of is equal to

ertilizer. How much of the mixture should be drained and replaced by an equal amount of water to dilute the mixture to 10% fertilizer? ___L of the 25% mixture should be drained and replaced by water. 2. Darren drives to school in rush hour traffic and averages 24mph. He returns home in mid-afternoon when there is less traffic and averages 39mph. What is the distance between his home and school if the total traveling time is 1hr 45min? The distance between his home and school is ___ mi.

to the bases b. has a length equal to the average of the base lengths

izon problems? In the standard model of cosmology (excepting accelerated expansion) there are three possible fates for the universe. For each fate, state the geometry (shape) of the universe (sphere, saddle, flat), the ulimtate fate of the universe (expand forever, expand forever ever-slowing, big cruch), and how the critical density compares with the actual density of the universe (greater than critical, less than critical, equal to critical). Explain the fates of a low-mass star like the Sun and a high-mass star like Rigel. Make sure to state the final elements produced during their lives and the identity of their ultimate stellar remnants.

for the universe. For each fate, state the geometry (shape) of the universe (sphere, saddle, flat), the ulimtate fate of the universe (expand forever, expand forever ever-slowing, big cruch), and how the critical density compares with the actual density of the universe (greater than critical, less than critical, equal to critical). Explain the fates of a low-mass star like the Sun and a high-mass star like Rigel. Make sure to state the final elements produced during their lives and the identity of their ultimate stellar remnants. Why is inflation necessary to explain our universe and how does inflation solve the flatness and horizon problems?

izon problems? Explain the fates of a low-mass star like the Sun and a high-mass star like Rigel. Make sure to state the final elements produced during their lives and the identity of their ultimate stellar remnants. In the standard model of cosmology (excepting accelerated expansion) there are three possible fates for the universe. For each fate, state the geometry (shape) of the universe (sphere, saddle, flat), the ulimtate fate of the universe (expand forever, expand forever ever-slowing, big cruch), and how the critical density compares with the actual density of the universe (greater than critical, less than critical, equal to critical).

