What is the scope of a local variable?

What do you understand by the term “scope of a variable”?

The study of food chains is an important topic in the determination of the spread and accumulation of environmental pollutants in living matter. Suppose that a food chain has three links. The first link consists of vegetation of types $v_{1}, v_{2}, \dots, v_{0},$ which provide all the food requirements for herbivores of species $h_{1}, h_{2}, \dots, h_{m}$ in the second link. The third link consists of carnivorous animals $c_{1}, c_{2}, \dots, c_{k},$ which depend entirely on the herbivores in the second link for their food supply. The coordinate $a_{i j}$ of the matrix

$$A=\left[\begin{array}{cccc}{a_{11}} & {a_{12}} & {\cdots} & {a_{1 m}} \\ {a_{21}} & {a_{22}} & {\cdots} & {a_{2 m}} \\ {\vdots} & {\vdots} & {} & {\vdots} \\ {a_{n 1}} & {a_{n 2}} & {\cdots} & {a_{n m}}\end{array}\right]$$

represents the total number of plants of type $v_i$ eaten by the herbivores in the species $h_j,$ whereas $b_{ij}$ in

$$B=\left[\begin{array}{cccc}{b_{11}} & {b_{12}} & {\cdots} & {b_{1 k}} \\ {b_{21}} & {b_{22}} & {\cdots} & {b_{2 k}} \\ {\vdots} & {\vdots} & {} & {\vdots} \\ {b_{m 1}} & {b_{m 2}} & {\cdots} & {b_{m k}}\end{array}\right]$$

describes the number of herbivores in species $h_i$ that are devoured by the animals of type $c_j.$ a. Show that the number of plants of type $v_i$ that eventually end up in the animals of species $c_j$ is given by the entry in the ith row and jth column of the matrix AB. b. What physical significance is associated with the matrices A−1,B−1, and (AB) −1= B−1A−1?

Pistol Corporation acquired 70 percent of Scope Corporation's voting stock on May 18, 20X1. The companies reported the following data with respect to intercompany sales in 20X4 and 20X5:

$$\begin{array}{llrlrr} & \textbf{Purchased} & \textbf{Purchase} & \textbf{Sold} & \textbf{Sale} & \textbf{Unsold at} & \textbf{Year Sold to}\\ \textbf{Year} & \textbf{by} & \textbf{Price} & \textbf{to} & \textbf{Price} & \textbf{End of Year}& \textbf{Unaffiliated Co.}\\ \\ \text{20X4} & \text{Scope Corp.} & \$120,000 & \text{Pistol Corp.} & \$180,000 & \$\hspace{6pt}45,000 & \text{20X5} \\ \text{20X5} & \text{Scope Corp.} & 90,000 & \text{Pistol Corp.} & 135,000 & 30,000 & \text{20X6} \\ \text{20X5} & \text{Pistol Corp.} & 140,000 & \text{Scope Corp.} & 280,000 & 110,000 & \text{20X6} \\ \end{array}$$

Pistol reported operating income (excluding income from its investment in Scope) of $160,000 and$220,000 in 20X4 and 20X5, respectively. Scope reported net income of $90,000 and$85,000 in 20X4 and 20X5, respectively.

Required

Compute the inventory balance reported in the consolidated balance sheet at December 31, 20X5, for the transactions shown.

On the scope display, identify when the SCR is conducting.

The Environmental Protection Agency (EPA) regulates the level of carbon dioxide $\left(\mathrm{CO}_2\right)$ emissions. Periodically these emissions measurements are under-reported due to leakage or faulty equipment. Such problems are often detected only by an expensive test (RATA) that is typically conducted only once per year. The EPA recently began applying an automated control chart methodology to detect the under-measurement of emissions data (EPRI CEM Users Group Conference, Nashville, TN, May 13, 2008). The EPA collects emissions data each day by measuring $C O_2$ concentration for each of 6 randomly selected hours. The daily average $\mathrm{CO}_2$ levels for each of the 30 days are shown in the table above. The EPA considers these values to represent emissions levels because the RATA test was recently performed and showed no problems with under-reporting. The averages' lower and upper control limits were established as $\mathrm{LCL}=12.26$ and $\mathrm{UCL}=13.76$.

|Daily Average CO2 Measurements for 30 consecutive days| | | | | | | | | | | | | | | - | - |- | - | - |- |-- | - | -- |- | - | -- |- | - |-| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |13 |14 | |12.9|13.2|13.4 | 13.3 | 13.1 | 13.2 | 13.1 | 13 | 12.5 | 12.5 | 12.7 | 12.8 | 12.7 | 12.9 |
| 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |28 |29 | | 12.9 |12.8 | 12.7|13.2 | 13.2 | 13.3 | 13 | 13 | 13.2 | 13.2 | 13.4 | 13.1 | 13.3 | 13.4 |

a. Construct a control chart for the daily average $\mathrm{CO}_2$ levels.

