B. F. Skinner (the behaviorist) contends that all human behavior is controlled by rewards and/or punishments. Therefore, he claims everything we do is to earn a reward or avoid a punishment. This means humans have no "free will" or "choices." Further, Skinner contends that we are simply and always controlled by the rewards/punishments in our environment. Excluding biological processes (breathing, sleeping, etc. ) name three behaviors you have ever "chosen" that were done without reward or punishment. Justify your response for each selected behavior.

The main issue with answering this question is that one encounters a paradox when one attempts to define the nature of rewards. This is an issue that philosophers as early as Immanuel Kant addressed in the area of ethics when considering whether any act is truly altruistic or whether we should argue that "altruistic" acts such as giving away money bring the giver pleasure and thus are not purely "altruistic."
When I go to the grocery store over the holidays, there is an option of donating extra money to feed poor families. I make a habit of doing this. On one hand, I could argue that giving money to feed to poor is purely altruistic with no external reward. On the other hand, I could also argue that feeling that I have done something positive for others actually gives me more emotional satisfaction than picking up a latte on the way home from the store. There is actually evidence that people who donate to charity are happier than those who do not.
Many other behaviors that can be thought of as forms of self-actualization, such as creating art, nurturing friendships, and engaging in spiritual practices, lack external rewards and punishments but may bring emotional satisfaction. Thus, while Skinner's model of behavioral psychology works well for training mice, a broader understanding of rewards, which includes emotional satisfaction, is needed to account for human behavior.
https://nypost.com/2015/09/03/people-who-donate-to-charity-are-much-happier-and-healthier/

While behaviorists like B. F. Skinner hold that people learn to associate physical behaviors with rewards and others with punishment, they tend to minimize the effect on mental processes. Nevertheless, they do consider many mental processes to be externally conditioned behaviors. In contrast to this behavioral approach, humanistic psychology focuses on the inner lives, goals, and hopes of people. It rejects the notion held by behavioral psychologists that behavior is determined primarily by forces beyond people's control.
In this area of humanistic psychology, as it is termed, the focus is on the inner lives, goals, and hopes of people. These are self-driven urges and behaviors, rather than outside sources. For instance, artists, inventors, and scientists are often involved with their crafts or inventions and are very self-motivated even when they repeatedly fail because they are convinced that they can create what they hope to do, arrive at a solution to a problem, or discover a critical breakthrough in science. One example of an artist who was self-driven is Vincent van Gogh. Despite only selling one of his paintings, van Gogh continued to paint. He died never having known his talent was recognized so highly.
In another example, some people have been known to have anonymously donated something as crucial as a kidney to a stranger. Their action is purely altruistic and seeks no reward.
https://www.artble.com/artists/vincent_van_gogh

Skinner believed that behaviors are reinforced by rewards, including positive and negative reinforcement. However, some behaviors aren't reinforced by positive reinforcement or the removal of negative reinforcements. There are some self-sacrificing or altruistic behaviors, for example, in which the person does not expect a reward and might even experience punishment. An example is sharing your food with a hungry person who you will never see again. You don't expect a reward or recognition for that behavior, but you do it anyway. You don't experience any external rewards, and you might even suffer as a result of going hungry. Another example is providing help to a hurt animal along the side of the road. In this example, you might arrive late to your destination or even brave the elements to help the animal, which causes you to suffer. A final example is giving money to a charity (without wanting the recognition that results). You might have less money to spend on yourself as a result, which is punishing, but you do it anyway. In each case, there might be no recognition or reward; instead, you are motivated by a sense of altruism rather than a desire to be rewarded or to avoid punishment. 

In which chapter of The Wednesday Wars by Gary Schmidt does Holling's sister almost get hit by a bus?

Holling Hoodhood's sister, Heather, almost gets hit by a bus in the chapter titled "January."  
January doesn't start off so great for either Holling or Heather.  Doug Swieteck's brother gets his hands on every single copy of the newspaper that he can because it has a full color picture of Holling "flying" through the air as Ariel. Obviously, Holling is mortified, but Heather is also upset: the image reflects poorly on her social image.  

