Final answer:
To administer 7.5 mg of diazepam, the nurse should administer 1.5 mL of the diazepam injection.
Step-by-step explanation:
To determine how many mL of diazepam the nurse should administer, we can use a simple ratio:
z mg : 1 mL = 7.5 mg : x mL
Cross-multiplying will give us:
5x = 7.5 * 1
5x = 7.5
x = 7.5 / 5 = 1.5
Therefore, the nurse should administer 1.5 mL of diazepam.