What did the banker and the young lawyer argue about in Chekhov's The Bet?

In "The Bet," the lawyer and the banker argue over the issue of solitary confinement versus the death penalty. Specifically, the banker believes that the death penalty is a more "humane" way of dealing with a criminal. In contrast, the lawyer argues in favor of solitary confinement, saying that it is better to "live anyhow" than to not live at all.
In response, the banker continues to disagree with this opinion. He believes that nobody could endure the conditions of solitary confinement.
As this heated discussion continues, the banker proposes the following bet to the lawyer:

 I'll bet you two million you wouldn't stay in solitary confinement for five years.

The lawyer is so confident in his belief that he ups the stakes. He says that if the banker is offering a serious bet, he will stay in solitary confinement for 15 years, three times that proposed by the banker. 
Their discussion about the death penalty versus solitary confinement has quickly turned into a high-stakes betting situation, therefore setting the scene for the rest of the story's action.

The banker and the young lawyer are arguing over whether the death penalty or imprisonment is the more humane method of punishment. The young lawyer argues that both forms of punishment are equally immoral, but if he had to chose between them, then he'd plump for imprisonment. The banker, probably thinking of the terrifying prospect of being deprived of his opulent lifestyle, opts for the death penalty. The fractious debate ends with a wager, the bet of the title. The banker bets the lawyer a whopping two million rubles that he couldn't manage to stay in solitary confinement for five years. The lawyer accepts the wager, but goes one better, vowing that he will stay in solitary confinement not for five, but fifteen years. The bet is on.

How does Dickens explore the theme of poverty through the Crotchet family in A Christmas Carol?

Charles Dickens was one of the most important social commentators of his time. Having a father who was placed in debtors' prison when he was quite young, Dickens had to work in a shoe-blacking house as a boy, and he experienced much deprivation that he never forgot. As a result, Dickens used his literary works to expose social ills and invalidate the idea that the poor were worthless and merely "surplus population."
The portrayal of the Cratchit family in A Christmas Carol demonstrates the love and charity that exists among the family members, as well as their true Christianity. When the Ghost of Christmas Present takes Scrooge to the four-room house of Bob Crachit's, Scrooge is amazed that the spirit would bless such a house. That the family is so excited and cheerful over their meager Christmas dinner also surprises Scrooge, as well as the loving atmosphere of the home. When Scrooge's employee, Bob Cratchit, enters the house, the children run into his arms, and two of the children carry Tiny Tim to the washhouse so that he can listen to the pudding "singing in the copper [pan]." In the meantime, Bob tells his wife that little Tim told him that he hoped the people in church would see him so that they would remember on Christmas Day "who made lame beggars walk and blind men see." 
Tiny Tim sits close to his father, who holds his "withered hand" with paternal care and love as though he wishes to hold him to his side from fear that the boy may be taken from him. Seeing this, Scrooge asks the Ghost if Tiny Tim will live. The Ghost replies, "If these shadows remain unaltered by the Future, the child will die." When Scrooge protests, the Ghost responds with Scrooge's earlier words, saying if the child is going to die, he should do it quickly and "decrease the surplus population." Shamed by his cruel words, Scrooge hangs his head and is "overcome with penitence and grief." Later, as he and the Ghost depart, Scrooge realizes how happy the family is despite their poverty because they are rich in love.

A hydrocarbon contains 14.2% hydrogen by mass. This compound has a relative molecular mass of 56g/mol. Calculate the empirical formula and the molecular formula.

The empirical formula of a compound gives the simplest whole number ratio of atoms and the molecular formula gives the actual number of atoms of each element in a molecule. The molecular formula is a whole-number multiple of the empirical formula.
To find the empirical formula one must calculate the number of moles of each element in the compound. We are told that this is a hydrocarbon, meaning it contains hydrogen and carbon, and that it is 14.2% hydrogen by mass. Therefore if we have 100 grams of this compound 14.2 grams will be hydrogen and the remaining 85.8 grams will be carbon.
Using the molar masses of hydrogen and carbon, convert both to moles:
14.2 g H x (1 mol/1.00g) = 14.2 moles H
85.8 g C x (1 mol/12.0 g) = 7.1 moles C
Now divide each number of moles by the smallest (7.1) to get a whole-number mole ratio:
(14.2 moles H)/(7.1) = 2
(7.1 moles C)/(7.1) = 1
The mole ratio of C to H is 2:1, so the empirical formula is CH_2.
To find the molecular formula, compare the given molar mass of the compound to the molar mass of the empirical formula:
Molar mass of compound = 56 g/mol
Molar mass of CH_2 = (12.0) + 2(1.00) = 14.0 g/mol
56/14.0 = 4, so the molecular formula is 4 times the empirical formula:
4(CH_2) = C_4H_8
https://www.thoughtco.com/calculate-empirical-and-molecular-formula-609503

The energy of a particle in the n = 3 excited state of a harmonic oscillator. Potential is 5.45 eV. What is the classical angular frequency of oscillation of this particle?

