Mariah Carey, who made her debut alongside Nicki Minaj and Keith Urban in the now-storied role of celebrity judge on “American Idol” on Wednesday night, was paid as many millions as she has lifetime No. 1 hits (18) to appear on this, the twelfth season of the long-running show. Eighteen million also happens to be the approximate number of viewers who tuned into the season premiere of the Fox show, down from 30 million just three years ago.