1. **State the problem:** Calculate the student's final grade based on the weighted categories. 2. **Identify the weights and scores:** - Homework: score = 87, weight = 30% = 0.30 - Project: score = 75, weight = 15% = 0.15 - Research Paper: score = 92, weight = 35% = 0.35 - Exam: score = 81, weight = 20% = 0.20 3. **Calculate the weighted contributions:** - Homework contribution = $87 \times 0.30 = 26.1$ - Project contribution = $75 \times 0.15 = 11.25$ - Research Paper contribution = $92 \times 0.35 = 32.2$ - Exam contribution = $81 \times 0.20 = 16.2$ 4. **Sum all contributions to find the final grade:** $$26.1 + 11.25 + 32.2 + 16.2 = 85.75$$ 5. **Final answer:** The student's final grade is **85.75**.