Based on the details provided, let's analyze each statement one by one according to the earnings mentioned for each profession:
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The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
- The plumber earns $60 per hour, while the lawyer earns $300 per hour. Therefore, for any number of hours worked, the lawyer always earns more than the plumber. False.
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The entry level worker has the same slope as the lawyer.
- The slope refers to the rate of change, which in this context is the hourly wage. The lawyer earns $300 an hour, and the entry-level worker earns $6 an hour. Therefore, the slopes are not the same. False.
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Bill Gates has the same y-intercept as the entry level worker.
- The y-intercept would refer to the initial amount earned before any hours are worked. However, if we consider the graph setup with their respective earnings, we don't have specific information on initial amounts from the graph description. With no specific initial earnings noted for Bill Gates versus the entry level worker, this cannot be definitively confirmed. Ambiguous/Not enough information.
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The plumber has a steeper rate of change than the entry level worker.
- The plumber earns $60 per hour, and the entry-level worker earns $6 per hour. Thus, the plumber has a steeper slope (rate of change) compared to the entry level worker. True.
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The lawyer has a greater initial amount of earnings than the plumber.
- The lawyer earns $300 per hour and the plumber earns $60 per hour. The lawyer will always earn more than the plumber for any amount of hours worked (given they work the same number of hours). However, if referring to the specific earnings at hour 0, both start at $0 earnings, which means neither initially has more. This statement can be misleading since it might imply starting earnings rather than the rate. False.
Summary:
- True Statements: The plumber has a steeper rate of change than the entry level worker.
- False Statements: The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked; The entry level worker has the same slope as the lawyer; The lawyer has a greater initial amount of earnings than the plumber.
- Ambiguous/Not enough information: Bill Gates has the same y-intercept as the entry level worker.