Question

Which best describes why the graph relating the total number of members on the yearbook club, m, and the number of days the booth is set up, d, will be continuous or discrete?

A) The graph will be continuous because an end day for the booth being set up is not given in the description.
B) The graph will be continuous because there can be any number of people signing up each day since we are only given the average.
C) The graph will be discrete because some day the number of available people to sign up for the club will run out.
D) The graph will be discrete because there is no such thing as a partial person to sign up, and the booth is set up once each day for sign-ups.

Answer 1

The graph showing the relationship between the number of members in a yearbook club and the number of days the booth is set up will be discrete, because members are counted in whole numbers and the days the booth is set up are also countable, whole units.

Step-by-step explanation:

The question seeks to determine if the graph that shows the relationship between the total number of members on the yearbook club, m, and the number of days the booth is set up, d, is continuous or discrete. The correct answer is D) The graph will be discrete because there is no such thing as a partial person to sign up, and the booth is set up once each day for sign-ups. This means that the number of people who can sign up for the yearbook club is counted in whole numbers for each day, making it a discrete set of data.

A discrete graph is used when the data points are countable and there's a limited number of values possible. In this case, since we cannot have a fraction of a person joining the club, the data will consist of whole numbers. Furthermore, the number of days is also a countable figure, as you can't set up a booth for a fraction of a day for the purpose of sign-ups, which further confirms the data's discreteness.