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Stock-Based Employee Benefit Plans - Assumptions Used to Estimate Fair Value of Stock Options (Details)
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Share-based Payment Arrangement [Abstract]      
Weighted average expected term (years) 4 years 3 months 3 days 4 years 9 months 10 days 5 years
Expected volatility (range), minimum 31.10% 33.60% 35.30%
Expected volatility (range), maximum 32.40% 35.10% 35.30%
Weighted average volatility 32.20% 34.60% 35.30%
Risk free interest rate, minimum 2.50% 2.03% 2.02%
Risk free interest rate, maximum 2.68% 2.65% 2.02%
Weighted average expected dividend yield 0.00% 0.00% 0.07%
Expected dividend yield (range), minimum 0.00% 0.00% 0.07%
Expected dividend yield (range), maximum 0.00% 0.00% 0.07%