What are the metaphors in Raymond’s run?

A metaphor is a figure of speech that makes a comparison between two things that are unrelated or different while still sharing a common characteristic. It is possible to make the comparison without using the words "like" or "as." If either of those words is used, then it is a special type of metaphor called a simile. "Raymond's Run" uses similes and "normal" metaphors.
In the fourth paragraph, Squeaky is telling readers about her brother, Raymond. He is mentally challenged, and he has an active spirit and imagination. We are told that he pretends that the "curb is a tightrope," which is a metaphor. Later in the story, Squeaky tells her readers that the city is a metaphorical "concrete jungle."
During Squeaky's race, she looks over at Raymond, and readers get a sentence that contains two similes that are describing Raymond. He is first compared to a gorilla and then to a dancer.

Then I hear Raymond yanking at the fence to call me and I wave to shush him, but he keeps rattling the fence like a gorilla in a cage like in them gorilla movies, but then like a dancer or something he starts climbing up nice and easy but very fast.

Which of these sentences from The Lady or the Tiger? by Stockton shows a cause and effect relationship?

Of the four sentences presented in the image attached, the cause and effect sentence is the fourth (bottom) sentence shown.  
A hint to readers that the fourth sentence is a cause and effect sentence is the fact that it starts with the word "if."  Sentences that are written in "if, then" format are often cause and effect statements.  That's one reason why I have my sixth grade students write scientific predictions in "if, then" format.  That format shows a cause and effect relationship between the two halves of the sentence.  
The fourth sentence pictured does the same thing.  There is a direct cause and effect between the first half of the sentence and the second half of the sentence.  If the person chooses a certain door, then he is guaranteed a violent and horrible death from a wild animal.  What was the effect? Death.  What was the cause of that death? Choosing the wrong door. 

In order to find the sentence which shows a cause and effect relationship, we must first understand what a cause-and-effect sentence is. A cause-and-effect sentences tells us about an action that occurred and what resulted because of that action. Therefore, in these sentences we are looking first for an action that makes something else happen (the cause) and the result of that action (the effect). Think of it as what happens when you accidentally knock a cup filled with water off a table. The cause is the action of your arm or hand hitting the cup and the effect, or the result of you hitting the cup, is that the cup falls to the ground and spills water onto the floor.
In the examples from your question above, we can go through each sentence one by one and decide if there are any cause-and-effect relationships in them. The first three sentences are explanatory or descriptive sentences that simply describe a situation or explain the abilities and surroundings of a person. In those sentences, there are no actions that take place, just descriptions. There are also no "sentence connectors" which are words such as "because" "since" "if" and "then" that show cause and effect. Those are words to look for when trying to find a cause-and-effect sentence. We cannot ask the question "what happens if ____?" because there is no action to ask that question about. Therefore, there is no cause and effect in any of these sentences.
If we look at the last sentence on your paper, we can immediately see one of those connector words ("if"), so this could very well be our cause-and-effect sentence, but let's read it through and find the cause and effect to confirm that this is the right answer. The cause in this sentence would be the action that makes something happen. The action is the person opening a door. What happens if they open the door? Out would come a hungry tiger that would spring on him and tear him to pieces as a punishment for his guilt. That is the effect. Therefore, this is our cause-and-effect sentence, which details an action and what happens as a result of that action.

How did the photocopier change society?

The photocopier was invented in October 1937 when Chester Carlson came up with the process called electrophotography, which was later called xerography in 1989 – developed from a Greek word that meant “dry writing." In order to further develop xerography, Carlson teamed up with a photo-paper manufacturer in New York that was called Haloid Corporation. Haloid grew over the years into what is today known as the Xerox Corporation. It worked to further improve the process of xerography, coming up with the first automated xerographic machine called Copyflo in 1955. The Copyflo was actually the world’s first office photocopier machine.
The photocopier has helped to automate the process of document reproduction. The processes used to reproduce documents in the pre-xerographic times required expensive supplies. Also, xerography brought with it the ability to use untreated office paper, which lowered total document reproduction costs. Copies of documents could then be sorted or stapled together, for storage purposes.
While copying makes document reproduction more accessible to people, it further enhances frivolous copying and resource wastage. Employees misuse the process by making copies of their personal documents and other non-important items just for the sake of it. This results in paper and ink wastage. Also, because anybody anywhere can make copies at minimal costs, there is increased violation of copyright laws for written texts. Through photocopying, written texts containing company secrets can easily be leaked to outsiders with dire consequences.
The photocopier has also helped to enhance communication by facilitating the growth of the print media. Small groups of people, such as school clubs, can come up with their own internal publications meant to put forth ideas that interest them.
https://www.smithsonianmag.com/history/duplication-nation-3D-printing-rise-180954332/

What are the differences between social policy and social welfare policy?