To solve, use the formula of energy level of harmonic oscillator.
E_n = (n + 1/2)hf
where 
E_n is the energy level of harmonic oscillator in Joules
n is the quantum level
h is the Planck's constant (6.623 xx 10^(-34) Js)
and f is the frequency of oscillator.
To be able to apply this formula, convert the given energy to Joules. Take note that 1eV = 1.602xx10^(-19)J .
E_n=5.45 eV * (1.602xx10^(-19)J)/(1eV)
E_n = 8.7309xx10^(-19) J
Plug-in this value of En to the formula of energy level of harmonic oscillator.
E_n = (n+1/2)hf
8.8309 xx10^(-19) J= (3+1/2)(6.623 xx 10^(-34) Js)f
8.7309 xx10^(-19) J=(2.31805 xx10^(-33) Js) f
Then, isolate the f.
f = (8.7309 xx 10^(-19)J)/(2.31805xx10^(-33)Js)
f=3.76648476xx10^14/ sec
f=3.76648476 xx 10^14Hz
So the frequency of the oscillator is 3.76648476xx10^14Hz .
To determine the angular frequency, apply the formula:
omega = 2pif
omega =2pi * (3.76648476xx10^14 Hz)
omega=2.366552170 xx10^15 rad/s
Rounding off to two decimal places, it becomes:
omega =2.37 xx10^15 rad/s
 
Therefore, the angular frequency of harmonic oscillator is 2.37xx10^15 radian per second.

Whats are Jack Merridew’s convictions and beliefs in Lord of the Flies?

At his core, Jack believes that he should be leader. That's partly because he's always been a leader. He tells all of the other boys that he should be chief because he's "chapter chorister and head boy." Being a leader and wanting to be a leader isn't a bad trait; however, Jack firmly believes that the best way to lead is through fear. Jack is a violent kid, and he uses that violence against pigs in hunts and other boys on the island. He is convinced that his way is always the right way, and anybody that disagrees with him deserves to either be cast out or die. Jack's convictions and beliefs are firmly rooted in the concept of "might makes right," and he doesn't care about any potential consequences or repercussions of his actions. He simply cares about being right, being followed, and keeping power.

Jack Merridew's convictions and beliefs concern the ability to act upon one's instincts without consequences or repercussions. Throughout the novel, Jack continually neglects the rules and rejects Ralph's authority in favor of participating in activities that please him. Jack is also unashamed to act like a savage and rules over his hunters as a tyrant. He thoroughly enjoys hunting, swimming, and being in control, which is exactly what he does throughout the novel. Jack believes in living an unrestrained lifestyle and taking advantage of opportunities without worrying how his decisions and actions may affect other people. Jack also believes that the strongest, most aggressive person should be in control. He views Ralph as being weak and timid, which is one reason he decides to establish his own tribe of savages. Overall, Jack has strong convictions concerning his personal freedom and independence. He also believes that the strongest, most physically intimidating person should lead the group.

Which stylistic devices are used in The Crucible?

Arthur Miller, the author of the play, writes a sort of narrator for this work -- someone who interjects frequently in Act I -- to introduce characters, give the audience background information, etc.  We can call it authorial intrusion; the dialogue stops and this narrator steps in to tell us something it would be helpful to know, something the character is unlikely to reveal to us themselves: for example, John Proctor thinks he's "a fraud," Abigail Williams has an "endless capacity for dissembling," etc. 
Miller also makes heavy use of irony.  Dramatic irony is created when the audience knows more than a particular character, and it heightens tension and helps to build suspense.  For example, when Proctor, Francis Nurse, and Giles Corey come to the court in Act III to present their evidence against the girls and in favor of their wives (namely, the testimony of Mary Warren), Deputy Governor Danforth refuses to believe them; he says that the state believes "that the voice of Heaven is speaking through the children."  However, we know that Proctor is right: the girls are lying, but Dadnforth doesn't know this.  This is dramatic irony. 
It is also terribly ironic that Danforth refuses to believe Mary Warren, the only girl who is telling the truth, especially when he makes statements like, "We burn a hot fire here; it melts down all concealment."  On the contrary, the entire proceedings are founded on the deception of the girls!  This is an example of situational irony: the people who tell the truth are thought to be liars, and the liars are seen as truthful by the court.  We would expect the reverse -- that the truth will out, as they say -- especially in a court, but it is not so.

What are the boys and girls of noble family taught?

In Lilliput, children are educated in large public nurseries where they are taught the skills and knowledge appropriate to their social standing. Boys and girls of the Lilliputian nobility are taught honor, justice, modesty, clemency, religion, and love of country. Life's pretty hard in the nursery for both sexes: they are never allowed out of the sight of their professors and must never talk to the servants; they only get to see their parents twice a year, and, even then, they're not allowed presents. Public displays of affection between parents and children are also not permitted.
Girls of the nobility are taught family life, to prepare them for their future lives as wives and mothers. Their education is almost identical to that of the boys, except that their exercises aren't quite as robust. The most important principle in a girl's education is that she should one day become a wife who will always be a reasonable and agreeable companion to her husband.
Upper-class boys remain in the public nursery until they're fifteen, which corresponds to twenty-one, in our years. The girls leave when they're twelve years old, which would be the equivalent of marriageable age in Gulliver's England.