Final answer:
The vagus nerve is the mixed cranial nerve that projects to and from internal organs, muscles, and glands, containing both sensory and motor fibers.
Step-by-step explanation:
The mixed cranial nerve that projects to and from internal organs, muscles, and glands is the vagus nerve. It is classified as a mixed nerve because it contains both sensory and motor fibers. This nerve is crucial for parasympathetic control over the heart, lungs, and digestive tract. The vagus nerve is also involved in the gag reflex, which is a visceral response to taste. Other cranial nerves involved in taste include the facial nerve, which is responsible for taste sensations in the anterior two-thirds of the tongue, and the glossopharyngeal nerve, which handles taste in the posterior one-third.