Is my 2004 original equipment CD player likely to be able to play Mp3
cds (in the car I just bought)?

There is one I want to buy (though I dont' have the url now) that had
far more songs on it, maybe 50 or 100, than the 15 that I'm used to, and
another poster made me realize that this might be a set of MP3 files.

The owners manual says nothing about mp3. That probably means no,
right?