The height of lava ejected from the Stromboli volcano can be modeled by the relation h= - 5t(t-11), where h is the height, in metres, of the lava above the crater and t is the time, in seconds, since it was ejected. a) Graph the scenario.
Include key information and show work below. Select an appropriate scale.

b) Find the maximum height reached by the
lava to the nearest metre.

c) How long does the lava take to reach the maximum height?

d) Is the length of time that the lava is in the air twice the answer from part c)? Explain why or why not.

How many times larger is 6 × 10^12 than 2 × 10^7? a. 30,000 b. 3,000 c. 3,000,000 d. 300,000

What is the distance between the points (2, 5) and (5,9)?

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.)