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Income Taxes - Schedule of Reconciliation of Federal Statutory Rate to Total Provision for Income Taxes (Details) - USD ($) $ in Millions | 12 Months Ended
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Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020
Income Tax Disclosure [Abstract] |  |  |
Federal income tax computed at statutory rate | $ 103.7 | $ 83.2 | $ 68.2
State income tax, net of federal income tax benefit | 13.5 | 10.7 | 9.7
Federal permanent differences | (4.3) | 0.6 | 0.9
Foreign permanent differences and rate differential | 4.3 | 2.4 | 2.4
Research and development tax credits | (7.6) | (7.6) | (7.1)
Unrecognized tax benefits | 2.1 | 0.7 | 1.8
Other, net | (1.8) | (0.1) | 0.5
Total provision for income taxes | $ 109.9 | $ 89.9 | $ 76.4

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