The azygos vein runs along the esophagus and spine in the thoracic cavity. It get oxygen-poor blood from the intercostal muscles and drains into the superior vena cava.

The brachial plexus is located in the axillary region near the clavicle. It is responsible for innervating the arm and forearm as well as certain muscles in the shoulder region. From this information we can infer that the five main nerves from the plexus are the: musculocutaneous, radial, median, axillary, and ulnar.

The gastrocnemius muscles is located in the superficial, posterior compartment of the leg. We can eliminate the deep femoral artery because it supplies the thigh and the anterior tibial artery because it supplies the anterior leg. Of our two remaining choices, the fibular artery supplies the lateral compartment of the leg. Thus, the answer is posterior tibial artery.

The ileocolic artery supplies the ileocecal junction. The right colic artery supplies the ascending colon. The left colic artery supplies the descending colon. The makes the correct answer the middle colic artery.

The superior mesenteric artery is responsible for supplying the midgut. The midgut starts from the second half of duodenum and continues until the two-thirds point of the transverse colon. The inferior mesenteric artery supplies the hindgut, while the celiac trunk supplies the foregut.

The inferior mesenteric artery supplies the hindgut. The hindgut region starts from the two-thirds point of the transverse colon and continues to the anus. The celiac trunk supplies the foregut, while the superior mesenteric artery supplies the midgut. 

The brachial plexus is a network of nerves that run though the axial region. This means the only correct choice is the ulnar nerve. The femoral and tibial nerves are located in the lower extremities and the phrenic nerve is located in the thoracic cavity.

The celiac trunk supplies blood to the stomach, liver, spleen, pancreas, and duodenum. It is located in the abdominal cavity above the left and right renal arteries. The renal artery branches off directly from the abdominal aorta.

The function of the oculomotor nerve is eye movement. It controls eye movement through innervating the superior, medial, and inferior rectus muscles, the inferior oblique, levator palpebrae and the pupillary and ciliary muscles. The optic nerve controls vision and the superior oblique and lateral rectus muscles are innervated by the trochlear and abducens nerves, respectively.

Veins take blood back to the heart, and in all but one case (pulmonary veins), they carry oxygen-poor blood. The external carotid artery supplies the face. Only the internal carotid artery goes directly up to supply the brain.