a program designed to provide a decent standard of living to all Americans by spreading the nation’s wealth among the people. Long proposed capping personal fortunes at $50 million each (roughly $600 million in today's dollars) through a restructured, progressive federal tax code and sharing the resulting revenue with the public through government benefits and public works. In subsequent speeches and writings, he revised his graduated tax levy on wealth over $1 million to cap fortunes at $5 - $8 million (or $60 - $96 million today). The full text of this speech, as printed in Long's official Share Our Wealth pamphlet (see right), appears below. “EVERY MAN A KING” Share Our Wealth Radio Speech by Senator Huey P. Long, of Louisiana, February 23, 1934 I s that a right of life when the young children of this country are being reared into a sphere which is more owned by 12 men than it is by 120,000,000 people?” Ladies and Gentlemen: — I have only 30 minutes in which to speak to you this evening, and I, therefore, will not be able to discuss in detail so much as I can write when I have all of the time and space that is allowed me for the subjects, but I will undertake to sketch them very briefly without manuscript or preparation, so that you can understand them so well as I can tell them to you tonight. I contend, my friends, that we have no difficult problem to solve in America, and that is the view of nearly everyone with whom I have discussed the matter here in Washington and elsewhere throughout the United States—that we have no very difficult problem to solve. It is not the difficulty of the problem which we have; it is the fact that the rich people of this country—and by rich people I mean the super-rich—will not allow us to solve the problems, or rather the one little problem that is afflicting this country, because in order to cure all of our woes it is necessary to scale down the big fortunes, that we may scatter the wealth to be shared by all of the people. We have a marvelous love for this Government of ours; in fact, it is almost a religion, and it is well that it should be, because we have a splendid form of government and we have a splendid set of laws. We have everything here that we need, except that we have neglected the fundamentals upon which the American Government was principally predicated. How many of you remember the first thing that the Declaration of Independence said? It said: "We hold these truths to be self-evident, that there are certain inalienable rights for the people, and among them are life, liberty, and the pursuit of happiness;" and it said further, "We hold the view that all men are created equal." Now, what did they mean by that? Did they mean, my friends, to say that all men are created equal and that that meant that any one man was born to inherit $10,000,000,000 and that another child was to be born to inherit nothing? Did that mean, my friends, that someone would come into this world without having had an opportunity, of course, to have hit one lick of work, should be born with more than it and all of its children and children's children could ever dispose of, but that another one would have to be born into a life of starvation? That was not the meaning of the Declaration of Independence when it said that all men are created equal or "That we hold that all men are created equal." Nor was it the meaning of the Declaration of Independence when it said that they held that there were certain rights that were inalienable—the right of life, liberty, and the pursuit of happiness. Is that right of life, my friends, when the young children of this country are being reared into a sphere which is more owned by 12 men than it by 120,000,000 people? Is that, my friends, giving them a fair shake of the dice or anything like the inalienable right of life, liberty, and the pursuit of happiness, or anything resembling the fact that all people are created equal; when we have today in America thousands and hundreds of thousands and millions of children on the verge of starvation in a land that is overflowing with too much to eat and too much to wear? I do not think you will contend that, and I do not think for a moment that they will contend it. Now let us see if we cannot return this Government to the Declaration of Independence and see if we are going to do anything regarding it. Why should we hesitate or why should we quibble or why should we quarrel with one another to find out what the difficulty is, when we know that the Lord told us what the difficulty is, and Moses wrote it out so a blind man could see it, then Jesus told us all about it, and it was later written in the Book of James, where everyone could read it? I refer to the Scriptures, now, my friends, and give you what it says not for the purpose of convincing you of the wisdom of myself, not for the purpose, ladies and gentlemen, of convincing you of the fact that I am quoting the Scriptures means that I am to be more believed than someone else; but I quote you the Scripture, or rather refer you to the Scripture, because whatever you see there you may rely upon will never be disproved so long as you or your children or anyone may live; and you may further depend upon the fact that not one historical fact that the Bible has ever contained has ever yet been disproved by any scientific discovery or by