The correct answer is D) vessel's displacement. The rate at which a vessel's speed through the water decreases when reducing speed without backing depends primarily on the vessel's displacement. A vessel with a larger displacement will have more inertia and take longer to slow down compared to a vessel with a smaller displacement, all else being equal. The number of propellers, horsepower, and sea state can also affect deceleration, but the vessel's displacement is the primary factor. The other answer choices are incorrect because they do not directly determine the rate of deceleration when reducing speed without backing. The number of propellers and horsepower can affect overall speed and maneuverability, but do not directly influence the rate of deceleration. The sea state can affect the vessel's movement through the water, but is not the primary factor in determining the deceleration rate.