Match each term to its correct description.

Here are the matches between Column A and Column B:

1. Concentration: b. The amount of one substance in a certain volume of another substance.

2. Saturated Solution: a. A solution with as much dissolved solute as it can hold at a given temperature. No more solute can be dissolved.

3. Unsaturated Solution: c. A solution that holds less solute than is possible at a given temperature. More solute can dissolve.

4. Supersaturated Solution: d. A heated solution that holds more dissolved solute than is possible at a lower temperature.

Consider the following scenario.

The fee for an upcoming science camp is $50 per participant. The total cost of the camp, in dollars, is a function of the number of participants. `C=50x` where your input is the number of students (x) and your output is the total cost (C)

1. Select all the possible outputs (Range values) for the cost function, and then explain why you chose those values.

(3 points)
Responses

80

50

0

150

210

To determine the possible outputs (range values) for the cost function \( C = 50x \), we need to consider the function's behavior based on the input (number of participants \( x \)).

1. Since \( x \) (the number of participants) must be a non-negative integer (you cannot have a negative or fractional number of participants), the smallest valid input is \( x = 0 \), which gives \( C = 50(0) = 0 \).
2. The outputs will increase in increments of $50 for each additional participant:
   • For \( x = 1 \), \( C = 50(1) = 50 \).
   • For \( x = 2 \), \( C = 50(2) = 100 \).
   • For \( x = 3 \), \( C = 50(3) = 150 \), and so on.

Based on these considerations, the possible outputs from the given options (80, 50, 0, 150, 210) can be evaluated:

• 0: Valid output because it corresponds to \( x = 0 \).
• 50: Valid output because it corresponds to \( x = 1 \).
• 150: Valid output because it corresponds to \( x = 3 \).
• 80: Not a valid output because there is no integer value of \( x \) such that \( C = 80 \) (since \( C \) increases in increments of $50).
• 210: Not a valid output because there is no integer value of \( x \) such that \( C = 210 \) (the closest values are 200 and 250).

Summary of Valid Outputs:

• Valid Outputs (Range values): 0, 50, 150
• Reason: These outputs correspond to non-negative integer values for \( x \) according to the function \( C = 50x \).

Consider the following scenario.

The fee for an upcoming science camp is $50 per participant. The total cost of the camp, in dollars, is a function of the number of participants. `C=50x` where your input is number of students (x) and your output is the total cost (C)

1. Select all the possible Inputs (Domain values) for the cost function, and then explain why you chose those values.

(3 points)
Responses

100

10.5

50 34

0

-20

25

To determine the possible inputs (domain values) for the cost function \( C = 50x \), we need to consider the nature of the input \( x \), which represents the number of participants in the science camp.

Possible Values for \( x \):

1. Non-negative Integers:
   • The number of participants cannot be negative or a fraction; it must be a whole, non-negative number. Therefore, \( x \) must be \( 0 \) or any positive integer.

Evaluating the Given Options:

• 100: Valid input because it is a non-negative integer representing 100 participants.
• 10.5: Not a valid input because it is not a whole number; you cannot have a fraction of a participant.
• 50 34: Not a valid input because it is not a single value; it appears to be a miscommunication—typically, the number of participants should be one singular value.
• 0: Valid input because it represents a scenario where there are no participants.
• -20: Not a valid input because the number of participants cannot be negative.
• 25: Valid input because it is a non-negative integer representing 25 participants.

Summary of Valid Inputs:

• Valid Inputs (Domain values): 100, 0, 25
• Reason: These values correspond to valid, non-negative integers that represent the number of participants in the science camp. Inputs like negative numbers or fractions are not applicable in this context.