reason of anything that has been disclosed to man through his own individual mind or through the wisdom of the Lord which the Lord has allowed him to have. But the Scripture says, ladies and gentlemen, that no country can survive, or for a country to survive it is necessary that we keep the wealth scattered among the people, that nothing should keep the wealth scattered among the people, that nothing should be held permanently by any one person, and that 50 years seems to be the year of jubilee in which all property would be scattered about and returned to the sources from which it originally came, and every seventh year debt should be remitted. Those two things the Almighty said to be necessary—I should say He knew to be necessary, or else He would not have so prescribed that the property would be kept among the general run of the people, and that everyone would continue to share in it; so that no one man would get half of it and hand it down to a son, who takes half of what was left, and that son hand it down to another one, who would take half of what was left, until, like a snowball going downhill, all of the snow was off of the ground except what the snowball had. I believe that was the judgment and the view and the law of the Lord, that we would have to distribute wealth ever so often, in order that there could not be people starving to death in a land of plenty, as there is in America today. We have in America today more wealth, more goods, more food, more clothing, more houses than we have ever had. We have everything in abundance here. We have the farm problem, my friends, because we have too much cotton, because we have too much wheat, and have too much corn, and too much potatoes. We have a home loan problem, because we have too many houses, and yet nobody can buy them and live in them. We have trouble, my friends, in the country, because we have too much money owing, the greatest indebtedness that has ever been given to civilization, where it has been shown that we are incapable of distributing the actual things that are here, because the people have not money enough to supply themselves with them, and because the greed of a few men is such that they think it is necessary that they own everything, and their pleasure consists in the starvation of the masses, and in their possessing things they cannot use, and their children cannot use, but who bask in the splendor of sunlight and wealth, casting darkness and despair and impressing it on everyone else. "So, therefore," said the Lord in effect, "if you see these things that now have occurred and exist in this and other countries, there must be a constant scattering of wealth in any country if this country is to survive." "Then," said the Lord, in effect, "every seventh year there shall be a remission of debts; there will be no debts after 7 years." That was the law. Now, let us take America today. We have in America today, ladies and gentlemen, $272,000,000,000 of debt. Two hundred and seventy-two thousand millions of dollars of debts are owed by the various people of this country today. Why, my friends, that cannot be paid. It is not possible for that kind of debt to be paid. The entire currency of the United States is only $6,000,000,000. That is all of the money that we have got in America today. All the actual money you have got in all of your banks, all that you have got in the Government Treasury, is $6,000,000,000; and if you took all that money and paid it out today you would still owe $266,000,000,000; and if you took all that money and paid again you would still owe $260,000,000,000; and if you took it, my friends, 20 times and paid it you would still owe $150,000,000,000. You would have to have 45 times the entire money supply of the United States today to pay the debts of the people of America and then they would just have to start out from scratch, without a dime to go on with. So, my friends, it is impossible to pay all of these debts, and you might as well find out that it cannot be done. The United States Supreme Court has definitely found out that it could not be done, because, in a Minnesota case, it held that when a State has postponed the evil day of collecting a debt it was a valid and constitutional exercise of legislative power. Now, ladies and gentlemen, if I may proceed to give you some other words that I think you can understand—I am not going to belabor you by quoting tonight—I am going to tell you what the wise men of all ages and all times, down even to the present day, have all said: That you must keep the wealth of the country scattered, and you must limit the amount that any one man can own. You cannot let any man own §300,000,000,000 or $400,000,000,000. If you do, one man can own all of the wealth that the United States has in it. Now, my friends, if you were off on an island where there were 100 lunches, you could not let one man eat up the hundred lunches, or take the hundred lunches and not let anybody else eat any of them. If you did, there would not be anything else for the balance of the people to consume. So, we have in America today, my friends, a condition by which about 10 men dominate the means of activity in at least 85 percent of the activities that you own. They either own directly everything or they have got some kind of mortgage on it, with a very small percentage to be