Evaluate the expression:

v ⋅ w
given the vectors:
r = < 8, 1, -6> ; v = < 6, 7, -3> ; w = < -7, 5, 2> (2 points)

This circle is centered at the origin, and the length of its radius is 6. what is the circle's equation? a. x^2+y^2=36 b x^2+y^2=6 c x+y=36 d x^6+y^6=1

An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)

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?