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Under adolf hitler, the nazis developed a carefully planned network of concentration camps. these were designed to hold all those deemed undesirable by the nazi leadership. an individual consigned to a camp was forced to work, given a specific uniform that was the same as all other prisoners, given a limited ration of food, no access to amenities, and faced a near certain death by poison gas. this tragic episode in human history is an extreme example of

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Under adolf hitler, the nazis developed a carefully planned network of concentration camps. these were designed to hold all those deemed undesirable by the nazi leadership. an individual consigned to a camp was forced to work, given a specific uniform that was the same as all other prisoners, given a limited ration of food, no access to amenities, and faced a near certain death by poison gas. this tragic episode in human history is an extreme example of

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Which measurement is most accurate to describe the amount that a teacup can hold?

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Which measurement is most accurate to describe the amount that a teacup can hold?

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A share of stock in the Lofty Cheese Company is quoted at 251/4. Suppose you hold 30 shares of that stock, which you bought at 201/4. If you sell your stock at 251/4, which one of the following statements would be true?

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A share of stock in the Lofty Cheese Company is quoted at 251/4. Suppose you hold 30 shares of that stock, which you bought at 201/4. If you sell your stock at 251/4, which one of the following statements would be true?

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Which statement best describes the difference between strong nuclear forces and weak nuclear forces? a) Weak nuclear forces hold protons and neutrons together; strong nuclear forces hold electrons in their shells. b) Strong nuclear forces are responsible for holding electrons in bonds; weak nuclear forces are involved when the bonds break. c) Weak nuclear forces hold the atoms’ nucleus together; strong nuclear forces tear them apart. d) Strong nuclear forces are responsible for holding together the nucleus of an atom; weak nuclear forces are involved when certain types of atoms break down.

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There are four types of fundamental forces in nature.These are named as gravitational force,electromagnetic force,strong nuclear force and weak nuclear force.

As per the question we have to understand the role of strong nuclear force and weak nuclear force.

An atom consists of a nucleus surrounded by extra nuclear part consisting of electrons in various orbits.The nucleus contains two basic particles called protons and neutrons .Protons are positively charged while neutrons are neutral.Protons being positively charged will impart repulsive force on each other and may come out of the nucleus.But the nucleus is stable.That is due to the strong nuclear force.

Strong nuclear force is a spin dependent and charge independent force which comes into existence due to the mutual interaction of gluons which binds the protons and neutrons .Hence it is attractive in nature.It’s 100 times more stronger than electromagnetic force also.

Weak nuclear force comes into existence during radio -active decay .This force is due to the exchange of ‘ w’ and ‘z’ bosons[the particles like protons and neutrons having integral or zero spin] which are heavier in nature.The role of it is to change protons into neutrons and vice versa.Its a short range force.

Hence the option D is right.

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Which powers did the pope hold over medieval monarchs? Select all that apply. indulgences interdicts simony excommunication sacraments

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Which powers did the pope hold over medieval monarchs? Select all that apply. indulgences interdicts simony excommunication sacraments

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An action movie production team needs glass spheres to hold a green liquid that looks like an explosive l. if all of the available 3,392’92 cubic inches of the liquid is to be poured into 30 glass spheres l, what should the diameter of each sphere be. assume that each sphere is filled to the top

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We need 30 glass spheres whose TOTAL volume = 3,392.92 cubic inches.
Therefore each of the 30 spheres must have a volume of  3,392.92 / 30 =



113.0973333333



cubic inches
Sphere Volume   =   4/3 • π • r³
radius^3 =
Sphere Volume / (4/3 • π)
radius^3 = 113.0973333333 /



4.1887902048




radius^3 =



26.9999994758




radius = 3 inches
diameter = 6 inches

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How did youth culture change during the 1920s? youth were expected to hold jobs that contributed to the welfare of the family. students were able to remain in school longer and an adolescent culture developed. both men and women were working outside the home, so youth were expected to shoulder greater responsibility. no real youth culture existed during the 1920s?

