Please show work. Trying to learn. Thank you.

1.You are a restaurant manager. You must pick 15 entrees for your menu. There are 18 meat offerings and 10 poultry offerings to choose from.

(a) In how many ways can 15 entrees be randomly selected out of the 28 meat and poultry offerings? Show work.

(b) In how many ways can 15 entrees be chosen, if 9 must be meat and 6 must be poultry? Show work.

(c) If 15 entrees are randomly selected from the 28 offerings, what is the probability that 9 are meat and 6 are poultry?

2."Safety, Ethical Considerations, and Application Guidelines for the Use of Transcranial Magnetic Stimulation (TMS) in Clinical Practice and Research" (Rossi, Hallett, Rossini, Pascual-Leone, Clinical Neurophysiology , Vol 120 Issue 12 (Dec 2009)) reports that the number of research papers addressing TMS was 30 in 1986. That number climbed to 3000 by 2008.

(a) Which of the following linear equations could be used to predict TMS research papers published y in given year x, where x = 0 represents year 1986? Explain/show work. A. y=0.0074x+1986

B. y=0.0074x+1986

C. y=135x+30

D. y=135x+1986

(b) Use the equation from part (a) to predict number of TMS research papers published in the year 2021. Round answer to nearest whole number. .

(c) Fill in the blanks to interpret the slope of the equation: The rate of change of TMS research papers published with respect to time is ______________________ per ________________. (Include units of measurement.)

3. According to the American Chemical Society, there is a 0.9 probability that in the United States, a randomly selected $1 dollar bill is tainted with traces of cocaine. Assume nine $1 dollar bills are randomly selected. What is the probability that exactly five (5) of the $1 dollar bills randomly selected will be tainted with traces of cocaine?

4. A network security specialist records the number of incoming e-mails containing links that six randomly-selected network users receive in a day. Numbers are 65, 39, 43, 81, 57, and 39.

(a) State the mode (if one exists).

(b) Find the median. Show work/explanation.

(c) Determine the sample mean. Show work

(d) Using the sample mean found in part (c), and given that the sample standard deviation of the data set above is 16.9, what percentage of the data set falls within one standard deviation of the mean?

A. 34.2%

B. 66.7%

C. 68.3%

D. 83.3%