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Each hygienist works 6 h−0.5 h=5.5 h=3306\text{ h} - 0.5\text{ h} = 5.5\text{ h} = 330 minutes of appointment time. With 45-minute slots, the number of whole appointments per hygienist is ⌊330/45⌋=7\lfloor 330/45 \rfloor = 7. Across 3 hygienists, total scheduled = 3×7=213 \times 7 = 21. With a 15% no-show rate, expected seen = 0.85×21=17.85≈180.85 \times 21 = 17.85 \approx 18. Option D (21) ignores no-shows; Option C (19) reflects rounding the expected value up, but in expectation problems, standard practice is to round to the nearest whole number unless instructed otherwise—18 is closest. Option A underestimates by double-counting breaks or misapplying the percentage. For QR on the DAT, translate operational constraints into time slots, compute an integer capacity, and then apply percentages to the total—not to each hygienist separately—to avoid compounding rounding errors.