Beginning Algebra With Applications, Chapter 5, 5.1, Section 5.1, Problem 36

The following table shows the projected population of adults 18 to 19 years old for selected years from 2005 to 2030.

$\begin{array}{c|cccccc}
\text{Year} & 2005 & 2010 & 2015 & 2020 & 2025 & 2030 \\
\hline\\
\text{Population projection, in millions} & 8.4 & 8.6 & 8.1 & 8.6 & 9.0 & 9.4
\end{array} $

a. Determine the average annual rate of change of the U.S. population of adults 18-18 years old from 2005 to 2030.


$
\begin{equation}
\begin{aligned}

\text{average annual rate of change} =& \frac{\text{population in 2030 - population in 2005}}{2030-2005}
\\
\\
=& \frac{9.4-8.4}{2030-2005}
\\
\\
=& \frac{1}{25}
\\
\\
=& 0.04

\end{aligned}
\end{equation}
$


This means that the population of 18-19 years old from 2005 to 2030 was increased by 40,000 per year.

b. In which five-year period shown did the average annual rate of change of this population decline? What was the average annual rate of change for that period?

The population decline from 2010 to 2015, the average annual rate of change is


$
\begin{equation}
\begin{aligned}

\frac{\text{population in 2015 - population in 2010}}{2015-2010} =& \frac{8.1-8.6}{2015-2010}
\\
\\
=& \frac{-0.5}{5}
\\
\\
=& -0.1

\end{aligned}
\end{equation}
$



The population of 18-19 years old from 2010-2015 was decreased by 100,000 per year.

In the novel Fifth Business what is the importance of the theme of sainthood?

In Fifth Business, the importance of the theme of sainthood has to do with two specific characters: Dunstable (Dunstan) Ramsay and Mary Dempster.  
Dunstable Ramsay (who is later referred to as Dunstan or Dunny) has to do with the theme of sainthood due to his study of saints. The irony is that Ramsay is not even a Roman Catholic, but his obsession with saints eventually brings him all over Europe. Ramsay's true interest in sainthood has more to do with the supernatural aspect of sainthood than the religious aspect of sainthood. Ramsay proves this when he begins to pursue magic as a career. As further proof, the reader finds Ramsay comparing the New Testament to the Arabian Nights and comparing Mary Magdalene to mythological archetypes. Dunstable Ramsay finally receives the name of Dunstan after he returns from the war as a crippled hero. As a kind of martyr for the cause, Dunstan's name was taken from a saint who supposedly caused the deformity in the devil's nose. It is at this point that Dunstan's obsession with saints takes over. Dunstan visits shrine after shrine in Europe, writes many books on saints, and is eventually considered a hagiographer. The other irony is that Dunstan does not act very holy, especially when he tries to convince Staunton to take the blame for causing the ill-fated snowball incident from their youth.
Mrs. Dempster, on the other hand, has her "sainthood" thrust upon her by a hard snowball that hits her and causes early labor. Mrs. Dempster already has her marriage to the Baptist minister going for her, and now her sainthood appears confirmed by many strange "miracles." First, Mrs. Dempster uses her "generosity" to give her body to people other than her husband (such as a vagrant). The vagrant then ceases his evil behavior and immediately becomes a missionary. Later, Mrs. Dempster "resurrects" Willy (who is on the verge of death) and eventually appears to Dunstan during the war in a kind of saintly apparition.
The theme of sainthood connects the two characters through the vision on the battlefield during World War I. It is this vision, more than any of the other "miracles," that makes Dunstan believe Mrs. Dempster is a saint. At this moment, Mrs. Dempster joins the throng of saints fueling Dunstan's obsession with saintly holiness.

Can you help me write a thesis statement and think about how to write 500 words about how a community problem should be solved?

To identify a problem in your community, you can read your local newspaper or visit its website. You might also know about a problem related to your school that you can write about.
Your thesis statement should include what the problem is, what people are doing to solve it, and whether that has been effective. For example, wildfires are a big concern on the West Coast of the United States right now. The thesis statement for an essay about wildfire concern would include the extent of the fires and the damage they are causing, as well as what can be done to help fight or prevent them.
You might want to think about dividing your essay into three main parts: background information, what's being done to solve the problem, and what the future holds. When examining any community problem, you first want to start with background information about that problem. For example, the California wildfires were caused in part by years of drought and high summer temperatures. Then, you want to discuss the extent of the problem, including the problem's effects on the community. For example, in the case of wildfires, you would mention the number of acres they have affected, their cost, and the number of people who have died due to wildfires. Then, you would speak about how your community is attempting to handle this problem. Finally, you might discuss what you propose for the future to help solve this problem, or what experts suggest to solve this problem. You would want to aim for about 150-200 words per section so you can come up with an essay of 500 words. 

How did the townspeople finally solve the problem with the smell?

Miss Emily Grierson is effectively the aristocracy of the small town of Jefferson, so her life is both highly scrutinized by the townspeople and veiled by the regard in which the upper class is held. When a sickening smell arises from her house shortly after the disappearance of her fiancé, Homer Barron, the townspeople are conflicted about how to deal with the problem. On the one hand, the smell must be dealt with, because it is a public nuisance. On the other hand, Miss Emily has just been jilted by her lover, is presumably going through a difficult time, and is a woman. More than that, she is a "lady" from a family of high degree. Social mores in the town of Jefferson (and the South more generally) prohibit bluntly confronting Miss Emily with the problem.
The townspeople believe the source of the smell is a dead animal of some kind, and after making a few complaints to the mayor, Judge Stevens, the Board of Aldermen approach him and ask him to take action:

"It's simple enough," [a young alderman] said. "Send her word to have her place cleaned up. Give her a certain time to do it in, and if she don't..."