"And now I'm the one who has a baby brother who wears yellow tights . . . Fix this or you die," she said. 

It appears that she hates Holling a lot, but she comes into his room a bit later and passionately explains why she cannot stand the thought of Holling going off to military school.  It is a quick moment in the chapter, but it shows readers that both Holling and Heather do indeed care for each other despite their public antagonism toward each other. 
January continues to roll on, and the weather gets worse and worse.  Unfortunately, the school does not allow the students a snow day, and the roads get progressively more and more icy and dangerous.  But for Doug Swieteck's brother, the weather is time for fun.  He enjoys grabbing on to the bumper of a bus and sliding around behind the bus on the icy roads.  Holling does not think his next move through. He compacts a snowball and throws it right at Swieteck's brother and hits him in the face.  Swieteck's brother eventually learns that it was Holling and tells Holling that he's "dead."
After school that day, Holling is hoping to avoid Swieteck's brother and his friends.  He does not have luck with that. The boys are waiting for Holling with balls of yellow snow. As Holling is taking in that information, he sees the school bus slipping and sliding on the ice.  The next thing that Holling notices is that the out of control school bus is heading straight for his sister.  She doesn't see the bus because her head is down and buried deep in layers of warm clothing. 

Because walking across Lee Avenue, in the middle of the road, her head down and her scarf pulled over her ears because she didn't want the wet snow to dampen her southern California hair, was my sister.  

Holling takes off like a shot toward his sister, and he shoves her out of the way of the bus just before she would have been hit.  Unfortunately, Holling is not able to get out of the way.  The right rear bumper of the bus hits Holling in the backside and propels him through the air across the rest of the street. Heather is humbled, thankful, scared, and relieved all at the same time.  Mrs. Baker then takes Holling to the hospital along with Heather and the school principal.  Once there, Holling is checked out by doctors and even has to have his backside x-rayed.  Holling is bruised, but overall he is okay.   

In the chapter entitled "January," Holling is walking home, about to be attacked by Doug Swieteck's brother and other boys holding snowballs, when he sees the school bus gliding into the intersection and going through a red light. He sees his sister in the middle of the intersection; she is walking with a scarf over her "southern California hair" to keep it dry. Holling races to push his sister out of the way of the bus into a snowbank, and he is hit by the bus's rear bumper in the buttocks. Mrs. Baker drives him to the hospital to get an X-ray, and his sister thanks him for saving her life. He is sore, but he is left without a serious injury and is featured in the town paper as a hero. 

According to Jefferson, what should people do if the government does not serve the people?

As a follower of Enlightenment philosophies put forth by such thinkers as John Locke and Voltaire, Thomas Jefferson had a strong belief that the proper role of government was to protect the natural rights of its citizens. In the Declaration of Independence, Jefferson states quite clearly what people should do if a government fails to do this: they should abolish or sever ties with that government and institute a new one.
Jefferson is quick to point out that people should not rebel against their government for trivial reasons. He knew the dangers that come from rebellion and that it is better to try to reform a government than to rebel against it. However, if that fails, then the people have no choice but to institute a new government that operates under the consent of the governed with the goal of protecting their rights.
Jefferson was not alone in this thinking. During the seventeenth and eighteenth centuries, there was a growing school of thought concerning the role of government. Previously, many rulers claimed that their right to rule was granted by God. This theory is often referred to as the Divine Right of Kings. However, as the Enlightenment era took shape, moral and political philosophers began to rethink this notion. They often came to the conclusion that ruler's power should be granted by the people themselves through a so-called "social contract." In order to win over the consent of the governed, a government must protect people's rights to "life, liberty, and the pursuit of happiness." Any government that refuses to do so should be abolished.

