Mariah Carey spontaneously sang standards for surprised guests at the classy Carlyle on Wednesday. The chanteuse was spotted at the hotel with husband Nick Cannon, Randy Jackson and Jermaine Dupri after an earlier performance at an NFL kickoff gig. “Mariah was loving the music, and the band invited her to join in,” said a spy. Carey crooned “Summertime” and “Lullaby of Birdland.” She’d also eaten at Mr. Chow to celebrate her new album’s chart performance in the UK.