(1.2: Solving linear equations) Consider the following linear system withaandbunknown non-zero constants. x1−3x2+x3=42x1−8x3=−2−6x1+ 6x2+ax3=b(a) For what values ofaandbdoes the system have infinitely many solutions?(b) Given an example ofaandbwhere the system has exactly one solution.(c) Give an example ofaandbfor which the system has no solutions.

True or false look at the picture pls : /

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.)

Now, martin can reasonably guess that the standard deviation for the entire population of people at the mall during the time of the survey is $1.50. what is the 95% confidence interval about the sample mean? interpret what this means in the context of the situation where 95 people were surveyed and the sample mean is $8. use the information in this resource to construct the confidence interval.