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Income Taxes (Narrative) (Details) - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2022
Nov. 30, 2021
Income Taxes [Abstract]    
Provision for income taxes 20.90% 19.80%
Tax shortfalls related to settlements of stock-based equity awards $ 0.7  
Unfavorable impact on effective tax rate due to tax shortfall 5.10%  
Favorable impact on effective tax rate due to charitable donation 4.20%  
Charitable donation amount $ 3.5  
Tax benefit related to charitable donation $ 0.7