In To Kill a Mockingbird, why has Atticus Finch given up shooting, despite his talent?

After the incident with the mad dog, Miss Maudie explains to the children: "If your father's anything, he's civilized in his heart. Marksmanship's a gift of God, a talent -- oh, you have to practice to make it perfect, but shootin's different from playing the piano or the like. I think maybe he put his gun down when he realized that God had given him an unfair advantage over most living things."

Atticus, a few chapters later, talks about what true courage is. He is talking about Mrs. Dubose. He says: "I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. it's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won.... According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew."

Not only does Atticus's statement about Mrs. Dubose disabuse the children of any lingering idea that guns are the props of brave men, he also foreshadows his own courageous struggle against injustice in Maycomb, despite being "licked" before he begins.

His choice to never shoot a gun relates to what real courage is, and to being a gentleman who would never take advantage of any living thing.

In "The Crucible," how does Proctor think Danforth is taking advantge of him?

Your question references Act IV of The Crucible when Danforth wants to use John Proctor to prove to the town of Salem that their actions against those who were accused and executed were valid. 

Danforth wants to use Proctor, who is a respectable citizen in Salem, to give his court and their rulings validity and authenticity.   Danforth needs John Proctor's confession nailed to the church door so that there will be no rebellious uprising in the town like there was recently in Andover, a neighboring town.

Danforth is frightened for his life, and seeks to use John Proctor to prove to the town of Salem, that there were witches in their midst, look, he is saying, even someone like John Proctor, an upstanding citizen admits to witchcraft.

One of the factors that contributed to the Salem witch hysteria was the confessions.  People confessed to witchcraft so that they could save their lives.  But once someone confessed, it made the existence of witchcraft more and more real.

So Danforth knows that if he uses John Proctor to prove the existence of witchcraft through his confession, no one in the town will question what the court has done, which was to hang innocent people on false charges based on the testimony of a girl, Abigail Williams, who has run away from Salem in disgrace.  

What was the purpose of the Halloween pageant? What practical joke had persuaded the grown ups to have an organized event? Chapter 27 " To Kill a...

In Chapter 27 of Harper Lee’s To Kill a Mockingbird, Scout explains that, in the past, the town of Maycomb made no effort to organize Halloween activities for the children, leaving them to their own devices.  As Lee’s narrator, Scout, explains, the change from previous years to an organized event this year was precipitated by a practical joke played at the expense of two elderly, deaf women:

“The second change in Maycomb since last year was not one of national significance. Until then, Halloween in Maycomb was a completely unorganized affair. Each child did what he wanted to do, with assistance from other children if there was anything to be moved, such as placing a light buggy on top of the livery stable. But parents thought things went too far last year, when the peace of Miss Tutti and Miss Frutti was shattered. . .some wicked children had waited until the Misses Barber were thoroughly asleep, slipped into their living room (nobody but the Radleys locked up at night), stealthily made away with every stick of furniture therein, and hid it in the cellar.”

In an effort at preventing a recurrence of such mischief, the school organized a play produced for the parents with the children each dressed-up to look like agricultural products.  Again, as Scout describes the scene:

 “Mrs. Grace Merriweather had composed an original pageant entitled Maycomb County: Ad Astra Per Aspera, and I was to be a ham. She thought it would be adorable if some of the children were costumed to represent the county’s agricultural products . . .”

So, the practical joke that resulted in an organized pageant involved some children breaking into Tutti and Frutti Barber’s home and moving their furniture into the basement.  The women were deaf, so didn’t hear to the sounds emanating from their living room, as the juvenile delinquents went about executing their plan at these two elderly women’s expense.

Please explain Hamlet's statement, "(T)he time is out of joint. O cursed spite, that ever I was born to set it right."

Hamlet has just finished talking to the ghost and finding out that his father was murdered by his uncle, Claudius. The ghost has left and Hamlet swears Marcellus and Horatio to an oath not to reveal what they have seen or what Hamlet is trying to do, even if he pretends to be mad:

HAMLET
    ...
    There are more things in heaven and earth, Horatio,
    Than are dreamt of in your philosophy. ...
    How strange or odd soe'er I bear myself,
    As I perchance hereafter shall think meet
    To put an antic disposition on,
    That you, at such times seeing me, never shall,
    ...
    ... by pronouncing of some doubtful phrase,
    As 'Well, well, we know,' ...
    ...
    Or such ambiguous giving out, to note
    That you know aught of me: this not to do,
    So grace and mercy at your most need help you, Swear.