Jefferson wrote in the Declaration of Independence that people are born with "inalienable rights," which refers to the Enlightenment idea of natural rights—rights that the government cannot take away. Jefferson defined these rights as "life, liberty, and the pursuit of happiness," similar to Locke's idea that people have a right to life, liberty, and property. Though people give up some of their freedoms to be ruled by a government, the government must protect these rights in return. Jefferson also wrote the following:

"That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness."

In other words, when a government does not protect the inalienable rights that are due to its constituents, the people have the right to change or get rid of it and to start a new government that will bring about their safety and happiness. Though Jefferson thought that people should not abolish or change their government without serious consideration, he felt that a despotic government with a long history of abuses, namely, the government of Great Britain ruling over the colonies, should be overthrown. 

In the Declaration of Independence, Thomas Jefferson wrote that all people have certain unalienable rights that can’t be taken away. These rights include the rights of life, liberty, and the pursuit of happiness. One of the main jobs of the government is to protect the rights of the citizens.
Thomas Jefferson stated that when the government fails to protect the rights of the people, the people have no option but to replace that government with one that will protect their rights. In the Declaration of Independence, there is a long list of grievances that the colonists had against the King of England. This list included examples of how the King of England abused the rights of the colonists. For example, the British taxed the colonists without allowing the colonists to have representatives in Parliament that could vote for the proposed taxes. As a result, Thomas Jefferson wrote in the Declaration of Independence that the colonists had to rebel against the British government in order to establish a new government that would protect the rights of the people.
https://www.archives.gov/founding-docs

What are some characteristics of Daniel and Rosh?

Daniel is a passionate, strong eighteen-year-old boy who joins Rosh's band after he flees his master, Amalek. Daniel is full of hate and bitterness directed towards the Romans after the death of his parents and vows to fight them for the rest of his life. Joel and Thacia's friendship gives Daniel hope, and he begins hearing Jesus preach. Daniel's attitude gradually begins to change, and he becomes more sympathetic to his sister's needs. Although Daniel is still an intense individual, he displays his kind, caring nature towards his close friends and family. Daniel is essentially a pure soul who has suffered traumatic experiences throughout his life. At the end of the novel, Daniel finally lets go of his hate and bitterness after Jesus heals his sister.
Rosh is an equally intense character but does not display a caring nature like Daniel. Rosh is selfish and violent throughout the novel. He is a ruthless individual, and his only concern is benefiting from others. Although he is a cunning and respected leader, Daniel realizes that Rosh's plans are self-serving and refuses to be a member of his band anymore.

Single Variable Calculus, Chapter 5, 5.5, Section 5.5, Problem 76

Find the integral $\displaystyle \int \frac{\sin x}{1 + \cos ^2 x} dx$

If we let $u = \cos x $, then $\displaystyle du = - \sin x dx$, so $\sin x dx = -du$. Thus,



$
\begin{equation}
\begin{aligned}

\int \frac{\sin x}{1 + \cos^2 x} dx =& \int \frac{1}{1 + \cos^2 x} \sin x dx
\\
\\
\int \frac{\sin x}{1 + \cos^2 x} dx =& \int \frac{1}{1 + u^2} \cdot -du
\\
\\
\int \frac{\sin x}{1 + \cos^2 x} dx =& - \int \frac{1}{1 + u^2} du
\\
\\
\int \frac{\sin x}{1 + \cos^2 x} dx =& - \tan^{-1} u + C
\\
\\
\int \frac{\sin x}{1 + \cos^2 x} dx =& - \tan^{-1} (\cos x) + C

\end{aligned}
\end{equation}
$

Describe Candy in chapter 2 in Of Mice and Men.

Candy is a kind old swamper who has lost a hand and identifies very strongly with his blind old dog. He is deeply saddened after it is shot as a smelly nuisance, though he agrees to have it killed. He sees in the dog's end his own ignoble demise when he can no longer work.
Candy, fearing he will be left poor and alone to die, is very much taken with the idea of going in on the farm George and Lennie dream of buying. For him, it would be a dream come true because it would provide him a stable and secure place to stay when grows old. It offers him the hope of independence and dignity.
Candy does menial tasks on the ranch, taking on whatever he can to make himself useful. He comes across as an unpretentious person who only asks for a fair deal in life—one it seems he is unlikely to get.

