A 90° counterclockwise rotation about the origin, and then a reflection across the x-axis performed on shape I proves that shape II is congruent to shape I. Which other sequences of transformations on shape I can also be used to prove congruence to shape II? a reflection across the y-axis and a 90° clockwise rotation about the origin a 90° counterclockwise rotation about the origin and a reflection across the y-axis a reflection across the y-axis and a 90° counterclockwise rotation about the origin a 90° clockwise rotation about the origin and a reflection across the x-axis a reflection across the x-axis and a 90° clockwise rotation about the origin

Joe has a rectangular chicken coop. the length of the coop is 4 feet less than twice the width. the area of the chicken coop is 510 square feet. what is the length of the chicken coop?

What value of x is in the solution set of –5x – 15 > 10 + 20x?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)