Final answer:
Black composers and entertainers became prevalent in the mainstream American entertainment industry in the 1920s, during the Harlem Renaissance. The correct answer for this question is option (A).
Step-by-step explanation:
Black composers and entertainers began to become prevalent in clubs, on stage, film, and Tin Pan Alley in the 1920s, marking the correct answer as a) 1920s. During this time, the Harlem Renaissance was in full swing, and African American culture strongly influenced the arts and entertainment industry. The 1920s saw the emergence of legendary jazz musicians like Duke Ellington and Cab Calloway performing in Harlem nightclubs such as the Cotton Club. Furthermore, the first all-black musical on a major Broadway stage, In Dahomey, was performed earlier in 1903, but it was the Harlem Renaissance that truly marked the era of widespread acceptance and popularity for black entertainers in mainstream American society.