"Social policy" is a phrase often used to describe policy that is related to society as a whole. It is usually intended to address some need or advance a societal priority. Education policy, for example, is social policy. So are policies such as affirmative action, which was instituted in the United States in the wake of the civil rights movement to promote employment opportunities for minorities. Title IX, the legislation that required equal access to educational programs for women, is another example of social policy.
"Social welfare policy" is usually used to refer to policy aimed at addressing people's material circumstances. Temporary Assistance for Needy Families (TANF), Medicaid, and Social Security are examples of social welfare policies. They support people who struggle, due to their circumstances, to provide for their families through public funds. SNAP, or the Supplemental Nutrition Assistance Program, is another example. It provides financial support for families to purchase nutritious food. It is an example of a direct aid program that attempts to benefit society by providing funds to help people who need them the most. These programs, then, are a specific kind of social policy.
https://www.usa.gov/benefits

Although the terms are often used interchangeably, social welfare policy is theoretically a subset of social policy. In other words, all social welfare policies are social policies but not all social policies are social welfare policies. The difference though is more theoretical than practical as it is rare to have social policies that are not believed to contribute to the well-being of society.
One set of social policies that one could argue are not necessarily social welfare policies are those regulating gender and sexuality. For example, whether restrooms are unisex or single gender and whether biology or gender identification should determine use of single-gender bathrooms a matter of social policy, as are gay marriage, the legal age of marriage, whether women are compelled to take their husbands last names, whether married couples hold property in common or can still hold property as individuals, or whether polygamy is legal. Various laws and policies vary across different regions and countries are intended to promote different ideals of sexual conduct, but while these are social policies, they are not necessarily social welfare policies but instead efforts to sustain local cultural norms. Racial segregation would be an example of a social policy informed by racism that did not enhance social welfare but actually harmed many United States citizens.
On the other hand, social policies that aim to reduce child hunger, provide prenatal care, reduce crime, or promote universal education all would be considered social welfare policies.

There is a difference between social policy and social welfare policy. A reference to social policy includes both the goals of collective responsibilities and the services that are needed to carry out these responsibilities. Social policies include the rules and the laws that define what public social welfare is and that authorizes groups to try to achieve the purpose of the social policies. An example of a social policy would be a tax credit to help families pay for the cost of child daycare or the cost of higher education.
Social welfare policy refers to the responsibilities that the government and the society have to each other. It includes the structures and measures that allow for these responsibilities to occur. These responsibilities could be carried out by either informal organizations or by formal organizations. These could be public organizations, for-profit organizations, or private nonprofit organizations. Examples of social welfare policies would include Social Security, Medicare, and Medicaid.

What is the red-headed league? How does Jabez Wilson find out about it? What are the conditions for getting and keeping a place in the league?

Jabez Wilson finds out about the Red-Headed League through an advertisement which had been placed in the newspaper. This advertisement said that a salary of £4 per week would be payable to members of the League who met its conditions, which were:
1. Members had to be sound in body and mind;
2. Members had to be over the age of twenty-one years, and;
3. Members had to be red-haired.
The advertisement also stipulated that membership of the league was open only to men, suggesting that red-haired women would not be eligible.
£4 a week was a significant sum in those days, which is why the advertisement caught Wilson's attention. Those wishing to become a member of the League would have to perform "nominal services" and would have to make an application in person at a stated time and place.
The League, supposedly, was founded by a red-haired American gentleman who wanted to leave his fortune to other men with red hair. When Wilson applies and is accepted, he is told that the work entails copying out the Encyclopaedia Britannica four hours a day.
This, naturally, struck Wilson as strange, particularly when, one morning, he arrived and found the offices closed and locked. In the course of his investigation, Holmes discovers that the League is in fact an invention; the criminals who thought of it had simply wanted to keep Wilson out of his shop so that they could receive stolen goods from a bank vault through a tunnel in the floor of said shop.

Single Variable Calculus, Chapter 7, 7.1, Section 7.1, Problem 30

Determine the explicit function for $f^{-1}$ if $f(x) = \sqrt{x^2 + 2x}$ for $x > 0$ and use it to graph $f^{-1}$, f and the line $y = x$ on the same
If $f(x) = \sqrt{x^2 + 2x}$, then

$
\begin{equation}
\begin{aligned}
f^{-1} (x) \quad \Longrightarrow \quad x &= \sqrt{y^2 + 2y}\\
\\
x^2 &= y^2 + 2y\\
\\
\text{by completing the square}\\
\\
x^2 + 1 &= y^2 + 2y + 1\\
\\
x^2 + 1 &= (y+1)^2\\
\\
\pm \sqrt{x^2+1} &= y + 1\\
\\
y &= -1 \pm \sqrt{x^2 + 1}
\end{aligned}
\end{equation}
$

We got the two values of $y$, however, the function is defined only for $x > 0$. The domain of $f$ is $x > 0$ and its range $y > \sqrt{0^2 + 2(0)} \Longrightarrow 0$. Thus, the domain of $f^{-1}(x)$ is $x > 0$ and range $y > 0$. Thus, the domain of $f^{-1}(x)$ is $x > 0$ and range $y > 0$. If we check both $y$,
when $ x = 1$,

$
\begin{equation}
\begin{aligned}
y &= -1 + \sqrt{1^2 + 1}\\
\\
y &= 0.4142
\end{aligned}
\end{equation}
$


when $ x = 1$,

$
\begin{equation}
\begin{aligned}
y &= -1 - \sqrt{1^2 + 1}\\
\\
y &= -2.4142
\end{aligned}
\end{equation}
$

Hence, $f^{-1}(x) = -1 + \sqrt{x^2+1}$

Who got killed in Grover Park?

It's just another ordinary day at work for aging 87th Precinct detective Steve Carella and his partner Artie Brown. They're out on the streets, investigating a particularly heinous—and unusual—homicide. A young woman's body has been found in Grover Park; she's been strangled to death. If this isn't bad enough, the autopsy reveals that the murder victim is a nun. Matters get even more complicated when it turns out that this sister of mercy had breast implants. It seems that Sister Mary Vincent—for it is she—had quite a few personal and financial problems in her life.
This complex, disturbing case will require Carella to use all his powers of deduction and draw upon his vast experience as a detective to get to the truth of the matter. That he's able to this while dealing with a serial burglar who leaves behind cookies for his victims, makes us admire Carella all the more.