Question

for the scenario given, determine the smallest set of numbers for its possible values and classify the values as either discrete or continuous.

the fuel efficiency, in miles per gallon, for a fleet of rental cars

choose the smallest set of numbers to represent the possible values.
☐ integers
☐ fractional numbers
☐ natural numbers
☐ rational numbers
☐ real numbers
☐ whole numbers

are the values continuous or discrete?
☐ continuous
☐ discrete

Explanation:

Step1: Analyze fuel efficiency values

Fuel efficiency (miles per gallon) can be a decimal (e.g., 25.5 mpg), so it's a real number (includes rationals/irrationals, decimals). Natural numbers are positive integers, which don't fit (e.g., 25.5 isn't natural). Real numbers are the smallest set here as they include all possible efficiency values (decimals, integers, etc.).

Step2: Classify as continuous

Continuous data can take any value in an interval (e.g., 25.3, 25.4, etc.), while discrete is countable (integers). Fuel efficiency is continuous (can have non - integer values, infinite possible in a range).

Answer:

Smallest set: real numbers; Values: continuous