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The Putnam Coffee House brews fresh-roasted coffee beans to serve to their patrons. The amount of coffee they will need to brew in a day depends on the number of patrons they have. \( c= \) the amount of coffee they will need to brew \( p= \) the number of patrons Which of the variables is independent and which is dependent? \( p \) is the independent variable and \( c \) is the dependent variable c is the independent variable and \( p \) is the dependent variable

Ask by Long Thornton. in the United States
Jan 21,2025

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Tutor-Verified Answer

Answer

\( p \) is the independent variable and \( c \) is the dependent variable.

Solution

In the context of the problem: - **\( p \)** represents the **number of patrons**, which is the factor that influences or determines the outcome. - **\( c \)** represents the **amount of coffee** that needs to be brewed, which depends on the number of patrons. Therefore: - **\( p \) (number of patrons)** is the **independent variable** because it is the variable you control or that influences the outcome. - **\( c \) (amount of coffee)** is the **dependent variable** because its value depends on the number of patrons. **Correct Choice:** - **\( p \) is the independent variable and \( c \) is the dependent variable.**

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Beyond the Answer

You've got it right! In this scenario, the number of patrons \( p \) is the independent variable because it can change without being influenced by any other factors in your coffee house. The amount of coffee \( c \), on the other hand, is the dependent variable since it varies based on how many patrons arrive. The more patrons you have, the more coffee you'll need to brew to keep everyone caffeinated and happy! Now here's the fun part! Many coffee shops actually use this relationship for forecasting. They analyze previous customer data to predict daily coffee demand based on trends—like special events or weather. This allows them to optimize their brewing quantities, avoid waste, and keep their customers satisfied with freshly brewed coffee exactly when they need it! Keep an eye on those patterns, and you’ll be brewing like a pro!

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