Judge Stevens is appalled by this breach of protocol:

"Dammit, sir," Judge Stevens said, "will you accuse a lady to her face of smelling bad?"

Unable to order Miss Emily to solve the problem herself, the townspeople take matters into their own hands, and a group of four men sneak onto her property under cover of darkness and spread powdered lime all around the house:

[After] midnight, four men crossed Miss Emily's lawn and slunk about the house like burglars, sniffing along the base of the brickwork and at the cellar openings while one of them performed a regular sowing motion with his hand out of a sack slung from his shoulder. They broke open the cellar door and sprinkled lime there, and in all the outbuildings.

This seems to resolve the issue—although not immediately—for "after a week or two the smell went away." Nobody knows until many years later that the corpse of Homer Barron was the source of the smell.

Explain the theme of death in the story "A Rose for Emily."

William Faulkner establishes a theme of death from the first sentence in "A Rose for Emily":

When Miss Emily Grierson died, our whole town went to her funeral.

Emily herself is described in deathlike terms, with the imagery connoting that she is a drowned woman—bloated and pale.
Emily dissociates herself from death. When her father dies and mourners arrive, she appears as usual, with no trace of grief on her face. She also adamantly asserts that her father is not dead and refuses to allow anyone to take his body. For three days, she maintains this assertion until finally ministers and other visitors create a "break" that allows them to take her father's body and dispose of him quickly.
When Emily faces the truth that her love interest is not a "marrying man," she plans his murder and executes it with seemingly cool and calculated tactics. Her subsequent actions following the murder do not arouse the suspicions of anyone in town, and she shows no sense of mourning, showing her disconnect from the death she has inflicted.
Only after her own death do people learn of the extent of Miss Emily's dissociation from death. Not only has she kept Homer's corpse in her house all those years, but she has also lain with him in the bed, as evidenced by the long gray hair found on the pillow.
Miss Emily has difficulty parting with tradition and with those whom she has grown to love, and her actions show her inability to accept the ultimate finality of death's power.

William Faulkner explores the theme of death throughout his short story "A Rose for Emily," which symbolically represents the decay of the Old South and the fall of the Confederacy following the Civil War.
The story begins as the community of Jefferson attends the funeral of the reclusive, southern aristocrat, Emily Grierson. Throughout the story, Emily's tragic life is revealed, and the audience gains insight into the nature of her downfall. Emily and her decaying home symbolically represent the culture and traditions of the Old South. Although the story is told out of sequential order, it is understood that Emily's mental breakdown begins following the death of her father. Interestingly, Emily refuses to acknowledge the death of her father.
Years after her father's death, Emily begins to date Homer Barron, a working-class Yankee. Emily then buys arsenic, which she uses to poison and kill her companion. After Homer's disappearance, the community council members visit her home and describe her as looking like a corpse. After Emily dies, citizens finally enter her home and discover Homer Barron's skeleton on a bed in an upstairs room with a piece of gray hair laying on the pillow beside it. The gray hair indicates that Emily Grierson had been sleeping next to Homer's skeleton. The theme of death is representative of the fall of the Old South and its traditions. Throughout the story, Emily attempts to freeze time by not acknowledging the death of her father and purposely killing her suitor so that he cannot leave her. Similarly to Emily's attempts to stop time, Faulkner metaphorically illustrates how southern citizens attempt to preserve their past. The antebellum society has been destroyed and the South will never return to its former glory. Emily, the "fallen monument," represents the decay of the Old South and its culture.

How does Atticus explain rape to Scout?

In Harper Lee's famous novel To Kill a Mockingbird, the main character, Scout, is very young. In chapter 14 of the book, she asks her father, the lawyer Atticus Finch, to explain what rape is after Calpurnia refuses to explain. As Scout tells us, "He sighed, and said rape was carnal knowledge of a female by force and without consent." 
Essentially, Atticus purposely does not explain to Scout what rape is. Obviously, if you repeated this quote from Atticus to a child, they would still be completely clueless. It makes sense that he wanted to avoid giving a straightforward answer—rape is a pretty tough subject to discuss with your young daughter. However, it does make Atticus a bit of a hypocrite. He specifically told Jack earlier in the book to not to beat around the bush when a child asks you a question.

How does Shelley include the theme of Love in her book? And how does it still mean something in Modern Society?

Although Frankenstein deals mostly with heavier themes, love plays a role in the novel's plot and character interactions. Here are some prominent examples:
1. Victor Frankenstein's family: Victor describes his young life as very happy and pleasant. His family loves each other, and this love shapes his early life. It serves as an ironic contrast to his adult life.
2. Victor's relationship with Clerval: Henry Clerval is Victor's best friend, and he loves him like a brother. It is a tragic twist when the monster kills Henry to get revenge on Victor.
3. Victor's relationship with Elizabeth: These two characters are close since childhood and eventually marry one another. Elizabeth is Victor's support system for part of his adult life, and she is very understanding and sympathetic. Unfortunately, Victor isolates himself and puts his wife at risk by not building the creature a mate; the monster reciprocates by killing Elizabeth on Victor and Elizabeth's wedding night.
4. Safie and Felix: Felix De Lacey and his beloved Safie are two of the members of the family that the monster observes when he lives outside their home. He learns about family and about true love between parents and children but also between husband and wife. The creature learns from Safie and Felix, as well as from his reading of Paradise Lost, that a man is meant to be paired with a female partner. He then petitions his creator, Victor, to build him a companion. Although disgusted, Victor originally agrees and works on the female creature; however, he eventually destroys her. This is a crucial plot point because after this, the creature's revenge knows no bounds.
5. Victor and the creature: The lack of love Victor has for his creature is also key to the novel as a whole. If Victor had cared for this being whom he brought to life and nurtured him like a real parent, the tragedies of the novel could have been avoided.