Write the chemical formula and Lewis structure of the following, each of which contains five carbon atoms: (a) an alkane (b) an alkene (c) an alkyne

Which of the following compounds are capable of cis-trans isomerism?
(a) 1-Hexene
(b) 2-Hexene
(c) 3-Hexene

Assume that the change in concentration of $\mathrm{N}_{2} \mathrm{O}_{4}$ is small enough to be neglected in the following problem. (a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of $\mathrm{N}_{2} \mathrm{O}_{4}$ with chloroform as the solvent. $\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$ $K_{c}=1.07 \times 10^{-5}$ in chloroform (b) Show that the change is small enough to be neglected.

Which of the following compounds are capable of cis-trans isomerism? (a) 1-Hexene (b) 2-Hexene (c) 3-Hexene

Are the concentrations of hydronium ion and hydroxide ion in a solution of an acid or a base in water directly proportional or inversely proportional? Explain your answer.

Consider the system

$$\mathbf{y}^{\prime}=\left(\begin{array}{ccc} 1 & -1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{array}\right) \mathbf{y}$$

. (a) Find the eigenvalues and eigenvectors. Use your numerical solver to sketch the half-lines generated by the exponential solutions $\mathbf{y}(t)=C_{i} e^{\lambda_{i} t} v_{i}$ for i=1, 2, and 3. (b) The six half-line solutions found in part (a) come in pairs that form straight lines. These three lines, taken two at a time, generate three planes. In turn these planes divide phase space into eight octants. Use your numerical solver to add solution trajectories with initial conditions in each of the eight octants. (c) Based on your phase portrait, what would be an appropriate name for the equilibrium point in this case?

Use the Distributive Property to write each expression as an equivalent algebraic expression. $5(x+y)$

Find each quotient. $-105 \div 15$

Solve. Check your solution. $6(m-2)=12$

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

A prisoner is told that he will be released at a time chosen uniformly at random within the next 24 hours. Let T denote the time that he is released. What is the hazard function for T ? For what values of t is it smallest and largest? If he has been waiting for 5 hours, is it more likely that he will be released in the next few minutes than if he has been waiting for 1 hour?

Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s but collides head-on with a padded goalpost and experiences a backward force of $1.76 \times 10^{4}\ \mathrm{N}$ for $5.50 \times 10^{-2}\ \mathrm{s}.$

Solve Ax = b, where A and b are given by

$$A=\left[\begin{array}{ll} 1 & 1 \\ 1 & 2 \end{array}\right], \ \mathbf{b}=\left[\begin{array}{l} 2 \\ 3 \end{array}\right]$$

Let $T: \mathbb{R}^{2} \longrightarrow \mathbb{R}^{2}$ be the transformation that performs a horizontal stretching by a factor of 3, followed by a vertical contraction by a factor of 2, followed by a reflection through the x axis. a. Find the matrix of T relative to the standard basis. b. Apply the transformation to the triangle with vertices (1, 0), (3, 0), and (2, 2), and give a sketch of the result. c. Find the matrix relative to the standard basis that reverses T.