Why admire Marie Antoinette?

There are many reasons not to admire Marie Antoinette. She was the embodiment of the French ancien regime, the monarchy whose lavish lifestyle, embodied by the palace at Versailles, stood in stark contrast to the widespread poverty of the French people in the late eighteenth-century. The attitude of many common French people toward Marie Antoinette is summed up by her (almost certainly apocryphal) response to bread riots of hungry Parisian crowds: "Let them eat cake." Her lavish lifestyle was seen as the epitome of all that was corrupt and decadent about the French Bourbon monarchy.
But there are certainly some things to admire about Marie Antoinette. First, it is important to remember that she was married into the French monarchy at a very young age—just fourteen years old. She struggled to settle into the role of queen after her husband, Louis XVI, became king, but she persisted, eventually becoming an active figure in politics, frequently advising her husband on diplomatic matters.
Perhaps the main thing to admire about Marie Antoinette is the way she responded to the chaos that descended on her life and family during the French Revolution. An almost impossibly haughty woman while queen, she faced one indignity after another beginning in 1789, when she and Louis were forced back to Paris from Versailles by an angry mob. As her situation worsened, she showed the dignity that her position demanded, even after Louis XVI was executed. She faced relentless insults and was accused at her trial (for treason) of having an incestuous affair with her own son. In the face of this treatment, she displayed pride and even humility, going to the guillotine with composure and grace. So while Marie Antoinette did not live the most laudable life, she redeemed herself during her fall from the heights of the Bourbon monarchy. Even some French revolutionaries admired her courage in the face of death.
https://www.biography.com/royalty/marie-antoinette

https://www.smithsonianmag.com/history/marie-antoinette-134629573/

What is symbolic about Jean de Satigny's perversion and why does Allende include it?

Initially, Blanca is quite happy in her marriage to Jean. But, as she discovers some rather unpleasant facts about his sexual predilections, she sees a totally different side to him. The precise nature of Jean's sexual perversions is never quite established. At the very least, though, he seems to have some kind of fetish for using indigenous men and getting them to pose for erotic photographs. On top of this, Blanca discovers Jean's drug abuse as well as his shady business practices.
The House Of The Spirits incorporates numerous examples of what is called magic realism. This is a literary style that uses elements of fairy tales, fables, and folktales to heighten the sense of realism being presented. And Allende uses this method in relation to Jean's sexual perversions. In doing this, she is engaging in social commentary on contemporary Latin America: Allende wants to highlight the serious plight of Latin America's indigenous populations. Their sexual exploitation at the hands of Jean is symbolic of their wider treatment in society.
Magic realism is an effective means of dealing with age-old themes in a way that is both imaginative and relevant to the present day. Dealing with social and political themes using traditional realism can often lead to their becoming quickly dated. However, Allende's use of magic realism allows her to tap into a deeper structure of meaning, one reflected in countless myths, fables, and stories that never truly age and whose important themes resonate through the ages.

The purpose of the second to last paragraph of chapter 5, "Hester at Her Needle," is to explain one of the fundamental lessons that wearing the scarlet letter has taught Hester. Identify this lesson and explain how Hawthorne's use of diction, syntax, figurative language, irony, and tone achieves his purpose.

As Hester Prynne walks "to and fro" in the community, she notices how certain people that she passes gaze at her scarlet A, "the ignominious brand" on her bosom. When these people look at the letter, there is often more than a quick glance. In their momentary pause, Hester notices that there is a reaction to this letter. Sometimes she believes that she observes "a momentary relief," and it is as though the other person shares her "agony." Perhaps they, too, are adulterers who are guilty of the same sin, though they wear no mark.
Also, Hester finds that her wearing of the scarlet letter somehow gives her

a sympathetic knowledge of the hidden sin in other hearts. (Ch. 5)

Since she dwells in a Puritan community where sin is strongly condemned, Hester does not want to think that in many a heart there is a secret sin. In fact, Hester now feels confused and disillusioned. In her mind she addresses the Devil:

O Fiend, whose talisman was that fatal symbol, wouldst thou leave nothing, whether in youth or age, for this poor sinner to revere? (Ch. 5)

Because her heart gives "a sympathetic throb" as she passes certain ministers or magistrates, and she feels "a mystic sisterhood" when she observes other women looking at her, Hester is especially concerned that many others may carry in their hearts a secret sin that resembles her transgression. This thought of the possibility of hidden sins in the hearts of others causes Hester to become disillusioned.