excepted. They own the banks, they own the steel mills, they own the railroads, they own the bonds, they own the mortgages, they own the stores, and they have chained the country from one end to the other until there is not any kind of business that a small, independent man could go into today and make a living, and there is not any kind of business that an independent man can go into and make any money to buy an automobile with; and they have finally and gradually and steadily eliminated everybody from the fields in which there is a living to be made, and still they have got little enough sense to think they ought to be able to get more business out of it anyway. If you reduce a man to the point where he is starving to death and bleeding and dying, how do you expect that man to get hold of any money to spend with you? It is not possible. Then, ladies and gentlemen, how do you expect people to live, when the wherewith cannot be had by the people? In the beginning I quoted from the Scriptures. I hope you will understand that I am not quoting Scripture to you to convince you of my goodness personally, because that is a thing between me and my Maker; that is something as to how I stand with my Maker and as to how you stand with your Maker. That is not concerned with this issue, except and unless there are those of you who would be so good as to pray for the souls of some of UK. Rut the Lord gave His law, and in the Book of James they said so, that the rich should weep and howl for the miseries that had come upon them; and, therefore, it was written that when the rich hold goods they could not use and could not consume, you will inflict punishment on them, and nothing but days of woe ahead of them. Then we have heard of the great Greek philosopher, Socrates, and the greater Greek philosopher, Plato, and we have read the dialogue between Plato and Socrates, in which one said that great riches brought on great poverty, and would be destructive of a country. Read what they said. Read what Plato said; that you must not let any one man be too poor, and you must not let any one man be too rich; that the same mill that grinds out the extra rich is the mill that will grind out the extra poor, because, in order that the extra rich can become so affluent, they must necessarily take more of what ordinarily would belong to the average man. It is a very simple process of mathematics that you do not have to study, and that no one is going to discuss with you. So that was the view of Socrates and Plato. That was the view of the English statesmen. That was the view of American statesmen. That was the view of American statesmen like Daniel Webster, Thomas Jefferson, Abraham Lincoln, William Jennings Bryan, and Theodore Roosevelt, and even as late as Herbert Hoover and Franklin D. Roosevelt. Both of these men, Mr. Hoover and Mr. Roosevelt, came out and said there had to be a decentralization of wealth, but neither one of them did anything about it. But, nevertheless, they recognized the principle. The fact that neither one of them ever did anything about it is their own problem that I am not undertaking to criticize; but had Mr. Hoover carried out what he says ought to be done, he would be retiring from the President's office, very probably, 8 years from now, instead of 1 year ago; and had Mr. Roosevelt proceeded along the lines that he stated were necessary for the decentralization of wealth, he would have gone, my friends, a long way already, and within a few months he would have probably reached a solution of all of the problems that afflict this country today. But I wish to warn you now that nothing that has been done up to this date has taken one dime away from these big fortune-holders; they own just as much as they did, and probably a little bit more; they hold just as many of the debts of the common people as they ever held, and probably a little bit more; and unless we, my friends, are going to give the people of this country a fair shake of the dice, by which they will all get something out of the funds of this land, there is not a chance on the topside of this God's eternal earth by which we can rescue this country and rescue the people of this country. It is necessary to save the government of the country, but is much more necessary to save the people of America. We love this country. We love this Government. It is a religion, I say. It is a kind of religion people have read of when women, in the name of religion, would take their infant babes and throw them into the burning flame, where they would be instantly devoured by the all-consuming fire, in days gone by; and there probably are some people of the world even today, who, in the name of religion, throw their own babes to destruction; but in the name of our good government, people today are seeing their own children hungry, tired, half-naked, lifting their tear-dimmed eyes into the sad faces of their fathers and mothers, who cannot give them food and clothing they both need, and which is necessary to sustain them, and that goes on day after day, and night after night, when day gets into darkness and blackness, knowing those children would arise in the morning without being fed, and probably go to bed at night without being fed. Yet in the name of our Government, and all alone, those people undertake and strive as hard as they can to keep