A washing machine has the following cycle: soak for 15 minutes, wash for 30 minutes, and rinse for 10 minutes. If you approach the machine at a random during the cycle, what is the probability that the cycle will be in the rinse phase when you arrive at the machine? Round your answer to the nearest hundredth.

To find the probability that the washing machine is in the rinse phase when approached randomly, we first need to calculate the total duration of the cycle. The cycle duration consists of soaking (15 minutes), washing (30 minutes), and rinsing (10 minutes), which totals up to 55 minutes. Now, since the rinse phase lasts 10 minutes, we can determine the probability by dividing the duration of the rinse phase by the total cycle duration: \[ P(\text{rinse}) = \frac{\text{duration of rinse}}{\text{total cycle duration}} = \frac{10}{55} = \frac{2}{11} \approx 0.1818. \] Rounding to the nearest hundredth, the probability is approximately 0.18.