Liza is playing a game in which she earns 3 points for each correct response but loses 2 points for each incorrect response. She missed the first 3 questions. Right now she just hopes to break even. Which statement is true? To break even, Liza must answer 3 questions correctly to cancel out the 3 she answered incorrectly.
To break even, Liza must answer 2 questions correctly to give her 6 points, because she now has –6 points and the result would be a score of 0.
To break even, Liza must answer 6 questions correctly to give her 6 points, because she now has –6 points and the result would be a score of 0.
To break even, Liza must answer 1 question correctly, because she needs 3 points to cancel out the 3 questions she answered incorrectly.

The table shows the webster family’s monthly expenses for the first three months of the year. they are $2,687.44, $2,613.09, and $2,808.64. what is the average monthly expenditure for all expenses?

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.

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.)