On pages 48–49 of The Other Wes Moore, we learn about the sacrifices Wes and Justin made to attend their school. What did this early experience teach Wes and Justin about the importance of goals?

Wes and Justin must travel to attend their school and be singled out by their peers but they realize these are things they must face in order to get their education. They quickly learn that they must step out of their comfort zone and work a little harder to achieve their goals. Even though they do not like to travel a ways to get to school or be picked on by their peers they must remain focused on their end-goal. They must face these current hardships in order to achieve their goal and be successful in the long-run. They must take advantage of the opportunity they were given and make the best of it.

Despite growing up in a loving family environment, the author Wes Moore has been getting into trouble. His mother's worried that he might end up falling into a life of crime like so many other young men of his age. She figures that the only way to prevent that from happening is by changing her son's environment. That means sending him off to military school.
Doing so involves making a lot of sacrifices. Unbeknownst to Wes, almost every member of his family has had to contribute financially to send him to military school; his grandparents gave up almost the whole of their life savings. Wes learns from this that it was only though such enormous sacrifices that he was able to change his path in life, a path that had led to achievement and success.
As for Justin, Wes's friend, he has to sacrifice his good grades at school in order to help out his family after his mother's diagnosed with Hodgkin's disease, a rare form of cancer. With his sister away at college and his father living in Harlem, Justin has to hold the family together, juggling basketball practice and study with making regular visits to the hospital to see his mom. Inevitably, this has a disastrous effect on his schoolwork, and his grades decline accordingly.
And yet despite his many trials and tribulations, Justin never gives up hope and remains determined to make something of himself. Despite being diagnosed with cancer himself, Justin also achieves much in life, eventually forging a successful career in education.

What is the role of an exhibitor in a research carnival? Do they need to present a paper or their achievement such as a conference paper?

A research carnival is the most informal type of academic symposium, less formal than a conference paper presentation or even a poster presentation.
Research carnivals, unlike research conferences, are designed to be accessible to the general, non-academic public and to present the findings of research in a way that is both understandable and compelling. Instead of papers or posters, participants in a research carnival present tangible examples of their research so that attendees can understand its practical implications and witness it "in action."
For instance, at a research carnival, an exhibiting robotics engineer would not present a paper on their studies, but they might present working examples of robotic devices they had built with the aid of their research and demonstrate how that research had contributed to their design and construction.

In A Midsummer Night's Dream, how is Hippolyta's reasoning concerning how quickly the next four days will pass different from that of Theseus?

Great question! At the beginning of William Shakespeare's comedy A Midsummer Night’s Dream, Hippolyta and Theseus are due to be married in four days. The upcoming royal wedding serves as the backdrop for the plot of the play, and most of the characters are involved with the wedding in some capacity.
In the opening lines of the play, Theseus bemoans that time seems to pass so slowly. He says that the moon "lingers my desires" and essentially says that he wishes to bed Hippolyta immediately rather than waiting until after the ceremony.
Hippolyta is much less anxious. She responds to Theseus's impatience by saying:

Four nights will quickly dream away the time

For Hippolyta, time is moving quickly. She refers to the night of the wedding as the "night of our solemnities." By using the word "solemnities" to describe a (normally) happy and joyful experience, Hippolyta reveals that she is not enthusiastic about her coming marriage.
For Theseus, four days seem like an eternity while for Hippolyta four nights will pass far too quickly. This is interesting, and the odd relationship between these two characters is revealed a few lines later when Theseus tells his betrothed:

Hippolyta, I woo'd thee with my sword,And won thy love, doing thee injuries;But I will wed thee in another key,With pomp, with triumph and with revelling.

This reveals that Hippolyta is not marrying Theseus willingly. The Queen of the Amazons has been kidnapped by Theseus and is being forced into marriage. This detail largely explains why Theseus and Hippolyta have different perspectives on the passage of time leading to the wedding.
I hope this helps!

What are some examples that highlight the theme of home and abroad in Robert Louis Stevenson's "The Beach of Falesa"?

One example that highlights the theme of home and abroad in "The Beach of Falesá" is the marriage of the protagonist John Wiltshire to the Island native Uma. Such unions were not uncommon in the colonies or the South Seas, in a way that would not have been possible at home because of the cultural prohibition of "miscegenation."
Another example of the theme of home and abroad is the power that the rogue character Case is able to exert over the native population through his manipulation of their belief in the ever-present influence of spirits and the supernatural. Although the use of luminous paint and other conjuring tricks was not unheard of in England at the time, it could hardly have been used to fool an entire society, as happens on the island.
Another home and abroad example is Wiltshire's relative lack of concern for the legal or other consequences of plotting to blow up Case's temple in the jungle, where Case beguiles and enchants the natives. When Case confronts Wiltshire and a fight ensues, Wiltshire kills Case and ends up living contentedly on another island. Such things can happen abroad with far fewer risks and consequences than in England, where plotting to blow up a man's construction and killing him when he resists would likely not go unpunished.

What kind of partnership does Paul have with Bassett?

