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Income Taxes - Effective Income Tax Rate Reconciliation (Details)
3 Months Ended 6 Months Ended
Feb. 29, 2024
Feb. 29, 2024
Income Tax Disclosure [Abstract]    
Higher tax rates in certain foreign jurisdictions from period to period 1.70% 1.40%
An increase in non-deductible performance based compensation 0.70%  
A non-recurring charitable donation made in the first quarter of fiscal year 2023   1.90%
Lower year to date shortfalls from the settlements of stock-based equity awards in fiscal year 2024 (0.80%) (1.30%)
Benefits related to income tax positions affected by expiring statutes of limitation (0.60%)