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Goodwill and Other Intangible Assets (Schedule of Intangible Assets and Weighted Average Remaining Life Finite and Infinite Excluding Goodwill) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Aug. 31, 2022 | Aug. 31, 2021
Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 2 years 8 months 12 days | 3 years 1 month 6 days
Total, gross carrying amount | $ 54,892 | $ 55,858
Definite lived intangible assets: accumulated amortization | (36,684) | (35,491)
Tradenames [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Indefinite lived intangible assets: gross carrying amount | $ 11,162 | $ 11,312
Patents and Developed Technology [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 3 years 3 months 18 days | 3 years 8 months 12 days
Definite lived intangible assets: gross carrying amount | $ 26,329 | $ 27,085
Definite lived intangible assets: accumulated amortization | $ (24,106) | $ (23,931)
Customer Relationships [Member] |  |
Finite And Indefinite Intangible Assets [Line Items] |  |
Definite lived intangible assets: weighted average years | 2 years 1 month 6 days | 2 years 7 months 6 days
Definite lived intangible assets: gross carrying amount | $ 17,401 | $ 17,461
Definite lived intangible assets: accumulated amortization | $ (12,578) | $ (11,560)

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- Definition Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(16)) -URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682 + Details
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