The five-number summary for the weights (in pounds) of the players on a high school soccer team is {113, 143, 152, 165, 210} Are there any outliers? Explain.

A candy of this type is selected at random from each of two newly opened bags. What is the probability that the two candies have the given color(s)? Neither is yellow.

What must be true of the foci of a hyperbola?

Draw the structure of a phospholipid (from any of the subclasses of phospholipids) that contains one saturated and one unsaturated fatty acid. (a) Draw the structure of all of the products that would be formed from your phospholipid if it were subjected to complete hydrolysis (choose either acidic or basic conditions). (b) Draw the structure of the product(s) that would be formed from reaction of the unsaturated fatty acid moiety of your phospholipid (assuming it had been released by hydrolysis from the phospholipid first) under each of the following conditions:

$$\begin{array}{l}\text { (i) } \mathrm{Br}_{2} \\ \text { (ii) } \mathrm{OsO}_{4} \text { , followed by } \mathrm{NaHSO}_{3} \\ \text { (iii) } \mathrm{HBr} \\ \text { (iv) Hor alkaline } \mathrm{KMnO}_{4} \text { , followed by } \mathrm{H}_{3} \mathrm{O}^{+} \\ \text {(v) } \mathrm{SOCl}_{2} \text { , followed by excess } \mathrm{CH}_{3} \mathrm{NH}_{2}\end{array}$$

Explain why the redox processes that occur during photosynthesis are vital to life.

For the following exercises, use Gaussian elimination to solve the system.

$$\begin{array}{l} \frac{x-3}{10}+\frac{y+3}{2}-2 z=3 \\ \frac{x+5}{4}-\frac{y-1}{8}+z=\frac{3}{2} \\ \frac{x-1}{4}+\frac{y+4}{2}+3 z=\frac{3}{2} \end{array}$$

The electrical conductivity of copper at room temperature is $5.96 \times 10^{7} \Omega^{-1} \mathrm{m}^{-1}$. Evaluate the average distance between electron scatterings. How many lattice spacings does this amount to?

Write the structure of the RNA dinucleotide G-C in which G has a free 5 '-hydroxyl group and C has a free 3 '-hydroxyl group.

For the following exercises, determine the value of k based on the given equation. Given $2 x^{2}+k x y+12 y^{2}+10 x-16 y+28=0,$ find k for the graph to be an ellipse.

Define a parabola in terms of its focus and directrix.

Complete the following for the indicated interval [a, b]. (a) Verify that the given function is nonnegative. (b) Use a calculator to find the LRAM, RRAM, and average approximations for the area under the graph of the function from x = a to x = b with 10, 20, 50, and 100 approximating rectangles. (c) Compare the average area estimate in part (b) using 100 approximating rectangles with the calculator MINT area estimate, if your calculator has this feature. $f(x)=\sqrt{x-2}; [3,6]$

Sequence the events of DNA replication. ___ Hydrogen bonds form between new nitrogen bases and the existing strand. ___ Two nucleotide strands unzip. ___ Nitrogen bases pair adenine with thymine, cytosine with guanine. 1 An enzyme breaks the hydrogen bonds between the nitrogen bases. ___ The nucleotide strands separate to expose the nitrogen bases. ___ Free nucleotides are delivered by enzymes from the surrounding environment.

For the following exercises, solve the system using the inverse of a $2 \times 2$ matrix.

$$\begin{array}{l} -3 x-4 y=9 \\ 12 x+4 y=-6 \end{array}$$

We will denote the set of all automorphisms of G by Aut(G). Prove that Aut(G) is a subgroup of $S_{G}$, the group of permutations of G.