a good government alive, and how long they can stand that no one knows. If I were in their place tonight, the place where millions are, I hope that I would have what I might say—I cannot give you the word to express the kind of fortitude they have; that is the word—I hope that I might have the fortitude to praise and honor my Government that had allowed me here in this land, where there is too much to eat and too much to wear, to starve in order that a handful of men can have so much more than they can ever eat or they can ever wear. Now, we have organized a society, and we call it "Share Our Wealth Society," a society with the motto "Every Man a King." Every man a king, so there would be no such thing as a man or woman who did not have the necessities of life, who would not be dependent upon the whims and caprices and ipsi dixit of the financial barons for a living. What do we propose by this society? We propose to limit the wealth of big men in the country. There is an average of $15,000 in wealth to every family in America. That is right here today. We do not propose to divide it up equally. We do not propose a division of wealth, but we propose to limit poverty that we will allow to be inflicted upon any man's family. We will not say we are going to try to guarantee any equality, or $15,000 to a family. No; but we do say that one third of the average is low enough for any one family to hold, that there should be a guarantee of a family wealth of around $5,000; enough for a home, an automobile, a radio, and the ordinary conveniences, and the opportunity to educate their children; a fair share of the income of this land thereafter to that family so there will be no such thing as merely the select to have those things, and so there will be no such thing as a family living in poverty and distress. We have to limit fortunes. Our present plan is that we will allow no one man to own more that $50,000,000. We think that with that limit we will be able to carry out the balance of the program. It may be necessary that we limit it to less than $50,000,000. It may be necessary, in working out of the plans that no man's fortune would be more than $10,000,000 or $15,000,000. But be that as it may, it will still be more than any one man, or any one man and his children and their children, will be able to spend in their lifetimes; and it is not necessary or reasonable to have wealth piled up beyond that point where we cannot prevent poverty among the masses. Another thing we propose is old-age pension of $30 a month for everyone that is 60 years old. Now, we do not give this pension to a man making $1,000 a year, and we do not give it to him if he has $10,000 in property, but outside of that we do. We will limit hours of work. There is not any necessity of having overproduction. I think all you have got to do, ladies and gentlemen, is just limit the hours of work to such an extent as people will work only so long as it is necessary to produce enough for all of the people to have what they need. Why, ladies and gentlemen, let us say that all of these labor-saving devices reduce hours down to where you do not have to work but 4 hours a day; that is enough for these people, and then praise be the name of the Lord, if it gets that good. Let it be good and not a curse, and then we will have 5 hours a day and 5 days a week-, or even less than that, and we might give a man a whole month off during a year, or give him 2 months; and we might do what other countries have seen fit to do, and what I did in Louisiana, by having schools by which adults could go back and learn the things that have been discovered since they went to school. We will not have any trouble taking care of the agricultural situation. All you have to do is balance your production with your consumption. You simply have to abandon a particular crop that you have too much of, and all you have to do is store the surplus for the next year, and the Government will take it over. When you have good crops in the area in which the crops that have been planted are sufficient for another year, put in your public works in the particular year when you do not need to raise any more, and by that means you get everybody employed. When the Government has enough of any particular crop to take care of all of the people, that will be all that is necessary; and in order to do all of this, our taxation is going to be to take the billion-dollar fortunes and strip them down to frying size, not to exceed $50,000,000, and if it is necessary to come to $10,000,000, we will come to $10,000,000. We have worked the proposition out to guarantee a limit upon property (and no man will own less than one-third the average), and guarantee a reduction of fortunes and a reduction of hours to spread wealth throughout this country. We would care for the old people above 60 and take them away from this thriving industry and give them a chance to enjoy the necessities and live in ease, and thereby lift from the market the labor which would probably create a surplus of commodities. Those are the things we propose to do. "Every Man a King." Every man to eat when there is something to eat; all to wear something when there is something to wear. That makes us all a sovereign. You cannot solve these things through these various and sundry alphabetical codes. You can have the