Assign oxidation states for all atoms in each of the following compounds. $\mathrm{Na}_{4} \mathrm{Fe}(\mathrm{OH})_{6}$

Find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use $\sigma$ in each case, rather than $s$.) The CD shipment data is in Table.

Transform the given equation

$$\begin{gather*} t^2 U'' + 3t U' + 5 U = t^2 + 4 \end{gather*}$$

into a system of first order equations.

Using clay (or glazing compounds), make a doughnut. Without puncturing or tearing the doughnut, reshape it into a topologically equivalent figure, a cut with a handle.

Which noble gas has the same electron configuration as each of the ions in the following compounds?

a. calcium bromide, $\mathrm{CaBr}_2$

Solve by the Laplace transform, showing the details and graphing the solution: y''+4y=δ(t-π)-δ (t-π), y(0)=1, y'(0)=0

When each of these compounds dissolves in water, what ions are released and in what ratio? (a)

$$NaF$$

(b)

$$Li_3N$$

(c)

$$FeCI_3$$

(d)

$$K_2O$$

Which compound or compounds in each of the following groups is (are) expected to be soluble in water?\

$$\mathrm{CuO}, \mathrm{CuCl}_2, \mathrm{FeCO}_3$$

Give the empirical formula of each of the following compounds if a sample contains 0.0130 mol C, 0.0390 mol H, and 0.0065 mol O;

Antidifferentiate using the table of integrals. You may need to transform the integrand first.

$$\displaystyle \int \sin3\theta \cos5\theta\ d\theta$$

Describe how to transform the graph of y=ln x into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.

$$f(x)=ln(x+3)$$

How would you prepare the following compounds starting with an appropriate carboxylic acid and any other reagents needed? (Reddish brown = Br.)

trans-Cyclodecene boils at 193°C, but cis-cyclodecene boils at 195.6 °C. Write stru ctural formulas for these two compounds.

Use the definition of the Laplace transform to find $\mathcal{L}\{f(t)\}$ for each of the given functions f(t). $f(t)=e^{t} \cos t$