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In human male skulls, the mastoid process is ____.

Why are strawberries ideal for DNA extraction in a lab experiment?

What is the most polar molecule in the chromatography lab with spinach leaves? spinach-leaf-chromatography.jpg

Q8-8 points Consider the graph shown below. Does it have an Euler path?                                                    Is it Eulerian (i.e., does it have an Euler circuit)? ​ Explain your answer.  

Q7-10 points Consider the function  f : ℝ → ℝ defined by f (x) = x³ – 2x + 3. Prove or provide a counter example that this function is onto (or surjective). Prove or provide a counter example that this function is one-to-one (or injective). 

Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2, 3, 4} to {​a​, ​b​, ​c​, ​d​} as follows: f (1) = a,  f (2) = b, f (3) = a,  f (4) = b g(1) = a,  g(2) = d, g(3) = c,  g(4) = b h(1) = d,  h(2) = a, h(3) = a, h(4) = a                                                                                                    Which of these functions are well-defined? ​                                                                                                                                              Which of these functions are onto?                      Which of these functions are one-to-one?         

Q14-5 points 14,890 people attended the first game of the 1984 NBA Finals between the Los Angeles Lakers and the Boston Celtics. Is it a mathematical certainty that at least two of those people shared the same three-letter set of initials (such as JFK or LBJ)? Justify your reasoning.

Q5-6 points What subset ​ ​ of the real numbers would you use to make the function

Q10-6 points Seven people attended a smaller dinner party. Is it mathematically possible that each person shook hands with exactly three people at the dinner? Explain why or why not.            

Q16-5 points Use the Binomial Theorem to write out the expansion of (2a + b)3 .