Squealer talks about "The joy of service" and the "dignity of labor". What is ironic about that in Chapter 7?

The irony is addressed by Orwell in Chapter 7 when he writes, "All that year the animals worked like slaves. But they were happy in their work; they grudged no effort or sacrifice, well aware that everything that they did was for the benefit of themselves and those of their kind who would come after them, and not for a pack of idle, thieving human beings."

It is true that they are not working for a pack of idle, thieving human beings. Instead they are working for a pack of idle, thieving pigs. The pigs have moved into the farm house and started trading with neighboring farms. When some of the animals remember the commandment that "no animal shall sleep in a bed", the commandment is simply changed to "no animal shall sleep in a bed with sheets." Squealer assures the animals that all the sheets have been removed. So the work continues and the animals "volunteer" to work up to 60 hours a week. Of course, if they don't "volunteer" their food rations are cut in half. Thus, the animals are coerced into the "joy of service" by the need for sheer survival.

What were the original prophecies given to Macbeth and Banquo?

The witches prophecy to Macbeth is straightforward:

"First Witch. All hall, Macbeth! hail to thee,
Thane of Glamis!
Sec. Witch. All hail, Macbeth! hall to thee,
Thane of Cawdor!
Third Witch. All hail, Macbeth! that shalt be
king hereafter." (Shakespeare) 

For Banquo, the message is more veiled: 

"Third Witch. Thou shalt get kings, though
thou be none:
So, all hail, Macbeth and Banquo!"

When the two of them talk about the prophecy, it is clear that Banquo will be father to kings, and therefore greater than Macbeth.

"Ban. Were such things here as we do speak
about?
Or have we eaten on the insane root
That takes the reason prisoner?
Macb. Your children shall be kings.
Ban. You shall be king." (Shakespeare) 

How do you predict the ones digit for the standard form of the number 7 to the 100 power?it's exponents

There is a pattern to this powers, if you use the base to the power of the index.

Like this:

1. 7^1=7


2. 7^2=49


3. 7^3=343


4. 7^4=2401


5. 7^5= 16807

As you can see, there is a pattern of 7,9,3,1 in the ones digit as it progress to the 100th power. For the power of 4, the ones digit is simply one. And as what cburr said above, 100 can also be divided by the number 4 (100/4=25)

So, we can say the last digit (ones) for the 100th power would be 1

In Macbeth, how does the sergeant characterize Macbeth in Act I? What images does he associate with Macbeth?

From the sergeant's description of Macbeth in battle, we can conclude that Macbeth is a strong and valiant soldier who does not retreat, despite the odds against him. Macbeth fights furiously in defense of his King and country, his sword smoking with "bloody execution." Fighting his way through the forces arrayed against him, Macbeth finds the traitor Macdonwald  and "unseamed him from the nave to th' chops, ' And fixed his head upon our battlements." Macbeth does not hesitate in battle; he is relentless in his destruction of the enemy. When Macdonwald is defeated, Macbeth's position, along with Banquo's, is then overwhelmed by a new assault of Norway's army. Rather than retreat, Macbeth fights even more furiously, winning the battle.

In his recounting of Macbeth in battle, the sergeant compares Macbeth (and Banquo) to an eagle in relation to a sparrow and to a lion in relation to a hare. Furthermore, he says Macbeth and Banquo were "[A]s cannons overcharged with double cracks [explosives]."

Approximately, how many African-Americans went to college in the 1800s?

In the 1620s and 1630s, European missionaries began efforts to convert Africans to Christianity and provide them with a basic education. The Pennsylvania Quakers began organizing educational meetings for people of African heritage in the early 1700. Then in 1774, they started a school for blacks in Philadelphia. “By the mid-1800s, the city had become a center for black learning, with public, industrial, charity, and private schools providing an education for more than 2,000 African American students.” Freedmen's organizations were formed to provide educational opportunities to former slaves. Because of the laws passed by Congress in the 1860s, more than 2,500 schools were begun in the South.  Soon, colleges began to opened their doors for Black Students and in the 1870s, religious organizations and other programs played  a part in the establishment and support of many early black institutions of higher learning. By 1900, more than 2,000 black Americans had graduated from college. That may sound like a lot but in 1790, “the black population approached 760,000, and nearly eight percent of all blacks in America were free. Free blacks, however, were bound by many of the same regulations that applied to slaves.”

Why does Hamlet say the ghost is the devil? What makes him say that?

When Hamlet says, "the devil hath power to assume a pleasing shape", he is interpreting a verse from the Bible that says "for even Satan disguises himself as an angel of light."( II Corinthians 11:14). During Elizabethan times, ghosts were thought of as evil spirits. This belief is echoed by Horatio when he warns Hamlet not to follow the ghost at the beginning of the play. He says:

What if it[ the ghost] tempt you toward the flood, my lord,(75)

Or to the dreadful summit of the cliff

That beetles o'er his base into the sea,

And there assume some other horrible form,

Which might deprive your sovereignty of reason

And draw you into madness?

Act I, Scene IV, Lines 75-80

Thus Hamlet calls the ghost the devil because that was a common belief at the time.

What is the summary for Chapter 7 of The Absolutely True Diary of a Part-Time Indian?This chapter is titled "Rowdy Sings the Blues".

Junior tells Rowdy about his plans to go to Reardan.  He knows that Rowdy might get angry, but Rowdy "was (his) best friend and (Junior) wanted him to know the truth".  He tells Rowdy that he is leaving the rez, and that he wants Rowdy to go with him.  Rowdy at first does not take Junior seriously.

When Junior thinks about Reardan, he has a picture in his mind of the school against which his own school played flag football, basketball, and baseball last year, and lost embarrassingly every time.  The only student from his own school who had any success at all in any of those games was Rowdy.  Junior remembers that even in the Academic Bowl competition in which the schools engaged the year before, his own school lost by "a grand total of 50-1".  When Junior thinks about the kids from Reardan, he thinks of kids who are "beautiful and smart and epic...filled with hope".

Rowdy "absolutely hate(s)" the idea of Junior going to Reardan.  He becomes violently angry, and when Junior reaches out to him, Rowdy starts crying.  When Rowdy realizing that he is crying, he begins to scream, making a sound that is "the worst thing (Junior'd) ever heard...it was pain, pure pain".  Junior tells Rowdy that he has to go, or he will die, and that Rowdy can go with him, but Rowdy, overcome by rage, punches his best friend in the face (Chapter 7).