Can ready-to-hand and present-to-hand coexist?

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Can readiness to hand and presence to hand both exist in the same being simultaneously? The example I thought of is the mathematician hard at work. While he's working he is ready to hand and there is no conscious awareness, just pure action. But the concepts he's writing about are highly associated with the present at hand mode.
Can we say that while the ready to hand mode dominates, he at some level present at hand in order to manipulate such explicit abstractions?