Final answer:
To determine how many weeks Cynthia needs to practice the violin to reach 35 hours, we divide 35 by the weekly practice time of 2\(\frac{3}{4}\) hours, which is 12.73 weeks. Rounding up, it would take her 13 weeks.
Step-by-step explanation:
The student, Cynthia, practices for 2\(\frac{3}{4}\) hours each week playing the violin. To find out how many weeks it will take her to accumulate 35 hours of practice, we will divide the total hours needed by the number of hours she practices per week.
First, we convert 2\(\frac{3}{4}\) hours to an improper fraction: \(\frac{11}{4}\) hours. Then, we divide 35 hours by \(\frac{11}{4}\) hours per week.
To perform the division, we multiply 35 hours by the reciprocal of \(\frac{11}{4}\), which gives: 35 \(\times\) \(\frac{4}{11}\) = 140/11, which simplifies to approximately 12.73 weeks.
Since Cynthia can't practice for a fraction of a week, we round up to the nearest whole number. Thus, it will take her 13 weeks of practice to reach 35 hours.