Sam claims that his cat can do single-digit multiplication. he shows the cat 10 cards with simple multiplication problems that are either correct or incorrect. the cat correctly identifies the correctness of the card 7 times out of 10. if the cat were simply guessing, how many would the cat be expected to get correct?

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?