Explain why this technique of graphing a system of equations or inequalities works to solve exponential equations and inequalities.

How are solving systems of two linear equations or inequalities and solving two systems of quadratic equations or inequalities alike? How are they different?

Indicate the concentration of each ion present in the solution formed by mixing 3.60 g KCl in 75.0 mL of 0.250 M

$$CaCl_2$$

solution. Assume that the volumes are additive.

Draw the products of the following reactions. If the products can exist as stereoisomers, show which stereoisomers are formed. a.

$$cis-2-pentene + HCl,$$

b.

$$trans-2-pentene + HCl,$$

c.

$$1-ethylcyclohexene + H_2O + H_2SO_4,$$

d.

$$2,3-dimethyl-3-hexene + H_2, Pd/C,$$

e.

$$1,2-dimethylcyclohexene + HCl,$$

f.

$$1,2-dideuteriocyclohexene + H_2, Pd/C,$$

g.

$$3,3-dimethyl-1-pentene + Br_2/CH_2Cl_2,$$

h.

$$(E)-3,4-dimethyl-3-heptene + H_2, Pd/C,$$

i.

$$(Z)-3,4-dimethyl-3-heptene + H_2, Pd/C,$$

j.

$$1-chloro-2-ethylcyclohexene + H_2, Pd/C$$

We want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. Parameter estimates:

$$\begin{matrix} \text{Parameter} & \text{Estimate} & \text{Std. Err.} & \text{Alternative} & \text{DF} & \text{T-Stat} & \text{P-value}\\ \text{Intercept} & \text{17.966577} & \text{6.4779134} & \text{$\ne$0} & \text{131} & \text{2.7735131} & \text{0.0064}\\ \text{Father} & \text{0.50354896} & \text{0.067077219} & \text{$\ne$0} & \text{131} & \text{7.507004} & \text{<0.0001}\\ \text{Mother} & \text{0.27714316} & \text{0.078318967} & \text{$\ne$0} & \text{131} & \text{3.5386467} & \text{0.0006}\\ \end{matrix}$$

Analysis of variance table for multiple regression model:

$$\begin{matrix} \text{Source} & \text{DF} & \text{SS} & \text{MS} & \text{F-stat} & \text{P-value}\\ \text{Model} & \text{2} & \text{320.94662} & \text{160.47331} & \text{37.637221} & \text{<0.0001}\\ \text{Error} & \text{131} & \text{558.54293} & \text{4.2636865}\\ \text{Total} & \text{133} & \text{879.48955}\\ \end{matrix}$$

Summary of fit: Root MSE: 2.0648696 R-squared: 0.3649 R-squared (adjusted): 0.3552 Identify the P-value corre ponding to the overall significance of the multiple regre sion equation.

The decomposition of hydrogen peroxide is catalyzed by iodide ion. The catalyzed reaction is thought to proceed by a two-step mechanism:

$$\mathrm { H } _ { 2 } \mathrm { O } _ { 2 } ( a q ) + \mathrm { I } ^ { - } ( a q ) \longrightarrow \mathrm { H } _ { 2 } \mathrm { O } ( l ) + \mathrm { IO } ^ { - } ( a q )$$

( slow )

$$\mathrm { IO } ^ { - } ( a q ) + \mathrm { H } _ { 2 } \mathrm { O } _ { 2 } ( a q ) \longrightarrow \mathrm { H } _ { 2 } \mathrm { O } ( l ) + \mathrm { O } _ { 2 } ( g ) + \mathrm { l } ^ { - } ( a q )$$

(fast) Identify the intermediate, if any, in the mechanism.

(a) Explain the role of methanogenic (methane producing) archaea in the carbon cycle: (b) Suggest another biological source of methane:

Suppose you are using algebra tiles to factor a quadratic trinomial. What do you know about the factors of the trinomial when the tiles form a square?

Pure competition has what two major differences from each of the following: monopolistic competition, an oligopoly, a monopoly?

Determine all eigenvalues and corresponding eigenvectors of the given matrix.

$$\left[ \begin{array} { r r } { 7 } & { 4 } \\ { - 1 } & { 3 } \end{array} \right].$$

Compare the molar solubility of AgOH in pure water with thatin a solution buffered at pH 7.00. Note the difference between the two: When AgOH is dissolved in pure water, the pH does not remain at 7.

State whether the annihilator method can be used to determine a particular solution to the given differential equation. If the technique cannot be used, state why not. If the technique can be used, then give an appropriate trial solution.

$$y ^ { \prime \prime } + 4 y = 7 \cos ^ { 2 } x.$$

Fill in the blanks with the terms that best complete the following sentence. ___________ causes cold, nutrient rich waters to move up to the ocean’s surface.

Jack is an actuary working for a corporate pension fund. He needs to have $14.6 million grow to$22 million in 6 years. What interest rate compounded annually does he need for this investment?