Jenny places \( 100 \) pennies on a table, with \( 30 \) showing heads and \( 70 \) showing tails. She chooses \( 40 \) distinct pennies uniformly at random and turns them over. That is, if a chosen penny was showing heads, she turns it to show tails; if a chosen penny was showing tails, she turns it to show heads. After this process, what is the expected number of pennies showing heads?

This problem is shared by Muhammad A.

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