Question

for each of the pairs of quantities, identify if they are directly, inversely, or not proportional. complete parts (a) through (j). (b) population of a region : area of a region directly proportional not proportional inversely proportional (c) average speed to work : time it takes not proportional inversely proportional directly proportional (d) population of new york city : population of new york state directly proportional inversely proportional not proportional (e) volume of water : weight of water inversely proportional directly proportional not proportional

Explanation:

Part (e)

Step 1: Recall Proportionality Definitions

Directly proportional: \( y = kx \) (constant \( k \)), inverse: \( y=\frac{k}{x} \). For water, density \(
ho=\frac{\text{weight (mass)}}{\text{volume}} \), so \( \text{weight} =
ho \times \text{volume} \) (constant \(
ho \) for water).

Step 2: Determine Relationship

Since weight of water = density (constant) × volume of water, it follows \( y = kx \) (direct proportion, \( k=
ho \)).

Answer:

directly proportional (Option: directly proportional)