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Anneliese's total expenses for the first year of school are $32,000.
The total amount covered by the scholarship, grant, and work-study program together is $16,000 + $4,000 + $2,500 = $22,500.
To calculate the percentage of expenses covered, we divide the total amount covered by the total expenses and multiply by 100:
($22,500 / $32,000) * 100 = 70.3%
Therefore, Anneliese's expenses are covered by 70.3% by the scholarship, the grant, and the work-study program combined.