Atrumpeter is placed on a moving sidewalk that moves at a constant velocity of 4.5 m/s. a listener is standing 6.0 m in front of the trumpeter on the same sidewalk. the trumpeter plays a note of frequency 290 hz. the air is still and the speed of sound is what frequency of the note does the listener hear?

You didn't actually include the speed of sound. But it doesn't matter for this question. If the trumpeter and the listener are on the same moving sidewalk then the distance between them is not changing. The Doppler shift only happens when the distance between the source and the Observer is changing. So the Listener hears the same 290 Hertz that the trumpeter is generating.