I have a class that consists only of static member variables and static methods. Essentially, it is serving as a general-purpose utility class.
Is i
Just don't get carried away with it. Notice that the java.lang.Math class is only about math functions. You might also have a StringUtilities class which contains common string-handling functions which aren't in the standard API, for example. But if your class is named Utilities, for example, that's a hint that you might want to split it up.