Question

for each of the pairs of quantities, identify if they are directly, inversely, or not proportional. complete parts (a) through (j). (a) tax ($) charged for buying an item cost ($) of an item choose the correct answer. not proportional directly proportional inversely proportional (b) population of a region area of a region directly proportional not proportional inversely proportional

Explanation:

Part (a)

Tax is calculated as a percentage of the item's cost (e.g., \( \text{Tax} = \text{Rate} \times \text{Cost} \)). As the cost of the item increases, the tax (at a constant rate) also increases. This fits the definition of direct proportionality (\( y = kx \), where \( k \) is the tax rate).

Population of a region depends on many factors (like density, resources, urbanization) beyond just the area. A larger area doesn't necessarily mean a larger population (e.g., a sparsely populated large desert vs a small densely populated city). So there's no consistent proportional relationship (direct or inverse) between population and area.

Answer:

directly proportional

Part (b)