Fourteen of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements for financial records and fraud protection. Assuming that these are a random sample of all publicly traded companies, construct a 95 percent confidence interval for the overall noncompliance proportion. See The New York Times, April 27, 2005, p. BU5.

Personal consumption expenditures (in billions of dollars) for several types of recreation from 2012 through 2017 are shown in the table, where $x$ is the expenditures on amusement parks and campgrounds, $y$ is the expenditures on live entertainment (excluding sports), and $z$ is the expenditures on spectator sports.

A model for the data is given by

z = 0.54x - 0.6y + 11.98

Find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$.

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.

In a right triangle, the measure of one acute angle is twice the sum of the measure of the other acute angle and 30. Find the measure of each acute angle in the right triangle.

A sample of dry air at $28^{\circ} \mathrm{C}$ in a sealed flask has a pressure of $90 \mathrm{kPa}$. Which of the following values is most likely the partial pressure of oxygen, $\mathrm{O}_2(\mathrm{~g})$, in the flask?

(a) $70 \mathrm{kPa}$

(c) $3 \mathrm{~Pa}$

(b) $19 \mathrm{kPa}$

(d) $0.8 \mathrm{kPa}$

For the given problem, determine the equations of the polynomials of degree two whose graphs pass through the given points.

$$(-1,-1),(0,1),(1,-3)$$

Determine the value of $y$ when $x=3.$

Verify the identity by transforming the lefthand side into the right-hand side.

$$\left(1-\sin ^2 \theta\right)\left(1+\tan ^2 \theta\right) = 1$$

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?

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 $\mathrm{CaSO}_4 \cdot 2 \mathrm{H}_2 \mathrm{O}$.

Turpentine at $77^{\circ} \mathrm{F}$ is flowing from $\mathrm{A}$ to $\mathrm{B}$ in a $3$ -in coated ductile iron pipe. Point $\mathrm{B}$ is $20\ \mathrm{ft}$ higher than point $\mathrm{A}$ and the total length of the pipe is $60\ \mathrm{ft}$. Two $90^{\circ}$ long-radius clbows are installed between $\mathrm{A}$ and $\mathrm{B}$. Determine the volume flow rate of turpentine if the pressure at $\mathrm{A}$ is $120$ psig and the pressure at $B$ is $105$ psig.

Evaluate by using the order of operation: $(2^2+8)\div 4-2$

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, $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$

When $25.0 \mathrm{~mL}$ of $0.500 \mathrm{M}$ iron(II) sulfate is combined with $35.0 \mathrm{~mL}$ of $0.332 \mathrm{M}$ barium hydroxide, two different precipitates are formed. (a) Write a net ionic equation for the reaction that takes place. (b) Estimate the mass of the precipitates formed. (c) What are the equilibrium concentrations of the ions in solution?

Express the answers to these operations in scientific notation:
(a) $0.0095+\left(8.5 \times 10^{-3}\right)$
(b) $653 \div\left(5.75 \times 10^{-8}\right)$
(c) $850,000-\left(9.0 \times 10^5\right)$
(d) $\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^6\right)$