The compound 2,6-dimethyl pyrazine gives chocolate its odor and is used in flavorings. A valid Lewis structure is
(c) Is the hybridization of each $\mathrm{C}$ in a $\mathrm{CH}_3$ group the same as that of each $\mathrm{C}$ in the ring? Explain.

Describe the transformations from the graph of

$$f ( x ) = \sqrt { x }$$

to the graph of h. Then graph h.

$$h ( x ) = 4 \sqrt { x + 2 } - 1$$

The volume of the cylinder is $48 \pi$ cubic feet. The area of the base is $12 \pi$ square feet. What is the height of the cylinder?

What are the slope and y-intercept of the graph of the linear function f(x) = 6x + 15?

A $1.0$ - L solution that is $1.6 \mathrm{M}$ in ammonia is mixed with $75.8 \mathrm{~g}$ of ammonium sulfate. a. What is the hydroxide-ion concentration of this solution? b. $0.058 \mathrm{~mol}$ of $\mathrm{MnCl}_2$ is added to the above solution. Assume that there is no volume change. After $\mathrm{Mn}(\mathrm{OH})_2$ has precipitated, what is the molar concentration of manganese ion? What percent of the $\mathrm{Mn}^{2+}$ is removed from solution $\left(K_{s p}\right.$ of $\mathrm{Mn}(\mathrm{OH})_2$ is $\left.4.6 \times 10^{-14}\right)$ ?

Find the slope and y- intercept of the graph of the linear equation. y = -3x + 9

Numerical Reasoning Consider a triangle of area 2 bounded by the graphs of y=x, y=0, and x=2.
Complete the table.

$$\begin{array}{|l|l|l|l|l|} \hline n & 5 & 10 & 50 & 100 \\ \hline s(n) & & & & \\ \hline S(n) & & & & \\ \hline \end{array}$$

Find $[g \circ h](x)$ and $[h \circ g](x)$, if they exist.

$$g(x)=x-2$$

$$h(x)=3 x^2+1$$

Determine whether the following is linear transformation from P₂ to P₃. L(p(x)) = p(x) + xp(x) + x²p'(x)

Use a calculator to approximate the radical. Round your answer to two decimal places.

$$\frac{\sqrt{5}-2}{\sqrt{2}+4}$$

Numerical and Graphical Analysis In Exercises, use a graphing utility to complete the table and estimate the limit as $x$ approaches infinity. Then use a graphing utility to graph the function and estimate the limit graphically.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline x & 10^9 & 10^1 & 10^2 & 10^3 & 10^4 & 10^5 & 10^6 \\ \hline f(x) & & & & & & & \\ \hline \end{array}$$

$f(x)=\frac{4 x+3}{2 x-1}$

Why must you know how to add and subtract radical expressions before you can rationalize denominators with two terms?

If $\textbf{r}_1$ and $\textbf{r}_2$ are the position vectors of two points, $P_1$ and $P_2$, and $\lambda$ is a real number, show that $\textbf{r}=(1-\lambda)\textbf{r}_1+\lambda\textbf{r}_2$ is the position vector of a point $P$ on the straight line joining $P_1$ and $P_2$. Where is $P$ if $\lambda=\dfrac{1}{2}$ ? if$\lambda=\dfrac{2}{3}$? if $\lambda=-1$ ? if $\lambda=2$?

Tell whether the points given are endpoints of a vertical line, a horizontal line, or neither.

(4, 3), (2, 1)