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Which sequence of translations, rotations, and reflections produces △P’Q’R’ from the pre-image △PQR?

1. a reflection across the y-axis followed by a clockwise rotation 90° about the origin
2. a reflection across the x-axis, followed by a counter-clockwise rotation 90° about the origin, followed by a translation 4 units down and 4 units to the left
3. a counter-clockwise rotation of 90° about the origin followed by a translation 4 units to the right
4. no sequence of translations, rotations, and reflections because the images are not congruent

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.)