On average, it takes a particular gem cutter 90 minutes to map the cutting of 11 gems. Find how many gems she can draw maps for in 7.5 hours. She can draw maps for \( \square \) gems. (Type an integer or a decimal.)

Given that it takes \(90\) minutes to map \(11\) gems, we can first find the mapping rate in gems per minute: \[ \text{Rate} = \frac{11 \text{ gems}}{90 \text{ minutes}} \] Next, we convert \(7.5\) hours to minutes: \[ 7.5 \text{ hours} = 7.5 \times 60 = 450 \text{ minutes} \] Now, using the rate, the number of gems mapped in \(450\) minutes is: \[ \text{Gems} = \text{Rate} \times \text{Time} = \frac{11}{90} \times 450 \] Simplify the expression: \[ \frac{11}{90} \times 450 = 11 \times \frac{450}{90} = 11 \times 5 = 55 \] Thus, she can draw maps for \( \boxed{55} \) gems.