Candy is the first one to greet George and Lennie when they arrive on the farm in John Steinbeck's novel Of Mice and Men. Candy is described as an "old swamper," which is a term for a ranch worker who does odd jobs. Readers first see him sweeping the bunkhouse. Later in chapter two, he is cleaning the washroom.
Candy is very old. He's lived his whole life as a ranch worker and doesn't have much of anything to show for it. He is straightforward and honest in his dealings with George and Lennie. George is suspicious when he sees a can of bug or rat killer on the beds that Candy points to them. He thinks Candy is giving them the worst bedd, possibly lice-infested ones. Candy could have used the opportunity to torment them or be mean, but he doesn't. Candy explains that the guy who left the can was fastidiously clean. When George inspects the bed, he finds what Candy says to be true. Candy also seems to be respectful and concerned with making sure George and Lennie know that he wasn't eavesdropping on their conversation after they meet Curley.
Candy is very thin and missing a hand. He lost the hand in a farm accident, and it is a significant handicap to be a ranch worker without a hand. Candy also has a dog, a very old do, who probably should be put down, but Candy can't bring himself to do it. This shows his tender heart. Here is the description of Candy's dog:

The old man came slowly into the room. He had his broom in his hand. And at his heels there walked a dragfooted sheepdog, gray of muzzle, and with pale, blind old eyes. The dog struggled lamely to the side of the room and lay down, grunting softly to himself and licking his grizzled, moth-eaten coat. The swamper watched him until he was settled. "I wasn't listenin'. I was jus' standin' in the shade a minute scratchin' my dog. I jus' now finished swampin' out the wash house."

In chapter 2, Candy is an old swamper missing a hand, which he lost during a farm accident. He is a relatively kind old man and immediately befriends George and Lennie when he initially meets them. Candy is by far the oldest worker on the ranch and has lost his money working for other people his entire life. Candy also has an old, useless dog, which stinks up the bunkhouse. Carlson encourages Candy to shoot his dog and put it out of its misery, but Candy refuses to do so. Unfortunately, Slim gives Carlson permission to kill the dog, and he takes the dog outside to kill it. Candy, who has been the dog's owner its entire life, is upset and regrets letting a stranger kill his beloved dog. Candy is similar to his dog because he is also old and relatively useless. Candy's age and handicap make him a liability on the farm, and it is only a matter of time before he is fired. Candy sympathizes with his dog and realizes that he will be the next to go. 

y = x^4/4 , y=0 , x=4 Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

To be able to use the shell method, we consider a rectangular strip from the bounded plane region which should be parallel to the axis of revolution.
By revolving multiple rectangular strip, it forms infinite numbers of hollow pipes or representative cylinder.
 In this method, we follow the formula: V=int_a^b  (length * height * thickness)
or V = int_a^b 2pi * radius*height*thickness
For the bounded region, as shown on the attached image, the rectangular strip is parallel to y-axis (axis of rotation). We can a let:
r = x
h =f(x) or h=y_(above) - y_(below)
h =x^4/4-0
h=x^4/4
For the boundary values, we have x_1=0 to x_2=4 .
Plug-in the values on V = int_a^b 2pi * radius*height*thickness, , we get:
V = int_0^4 2pi* x*x^4/4*dx
V = int_0^4 (2pix^5)/4*dx
V = int_0^4 (pix^4)/2*dx
 
Apply basic integration property: intc*f(x) dx = c int f(x) dx .
V = pi/2 int_0^4 x^5*dx
Apply power rule for integration: int x^n dy= x^(n+1)/(n+1) .
V = pi/2* x^(5+1)/(5+1)|_0^4
V = pi/2 *x^6/6|_0^4
V =(pix^6)/12|_0^4
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V =(pi(4)^6)/12-(pi(0)^6)/12
V = (1024pi)/3 -0
V = (1024pi)/3 or 1072.33 (approximated value)