N. R. A. and P. W. A. and C. W. A. and the U. U. G. and G. I. N. and any other kind of dad-gummed lettered code. You can wait until doomsday and see 25 more alphabets, but that is not going to solve this proposition. Why hide? Why quibble? You know what the trouble is. The man that says he does not know what the trouble is is just hiding his face to keep from seeing the sunlight. God told you what the trouble was. The philosophers told you what the trouble was; and when you have a country where one man owns more than 100,000 people, or a million people, and when you have a country where there are four men, as in America, that have got more control over things than all the 120,000,000 people together, you know what the trouble is. We had these great incomes in this country; but the farmer, who plowed from sunup to sundown, who labored here from sunup to sundown for 6 days a week, wound up at the end of the time with practically nothing. And we ought to take care of the veterans of the wars in this program. That is a small matter. Suppose it does cost a billion dollars a year—that means that the money will be scattered throughout this country. We ought to pay them a bonus. We can do it. We ought to take care of every single one of the sick and disabled veterans. I do not care whether a man got sick on the battlefield or did not; every man that wore the uniform of this country is entitled to be taken care of, and there is money enough to do it; and we need to spread the wealth of the country, which you did not do in what you call the N. R. A. If the N. R. A. has done any good, I can put it all in my eye without having it hurt. All I can see that the N. R. A. has done is to put the little man out of business—the little merchant in his store, the little Italian that is running a fruit stand, or the Greek shoe-shining stand, who has to take hold of a code of 275 pages and study it with a spirit level and compass and looking-glass; he has to hire a Philadelphia lawyer to tell him what is in the code; and by the time he learns what the code is, he is in jail or out of business; and they have got a chain code system that has already put him out of business. The N. R. A. is not worth anything, and I said so when they put it through. Now, my friends, we have got to hit the root with the ax. Centralized power in the hands of a few, with centralized credit in the hands of a few, is the trouble. Get together in your community tonight or tomorrow and organize one of our Share Our Wealth Societies. If you do not understand it, write me and let me send you the platform; let me give you the proof of it. This is Huey P. Long talking, United States Senator, Washington, D. C. Write me and let me send you the data on this proposition. Enroll with us. Let us make known to the people what we are going to do. I will send you a button, if I have got enough of them left. We have got a little button that some of our friends designed, with our message around the rim of the button, and in the center "Every Man a King." Many thousands of them are meeting through the United States, and every day we are getting hundreds and hundreds of letters. Share Our Wealth Societies are now being organized, and people have it within their power to relieve themselves from this terrible situation. Look at what the Mayo brothers announced this week, these greatest scientists of all the world today, who are entitled to have more money than all the Morgans and the Rockefellers, or anyone else, and yet the Mayos turn back their big fortunes to be used for treating the sick, and said they did not want to lay up fortunes in this earth, but wanted to turn them back where they would do some good; but the other big capitalists are not willing to do that, are not willing to do what these men, 10 times more worthy, have already done, and it is going to take a law to require them to do it. Organize your Share Our Wealth Society and get your people to meet with you, and make known your wishes to your Senators and Representatives in Congress. Now, my friends, I am going to stop. I thank you for this opportunity to talk to you. I am having to talk under the auspices and by the grace and permission of the National Broadcasting System tonight, and they are letting me talk free. If I had the money, and I wish I had the money, I would like to talk to you more often on this line, but I have not got it, and I cannot expect these people to give it to me free except on some rare instance. But, my friends, I hope to have the opportunity to talk with you, and I am writing to you, and I hope that you will get up and help in the work, because the resolutions and bills are before Congress, and we hope to have your help in getting together and organizing your Share Our Wealth Societies. Now, that I have but a minute left, I want to say that I suppose my family is listening in on the radio in New Orleans, and I will say to my wife and three children that I am entirely well and hope to be home before many more days, and I hope they have listened to my speech tonight, and I wish them and all of their neighbors and friends everything good that may be had. I thank you, my friends, for your kind attention, and I hope you will enroll with us, take care of your own work in the work of this Government, and share or help in our Share Our Wealth Societies. I thank you.

