Repentance and faith, must both exist?

I understand faith (to believe) as being convinced or persuaded that something is true.  Repentance is a resolve to think or do differently.   

I believe it can be said that faith precedes repentance, for one must believe the message that causes them to resolve to think or do differently.  An example is the Ninevites who believed Jonah's message and then repented. One text says they believed, and another says they repented.  They did both, because they believed the message of Jonah, and then they repented, which then resulted in them changing their behavior.

But one can believe something and not repent.  One could believe the message they hear but not resolve to think or do differently.  An example would be that one could hear the warning that a hurricane is coming their way, but they do not resolve to leave their home.   It's not that they don't believe the message, it's just that they are not going to do anything about it.  It could be that they are not convinced it is a threat, but in that case, it's another issue to be believed.  And that is something to consider when it comes to the relationship between faith and repentance.  It depends on what is being believed or not believed.  The repentance depends on what is being believed.  I think one could believe something that doesn't result in a change of thought or behavior, for whatever reason.

So repentance to involve belief, but belief, it seems, doesn't necessarily involve repentance.