Question

1. select all of the possible types of numbers that are appropriate input values for the given situation. a flower - delivery service charges $39.95 per flower arrangement and $2.99 for delivery. the total cost y is represented by the function $y = 39.95x + 2.99$, where x is the number of flower arrangements. whole numbers integers rational numbers positive integers negative numbers only zero

Explanation:

1. Whole numbers: The number of flower arrangements can be 0, 1, 2, ..., so whole numbers (non - negative integers) are appropriate. Since \(x\) represents the number of flower arrangements, it can be 0 (no arrangements) or positive whole numbers.
2. Integers: But integers include negative numbers, and we can't have a negative number of flower arrangements. However, the set of whole numbers is a subset of integers, and the valid integer values here are non - negative integers (whole numbers). But when considering the broader set, since the valid integer values (non - negative) are included, and the function can take \(x = 0,1,2,\cdots\) (which are integers), we can say integers in the sense of non - negative integers. But more precisely, the valid integers are non - negative.
3. Rational numbers: The number of flower arrangements \(x\) is a non - negative integer, and all integers are rational numbers (since any integer \(n\) can be written as \(\frac{n}{1}\)). Also, if we consider the context, even though \(x\) is an integer, it is a rational number.
4. Positive integers: The number of flower arrangements can be 1, 2, 3, ... (positive integers) as well as 0. But positive integers are part of the valid values (when \(x\gt0\)).
5. Negative numbers: We can't have a negative number of flower arrangements, so negative numbers are not appropriate.
6. Only zero: We can have more than zero flower arrangements (e.g., 1, 2, ...), so this is not correct.

Answer:

whole numbers, integers, rational numbers, positive integers