The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs nine times as much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (Enter the dimensions as a comma separated list.)

On her way to work, mrs. larsen gets a green light at a certain traffic light only 30% of the time. she wants to find the probability that she will get a green light at this traffic light all five mornings that she travels to work next week. use the following randomly generated list of 200 five-digit numbers to answer the questions and find the probability. select the digits you will use to represent a favorable outcome. how many favorable outcomes are on this list? what are they? given this simulation, what is the probability that mrs. larsen will get a green light at this traffic light all five mornings next week?