A brine solution of salt flows at a constant rate of 6 L/mi…

 A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held 50 L ofbrine solution in which was dissolved 0.5 kg of salt. The solution inside the tank is kept well stirred andflows out of the tank at the same rate. a) If the concentration of salt in the brine entering the tank is 0.05 kg/L, determine the mass of salt in the tankafter t min. (Let x be the mass of salt at time t. Write the ODE that x satisfies and solved it.) b) When will the concentration of salt in thetank reach 0.03 kg/L

Problem 1 An urn contains two type A coins and one type B co…

Problem 1 An urn contains two type A coins and one type B coin. When a type A coin is flipped, it comes up heads with probability 1/4. When a type B coin is flipped, it comes up heads with probability 3/4. A coin is randomly chosen from the urn and flipped. Given that the flip landed on heads, identify the probability that it was a type A coin. Write out you work to solve the problem on scratch paper to be scanned and uploaded at the end of the exam time.Please include your Full Name, PSU ID, and Problem Number on each sheet of paper.