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To find the total cost, we first calculate the tip based on the haircut price of $13.99.
1. Calculate the amount of the tip:
\[
\text{Tip} = 20\% \text{ of } 13.99 = 0.20 \times 13.99 = 2.798
\]
2. Now, round the tip to the nearest hundredth:
\[
\text{Tip} \approx 2.80
\]
3. Add the tip to the original cost of the haircut to find the total cost:
\[
\text{Total Cost} = \text{Haircut Cost} + \text{Tip} = 13.99 + 2.80 = 16.79
\]
Thus, Kyrian's total cost is **$16.79**.