What signals the end of the duty day and serves as a ceremony for paying respect to the flag?

The correct choice is the signal known as Retreat. Retreat is a ceremonial event that signals the end of the duty day and includes the lowering of the national flag. It is observed by military personnel and those in uniform, who typically salute the flag as it is being lowered. The ceremony serves to honor the flag and to reflect on the sacrifices made by those who serve.

Understanding the context of other terms helps clarify why Retreat is the right answer. Reveille, for instance, is the ceremonial call that marks the beginning of the duty day, indicating it is time to rise and start the day's activities. Colors refers to the hoisting of the national flag, which usually happens in the morning at sunrise. Taps, while it is a bugle call associated with military funerals or indicating the end of the day, does not involve the formal lowering of the flag like Retreat does. Thus, Retreat distinctly serves as a ceremony both signaling the day's end and paying respect to the flag.