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yes. usually you will work with an equal amount of dependent and independent variables. (ie, one dependent variable for every independent variable, and such that there is some kind of relationship between each..) If only. Usually a variable depends on many other variables. Such as, the price of a house depends on its size, number of rooms, distance to schools, age, windows etc.
The dependent variable is the number of bottles filled. It depends on the time elapsed since the run began.
It depends on what you are doing with the cheese. For example, if you were studying the effects of different temperatures of a specific cheese, cheese would be the dependent variable. Or, if you were studying the number of mice attracted to different amounts of cheese, cheese would be the independent variable.
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Yes, the usual case in mathematics is to use the the y-axis variable as the dependent variable.