At first, the two men see no reason for swearing an oath but both Hamlet and the ghost insist. The ghost requires they swear:

GHOST [Beneath.]
    Swear.
[They swear.]

Hamlet then laments that he is alive during this time ("O time is out of joint"). It's the time in which his father was murdered and, being the king's son, he is the culturally required person to "set things right." But he is not happy about it and laments being born at the time--out of joint, out of proper alignment--that requires he avenge his father's murder.

Culturally, revenge killings were the norm, as illustrated by Fortinbras. It is Hamlet's relatively new religious beliefs--beliefs in time out of joint, time out of alignment--that make revenge killing something to lament: Fortinbras accepts revenge killing for his father/King's death as an honor.

What does Hamlet's first soliloquy tell us about his depression? Does he feel isolated in his grief? "O that this too too solid flesh..." Act I...

This is Hamlet's statement that he wishes he were dead, that his body, all too physical, could just melt away "into a dew" or that God had not forbidden suicide, "fixed his canon against self-slaughter" as he will say later.  He has lost all interest in the things of this world ("weary, stale, flat and unprofitable" says it all).  What was once, by implication, a flourishing garden is now gone to seed with only things "disguisting and decaying" growing there.

This tells us that his depression is very serious.  It also tells us that he does feel very isolated and alone in his grief: "an unweeded garden / That is going to seed."  He has lost interest in the things that once gave him pleasure (a classic sign of depression), and he is contemplating suicide, stopped only by the fact that he just can't "disappear," and that God has forbidden him to act on his desire to die.  And this is a theme we will see developed in other parts of the play.

What is the definition of scientific method?In the field of earth science..

I teach scientific method to my sixth graders each year, and although the steps vary by what they are called, the scientific method is an orderly process that one follows in an experiment to prove their educated guess (also called a hypothesis) to a question.  In order for others to be able to duplicate your experiment and results, the scientific method is an agreed upon method of steps to follow while conducting your experiment.

All scientific experiments begin with a question and from that question, you come up with your hypothesis after researchingi nformation or observing if needed.

Once a testable hypothesis has been formed, then a scientist would begin creating an experiment that consists of different elements, including a control and experimental group.

Once the experiment has been conducted and the researcher is able to see consistent results, then a summary is written describing the results.

Every scientist may add or delete a few elements to their scientific method, but the major elements again are:

Question

Gather info/Research

Form a Hypothesis (Cause and Effect answer to your question)

Design an Experiment

Report Findings 

What is an expanding universe?I need lots of information. Please Help!

An expanding universe implies some physical characteristics:
1.  The bulk of atoms are made up of electrons moving about protons and neutrons ("Matter")
2.   Gravity is attractive (Matter clumps together)
3.   Time moves only forward
4.   Red Shift is apparent when measuring large distances
5.   Entropy (disorder) increases
6.   Enthalpy (energy content) decreases

So in this universe, to use a classic example, in dropping a teacup gravity causes it to move towards Earth and smash to pieces (increase entropy) while time moves forward.  In space, large clumps of matter (galaxies) are accelerting away from us (Red Shift) and energy content decreases, as the stars burn their nuclear fuel.

In contrast, a contracting universe is one where:

1.  The bulk of atoms are made up of  positrons moving about antiprotons and antineutrons ("AntiMatter")
2.   Gravity is repulsive (Matter spreads out)
3.   Time moves only backward
4.   Blue Shift is apparent when measuring large distances
5.   Entropy (disorder) decreases
6.   Enthalpy (energy content) increases

In this universe, broken china shards on the floor reassemble into a teacup (decrease entropy) while moving away from Earth (Antigravity) while time moves backward.  In space, Antimatter galaxies accelerate towards us (Blue Shift) dispersing into atoms, and  energy content increases as uniform clouds of gas in this contracting universe are squeezed together.
"A Brief History of Time,"  Stephen Hawking, 1990