}{5 \mathrm{em}} \) The units on the measurements are incorrect. The 5 cm should be in the numerator. The multiplication was done incorrectly The division was done incorrectly Write the correct answer to fix the error. The actual distance that corresponds to 5 centimeters is \( \qquad \) meters.

Ask by Ward Page. in the United States
Jan 23,2025

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Answer

The actual distance that corresponds to 5 centimeters is 100 meters.

Solution

The error in the original setup is **"The 5 cm should be in the numerator."** This means that when setting up the proportion, the 5 cm should be placed in the numerator to correctly represent the relationship between the scale and the actual distance. **Correct Proportion Setup:** \[ \frac{1 \text{ cm}}{20 \text{ m}} = \frac{5 \text{ cm}}{x \text{ m}} \] **Solving for \( x \):** \[ x = \frac{5 \text{ cm} \times 20 \text{ m}}{1 \text{ cm}} = 100 \text{ m} \] **Final Answer:** The actual distance that corresponds to 5 centimeters is \( 100 \) meters.

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Bonus Knowledge

When working with a scale of \( 1 \mathrm{~cm}: 20 \mathrm{mh} \), it’s essential to keep track of the units. If \( 1 \mathrm{~cm} \) represents \( 20 \mathrm{mh} \), then for \( 5 \mathrm{~cm} \), you multiply 5 by 20. So, \( 5 \mathrm{~cm} = 5 \times 20 \mathrm{~mh} = 100 \mathrm{mh} \). Therefore, the actual distance that corresponds to \( 5 \mathrm{~cm} \) is \( 100 \mathrm{~mh} \). To avoid mistakes, always ensure consistency in your unit measurements. Keep your conversions organized and double-check that you’re using the correct scale proportions. It helps to write down the scale conversion clearly before performing mathematical operations. This way, you can step back and check if you’ve calculated the figures correctly!

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