ame length, then the object is called a rhombus. Some authors restrict kites to being convex. However, a quadrilateral defined as above could be either convex or concave. Concave kites are often called arrowheads or darts. (Note: all rhobmi must be convex.)

properties: f is differentiable everywhere f(x+y)=f(x)f(y) f(0) doesn't equal 0 f'(0) = 1 Show that f(0)=1 Show that f(x) > 0 Use the limit definition of a derivative to show that f'(x) = f(x) for all values of x

C D Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with ∠DAB = x, and ∠ABC = 90◦ , and AD = BC. Say the perpendicular bisector to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C = P D. So the triangles P AD and P BC have equal sides and are congruent. Thus ∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦ . This is a preposterous conclusion – just where is the mistake in the “proof” and why does the argument break down there?

a) (-3,0) b) (0,0) c) (1, -16) d) (3,0)

hooses a card and gets a number. Each spinner outcome is numbered 1-8. If the player's card choice is equal to the spinner outcome they win a $5. If the card number is over the number on the spinner, they win $2. If the roll is under the number on the spinner, they win $1. If the player chooses the card Ace, or they land on 1, they will win nothing. I have to figure out the Theoretical probabilities table for this example but I do not know how, please help!!

ses a card and gets a number. Each spinner outcome is numbered 1-8. If the player's card choice is equal to the spinner outcome they win a $5. If the card number is over the number on the spinner, they win $2. If the roll is under the number on the spinner, they win $1. If the player chooses the card Ace, or they land on 1, they will win nothing. I do not know how to Theoretical probabilities table, please help

ng the package. Packages above 50 pounds will not be shipped. You need to write a program in C that calculates the shipping charge. The shipping rates are based on per 500 miles shipped. They are not pro-rated, i.e., 600 miles is the same rate as 900 miles or 1000 miles. Here are the shipping charges - Package Weight Rate per 500 miles shipped Less than or equal to 10 pounds $3.00 More than 10 pounds but less than or equal to 50 pounds $5.00 If the shipping distance is more than 1000 miles, there is an additional charge of $10 per package shipped.

he efficacy of this spending is therefore relatively important. When it comes to contagious diseases, there are generally two strategies that can be adopted. The first involves prevention, which includes vaccinations to lower or eliminate the risk of contracting a disease. The second involves treatment of those unfortunate enough to get sick, treatment typically requires some form of a drug. Since pharmaceutical companies can produce both vaccines and drugs, we would like to understand the incentives they have to develop each type of medicine. To explore this question, consider a population of 100 consumers, 90 of whom have a low disease risk, say 10%. The remaining ten have a high risk – to make things simple, assume they are certain to contract the disease. In addition, suppose the disease generates personal harm equal to the loss of $100 for each individual when they are infected. Suppose also that pharmaceuticals of either form (vaccines or drugs) are costless to produce (once R & D has occurred) and are perfectly effective Question 2. What price would a profit maximising monopolist charge for a vaccine? What are the monopoly profits on the vaccine? What is the efficient outcome (i.e. SMB = SMC)? What is the welfare under the monopoly and at the efficient allocation? Question 3.Now consider the demand for the drug (assume that the vaccine is not available). Construct the demand function for the drug and plot it on a diagram. What price would a profit maximising monopolist charge for the drug? What are the monopoly profits from the drug? What is the efficient outcome? What is the welfare under the monopoly and at the efficient allocation? Question 4. If the R&D costs of the vaccine and drug are the same, what will the pharmaceutical company do? Explain your answer in terms of the variation in the willingness to pay and the size of the R& D costs. What would a social planner do? Question 5. What are the R&D cost for the vaccine and the R&D cost for the vaccine drug that would make a pharmaceutical company indifferent between developing the vaccine and the drug? Is the social planner indifferent in this case? Explain any difference.