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The correct answer should be
Students were able to remain in school longer and an adolescent culture developed

These were people who started asking for permission less and less and developing their own youth culture that consisted of staying out long, dancing, they started dating and marrying as they saw fit, they could stay in school longer, both high school and college, and ultimately had more fun and less responsibilities.

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What belief did the romantics hold about humanity

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What belief did the romantics hold about humanity

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Brian Wilson has a baseball card collection passed down to him from his grandfather. He is particularly proud of the signed Hank Aaron baseball card that he has. What type of investment does he hold? A. Direct investment in real estate B. Indirect investment in real estate C. Investment in precious metals D. Investment in collectibles

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The Contribution Margin per unit (CM) can be calculated
from the difference of Selling Price per unit (SP) and Total Expenses per unit
(TE).

 

First, let’s calculate the value of SP:

SP = Sales / Units sold

SP = $1,043,400 / 22,200 units sold

SP = $47

 

Second, calculate all expenses:

Direct materials per unit = $234,948 / 27,970 units
manufactured = $8.4

Direct labor per unit = $131,459 / 27,970 units
manufactured = $4.7

Variable manufacturing overhead per unit = $240,542 / 27,970
units manufactured = $8.6

Variable selling expenses per unit = $113,220 / 22,200
units sold = $5.1

TE = $26.8

 

Therefore the CM is:

CM = SP – TE

CM = $47 – $26.8

CM = $20.2 per unit

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Many people urged America to fight the British to hold the northern boundary of Oregon at: 36° 30′ 49° 54° 40′

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The Reformation actually started after Columbus’s landing in North America. 

Treaty of Tordesillas in 1494 was forced on Spain and Portugal by the Pope. The Pope basically said that all lands in the New World belonged to Spain and all new non-Christian lands in the Eastern Hemisphere belong to Portugal. No other Catholic countries can do anything in those areas without the approval of the owner. 

The pope basically drew two lines on the globe setting the border. The western line started at the north pole cut half way through Greenland and ended at the south pole. The new world was everything to the west. Problem is that it ran through a chunk of Brazil which is why Brazil is an ex-Portuguese colony. 

The Eastern line starts at the North Pole runs through siberia, through the pacific just west of Japan, and cuts Australia in half. Of course, Australia hadn’t been discovered yet. Everything to the the east of this line is the new world. 

Obviously, this treaty didn’t hold up well, but the reformation gave the protestant countries an excuse to explore the new world since they didn’t have to take orders from the Pope. Even so, France, a catholic country, ignored it too. 

Really, the only country that was effected by the reformation in the exploration of the Americas was England. All the other countries, changed their religion once and then went to war with the nearest catholic country. Sweden became Lutheran and stayed that way. The Dutch Republic became Calvinists and stayed that way. 

England kept switching. First it was Catholic. Then, Henry VIII made it protestant. Then, Henry’s daughter Mary I made it catholic again. Henry’s other daughter Elizabeth I (with the two hit movies) made it Protestant again. 

Years latter, Oliver Cromwell over through the monarchy, executed the King Charles I, and established a Protestant fundamentalist religious military dictatorship. He outlawed drinking,smoking, gambling, theater, dirty books, sports, prostitution, and anything generally fun. He would have made Saudi Arabia proud. Basically, all you could do is work, pray, and die. Sex was allowed for creating children, but you couldn’t enjoy it. 

When Cromwell died, the people of England said enough was enough and brought back the King. Charles II kicked out the fundamentalists and brought back drinking, smoking, gambling, dirty books, sports, prostitution, and having fun during sex. Incidentally, those were also all his hobbies. 

This brings us to the famous Pilgrims. They were part of Cromwell’s crowd. They kept agitating a return to the no-fun policy. They annoyed everybody. They weren’t persecuted for practicing their religion, they were persecuted because they kept trying to force their religion on everyone else. Sort of like Southern Baptists. 

Charles II was the most easy going monarch in British history. Do realize how annoying you have to be to get him to throw you out. 

