Based on the description of the Assyrian relief sculpture, the three correct inferences about Assyrian culture are:
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Assyrians could depict people realistically. - The mention of a hand holding a bucket suggests a level of realism in the sculptural representation.
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Assyrians used a written language. - The presence of lettering surrounding the hand and bucket indicates that they had a written language.
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Assyrians sometimes wore accessories. - The detail about the bracelet with a sun- or flower-like object on the wrist suggests that personal adornments were valued in their culture.
The other statements about the Assyrians not valuing art or being unskilled sculptors are incorrect based on the provided information about their artistic capabilities.