In the movie Fight Club by David Fincher, the protagonist has Dissociative Identity Disorder. Can anyone out there give examples of how this movie accurately portrays the illness and also give some examples of how this movie makes a mockery of mental illness, only adding to the already negative stigma attached to mental illness?

Dissociative Identity Disorder (DID) used to be referred to as Multiple Personality Disorder (MPD), but was renamed when psychologists realized that DID was more accurately causing a fragment or fracture in an individual's sense of self, rather than growing secondary or new personalities (as MPD implies).
Much of the way Tyler Durden's DID is portrayed in Fight Club is largely accurate, according to the National Institute of Mental Health.
He experiences two distinct and separate identities.

The disruption in identity involves a change in sense of self, sense of agency, and changes in behavior, consciousness, memory, perception, cognition, and motor functions. ("I look like you want to look, I fuck like you want to fuck, I am smart, capable, and most importantly, I am free in all the ways that you are not.")

Frequent gaps are found in memories of personal history, including people, places, and events, for both the distant and recent past. (Edward Norton's character has either absent or inaccurate memories of Fight Club and Operation Mayhem.)

These symptoms cause clinically significant distress or impairment in social, occupational, or other important areas of functioning (this is well played out in the final confrontation between the two). 
One key difference is that Edward Norton's character did not seem to experience any significant childhood trauma, which is noted as one of the leading causes of DID. The implication here is that the culture of consumerism enacts that trauma on all American men. However, this is where the narrative philosophy of the film (and book) does start to stray from psychology. It also somewhat makes the condition seem "cool" by giving Edward Norton's character a sexy anarchist gangster as his alter-ego, possibly downplaying the remarkably difficult struggle it is to live with DID. 

Hydrogen sulfide is composed of two elements, hydrogen and sulfur. In an experiment, 5.485 g of hydrogen sulfide is fully decomposed into its elements. How many grams of sulfur must be obtained if 0.307 grams of hydrogen are obtained?

To solve, apply conservation of mass. It states that in a chemical reaction, mass is neither destroyed nor created. So the mass of the reactants at the beginning is equal to the mass of the products at the end of the reaction.
mass of  reactants = mass of products
In this problem, the chemical reaction is:
Hydrogen sulfide -> Hydrogen  + Sulfur
Applying conservation of mass, the equation is:
mass of hydrogen sulfide = mass of hydrogen + mass of sulfur
5.485g = 0.307g + mass of sulfur
mass of sulfur = 5.485g - 0.307g
mass of sulfur = 5.178g
 
Therefore, at the end of the reaction, 5.178 grams of sulfur is obtained.

College Algebra, Chapter 1, 1.6, Section 1.6, Problem 68

Solve the nonlinear inequality $\displaystyle \frac{x}{2} \geq \frac{5}{x+1} +4 $. Express the solution using interval notation and graph the solution set.

$
\begin{equation}
\begin{aligned}
\frac{x}{2} & \geq \frac{5}{x+1} +4\\
\\
0 & \geq \frac{5}{x+1} + 4 - \frac{x}{2} && \text{Subtract } \frac{x}{2}\\
\\
0 & \geq \frac{5(2) + 4(2)(x+1)-x(x+1)}{2(x+1)} && \text{Multiply the LCD } 2(x+1)\\
\\
0 & \geq \frac{10+8x+8-x^2-x}{2(x+1)} && \text{Simplify the numerator}\\
\\
0 & \geq \frac{-x^2 + 7x + 18}{2(x+1)} && \text{Factor out } -1\\
\\
0 & \geq \frac{-(x^2 - 7x - 18)}{2(x+1)} && \text{Divide } -1\\
\\
0 & \leq \frac{x^2 - 7x - 18}{2(x+1)} && \text{Factor out}\\
\\
0 & \leq \frac{(x-9)(x+2)}{2(x+1)} && \text{Multiply both sides by } 2\\
\\
0 & \leq \frac{(x-9)(x+2)}{(x+1)}
\end{aligned}
\end{equation}
$


The factors on the left hand side are $x-9$, $x+2$ and $x+1$. These factors are zero when $x$ is 9,-2 and -1 respectively. These numbers divide the real line into intervals
$(-\infty, -2], [-2,-1),(-1,9],[9,\infty)$




From the diagram, the solution of the inequality $\displaystyle 0 \leq \frac{(x-9)(x+2)}{(x+1)}$ are
$[-2,-1) \bigcup [9,\infty)$

When seeing Scout and Jem in town, a man on the street mumbles, “They c’n go loose and rape up the countryside for all of ’em who run this county care” (180). What does he mean? Why does this man say such a thing at the sight of Scout and Jem? Who is this man accusing of being rapists?

At the beginning of chapter 14, Scout mentions that every time she and Jem went into town, they would hear various farmers and countrywomen in straw hats commenting on them being Atticus's children as they walked to the store. Scout recalls hearing one skinny gentleman say,

They c’n go loose and rape up the countryside for all of ‘em who run this county care (Lee, 136).