Charles’s brother James II was obsessed with turning Great Britain catholic again. After four years of trying, they kicked him and his followers out. 

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For your fundraiser, you decide to hold a bake sale. In order to make bakery items, you had to purchase 12 pounds of sugar and 15 pounds of flour. Your total cost was $9.30. On a second trip to the grocery store, you purchased 4 pounds of sugar and 10 pounds of flour for a total cost of $4.60. Which of the following represent the system of equations for this problem.

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Answer:

C. Yes, because the population values appear to be normally distributed.

Step-by-step explanation:

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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The statement we hold these thruths to be self evident that all men are created equal that they are endowed by their creator with certain unalineable rights that among these are life liberty and the pursuit of happiness comes from which important document A.The Articles Of Confederation B.The Bill Of Rights C.The Declaration Of Independence D.The Constitution

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Answer:

According to the US Constitution federal election laws regulate the election of members of Congress.

Explanation:

The Constitution of the United States in Article 1, Section 4, grants the States the power to regulate, through what it is known as federal election laws, the congressional election process. Section 4 also establishes that both Congress and State legislatures can regulate the “times, places, and manners of holding elections for Senators and Representatives”. The federal election laws that the Constitution gives in order to regulate the election of members of the Congress cover all the aspects of the voting process, such as voter registration, prevention of fraud and methods to organize the results. The Constitution also gives the guarantees and rights for voting and for participating in a Congress election regarding citizenship, residency and age requirements.

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To avoid succumbing to negative self-talk, make sure that the expectations you hold yourself to are:

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However, they also point out that it’s OK to have an unusual kind of family structure. On One Tree Hill, for example, Lucas is being raised by a single mom, and he has a close relationship with his uncle, but his dad isn’t completely out of the picture. On a teen show such as iCarly, on Nick, Carly’s older brother plays the role of guardian, because her dad is in the Air Force. Her mom is never really spoken of. 

2. I do feel that most of the portrayal of family is accurate, on TV. Modern shows have steered away from the conventional “Mom, Dad, 2.5 kids plus dog” formula, which is accurate, because not all TV watchers are fortunate enough to have that kind of situation. See above answer for specific examples. 

3. I think that a definite negative theme in today’s modern shows, revolve around views on alcohol and drugs. Obviously everyone is entitled to their own views, but more often than not, after a character drinks, or does something they shouldn’t, they panic about what their parents will do once they find out. This panic may lead them to increasingly dangerous situations. For example, in OTH, Nathan is drinking, and then goes out to drive his girlfriend’s car. When he crashes it into another car, he realizes the trouble he is in, and leaves the scene of the accident; thus potentially getting him in even more trouble. I realize that TV is in no way an accurate depiction of all life aspects, and it is “only TV”, but I think Nathan should have faced the consequences right away, because by running from the scene, he only put himself in danger of being caught, or arrested. Again, though, I’m reading too much into it. 

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Who has the power to hold the federal bureaucracy accountable for its actions and policies?

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1- The correct answer is B, as one result of the Great Society was that the lives of many underprivileged Americans improved.

The Great Society was a set of US national reform programs announced by President Lyndon B. Johnson for the first time in a speech at Ohio University on May 7, 1964 and more fully illustrated on May 22, 1964 at the University of Michigan. These reform programs were subsequently presented to the Congress of the United States and largely approved during the 1960s, thanks to the consent of its supporters of the Democratic Party.

Two main goals of social reforms were the elimination of poverty and racial injustice. During this period new large spending programs were launched in the fields of education, medical care, urban problems and transport. Johnson’s “Great Society” was linked, in its objectives and policies, to President Franklin Delano Roosevelt’s New Deal program.

Some proposals of the Great Society resumed initiatives contained in the New Frontier program, interrupted by the tragic death of President John F. Kennedy. Johnson’s success in promoting and endorsing his reforms depended on his considerable congressional political influence, his persuasion, and the favorable historical circumstances resulting from the 1964 presidential elections, which allowed the Democratic Party to dominate Congress and to elect the House of Representatives with the largest number of exponents of the liberal current since 1938.

