Question

The amount of caffeine in a cup of coffee from Joe’s diner is directly proportional to the number of ounces in the cup as shown. Which statement is not true?

a) Larger cups have more caffeine.
b) Smaller cups have less caffeine.
c) The proportionality constant remains the same for every cup size.
d) Larger cups have less caffeine.
e) Smaller cups have more caffeine.

Answer 1

The correct answer is that either Statement d) Larger cups have less caffeine or Statement e) Smaller cups have more caffeine is not true, because the amount of caffeine is directly proportional to the cup size.

Step-by-step explanation:

The question asks about the relationship between the amount of caffeine in coffee and the size of the coffee cup. When it is stated that the amount of caffeine is directly proportional to the number of ounces in the cup, it means that as the number of ounces increases, so does the amount of caffeine, always with the same proportionality constant. Therefore, larger cups have more caffeine (Statement a), and smaller cups have less caffeine (Statement b). The proportionality constant indeed remains the same for every cup size (Statement c). So, the statement that is not true is either (Statement d) Larger cups have less caffeine or (Statement e) Smaller cups have more caffeine, as they are in direct contradiction with the concept of direct proportionality.