Interested in a sporty car? Worried that it might use too much gas? The Environmental Protection Agency lists most such vehicles in its "mini-compact" or "two-seater" categories. Table 4.1 gives city and highway gas mileages (in miles per gallon) for all model year 2009 cars in these two groups.

$$\begin{matrix} \text{} & \text{Mini/subcompact cars } & \text{} & \text{Two-seater cars} & \text{} & \text{}\\ \text{Model } & \text{City} & \text{Highway} & \text{Model } & \text{City} & \text{Highway}\\ \text{Audi TT coupe} & \text{23} & \text{31} & \text{Aston Martin DBS Coupe} & \text{17} & \text{24}\\ \text{BMW 328 $\mathrm{CI}$ Convertible} & \text{18} & \text{27} & \text{Aston Martin V8 Vantage} & \text{13} & \text{19}\\ \text{BMW 335 $\mathrm{CI}$ Convertible} & \text{17} & \text{26} & \text{Audi TT Roadster} & \text{22} & \text{30}\\ \text{BMW M3 Convertible} & \text{14} & \text{20} & \text{Cadillac XLR} & \text{14} & \text{23}\\ \text{Jaguar XK Convertible} & \text{16} & \text{25} & \text{Chevrolet Corvette} & \text{15} & \text{25}\\ \text{Jaguar XKR Convertible} & \text{15} & \text{23} & \text{Dodge Viper} & \text{13} & \text{22}\\ \text{Mercedes-Benz CLK350} & \text{17} & \text{25} & \text{Ferrari GTB Fiorano} & \text{11} & \text{15}\\ \text{Mercedes-Benz CLK550} & \text{15} & \text{22} & \text{Ferrari F430} & \text{11} & \text{16}\\ \text{Mitsubishi Eclipse Spyder} & \text{19} & \text{26} & \text{Honda S2000} & \text{18} & \text{25}\\ \text{Porsche 911 Carrera} & \text{18} & \text{26} & \text{Lamborghini Gallardo Coupe} & \text{14} & \text{20}\\ \text{Porsche 911 Turbo} & \text{15} & \text{23} & \text{Mercedes-Benz SL500} & \text{13} & \text{21}\\ \text{} & \text{} & \text{} & \text{Mercedes-Benz SL600} & \text{11} & \text{18}\\ \text{} & \text{} & \text{} & \text{Mercedes-Benz SLK320} & \text{19} & \text{26}\\ \text{} & \text{} & \text{} & \text{Nissan 350 Z Roadster} & \text{17} & \text{23}\\ \text{} & \text{} & \text{} & \text{Pontiac Solstice} & \text{19} & \text{27}\\ \text{} & \text{} & \text{} & \text{Porsche 911 GT2} & \text{16} & \text{23}\\ \text{} & \text{} & \text{} & \text{Saturn Sky} & \text{19} & \text{27}\\ \text{} & \text{} & \text{} & \text{Smart fortwo convertible} & \text{33} & \text{41}\\ \text{} & \text{} & \text{} & \text{Spyker C8} & \text{13} & \text{18}\\ \end{matrix}$$

(a) Make a scatterplot that shows the relationship between city and highway mileage for minicompact cars using city mileage as the explanatory variable. Be sure to label your axes. (b) On the same graph, make a scatterplot that shows the relationship between city and highway mileage for two-seater cars. Use a different color or plotting symbol. ( c) Describe what you see in the scatterplot. Is the form of the relationship similar for the two types of car? What is the most important difference between the two types?

