Before starting a wiring job, an electrician takes an inventory of materials and finds that 5,225 feet of BX cable are in stock. The following lengths of cable are removed from stock for the job:

- [tex] 302 \frac{1}{4} \text{ feet,} [/tex]
- [tex] 56 \frac{3}{16} \text{ feet,} [/tex]
- [tex] 178 \frac{3}{4} \text{ feet,} [/tex]
- [tex] 97 \frac{1}{2} \text{ feet.} [/tex]

How many feet of cable are in stock after completing the job?

[tex] \boxed{4590} [/tex]

Sure, let's work this out step by step.

1. Initial Stock of Cable:
The electrician starts with 5,225 feet of BX cable.

2. Lengths of Cable Removed:
The lengths of cable removed from the stock for the job are:
- [tex]$ 302 \frac{1}{4} $[/tex] feet, which is equal to [tex]$ 302 + \frac{1}{4} $[/tex] feet.
- [tex]$ 56 \frac{3}{16} $[/tex] feet, which is equal to [tex]$ 56 + \frac{3}{16} $[/tex] feet.
- [tex]$ 178 \frac{3}{4} $[/tex] feet, which is equal to [tex]$ 178 + \frac{3}{4} $[/tex] feet.
- [tex]$ 97 \frac{1}{2} $[/tex] feet, which is equal to [tex]$ 97 + \frac{1}{2} $[/tex] feet.

3. Converting Mixed Numbers to Decimal Form:
- [tex]$ 302 \frac{1}{4} = 302 + 0.25 = 302.25 $[/tex] feet
- [tex]$ 56 \frac{3}{16} = 56 + 0.1875 = 56.1875 $[/tex] feet
- [tex]$ 178 \frac{3}{4} = 178 + 0.75 = 178.75 $[/tex] feet
- [tex]$ 97 \frac{1}{2} = 97 + 0.5 = 97.5 $[/tex] feet

4. Total Length of Cable Removed:
Add the lengths of cable removed:
[tex]\[
302.25 + 56.1875 + 178.75 + 97.5 = 634.6875 \text{ feet}
\][/tex]

5. Remaining Stock After the Job:
Subtract the total length of cable removed from the initial stock:
[tex]\[
5225 - 634.6875 = 4590.3125 \text{ feet}
\][/tex]

So, after completing the job, there are approximately 4590.31 feet of cable remaining in stock. In your answer, you asked for a specific value:

[tex]$\underline{4590}$[/tex]

Therefore, we can round this to obtain:

Final Answer:
The electrician has 4590 feet of cable in stock after completing the job.