The evolution of the Vietnam war and the massive involvement of the American military machine in the conflict, however, partly undermined the success of the “Great Society” program. Growing, huge expenditures for the continuation of the war made more difficult to finance the reform programs. Representatives of the Democratic Party against the war in Vietnam complained that military spending decisively stifled the Great Society program. On the whole, however, despite growing political and economic difficulties, which forced the administration to eliminate or reduce the financing of some projects, President Johnson managed to activate a series of programs of great importance, including Medicare, Medicaid, the Older Americans Act and the federal education funding, which are still active.

2- The correct answer is C, as the Immigration and Nationality Act of 1965 was necessary because the previous existing American immigration policies were discriminatory.

On October 3, 1965, President Lyndon B. Johnson signed the law into effect, saying: “The [old] system violates the basic principle of American democracy, the principle according to which the valuation and reward of each man should be established on the basis of his merits as a man. It has been anti-American in the highest sense, because it has been unfaithful to the faith that led thousands to these shores, even before we were a country. ”

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Which characteristic of water allows its molecules to form hydrogen bonds? The water molecule is polar. Water has a low specific heat. Ionic bonds hold the water molecule together. Water expands as it freezes.

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Answer:

1) Water has very high specific heat.

2) It expands when it freezes

3) ability to dissolve in ionic substances

4) Water molecules at the surface experience fewer hydrogen bonds than water molecules within the liquid.

Explanation:

1) Water molecules due to their high specific heat , undergo relatively less increase in temperature after absorbing heat. So they prevent their adjoining area to experience sharp increase in temperature.

2) Water is an example which expands on freezing. In it , large spaces are left between molecules when it cools. It happens because hydrogen bonds prevent any two molecules to come very close thereby  creating gaps. This gap is filled up when ice melts , which results in overall reduction in volume of water.

3) Uneven distribution of charge results in water molecules becoming polar in nature . A polar substance  can be dissolved in polar solvents only.

4) It is due to property of surface tension. Property  of surface tension results due to molecules of water near the surface experiencing a  net downward  force due to hydrogen bonds . It is due to fewer hydrogen bonds made by them.

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What is a solution that has the capacity to hold additional solute at a given temperature called? A. Unsaturated B. Saturated C. Supersaturated D. Oversaturated E. Undersaturated

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This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

Answer: 30.6 torr

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How much data can an lto ultrium 5 tape hold, native and compressed?

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Answer:

data encryption and virus scanning utilities

Explanation:

In this scenario, Jack has determined that a virus has infiltrated his computer and corrupted several data files, but he doesn’t know what to do.

The two most helpful utilities are data encryption and virus scanning.

If Jack encrypted his data files and use virus scanning to scan the computer for viruses, the computer’s firewall will quarantine and delete the virus.

So, the correct answer is data encryption and virus scanning.

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Areas near oceans or large lakes tend to have more moderate climates than do areas far from large bodies of water. Which of these statements best explains this observation? Hydrogen and oxygen atoms share electrons in a water molecule. Lakes and oceans contain dissolved solids. Water has a very high specific heat. Water produces buoyant forces. Question 2(Multiple Choice Worth 2 points) A scientist discovers a new substance. The molecules of the substance form hydrogen bonds with each other. When the molecules lose a lot of energy, the hydrogen bonds hold them relatively far apart. Based on this information, what can the scientist infer about the substance? It expands when it freezes. It is highly colored. It exists only as a gas. It does not dissolve ionic compounds. Question 3(Multiple Choice Worth 2 points) Which of the following properties of water is due primarily to the uneven distribution of charge between the hydrogen and oxygen atoms? its color its taste its ability to dissolve ionic substances its ability to produce buoyant forces Question 4(Multiple Choice Worth 2 points) A drop of water placed on a smooth, dry surface will form a dome-shaped droplet instead of flowing outward in different directions. Which of these best explains this observation? The bonds between hydrogen and oxygen atoms are very strong. The electrons in the atoms attract the electrons in the other atoms. Water molecules at the surface experience fewer hydrogen bonds than water molecules within the liquid. Water molecules near the surface produce more buoyant force than water molecules within the liquid.

