To find out how much vinegar Tony would use to make 4 recipes, we need to multiply the amount of vinegar used in one recipe by the number of recipes.
The amount of vinegar used in one recipe is \(4 \frac{1}{4}\) cups. First, we convert this mixed number to an improper fraction.
To convert \(4 \frac{1}{4}\) to an improper fraction, we multiply the whole number part by the denominator and add the numerator:
\[ 4 \times 4 + 1 = 16 + 1 = 17 \]
So, \(4 \frac{1}{4}\) can be expressed as \(\frac{17}{4}\) cups.
Now, we multiply this amount by 4:
\[ \frac{17}{4} \times 4 = \frac{17 \times 4}{4} = 17 \]
Thus, Tony would use \(17\) cups of vinegar to make 4 recipes.
The final answer is:
\[ \boxed{17} \]