NEW YORK (AP) _ Mariah Carey and Caesars Palace are hoping to revive their livelihoods together. Carey will do a residency at The Colosseum in Las Vegas beginning May 16. The show is called “Mariah Carey Number Ones” and will feature her 18 number-one hits. The Caesars subsidiary that owns and manages The Colosseum filed for Chapter 11 bankruptcy yesterday. The company’s C-E-O says its lineup of entertainers will continue to perform as scheduled.