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The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies. 

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface. 

m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h. 

So the time for the pencil and eraser to touch is T=1.3449 hours. 

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

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Read this statement again: “We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness.” In a Word document, identify why this statement is more true today than it was when the framers first wrote it. Give at least 3 examples to back your explanation.

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1. We are all free and equal. We are all born free. We all have our own thoughts and ideas. We should all be treated in the same way.

2. Don’t discriminate. These rights belong to everybody, whatever our differences.

3. The right to life. We all have the right to life, and to live in freedom and safety.

4. No slavery – past, and present. Nobody has any right to make us a slave. We cannot make anyone our slave.

5. No Torture. Nobody has any right to hurt us or to torture us.

6. We all have the same right to use the law. I am a person just like you!

7. We are all protected by the law. The law is the same for everyone. It must treat us all fairly.

8. Fair treatment by fair courts. We can all ask for the law to help us when we are not treated fairly.

9. No unfair detainment. Nobody has the right to put us in prison without a good reason and keep us there or to send us away from our country.

10. The right to trial. If we are put on trial this should be in public. The people who try us should not let anyone tell them what to do.

11. Innocent until proven guilty. Nobody should be blamed for doing something until it is proven. When people say we did a bad thing we have the right to show it is not true.

12. The right to privacy. Nobody should try to harm our good name. Nobody has the right to come into our home, open our letters or bother us or our family without a good reason.

13. Freedom to move. We all have the right to go where we want in our own country and to travel as we wish.

14. The right to asylum. If we are frightened of being badly treated in our own country, we all have the right to run away to another country to be safe.

15. The right to a nationality. We all have the right to belong to a country.

16. Marriage and family. Every grown-up has the right to marry and have a family if they want to. Men and women have the same rights when they are married, and when they are separated.

17. Your own things. Everyone has the right to own things or share them. Nobody should take our things from us without a good reason.

18. Freedom of thought. We all have the right to believe in what we want to believe, to have a religion, or to change it if we want.

19. Free to say what you want. We all have the right to make up our own minds, to think what we like, to say what we think, and to share our ideas with other people.

20. Meet where you like. We all have the right to meet our friends and to work together in peace to defend our rights. Nobody can make us join a group if we don’t want to.

21. The right to democracy. We all have the right to take part in the government of our country. Every grown-up should be allowed to choose their own leaders.

22. The right to social security. We all have the right to affordable housing, medicine, education, and child care, enough money to live on and medical help if we are ill or old.

23. Workers’ rights. Every grown-up has the right to do a job, to a fair wage for their work, and to join a trade union.

24. The right to play. We all have the right to rest from work and to relax.

25. A bed and some food. We all have the right to a good life. Mothers and children, people who are old, unemployed or disabled, and all people have the right to be cared for.

26. The right to education. Education is a right. Primary school should be free. We should learn about the United Nations and how to get on with others. Our parents can choose what we learn.

27. Culture and copyright. Copyright is a special law that protects one’s own artistic creations and writings; others cannot make copies without permission. We all have the right to our own way of life and to enjoy the good things that “art,” science and learning bring.

28. A free and fair world. There must be proper order so we can all enjoy rights and freedoms in our own country and all over the world.

29. Our responsibilities. We have a duty to other people, and we should protect their rights and freedoms.

30. Nobody can take away these rights and freedoms from us.

I’m unsure of what you were asking for specifically.

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If you have several calls coming in at one time, you should A. answer each call by placing the caller on hold. B. ask someone else to help you. C. answer each call as soon as possible, saying, “Good Morning, Mr. Smith’s office, will you hold, please?” D. handle one call at a time.

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The answers to the blank provided above are SHORT RUN, and LOSSES ARE SMALLEST, respectively. So in the short run, if profits are not possible, the perfectly competitive firm will seek out the quantity of output where losses are smallest. Provided that the given firm is perfectly competitive, this means that it has already stabilized its processes even if there are instances that there is no gain acquired. BUT, this instance is only possible in the short run. In the long run, this small losses would turn into big ones as well, making the firm unstable.

