1) Belle is building a trophy case for her son. The number of shelves in the case will be dictated by how many trophies Belle's son has. (1) \( s \) = the number of shelves (1) \( t \) = the number of trophies Which of the variables is independent and which is dependent? \( s \) is the independent variable and \( t \) is the dependent variable \( t \) is the independent variable and \( s \) is the dependent variable

To determine which variable is independent and which is dependent, we need to analyze the relationship between the two variables \( s \) (the number of shelves) and \( t \) (the number of trophies). 1. **Independent Variable**: This is the variable that can be changed or controlled in an experiment. It is the cause or input in the relationship. 2. **Dependent Variable**: This is the variable that is affected by the independent variable. It is the effect or output in the relationship. In this scenario: - The number of trophies \( t \) dictates how many shelves \( s \) Belle will need. This means that the number of trophies is the factor that influences the number of shelves. - Therefore, \( t \) (the number of trophies) is the independent variable because it can vary independently of the shelves. - Conversely, \( s \) (the number of shelves) is the dependent variable because it depends on the number of trophies. Thus, the correct identification is: - \( t \) is the independent variable and \( s \) is the dependent variable.