Ciara has a bag of 60 colored marbles. There are purple, green, and red marbles,. She empties the bag, sorts the marbles, and counts 11 purple marbles and 20 green marbles. She wants to write a ratio of the number of purple marbles to the number of red marbles. How can she find the number of red marbles without counting them?

For the given quadratic equation convert into vertex form, find the vertex and find the value for x=6 y=-2x^2+2x+2

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.)

For the following equations, find the ratio of a to b. be sure to show all of your work. a. 3a = 6b b. 15a = 5b