A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 40 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance. How many error-free parts did it produce yesterday?

Solve the problem by making up an equation. a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 3 times the age of the child?

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).