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At the age of 15 months, anita repeatedly cries hoy when she wants her mother to hold her. anita is most likely in the ________ stage of language development.

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Answer:

The answer is C. In order to carefully control conditions and confirm or disconfirm a hypothesis about the causes of behavior, one must perform an experiment.

Explanation:

Experimental research allows the researcher to control all the variables in order to create the conditions that can confirm or disconfirm a hypothesis. This method aimes to establish a relation of causality between two variables, which means that one variable is generated and determined by the other; this is posible because all of the other variables that can influence it have been controlled.

When a researcher conducts a survey or engages in naturalistic observation, he can’t control the variables, therefore, he can only establish a correlation between two variables, but not of causality.

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After the yalta conference, which leader went back on the allied agreement to hold free elections in eastern europe?

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After the yalta conference, which leader went back on the allied agreement to hold free elections in eastern europe?

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Which of these facts BEST supports Congresswoman Chisholm’s thesis statement that there is a need for legislation that supports equal rights for women? A. “When women apply for a job they are asked if they can type.” B. “More than half the population is female but only two percent of them hold managerial positions.” C. “There is an unspoken assumption that women do not have executive ability.” D. “Women have not been aggressive in demanding their rights.”

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Answer:

  Set only in the South.

  Disturbed and twisted characters who are outcasts.

Explanation:

  Southern Gothic literature was a style of writing used by the American South and the stories were set in that region.

  Common themes of that type of literature were about disturbed and deeply flawed characters involved in Hoodoo, grotesque situations and events related to poverty, violence, and crime.

  Some of the most known authors of this style are Tennessee Williams, Truman Capote and Carson McCullers.

  I hope this answer helps you.

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How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members? assume that no member can hold more than one office?

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Let the boxes be Box 1, Box 2, Box 3. 

consider the 3 white balls. They can be all of them in one box:

(3, 0, 0) (3 in Box 1, 0 in box 2 and 0 in box 0)
(0, 3, 0)
(0, 0, 3)

We can have 2 in one box, and 1 in one of the remaining boxes:

(2, 0, 1)
(2, 1, 0)
(0, 2, 1)
(1, 2, 0)
(0, 1, 2)
(1, 0, 2)

and there is only one way: (1, 1, 1) to place one white ball in each box

In total there are: 3+6+1=10 ways to place the white balls. Similarly there are 10 ways to place the black ones.

Since every placement of the white balls can be combined with any placement of the black balls, there are 10*10=100 ways to place the 3white balls and the 3 black bals in the boxes.

Answer: 100

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A man weighs 78 kg and his two sons weighing 45 kg each were stranded on a river crossing. All they had to cross the river was a small boat, but it could only hold 90 kg. How did the man and his sons cross the river?

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Recall your d = rt, distance = rate * time

let’s say the boat’s rate is “b” in still water, and the current’s rate is “c”

as the boat goes upstream, is not really going “b” fast, the water is not still anyway, is going much slower, is going ” b – c “, because the current’s rate is eroding speed because is going against the current.

as the boat goes downstream, is not going “b” fast either, is going faster, is going ” b + c ” fast, because is going downstream and thus with the current and the current is adding speed to it.  notice, it takes longer going up, 5hrs, then coming down, 3hrs, same 150 on each way.

bf begin{array}{llll}
&distance&rate&time\
&-----&-----&-----\
upstream&150&b-r&5\
downstream&150&b+r&3
end{array}
\\\

begin{cases}
150=(b-r)5\
qquad frac{150}{5}=b-r\
qquad 30=b-r\
qquad 30+r=boxed{b}\
150=(b+r)3\
qquad frac{150}{3}=b+r\
qquad 50=b+r\
qquad 50=boxed{30+r}+r
end{cases}

solve for “r”

what’s the boat’s rate? well, 30+r = b

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