The man is alluding to the Tom Robinson case, in which a black man is accused of raping a white woman. In the prejudiced town of Maycomb, the majority of the citizens automatically assume that Tom raped Mayella, because he is black. During the trial, Atticus refers to this prejudiced way of thinking as the "evil assumption."
The skinny man is essentially saying that the authority figures in Maycomb county, like Judge Taylor, Sheriff Tate, and Atticus Finch, could care less if any black person is traveling throughout the countryside raping innocent white women. The racist man does not agree with Judge Taylor's decision to allow Atticus to represent Tom Robinson and feels like the authority figures in Maycomb are favoring the black community. The rude man is clearly upset that Atticus plans on defending Tom Robinson and feels the need to express his outrage in front of Jem and Scout. He may also be attempting to intimidate Jem and Scout or indirectly influence them into thinking that their father is wrong for defending Tom Robinson. Overall, the racist man is commenting on his beliefs that the authority figures in Maycomb are supporting and enabling black men to rape white women.

What is a federalist?

In the context of American history, a Federalist was someone who believed in a stronger Federal government and that political power should become more centralized. To this end, Federalists tended to be staunch supporters of the Constitution.
After the Revolutionary War the United States needed to take its place among the community of nations. However, under the loose governmental structure of the Articles of Confederation, it was unable to do so. Ultimate authority resided with each state, so it was impossible for the United States to pay off debts incurred during the war, to settle territorial disputes with foreign countries, or even to maintain good order against the threat of domestic sedition. The United States needed to speak with one voice in so many important areas of policy, but couldn't.
It was these conditions that gave rise to changes in American government as set out in the Constitution. These changes were generally welcomed by the Federalists. Opposing them were the Anti-Federalists. They thought that the Federalists wanted to invest central government with too much power. To them, this smacked of tyranny; and as Americans had just fought a war against what they perceived as British tyranny, the last thing the Anti-Federalists wanted to see was its return to American soil under a different guise.
Anti-Federalists strongly believed in "The Spirit of '76," the ideal of republican liberty set out by Thomas Jefferson in the Declaration of Independence. According to this principle, ultimate political authority must reside with the individual states, and not with a remote, potentially despotic federal government. It was to assuage the concerns of the Anti-Federalists that the framers of the Constitution added the Bill of Rights as amendments to the original charter, ensuring that the final document was a compromise incorporating both Federalist and Anti-Federalist elements.
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What would happen if we eliminated the use of fire and the wheel from everyday activity?

With as far as technology has advanced, I would argue that it is possible to survive and have a good quality of life without fire or the wheel, but it's really not practical or sustainable. 
Some people manage to live their lives with no fire at all. Food may be cooked on an electric stove-top, water may be heated by electricity, and there are a number of energy sources which do not requite combustion. At least when we consider fire that occurs on Earth, it is possible to live without it. If certain fires-- like the Sun-- were to cease to exist, we would certainly die. With all of that being said, the number of people on this planet who could live without fire is significantly smaller than those who rely on fire on a daily basis. Much of the world uses fire on a daily basis to cook food, heat and sterilize water, and provide warmth in the home. If fire were to cease to exist, these people might not have a secondary course of action and would certainly suffer.
I think that the wheel would be much harder to remove from our lives while maintaining the quality we're accustomed to. Wheels aren't only vital to transportation, they are a simple machine incorporated in most modern conveniences. Wheels are a part of industrialized life, so unless people are willing to adopt a mechanically simpler and far more labor intensive lifestyle, I don't think that we could get by as easily without the wheel. 
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Why does Golding decide to introduce the parachutist in chapter 6?

The entrance of the parachutist in chapter six is notable for both its timing and its symbolism. In chapter five, Ralph begins to understand his limits as a leader. He has the ability to get the other boys to listen to him, but he relies on Piggy's intelligence to make good choices and set policies on the island. Jack becomes more of an impediment, because he does not understand the fear that some of the boys have. His lack of regard for the dangers of psychological harm is becoming a threat because of the sadistic behavior he, Roger, and Maurice exhibit. Chapter five ends with Piggy worrying aloud that Jack will turn to physical violence against himself and the others.
Chapter six opens with imagery of a faraway dogfight, which provides the circumstances that make the appearance of the dead parachutist plausible. It also reinforces the mood of foreboding already established in chapter five. It is another reminder of the essential conflict of man versus man, playing out in both the adult world of military might between warring nations and the escalating tensions among the boys on the island. When the parachutist is observed by the boys, their perception is that the corpse is alive, as it moves up and down, entangled in the parachute cords and foliage. They don't understand what they are seeing, and fear overtakes rationality. This "beast from the air" rattles the boys so much that the conch is dispensed with, and the tenuous democracy of the island becomes doomed.

In chapter 5, Ralph holds an assembly to discuss why the boys are neglecting their responsibilities and address their fear of the beast. Essentially, the boys' attempt at creating a civil society is failing, and they are gradually descending into savagery. Towards the end of the meeting, Jack openly defies Ralph and leaves the assembly unexcused. After the hunters follow Jack, Ralph and Piggy lament about their terrible situation and ask for a sign from the adult world.
At the beginning of chapter 6, a paratrooper is shot out of the sky and lands on the top of the mountain. The dead paratrooper's arrival is both ironic and significant. The dead paratrooper's ominous arrival symbolizes the presence of evil on the island and indicates that the boys' situation will only get worse. Golding strategically chose to introduce the dead paratrooper in chapter 6 because it is a turning point in the novel when the boys' circumstances become dramatically worse. Once the paratrooper lands on the island, the boys becoming increasingly savage and end up brutally murdering Simon three chapters later.