The Department of Energy and the U.S. Environmental Protection Agency’s 2012 Fuel Economy Guide provides fuel efficiency data for 2012 model year cars and trucks (Department of Energy website, April 16, 2012). The file named 2012FuelEcon provides a portion of the data for 309 cars. The column labeled Manufacturer shows the name of the company that manufactured the car; the column labeled Displacement shows the engine’s displacement in liters; the column labeled Fuel shows the required or recommended type of fuel (regular or premium gasoline); the column labeled Drive identifies the type of drive (F for front wheel, R for rear wheel, and A for all wheel); and the column labeled Hwy MPG shows the fuel efficiency rating for highway driving in terms of miles per gallon.

a. Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine’s displacement. Test for significance using $\alpha$ = .05.

b. Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the required or recommended type of fuel is premium gasoline and 0 if the type of fuel is regular gasoline. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine’s displacement and the dummy variable FuelPremium.

c. Use $\alpha$ = .05 to determine whether the dummy variable added in part (b) is significant.

d. Consider the addition of the dummy variables FrontWheel and RearWheel. The value of FrontWheel is 1 if the car has front wheel drive and 0 otherwise; the value of RearWheel is 1 if the car has rear wheel drive and 0 otherwise. Thus, for a car that has all-wheel drive, the value of FrontWheel and the value of RearWheel is 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine’s displacement, the dummy variable FuelPremium, and the dummy variables FrontWheel and RearWheel.

e. For the estimated regression equation developed in part (d), test for overall significance and individual significance using $\alpha$ = .05.

An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen, nitrogen, oxygen, and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Dulong formula: $H H V(\mathrm{kJ} / \mathrm{kg})=33,801(\mathrm{C})+144,158[(\mathrm{H})-0.125(\mathrm{O})]+9413(\mathrm{S})$ where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125(O) term accounts for the hydrogen bound in the water contained in the coal. a) Derive an expression for the higher heating value (HHV) of a coal in terms of C, H, O, and S, and compare your result with the Dulong formula. Suggest a reason for the difference. b) A coal with an ultimate analysis of 75.8 wt% C, 5.1% H, 8.2% O, 1.5% N, 1.6% S, and 7.8% ash (noncombustible) is burned in a power-plant boiler furnace. All of the sulfur in the coal forms $\mathrm{SO}_{2}$. The gas leaving the furnace is fed through a tall stack and discharged to the atmosphere. The ratio $\phi$ (kg $\mathrm{SO}_{2}$ in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate $\phi$, using the Dulong formula for the heating value of the coal. c) An earlier version of the EPA regulation specified that the mole fraction of $\mathrm{SO}_{2}$ in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.

Ethylene glycol and propylene glycol are liquids used in antifreeze and deicing solutions. Ethylene glycol is listed as a hazardous chemical by the Environmental Protection Agency, while propylene glycol is generally regarded as safe. Table lists the freezing temperature for various concentrations (as a percentage of total weight) of each chemical in a solution used to deice airplanes. A linear regression model for the ethylene glycol data in Table is $E=-0.55 T+31$ where E is the percentage of ethylene glycol in the deicing solution and T is the temperature at which the solution freezes. $$ \begin{matrix} \text{Freezing Temperature }{\left(^{\circ} \mathbf{F}\right)} & \text{Ethylene Glycol (\\% Wt.) } & \text{Propylene Glycol (\\% Wt.)}\\ \text{-50} & \text{56} & \text{58}\\ \text{-40} & \text{53} & \text{55}\\ \text{-30} & \text{49} & \text{52}\\ \text{-20} & \text{45} & \text{48}\\ \text{-10} & \text{40} & \text{43}\\ \text{0} & \text{33} & \text{36}\\ \text{10} & \text{25} & \text{29}\\ \text{20} & \text{16} & \text{19}\\ \end{matrix} $$ (A) Draw a scatter plot of the data and a graph of the model on the same axes. (B) Use the model to estimate the freezing temperature to the nearest degree of a solution that is 30% ethylene glycol. (C) Use the model to estimate the percentage of ethylene glycol in a solution that freezes at $15^{\circ} \mathrm{F}$.

The following story and questions are designed to stimulate critical thinking through class discussion or as a brief essay response. There are no right or wrong answers to these questions.
Sylvia Gaylord works as a legal aide on the 12th floor of a tall glass-and-steel monument to modern architectural technology. On clear days, the views are spectacular. From her cubicle, Sylvia’s eye catches the edge of the beautiful blue-and-white skyscaper as she reaches for her inhaler. This is the third attack since she returned from lunch 4 hours ago—her asthma is really bad today. But if she leaves work early again, her boss will write her up for it. Sylvia concentrateson breathing normally.
Her roommate, Kelly, is a respiratory therapist at the county hospital. Kelly says Sylvia’s asthma attacks are probably triggered by the city’s high level of air pollution. That can’t be true. They both run in the park every morning before work, and Sylvia rarely needs to use her inhaler. The problems start when she gets to work. The wheezing and coughing were so bad today that by the time she got up the elevator and into her cubicle, she could hardly breathe. Last night, the cable news ran a story on the unhealthy air found in some buildings. They called it “sick building syndrome” and reported that certain employees developed allergic reactions just by breathing the air. “Hmmm,” she thought, “It seems like more and more people are getting sick in our office. John has had the flu twice. Sid’s bronchitis turned into bronchopneumonia, and Hui complains of sinusitis. Could this building have an air quality problem?”
Discuss which environmental factors might cause an asthma attack.

