Let's break down the scale notation: [tex]\(1^{\prime \prime}=20^{\prime}-0^{\prime \prime}\)[/tex].
To understand what this scale means, we need to interpret the symbols used:
- [tex]\(1^{\prime \prime}\)[/tex] represents an inch.
- [tex]\(20^{\prime}-0^{\prime \prime}\)[/tex] represents 20 feet and 0 inches.
Therefore, the notation [tex]\(1^{\prime \prime}=20^{\prime}-0^{\prime \prime}\)[/tex] indicates the relationship between a measurement on the plan and the actual measurement on the ground.
Here's a step-by-step explanation:
1. An inch on the plan is represented by [tex]\(1^{\prime \prime}\)[/tex].
2. [tex]\(20^{\prime}-0^{\prime \prime}\)[/tex] is equivalent to 20 feet in standard notation.
Now let's interpret the given choices:
1. Every inch represents 20": This statement implies that every inch on the plan equals 20 inches in reality, which is not correct.
2. Every inch represents [tex]\(20^{\prime}\)[/tex]: This indicates that every inch on the plan equals 20 feet in reality. This matches our interpretation of the scale notation.
3. Every foot represents 20": This statement implies that every foot on the plan equals 20 inches in reality, which is incorrect because the scale we are given is in inches.
4. Every foot represents [tex]\(20^{\prime}\)[/tex]: This implies that every foot on the plan equals 20 feet in reality, but we are given a scale in inches.
Given the scale [tex]\(1^{\prime \prime} = 20^{\prime}-0^{\prime \prime}\)[/tex], the correct interpretation is:
Every inch on the plan represents 20 feet in real life.
Thus, the answer is:
Every inch represents [tex]\(20^{\prime}\)[/tex].