In D. H. Lawrence's "The Rocking-Horse Winner," Paul and Bassett—the young protagonist and his family's gardener—have partnered together to gamble on horse racing. The partnership is equal in the sense that its success hinges upon both partners holding up their end of the agreement.
Paul is too young to make the bets himself. He also does not wish his mother to find out, as he believes she would put a stop to it. For these reasons, he must rely on Bassett to place the bets for him. On the other hand, Bassett must also rely on Paul, as he is the one picking the winners.
Bassett used to be "batman" (i.e., servant to a British Army officer) to Paul's uncle, Oscar Cresswell. After injuring his foot, Oscar helped Bassett get a job as a gardener for Paul's family. At the start of "The Rocking-Horse Winner," the pair have already been partners for a while, building up quite a stockpile of money. In a sense, Bassett has now also become "batman" to Paul, though it does not take away from the latter's reliance on the former.
The pair's process is as follows: Paul rides his rocking horse, where he gets an idea of who to bet on:

"Sometimes I'm absolutely sure, like about Daffodil," said the boy; "and sometimes I have an idea; and sometimes I haven't even an idea, have I, Bassett? Then we're careful, because we mostly go down."

As Paul is too young to do so, Bassett is the one who must go place the bets. He is also responsible for holding on to their winnings for safe keeping. The two of them only place large bets on horses that Paul is "absolutely" certain will win. Until Uncle Oscar discovers Paul's gift of luck, the pair keep this a secret from everyone else in the family.

Bassett and Paul have a partnership to place bets on horse races. Paul can determine the winner of an upcoming horse race by riding his rocking horse very hard. But he is too young to go to the racetrack and bet, so Bassett does that for him.
We learn that Bassett is the young gardener for Paul's family. His foot was wounded in World War I. Uncle Oscar helped him get him the job with Paul's family, because Bassett had been his batman in the war. (A batman was a personal servant the British army assigned officers like Uncle Oscar.)
Because Bassett and Uncle Oscar had a prior close relationship, Oscar is inclined to support their betting partnership. When Oscar questions Paul about it, he learns that Bassett had lent Paul the money—five shillings—to make his first bet. Oscar is surprised to find out the large sums the two are now winning on the races.

How did the terms “Democrat” and “Republican” change from 1776 to 1850? Who were the Whigs? Of the people and parties encompassed by these terms, what were they for and against? Give specific examples of key people, elections, debates, and so on.

During the establishment of the United States from 1776 to 1789, there were no Democrats and Republicans as we currently understand them. There were Federalists and anti-Federalists, the latter later forming the nucleus of the Democratic-Republicans. Well-known Federalists included John Adams and Alexander Hamilton. Federalists believed in a strong, centralized government with infrastructural services, such as a national bank. Federalists were often urban types—Adams was from Boston and Hamilton was from New York—and they were less likely to be sympathetic to the needs of slave owners.
Thomas Jefferson and James Madison are the most well-known Democratic-Republicans. Members of this party were more agrarian and more likely to be slave owners. They came from less populous states and states, such as Virginia and South Carolina, that often had large populations of black slaves. This situation inspired the "three-fifths compromise" in the Constitution, which declared slaves three-fifths of a person so that the Democratic-Republicans could have better representation in Congress. Both Jefferson and Madison were wealthy Virginia planters.
Democratic-Republicans believed in a less centralized government and supported allowing states more power. Jefferson and other members of this party believed that the citizens of an individual state were best positioned to determine their needs and did not need a distant government, then in Philadelphia, to direct their functioning. Democratic-Republicans were averse to involving themselves in foreign affairs, but the demands of the period, including the Louisiana Purchase in 1803, forced them to become more internationally engaged.
The Whig Party was active from 1834-1854. They developed in opposition to Andrew Jackson, whose populist appeal led to what Whigs perceived as an overreach of presidential powers. They borrowed the term "Whig" from British parliamentarians who opposed extensive royal power. The Whigs were usually antislavery, but they expressed a willingness to compromise—a political instinct best expressed by the party's founder, Kentucky Senator Henry Clay, who was nicknamed The Great Compromiser due to his ability to secure sectional compromises, particularly during the Missouri Compromise of 1850. Whigs were sympathetic to sectarian interests, like the Democratic-Republicans before them, but less sympathetic to slavery.
The Whig Party died in the 1850s and was absorbed by the Republican Party. The Whigs' key figures, Clay and Daniel Webster—who represented New Hampshire and Massachusetts in Congress—died. The party subsequently split between its proslavery and antislavery wings. The former joined the Republicans, who dominated in the Northern states; the latter went to the Democrats, who dominated in the South.
The Republicans were, at that time, against slavery. The Democrats, at that time, were for slavery. Democrats were adamant in their support of states' rights—a lingering Constitutional argument that they used to justify their right to have slaves and the perceived right of newly admitted states to decide for themselves if they wished to have slavery.
https://www.britannica.com/topic/Democratic-Republican-Party

What leadership style did Erin Brockovich have?

In leadership as an academic discipline, there are ten widely recognized styles of leadership: transactional, transformational, democratic, autocratic, bureaucratic, laissez-faire, servant, situational, cross-cultural, and charismatic.
It is rare for a leader to operate exclusively within one style of leadership. A more common occurrence is a blended style that leans more in the direction of one style. This is the case with Erin Brockovich.
Erin Brockovich's leadership blends transformational, servant, situational, and charismatic styles, and it leans more toward the charismatic style than it does the other three. Her style is transformational in the sense that her leadership and actions are focused on substantial and meaningful change. It is servant in the sense that her mission is grass-roots and serves to accommodate and empower the powerless. It is situational in that her move into a leadership role is influenced entirely by the circumstances of her life and community. Lastly, her style is charismatic in that she is able to effect change as a result of her personality, passion, compassion, and personal investment in her cause.
https://thebestschools.org/magazine/organizational-leadership-styles-study-starters/