Calcium sulfate, $\mathrm{CaSO}_4$, is a white, crystalline powder. Gypsum is a mineral, or natural substance, that is a hydrate of calcium sulfate. A 1.000-g sample of gypsum contains $0.791 \mathrm{~g} \mathrm{CaSO}_4$. How many moles of $\mathrm{CaSO}_4$ are there in this sample? Assuming that the rest of the sample is water, how many moles of $\mathrm{H}_2 \mathrm{O}$ are there in the sample? Show that the result is consistent with the formula $\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}$.

Calculate the amount concentration of the cations in the following solutions:

(a) $0.5 \mathrm{~mol} / \mathrm{L}$ sodium carbonate, $\mathrm{Na}_2 \mathrm{CO}_3$

(b) $0.2 \mathrm{~mol} / \mathrm{L}$ ammonium sulfite, $\left(\mathrm{NH}_4\right)_2 \mathrm{SO}_3$

(c) $1.5 \mathrm{molL}$ iron(III) sulfate, $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$

For the following exercise,

Simplify the expression.

$$\frac{\tan \left(\frac{1}{2} x\right)+\tan \left(\frac{1}{8} x\right)}{1-\tan \left(\frac{1}{8} x\right) \tan \left(\frac{1}{2} x\right)}$$

a) Find pairs of equivalent ratios:

$$\begin{array}{ll}2: 3: 4 & 9: 12: 15 \\ 8: 5: 4 & 1: 2: 3 \\ 3: 2: 1 & 16: 10: 8 \\ 3: 6: 9 & 6: 9: 12 \\ 5: 8: 4 & 3: 4: 5\end{array}$$

b) Explain how you know they are equivalent.

A 50 -cm-diameter pipeline in the Arctic carries hot oil at $30^{\circ} \mathrm{C}$ and is exposed to a surrounding temperature of $-20^{\circ} \mathrm{C}$. A special powder insulation $5 \mathrm{~cm}$ thick surrounds the pipe and has a thermal conductivity of $7 \mathrm{~mW} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$. The convection heat transfer coefficient on the outside of the pipe is $9 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Calculate the energy loss from the pipe per meter of length.

Predict how the relative volumes of the large intestines of herbivores and carnivores would compare, and explain your reasoning.

The italicized portion of each sentence below contains some flaw. Select the answer that best corrects the flaw.

Our boss called a meeting in relation to the sales project.

A. a meeting about

B. a discussion session in relation to

C. to tell us to meet to talk about

D. a meeting, which was on the topic of

Solve the problem below using Guess and Check. State your solution in a sentence. Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75 . Find the numbers.

Find all solutions of the equation

$$y y^{\prime \prime}-2\left(y^{\prime}\right)^{2}=0$$

that pass through the point x=1, y=1.

Most of the given sentences contain an error in subject-verb agreement. Draw a line through the incorrect verb, and write above it the correct form. If a sentence is already correct, write C above the number.

$\lbrack15\rbrack$ Where's the shirts and pants for the dry cleaners?

Specifies a functional relationship between the two variables $u$ and $v$.
(a) Find $\int_a^b u d v$.
(b) Find $\int_b^a u d v$.
(c) Find $\int_a^b v d u$.

The reaction

$$2 \mathrm { Fe } _ { 2 } \mathrm { O } _ { 3 } ( s ) + 3 \mathrm { C } ( s ) \longrightarrow 4 \mathrm { Fe } ( s ) + 3 \mathrm { CO } _ { 2 } ( g )$$

is involved in the smelting of iron. Use

$$\Delta H _ { f }$$

values given in Appendix Table B–14 to calculate the enthalpy change during the production of 1 mol of iron.

The equation for the reaction of iron and oxygen gas to form rust $\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ is written as

$$4 \mathrm{Fe}(s)+3 \mathrm{O}_2(g) \longrightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s) \quad \Delta H=-1.7 \times 10^3 \mathrm{~kJ}$$

How many grams of rust form when 150 kJ are released?

State the first term of each product. a. $(2 x+1)(3 x+4)$ b. $\left(x^{4}+x^{2}\right)\left(3 x^{8}+x^{11}\right)$ c. $x(x+9)$ d. $\left(x^{2}+9\right)(3 x+4)(2 x+6)$ e. $\left(x^{3}+4\right)\left(x^{2}+6\right)(x+5)$