Final answer:
The initial treatment should be high-flow oxygen via a nonrebreathing mask, followed by positive-pressure ventilatory support if needed, to ensure adequate oxygenation and stabilization of vital functions.
Step-by-step explanation:
The initial treatment for a 39-year-old woman presenting with signs and symptoms of an acute hemorrhagic stroke, who is responsive only to deep painful stimuli with bilaterally dilated and sluggishly reactive pupils, slow and irregular respirations, blood pressure at 80/50 mm Hg, and a pulse of 40 and bounding, involves high-flow oxygen via a nonrebreathing mask.
This immediate intervention is crucial to ensure the maximum amount of oxygen is delivered to the brain to minimize brain cell death due to hypoxia. Following oxygen administration, positive-pressure ventilatory support may be necessary to stabilize the patient's breathing if her condition does not improve. Additional treatments may include the control of blood pressure and intracranial pressure, as well as addressing the underlying cause of the hemorrhage.