list uses dynamic memory allocation to grow as the size of the data set grows. Unlike linked lists, a binary search tree is very fast to insert, delete and search. Project Description When an author produce an index for his or her book, the first step in this process is to decide which words should go into the index; the second is to produce a list of the pages where each word occurs. Instead of trying to choose words out of our heads, we decided to let the computer produce a list of all the unique words used in the manuscript and their frequency of occurrence. We could then go over the list and choose which words to put into the index. The main object in this problem is a "word" with associated frequency. The tentative definition of "word" here is a string of alphanumeric characters between markers where markers are white space and all punctuation marks; anything non-alphanumeric stops the reading. If we skip all un-allowed characters before getting the string, we should have exactly what we want. Ignoring words of fewer than three letters will remove from consideration such as "a", "is", "to", "do", and "by" that do not belong in an index. In this project, you are asked to write a program to read any text file and then list all the "words" in alphabetic order with their frequency together appeared in the article. The "word" is defined above and has at least three letters. Note: Your result should be printed to an output file named YourUserID.txt. You need to create a Binary Search Tree (BST) to store all the word object by writing an insertion or increment function. Finally, a proper traversal print function of the BST should be able to output the required results. The BST class in the text can not be used directly to solve this problem. It is also NOT a good idea to modify the BST class to solve this problem. Instead, the following codes are recommended to start your program. //Data stored in the node type struct WordCount { string word; int count; }; //Node type: struct TreeNode { WordCount info; TreeNode * left; TreeNode * right; }; // Two function's prototype // Increments the frequency count if the string is in the tree // or inserts the string if it is not there. void Insert(TreeNode*&, string); // Prints the words in the tree and their frequency counts. void PrintTree(TreeNode* , ofstream&); //Start your main function and the definitions of above two functions. Sample Run Please type the text file name: Lincoln.txt Please give the output text file name: mus11.txt You are done! You can open the file "mus11.txt" to check. Press any key to continue ------------------------------------------------------------------------------------------------------------------------------------------------ lincoln.txt--- The Gettysburg Address Gettysburg, Pennsylvania November 19, 1863 Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us -- that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion -- that we here highly resolve that these dead shall not have died in vain -- that this nation, under God, shall have a new birth of freedom -- and that government of the people, by the people, for the people, shall not perish from the earth. ------------------------------------------------------------------------------------------------------------------------------------------------ mus11.txt 1863 1 Address 1 But 1 Four 1 Gettysburg 2 God 1 Liberty 1 November 1 Now 1 Pennsylvania 1 The 3 above 1 add 1 advanced 1 ago 1 all 1 altogether 1 and 6 any 1 are 3 battle-field 1 before 1 birth 1 brave 1 brought 1 but 1 can 5 cause 1 civil 1 come 1 conceived 2 consecrate 1 consecrated 1 continent 1 created 1 dead 3 dedicate 2 dedicated 4 detract 1 devotion 2 did 1 died 1 earth 1 endure 1 engaged 1 equal 1 far 2 fathers 1 field 1 final 1 fitting 1 for 5 forget 1 forth 1 fought 1 freedom 1 from 2 full 1 gave 2 government 1 great 3 ground 1 hallow 1 have 5 here 8 highly 1 honored 1 increased 1 larger 1 last 1 little 1 live 1 lives 1 living 2 long 2 measure 1 men 2 met 1 might 1 nation 5 never 1 new 2 nobly 1 nor 1 not 5 note 1 our 2 people 3 perish 1 place 1 poor 1 portion 1 power 1 proper 1 proposition 1 rather 2 remaining 1 remember 1 resolve 1 resting 1 say 1 score 1 sense 1 seven 1 shall 3 should 1 struggled 1 take 1 task 1 testing 1 that 13 the 9 their 1 these 2 they 3 this 4 those 1 thus 1 under 1 unfinished 1 vain 1 war 2 what 2 whether 1 which 2 who 3 will 1 work 1 world 1 years 1

s, you run the following re- gression on a sample of 65 countries for the year 2012: books = 8.2314 + (1.0329) + 0.3149 age (0.4111) 8.1391 (0.5812) ? income 4.8121 (0.3543) + ereaders, 3.4125 educ (0.7314) where books is the number of paperback novels purchased in 2012, income is per capita GDP in 2012, educ is the average number of years of education for the population in 2012, age is the average age of the population in 2012 and ereaders is the number of electronic readers (e.g. Kindles) sold in 2012. The numbers in parentheses refer to standard errors corresponding to the estimated coefficients. You also find that R2 = 0.7231 and SSR = 1, 231. (a) Which of the slope coefficients are statistically different from zero at the 5% level of significance? Perform statistical tests to answer this question. [8 marks] Solution: Each test carries 2 marks. t ratios are: 14.0039, 4.66, 0.7659, -13.5819. The 2.5% critical value for a tn?k=65?5=60 distribution can be seen to be 2.0000, implying that all coefficients except the one on age are significant. (b) Does the intercept have a plausible interpretation? Explain briefly. [4 marks] Solution: The intercept indicates that demand for paperback novels equals 8.2314 when income, educ, age and ereaders all equal zero. Clearly this is not plausible. (c) Construct a 95% confidence interval for the coefficient on age. [8 marks] Solution: CI is given by [bage