Final answer:
The expressions represent volumes and counts of water jugs filled by a company. Expressions a and d signify combined capacities and total volumes, which are continuous values, whereas expression b represents a total count of jugs, which is discrete. Expression c gives a total volume for one size of jugs, also a continuous value.
Step-by-step explanation:
The expressions given in the problem relate to the volume of water jugs being filled by a water company. Expression a. x + y simply adds the capacity of the two different sized jugs together. This expression might be used if you want to know the total capacity if you combined one jug of each size. However, this does not represent a real-world scenario since the volumes of the jugs are discrete and not summable in this context. The capacity is a continuous value in liters or gallons but when referring to the jugs, it becomes discrete as you can't have a fraction of a jug.
Expression b. A + B refers to the total number of jugs filled, which represents a discrete value, as you cannot fill a fraction of a jug. The total is a count of the jugs, regardless of their size or volume capacity.
Expression c. Ax gives the total volume of water for A jugs of the first size, and is a continuous value, denoting the volume of water held in a certain number of jugs, which can be in liters or gallons.
Expression d. Ax + By signifies the combined total volume of water for A jugs of the first size and B jugs of the second size. Like expression c, this represents a continuous value of the combined water volume.