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Find for the following piecewise equation:

The graph of has been transformed to

**This is a show your work question. Write out your work on a scratch piece of paper and hold it up to the camera when you are finished. You can type your answer in best you can in the box or type in “I held up my answer”. Ensure your camera focuses on your scratch paper so Professor Bramall can clearly read it when she pauses the recording.**   Find a formula for

Which of the following functions does not have a domain that is

If you are given a volume in liters and need to find the moles of a compound in a solution, what conversion factor can you use to go from liters to moles? 

Everyone’s skin contains about the same number of melanocytes even though people come in many different colors. How is this possible?

What methods might be used to cool the skin of a child experiencing a high fever? For each method you list, identify the means by which it promotes heat loss—radiation, conduction, convection, or evaporation.

Suppose you were to flip a fair coin 5 times and record the number of tails that you got. The table below shows the corresponding probability distribution. Calculate the mean of this discrete probability distribution.    Probability Distribution Table Outcomes = # of Tails Probability 0 0.03125 1 0.15625 2 0.3125 3 0.3125 4 0.15625 5 0.03125   Make sure to round your final answer to 2 decimal places. For example, if your answer was , then you would type in 3.21 as your final answer. 

Suppose you are hired to determine the true average amount of money that college students make while working on-campus jobs. If you want to be 95% confident that you are within $100 of the actual value, how many students would you need to survey? Assume that the true standard deviation is $600.  Reminder: It’s impossible to survey a fraction of a college student.    

Part 1. Provide the curved arrow mechanism for 2 of the following 4 reactions. No response is required below, all work needs to be shown on scratch paper sent to Dr. Metz. Part 2. How many curved arrows are included for each mechanism provided. (Answers to this question must be provided below in order to receive credit for both parts 1 and 2. (Answers provided for part 1 must align with part 2 in order to receive credit for part 1 responses.)