Let's carefully analyze the reimbursement package offered by Dean's company. According to the given information, the company offers:
1. A fixed rate of \[tex]$0.59 per mile.
2. An additional annual maintenance fee of \$[/tex]275.
We need to determine the total amount of reimbursement, [tex]\( C \)[/tex], which depends on the number of miles driven, [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Understand the fixed rate per mile:
- For every mile driven, the company reimburses \[tex]$0.59.
- So, if Dean drives \( x \) miles, the reimbursement for mileage is \( 0.59 \times x \).
2. Understand the annual maintenance fee:
- Regardless of the miles driven, Dean receives an additional fixed reimbursement of \$[/tex]275 for maintenance.
3. Combine both components:
- The total reimbursement [tex]\( C \)[/tex] is the sum of the mileage reimbursement and the maintenance fee.
- Mathematically, this can be expressed as:
[tex]\[
C = 0.59x + 275
\][/tex]
4. Match the equation with the provided options:
- Option A: [tex]\( C = 59x + 275 \)[/tex]
- This is incorrect because the coefficient for [tex]\( x \)[/tex] should be 0.59, not 59.
- Option B: [tex]\( C = 0.59 + 275x \)[/tex]
- This is incorrect because it improperly places the [tex]\( x \)[/tex] with the annual maintenance fee.
- Option C: [tex]\( c = 59x + 275 \)[/tex]
- This is incorrect for the same reason as option A and additionally has a lowercase [tex]\( c \)[/tex] which does not match our notation [tex]\( C \)[/tex].
- Option D: [tex]\( c = 0.59x + 275 \)[/tex]
- This one correctly represents the equation as [tex]\( 0.59x + 275 \)[/tex]. Even though it uses a lowercase [tex]\( c \)[/tex], this is a minor notation difference likely meant to be [tex]\( C \)[/tex].
Thus, the correct model for the total reimbursement [tex]\( C \)[/tex], based on the given information, and matching the correct option structure, is:
Option D: [tex]\( c = 0.59x + 275 \)[/tex].