Such loss of faith is ever one of the saddest results of sin. . . . Hester Prynne yet struggled to believe that no fellow-mortal was guilty like herself. (Ch. 5)

As Hester walks, her observations are shaded by a pessimistic tone, for Hester feels discouraged that others may be no better than herself. Certainly, Hawthorne's diction, his use of such words as "loss," "saddest," "fatal," and "hidden sin," suggests a new gloom that pervades Hester's spirit. For she has lost her faith in mankind as she realizes that in many a heart there lies a secret sin. Also, there is a bitter irony to her thoughts, as she is the only one wearing the ignominious symbol that figuratively "burns into her heart" with her shame and the scorn of others, who in fact may be sinners themselves.

What is a summary for The Dreamer by Pam Muñoz Ryan?

The Dreamer is a fictional tale based on the life of Pablo Neruda (originally Neftalí Ricardo Reyes Basoalto), a revered Chilean poet.
In short, “the dreamer” is Neftali, who is lost in a maze of thoughts. Since childhood, Neftali has wanted to pursue his poetry dream, but his domineering father objects to it. Neftali is intrigued by fantasy and uses his great imagination to escape reality. He explores nature to beat loneliness and illnesses, and to eschew his father’s wrath. The father does not want to tolerate Neftali's behavior, and he occasionally uses epithets to berate Neftali for his (Neftali's) absentmindedness. Throughout the text, Neftali is bullied by his own father, his brother, and a schoolmate. As he grows up, Neftali receives much inspiration from his uncle, a progressive journalist. Despite his father’s disapproval, Neftali manages to pursue his dream and finds happiness.

The Dreamer by Pam Muñoz Ryan is a fictionalized telling of Pablo Neruda's childhood in Temuco, Chile. Born Neftali Reyes, the child grew to be called Pablo Neruda (1904–1973), a Chilean poet, diplomat, and politician. As a rebellious young boy, Neruda uses his father's disapproval of his love for reading and writing as motivation to excel as a poet. His strained relationship with his father and brother is countered by his tender and loving relationship with his stepmother and uncle. These role models teach him the importance of believing in yourself and others. They instill in him the value of questioning authority and respecting one another. Neruda finds a voice within himself that guides him on adventures. His curiosity is inspired by the natural world around him. Muñoz utilizes sound in her writing, encouraging the readers to hear the ocean and forests that inspired Neruda himself. Ultimately, The Dreamer is a coming-of-age story of a shy young boy who struggles for independence and freedom.

The Dreamer, written by Pam Muñoz Ryan, is the fictionalized biography of the Nobel Prize–winning Chilean poet Pablo Neruda. The book traces the life of a tender-hearted boy, Neftali, and the arduous path he traverses to become Pablo Neruda. Neftali is by no means a conventional boy and distinctively stands out from others. He spends most of his time alone, finding beauty and wonder in even the most seemingly insignificant things. For this, however, Neftali is not only taunted by his peers but also derided by his strict and authoritative father. Right from childhood, however, he knows he has a "calling," which is symbolized in the book as a mysterious voice. The voice takes Neftali through an experiential sensory journey, and his journey leads him to a turning point in his life. Neftali fights against his father's cruel wishes and his own perceived inadequacies to become Pablo Neruda, one of the world's most celebrated poets.

The Dreamer is a fictional biography of the author Pablo Neruda, the poet.  It is about a shy boy (originally named Neftali Reyes) who is born in Chile and who deals with his pessimistic father. Neftali is always dreaming and using his senses to experience poetry all around him; from the time he is very young, this is often through a "mysterious voice" he hears. The children living near Neftali always taunt him for being dreamy. Neftali's father ridicules him as well. Both of these things cause Neftali to doubt himself and his abilities as a poet. Luckily, Neftali's uncle and stepmother encourage him (and teach Neftali about the Mapuche tribe and the rights they deserve). "The voice" Neftali hears leads him into the rain forest, the ocean, and the Chilean rain to give him the sensory experiences he needs to become a great poet. When Neftali becomes a teenager, he finally takes on the name he is famous for: Pablo Neruda.

What are some of the events and social practices that occur in the city and in the jungle in the novel Lost City Radio? How can I analyze the metaphors and symbols, the tone and/or feeling of each scene?

