]you are in charge of erecting a radio telescope on a newly discovered planet. to minimize interference, you want to place it where the magnetic field on the planet is the weakest. the planet is spherical, with a radius of 6 units. based on a coordinate system whose origin is at the center of the planet, the strength of the magnetic field is given by m (x, y, z) = 6 x − y 2 + xz + 60 . use the method of lagrange multipliers to determine where you should locate the telescope.

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?