A candle burns down at the rate of 0.75 inches per hour. The original height of the candle was 9 inches. Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs.

Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A.

Part C: If the rate at which the candle burned was 0.5 inches per hour instead of 0.75 inches per hour, would the relation be a function? Explain your answer using input and output values.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Acertain volume of water contains 100000 hydrogen atoms and 50,000 oxygen atoms how many hydrogen atoms are in a volume of water containing 4 million oxygen atoms

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.