Was the Compromise of 1850 a good compromise?

The Compromise of 1850 did several things. It allowed California to enter the Union as a free state. It stated that the land we received from Mexico would be divided into the New Mexico and the Utah territories. The people would determine if there would be slavery in these territories. The Compromise of 1850 ended slave trading in Washington, D.C. It also included the passage of the Fugitive Slave Act. This law required northerners to help capture runaway slaves.
While a compromise is designed to give both sides part of what they wanted, this compromise created many problems. The northerners were furious that they had to help capture runaway slaves. This meant that no slave who had escaped was safe in the North. Many northerners refused to obey this law. This made the South unhappy because they relied on the enforcement of this law to capture the slaves that had escaped. The North also had a majority of states in the Senate. It is fair to say there was unhappiness with this compromise after it was created.
https://www.ushistory.org/us/30d.asp

Depreciation of the US dollar will

The depreciation of money, also known as currency depreciation, occurs when a country's currency decreases in value. For example, if the US dollar depreciated, then it lost some of its value compared to the currency of another country.
Depreciation of the US dollar will have a ripple effect. In other words, it will impact other aspects of the economy. For example, depreciation of the dollar will:
Increase the price of products being imported into the US from other countries.
Decrease the price of products being exported from the US to other countries.
Impact the amount being imported and exported from the US (i.e., fewer imports and greater exports).
Lead to an increase in real GDP if US-based production increases to replace products that may have otherwise been imported.
Cause the currencies of other countries to fluctuate in tandem with the decreasing value of the US dollar if these counties try to keep their currencies stable relative to the US.

What is the theme of "The Way Up To Heaven" by Roald Dahl?

The theme of "The Way Up to Heaven" is essentially revenge. Mr. Foster has been secretly tormenting his wife for years with his procrastination and deliberate delays. She doesn't resent his behavior because she can't be sure whether he is doing it intentionally or it is just an annoying character trait. One morning, she find definite evidence that he is a sadist who enjoys torturing her because he knows how important it is to her to be on time for appointments.
Since Mr. Foster uses passive aggression to torment his wife, it is poetic justice that she should get revenge through the same passive aggression. She doesn't actively do anything to kill her husband; she only refrains from doing something. When Mr. Foster delays their trip to the airport by pretending he left something behind in their house, Mrs. Foster, waiting in the car, hears a sound of the elevator getting stuck between the floors. Instead of helping him, she proceeds to the airport, thereby letting him die.
Mrs. Foster's deadly revenge might be considered excessive, but Roald Dahl takes pains to show that Mr. Foster has been using his sadistic passive aggression against his poor, long-suffering wife systematically. Her revenge is a reaction to a whole series of injuries she has suffered at the hands of this petty tyrant over many years.

In Lord of the Flies, how did the choir boys, Ralph, and the other boys get separated? Why did the choir boys not look like they had just been in a plane crash?

Golding does not spend a great deal of time describing the actual events of the plane crash, so it is difficult to know exactly what happened prior to the boys coming out of the jungle for the first meeting.
It is clear that the plane broke into pieces, according to the conversation between Ralph and Piggy. It is also clear that at least one piece of it hit the island and made the "scar" in the jungle. During the crash, it is also clear that the boys were separated, either thrown out of different parts of the plane or perhaps they simply scattered when the plane hit the ground.
The choir boys somehow managed to save their "togs" and Jack forces them to put these on before they march to the meeting in formation. The uniformity allows them to appear as though they'd just come from a performance rather than coming out of the jungle following a plane crash.

What prior knowledge do readers have when they begin Anne Frank's diary?

Many readers have heard of Anne Frank.  In many ways, she is a human symbol of the Holocaust.  She is considered one of the most famous Holocaust victims.  The basic information of her story is known throughout the world, even by those who have not read her diary.
In addition to information about Anne Frank herself, most readers will also have prior knowledge about Nazism and the Holocaust.  In the study of world history, World War II, Nazism, and the Holocaust are important topics.  People who have not read Anne Frank's diary will most likely know about Hitler's rise to power and Nazi Germany.  They will know that the Nazis had a platform of antisemitism, and this led to them restricting the lives of German Jews.  Jews were banned from schools and public places, and they were eventually removed from their homes and sent to concentration camps.  World War II began, and the Nazis started invading other countries.  The Nazis invaded Holland, where Anne and the Frank family lived.  They placed restrictions on Jews in Holland, and eventually they sent many of them to work camps.  Anne and her family went into hiding to escape being sent away by the Nazis.

What effect does the house's repetition of the time have on the mood of the story?

In literary terms, "mood" is the emotional atmosphere evoked by a piece. In this story, the house's repetition of the time draws our attention to a devastating, sad change. It also contributes to the feeling that the house -- while managing to keep its operations under control -- is disoriented and abandoned. Let's look more closely at the details.
First, consider the context. The house is a mechanical servant to its human masters, but its masters are dead, killed in a nuclear holocaust. Thus, the time announcements underscore what is missing now -- the people who used to live by this schedule, and the wider civilization that made this schedule possible. You can observe this at various points in the story.
Sometimes, the voice-clock doesn't just tell the time. It also urges its potential listeners to do something:

"Eight-one, tick-tock, eight-one o'clock, off to school, off to work…"

On other occasions, the voice-clock states only the time of day. But nevertheless, the house performs specific services at these times.

"Five o'clock. The bath is filled with clear hot water."

Either way, the time messages remind us of the schedules these people followed, and the daily activities they engaged in. We recognize these schedules and activities, and so we feel empathy.
In addition, we are aware of the scale the loss. It isn't just one family that died. Very likely, civilization has been destroyed, in which case the schedule is no longer relevant to anyone. Thus, the time updates highlight this sense of irrelevance, and help contribute to an atmosphere of futility. Time is passing, but there is no one left for whom this passage has any meaning.
Finally, the time messages help emphasize the house's ignorance of what is going on. This contributes to the impression that the house is a confused or deranged -- and possibly lonely -- being. And it heightens the sense of sadness.
 

Precalculus, Chapter 7, 7.3, Section 7.3, Problem 26

You may use the substitution method to solve the system, hence, you need to use the first equation to write x in terms of y and z, such that:
x + y + z = 5 => x = 5 - y - z
You may now replace 5 - y - z for x in equation x - 2y + 4z = 13 , such that:
5 - y - z - 2y + 4z = 13 => -3y + 3z = 8
You may use the third equation, 3y + 4z = 13 , along with -3y + 3z = 8 equation, such that:
-3y + 3z + 3y + 4z = 8 + 13 => 7z = 21 => z = 3
You may replace 3 for z in equation 3y + 4z = 13:
3y + 12 = 13 => 3y = 1 => y = 1/3
You may replace 3 for z and 1/3 for y in equation x = 5 - y - z:
x = 5 -1/3 - 3 => x = 2 - 1/3 => x = 5/3
Hence, evaluating the solution to the given system, yields x = 5/3, y = 1/3, z = 3.