One of the practices in the city portrayed in Lost City Radio is the beating of children. Alarcon writes, "The government counseled solid beatings of children, in the name of regaining the discipline that had been lost in a decade of war. The station ran public service announcements on the subject" (page 12). The government uses the beating of children to try to reinvigorate a sense of discipline after the wayward years of the war, and the city radio station supports the government's message in an attempt to regain order in the society.
The government has instituted other social practices, including the outlawing of traditional native rituals. For example, villagers use a hallucinogenic plant called "tadek" to identify criminals. After a crime has been committed, the villagers feed "tadek" to a boy who then points out the criminal. Then, the criminal's arms are summarily chopped off. Manau meets a man named Mr. Zahir who has suffered this fate. Alarcon writes of Mr. Zahir, "He motioned with a waving stump, and Manau saw the scarred flesh, dimpled and leathery, that closed around the place where his hands ended so abruptly" (page 94). Mr. Zahir's hands are a symbol of the ways of the jungle, which are both mysterious and sometimes savage. They are also a symbol of the current post-war state of the country, particularly the jungle, and convey a tone of sadness about the devastation that the civil war caused in the jungle, where countless people were murdered or disappeared. 
Another event that occurs regularly in the city is each Saturday night, Norma broadcasts her show, which helps people find others who were lost in the war. Alarcon writes, "And Norma listened, and then repeated the names in her mellifluous voice, and the board would light up with calls, lonely red lights, people longing to be found" (page 9). The red lights symbolize people hoping to find others, though some are impostors. This ritual brings hope, though some of it is illusory, to the people who live in the city and to the former inhabitants of the jungle who have fled to the city. 

Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 68

Solve the equation $\displaystyle \frac{4}{9} + a = -\frac{2}{9}$ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
\frac{4}{9} + a &= -\frac{2}{9} - \frac{4}{9} && \text{Subtract $\displaystyle \frac{4}{9}$ from each side} \\
\\
a &= \frac{-6}{9} && \text{Simplify}\\
\\
a &= -\frac{2}{3} && \text{Divide both sides by 3}
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
\frac{4}{9} + \left( - \frac{2}{3} \right) &= - \frac{2}{9}&& \text{Replace the variable by the given number, } \frac{-2}{3}\\
\\
\frac{4-2(3)}{9} &= \frac{-2}{9} && \text{Evaluate the numerical expressions}\\
\\
\frac{-2}{9} &= -\frac{-2}{9} && \text{Compare the results}
\end{aligned}
\end{equation}
$


The results are same; Therefore, $\displaystyle -\frac{2}{3}$ is a solution of the equation $\displaystyle \frac{4}{9} + a = -\frac{2}{9}$

What are the best and the easiest ways to recycle batteries?

In states other than California, it is legal to dispose of single-use alkaline and lithium batteries in the trash, as they do not contain heavy metals. However, it is advisable from an environmental point of view to recycle them. In addition, automotive and rechargeable batteries (such as lead acid batteries, Li-Ion, Ni-MH, Ni-ZN, Ni-Cd) batteries should be recycled.
Many cities have events or locations at which they collect hazardous waste (see the link for New York City below). You can find out more about these events by visiting the website of your town, county, or city. In addition, you may be able to mail hazardous waste materials such as batteries to a collection site that will recycle them. Single-use batteries contain materials such as steel and zinc that can be recycled. When you bring in non-alkaline batteries to be recycled, place clear tape (not opaque tape) over the terminals to prevent the risk of fire. Place each battery in a bag. You do not need to bag or tape alkaline batteries. 

The way you dispose of batteries depends on the type of battery. According to Duracell, alkaline batteries can be disposed of with household waste. Due to the fact that batteries can explode if exposed to fire, throwing used batteries in a fire would not be acceptable. Although batteries contained mercury in the past, many manufacturers have eliminated it. You can check with a manufacturer online. It is important not to throw large numbers of batteries away at the same time since the batteries may not be completely used.
Other types of batteries such as rechargeable batteries, lithium, lithium ion and zinc air batteries should not be disposed of in the trash. These types should be recycled. This is due to the chemicals these types contain. A label on the battery should mark them as recyclable. They are commonly found in laptops, cell phones, power tools and cameras. There are recycle centers in most areas where you can bring the batteries for disposal. 
Large batteries, such as car batteries, contain lead. They should be brought to a local waste management or recycling center.
https://www.duracell.com/en-us/technology/battery-care-use-and-disposal/