Raphael is twice as old as his sister is. the sum of their ages is less than 30. what is the greatest age raphael’s sister can be?

If the measure of angle 1 is 110 degrees and the measure of angle 3 is (2 x+10 degree), what is the value of x?

Click the arrows to advance or review slides. mapping carbohydrates to food carbohydrates (grams) 15 food (quantity) bread (1 slice) pasta (1/3 cup) apple (1 medium) mashed potatoes (1/2 cup) broccoli (1/2 cup) carrots (1/2 cup) milk (1 cup) yogurt (6 oz.) 12 12 is jennifer's relation a function? yes no f 1 of 2 → jennifer figure out the difference between a function and a relation by answering the questions about her food choices

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.)