What breakthroughs has Jerry achieved by the story's end?

On a basic level, Jerry has accomplished the physical feat he set out to complete. He has conditioned himself to be able to hold his breath for several minutes and overcome his fears to swim through the tunnel in the rock: an unbelievably dangerous and difficult thing.

Further, Jerry no longer craves the acceptance of the older, local boys with whom he so much wanted to fit when he first went to the wild bay. This is pretty significant. He attempted such a dangerous feat because they were doing it, and he felt childish and rejected when he could not do it before. However, he no longer links this experience to their recognition of him as an equal. This lack of concern for what they think is an achievement, as it shows the maturation that has resulted from Jerry's dangerous experience. He has also developed the ability to delay gratification, something he couldn't do at the beginning (consider his behavior when he wanted goggles). But now, he's developed "A curious, most unchildlike persistence, a controlled patience," and this is definitely the sign of a mature person.

Who sits with George all night after the accident?

Michaelis, a young Greek who runs the "coffee joint" next to the ashheaps and in the same building as Wilson's Garage, stays with George Wilson the night that Myrtle Wilson is killed. Michaelis is also one of the first to reach Myrtle after she is hit by Daisy Buchanan, who was driving Gatsby's car. Michaelis is subsequently questioned by police. He tries to keep George occupied by asking him questions about his marriage and whether he had any kids. He also tells George it would be good if he had a church "for times like this." He tries to convince George that Myrtle's death was just an accident but George suspects that Myrtle had been cheating on him. George shows Michaelis an expensive dog collar which he found in a drawer (presumably for the dog Tom bought for her in New York). George thinks the collar is evidence that she was seeing another man. 

How would you explain the Incan social system?

The Incan social system was based around various classes. There was a nobility class at the top. The ruler was at the very top of this class. The commander of the military and the high priest were among those in the nobility class. It also included the ruler's family. People in this highest class were exempt from paying taxes.

Next in the social class system were government officials. Those in this class included tax collectors and individuals who kept records. Skilled laborers were also in this middle class in Incan society. Engineers and architects, who were essential to the building of cities, were considered skilled laborers.

Below government officials and skilled laborers were the common people. These were the laborers and artisans.

The farmers and slaves were at the very bottom of the social class system. Those in this class paid most of the taxes.

What might Roger's behavior suggest about his future potential in Langston Hughes's short story "Thank You, M'am"?

In Langston Hughes's short story "Thank you, M'am," Roger is so stunned by Mrs. Jones's actions that he can barely speak, which signifies just how much she has positively influenced him.

The first moment in which he is too shocked to speak is when she shows compassion by confiding in him that when she was young, she was equally in need and "wanted things [she] could not get." He is further unable to speak when, contrary to what he expects her to say, she doesn't say she didn't rob people to get what she wanted but rather confides that she too did things she was ashamed of.

At that point, he feels a need to be trusted by her and sits in a corner of the room where she can see him, far away from her purse. Yet, he is still unable to speak much. Instead, during their shared dinner, she is the one who does the conversing by telling him all about where she works.

His greatest moment of stunned near-silence is when she hands him the 10 dollars and tells him to buy the blue suede shoes he wants, warning him to "behave" himself in the future. He is so stunned that he can barely say, "Thank you, m'am," as she closes the door to her rented room.

We know from his stunned near-silence and his desire to be trusted that Mrs. Jones's actions significantly influenced him; her actions moved him so much that he is barely able to speak, just as one might be moved to silence in the presence of God. For the first time in his life, he was shown empathy, compassion, and care, which will help him in the future to think twice about the people he meets. While before he distrusted everyone because of his situation, he now sees that there truly are some goodhearted people in the world. Seeing that there are goodhearted people in the world will help him to become goodhearted himself. Due to her compassionate influence, in the future, he is likely to do just as she wants him to do, "behave" himself and emulate her compassionate actions.

What units are used to describe the solubility of a substance in a given solution?

The solubility of a substance in a given solvent refers to the amount of solute (or substance) that can be added to a unit quantity of the solvent. Thus, solubility can be described in terms of amount of solute per unit amount of solvent. In other words,

solubility = amount of solute / amount of solvent

We commonly use g/l (gram per liter) and mg/l (milligram per liter) as units of solubility of a substance in a solvent. For example, the solubility of sodium chloride (NaCl) in water at room temperature (25 degrees Celsius) is 0.36 g/ml. 

The solubility of a solute in a solvent is a function of the temperature. As the temperature increases, the solubility of solutes in a given solvent increases. We can also increase the rate of dissolution by stirring the solution.

Hope this helps. 

Describe the setting of the opening scene in The Scarlet Letter, the people surrounding the prison, and any other notable imagery. Given the...

In the first scene of Nathaniel Hawthorne's The Scarlet Letter, the reader is shown a prison surrounded by the people of the community. Hawthorne's heavy use of imagery paints a clear picture and molds the reader into a specific mood. 

The prison itself is described as heavy, made of wood and metal, and dark. The people around the prison mirror its presentation, darkly attired in gray and pointed "steeple-crowned hats". The correlation between the prison, the people, and the dark, heavy images produces a foreboding tone that immediately sets the reader against this setting. 

In contrast to all of this is the rose-bush, meticulously detailed by Hawthorne as light and beautiful. Hawthorne goes out of his way to paint the contrast here, bluntly telling the reader the figurative meaning of this wild and delicate juxtaposition, which symbolizes a "sweet moral blossom". 

How is the society in the book responsible for the current rules on time?

The society in “’Repent, Harlequin!’ said the Ticktockman” is a society in which the members of that society have sacrificed personal liberty for order and timeliness. The story is representative of the constant tension between being able to do as one wishes and adhering to the rules of society for the collective benefit of all the members of society.

Humans are group animals. We depend on group structure for survival. The rules of any given group of humans exist to redirect our individualist tendencies (i.e. survival goals) toward group benefit. The story “’Repent, Harlequin!’ said the Ticktockman” shows us a world in which a society has taken this to the extreme.

Given the structured nature of the society, any disruption to the schedule on an individual level has a ripple effect on the society as a whole. All activities by members of the Ticktockman’s society are intended to be for the benefit of the collective; therefore, any activities that interfere with the orderliness of the society directly impact the survival of the offending individual via the loss of time from the individual’s life. The rules against disrupting others and not wasting time are thus an aspect of this nearly total subversion of the individual’s survival for the benefit of the collective.