A power plant is driven by the combustion of a complex fossil fuel having the formula $\mathrm{C}_{11} \mathrm{H}_7 \mathrm{~S}$. Assume the air supply is composed of only $\mathrm{N}_2$ and $\mathrm{O}_2$ with a molar ratio of $3.76: 1.00$, and the $\mathrm{N}_2$ remains unreacted. In addition to the water produced, the fuel's $\mathrm{C}$ is completely combusted to $\mathrm{CO}_2$ and its sulfur content is converted to $\mathrm{SO}_2$. In order to evaluate gases emitted at the exhaust stacks for environmental regulation purposes, the nitrogen supplied with the air must also be included in the balanced reactions.

Including the $\mathrm{N}_2$ supplied in the air, write a balanced combustion equation for the complex fuel assuming $100 \%$ stoichiometric combustion (i.e., when there is no excess oxygen in the products and the only $\mathrm{C}$-containing product is $\mathrm{CO}_2$ ). Except in the case of $\mathrm{N}_2$, use only integer coefficients.

Including $\mathrm{N}_2$ supplied in the air, write a balanced combustion equation for the complex fuel assuming $120 \%$ stoichiometric combustion (i.e., when excess oxygen is present in the products and the only $\mathrm{C}$-containing product is $\mathrm{CO}_2$ ). Except in the case of $\mathrm{N}_2$, use only integer coefficients.

Calculate the minimum mass (in $\mathrm{kg}$ ) of air required to completely combust $1700 \mathrm{~kg}$ of $\mathrm{C}_{11} \mathrm{H}_7 \mathrm{~S}$.

Calculate the air/fuel mass ratio, assuming $100\%$ stoichiometric combustion.

Calculate the air/fuel mass ratio, assuming $120 \%$ stoichiometric combustion.

Please refer to the example below.

a. Assume you analyzed the data by focusing on boys rather than girls. How would the percent in Part A change? How would the percents in Part B change? How would the conclusions in Part C change?

b. About how many girls would have to prefer each type of pet for pet preference to be completely uninfluenced by gender? Discuss.

Example:

Jenna conducted her survey because she was interested in the question, "Does gender influence what type of pet people prefer?" If there is no influence, then the distribution of gender within each subgroup of pet preference should roughly equal the distribution of gender within the whole group. Use the results of Jenna's survey to investigate possible influences of gender on pet preference.

A Identify the percent of all students surveyed who are girls:

B Determine each conditional relative frequency.

Of the 18 students who prefer dogs as pets, 8 are girls. Percent who are girls, given a preference for dogs as pets:

Of the 12 students who prefer cats as pets, 7 are girls. Percent who are girls, given a preference for cats as pets:

Of the 10 students who prefer other pets, 1 is a girl. Percent who are girls, given a preference for other pets:

C Interpret the results by comparing each conditional relative frequency to the percent of all students surveyed who are girls.

The percent of girls among students who prefer dogs is fairly close to 40%, so gender does not appear to influence preference for dogs.

The percent of girls among students who prefer cats is much greater than 40%. What conclusion might you draw in this case?

The percent of girls among students who prefer other pets is much less than 40%. What conclusion might you draw in this case?

The U.S. Environmental Protection Agency (EPA) monitors levels of pollutants in the air for cities across the country. Ozone pollution levels are measured using a 500-point scale; lower scores indicate little health risk, and higher scores indicate greater health risk. The following data show the peak levels of ozone pollution in four cities (Birmingham, Alabama; Memphis, Tennessee; Little Rock, Arkansas; and Jackson, Mississippi) for 10 dates in 2012 (U.S. EPA website, March 20, 2012).

	City
Data	Birmingham AL	Memphis TN	Little Rock AR	Jackson MS
Jan 9	18	20	18	14
Jan17	23	31	22	30
Jan 18	19	25	22	21
Jan 31	29	36	28	35
Feb 1	27	31	28	24
Feb 6	26	31	31	25
Feb 14	31	24	19	25
Feb 17	31	31	28	28
Feb 20	33	35	35	34
Feb 29	20	42	42	21

Use $\alpha$ = .05 to test for any significant difference in the mean peak ozone levels among the four cities.