Deposit $150 at the end of every month for ten years into a savings account that earns 3% compounded monthly. At the end of the ten years, transfer the accumulated money into an investment fund that earns 6% compounded quarterly, and allow the money to grow in this fund until retirement.
b. How long (in years and months) would it take to accumulate the required amount of $45,000.
c. To ensure that the amount accumulates to only $45,000 at the time of retirement, by how much should he change his monthly deposit?

Which expression gives the area of the triangle shown below

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.)

Proving the congruent supplements theorem