College Algebra, Chapter 7, 7.4, Section 7.4, Problem 62

An outdoors club is purchasing land to set up a conservation area. The last remaining piece they need to buy is the triangular plot shown in the figure. Use the determinant formula for the area of a triangle to find the area of the plot.







Based from the graph, the triangular plot has a vertices $(1000,2000), (2000,6000)$ and $(5000,4000)$. Using the formula for areas of triangles using determinants, we get


$
\begin{equation}
\begin{aligned}

\text{area } =& \pm \frac{1}{2} \left| \begin{array}{ccc}
1000 & 2000 & 1 \\
2000 & 6000 & 1 \\
5000 & 4000 & 1
\end{array} \right|
\\
\\
=& \pm \frac{1}{2} \left[ 1000 \left| \begin{array}{cc}
6000 & 1 \\
4000 & 1
\end{array} \right| - 2000 \left| \begin{array}{cc}
2000 & 1 \\
5000 & 1
\end{array} \right| + 1 \left| \begin{array}{cc}
2000 & 6000 \\
5000 & 4000
\end{array} \right| \right]
\\
\\
=& \pm \frac{1}{2} \left[ 1000 (6000 \cdot 1 - 1 \cdot 4000) - 2000 (2000 \cdot 1 - 1 \cdot 5000) + (2000 \cdot 4000 - 6000 \cdot 5000) \right]
\\
\\
=& \pm \frac{1}{2} (-14,000,000)

\end{aligned}
\end{equation}
$


To make the area positive, we choose the negative sign in the formula. Thus, the area of the triangular plot is

area = $7,000,000 ft^2$

What symbol is critical to the theme of heritage in "Everyday Use"?

Names are also symbols of heritage in the story "Everyday Use." Mama, the narrator of the story, names her older daughter Dee. However, when Dee, who is better educated than her mother and younger sister, Maggie, comes to visit, Dee says her name is now Wangero Leewanika Kemanjo. Dee claims that the name Dee is symbolic of her oppression, so she takes an African-influenced name. In abandoning her name, Dee also abandons family tradition. She is named after her aunt Dicie, Mama's sister. Her aunt was named after her Grandmother Dee, who was named after her mother. The name "Dee" goes back in the family to the Civil War. By changing her name, Dee is abandoning her family's traditions and heritage. Her mother can't even pronounce her daughter's new name, and it's as if Dee doesn't appreciate the value of what came before her. 

The Johnson family quilts are a crucial symbol to understand heritage in this story. For Mama and Maggie, these quilts are meant to be used, just as heritage is something that continues to exist and is alive in the present. Dee, on the other hand, considers the quilts to be representative of a heritage that is in the past. She thinks the quilts should not be used as they were intended; instead, they should be preserved and displayed. Mama and Maggie do not put their heritage on display; rather, they live it by using these quilts (as well as other items that have been handmade by members of the family through the years) every day; this accounts for the story's title, "Everyday Use." Dee thinks it's "backward" of Maggie to use the quilts because they will fall apart, but Mama and Dee believe it only makes sense to use them and remember the people who made them (Dee doesn't even know the family stories). Although Maggie and Dee both appreciate the quilts, they see those quilts—and the concept of heritage—quite differently.

What is a summary for the article "Preventing Criminal Recidivism Through Mental Health and Criminal Justice Collaboration"?

This article assesses how criminal recidivism can be tackled through collaboration between criminal justice and mental health professionals. There are a number of intervention strategies used to help treat those with serious mental illnesses within communities, such as courts for the mentally ill, specialized parole and probation, conditional release, and so on. Most of these services require the person, legally, to attend sessions and adhere to the strategy. However, studies have found that there is little evidence of these "jail diversion" programs actually reducing recidivism in the mentally ill. Likewise, among such strategies used in civil law cases to prevent recidivism, only one of two trials showed reduced rates of arrest and violence. Arguably, how effective these "leverage-based" programs can be will depend upon how well mental health and criminal justice staff can collaborate. Often these professionals have very different goals, and the involvement of criminal justice staff in mental health programs may result in threats and sanctions which can cause work to backslide. As such, new programs have been set up to help the groups integrate. This means there is a need for a framework to help them build these types of programs in a way which will be effective.
The article then goes on to set out a set of "steps" for what has been proven to work in terms of collaboration between mental health and criminal justice providers, incorporating best practice from both fields. These steps are:

Engagement. It is vital to ensure that "justice-involved individuals" are completely engaged in the process of collaboration and share the common goal of their criminal justice and mental health staff. Within this approach, the patient and the professionals must all choose to work towards both public health and public safety. Accountability should be provided for all involved and a good rapport should be built with the client by ensuring they understand the purpose of what is being offered to them and how their information will be used. Poor understanding on the part of the patient can diminish chances of success. Individuals should be catered to on an individual level, including using visual aids of explanation where necessary.


Assessment. It is very important to identify and target "crimogenic" risk factors in perpetrators or potential perpetrators of crime, whether or not they are mentally ill. Patients should be assessed for history of antisocial behavior or personality, criminal associates, problems at work and school or in a relationship, substance abuse, lack of recreational hobbies, and similar. This "risk assessment" should be conducted in any program, as it helps predict likelihood of recidivism and gear the professionals' approach to the particular patient. It also assesses how likely the patient is to commit violence to others or suicide and establishes which elements in the patient's background need to be addressed in treatment.


Planning and treatment. It is vital that criminal justice and mental health staff identify who should address what. Mental health professionals generally address substance abuse, work/school problems, relationship problems, lack of recreational pursuits, and they recommend treatment for any disorders, family-based intervention, placements and support for the unemployed. They also treat factors such as trauma and homelessness which can increase recidivism. But it is less clear who should help address the thinking that generates antisocial behavior. Criminal justice professionals sometimes develop cognitive behavioral treatment regimes among prison populations to help change attitudes, and some of these have been promising, but mental health professionals outside of prison populations rarely use such interventions. Instead, they tend to use behavioral management principles. Given that both have been successful, good planning would indicate that the two professional groups should work closely together to develop a treatment plan which includes intervention from both.


Monitoring. Monitoring has been proven to reduce recidivism, but only where a sense of collaboration is encouraged. Threats and sanctions make the patient feel attacked, whereas face-to-face meetings which encourage mutual trust help the patient feel supported in adhering to the program.


Problem solving. There will always be setbacks involved in setting a mentally ill patient on a program of this kind. It is important to address these problems through collaboration between mental health professionals, criminal justice staff, and the patient himself. Options should be weighed up and analyzed by both sets of staff. They should then attempt to recommend therapeutic alternatives to punishment, as behavioral problems can often relate to an underlying and untreated issue in the patient. Rewards and the gradual removal of sanctions have also been shown to be more effective than increased threats and punishments in helping a patient adhere to a program.


Transition. This is the point in the process at which the criminal justice staff step back from their role in supporting the patient. This is a significant point for patients and can thrust them back into relapse, so it is important to collaborate and prepare clients for this change with extra outpatient appointments and the involvement of family members as additional emotional resources. Appointing a "representative payee" for potential substance abusers can also help support these people and reduce likelihood of reoffending.

In conclusion, then: current outpatient mental health treatment does not greatly reduce criminal recidivism on its own, because only 18% of crimes among the mentally ill are motivated directly by that mental illness. In order to effectively prevent recidivism among the mentally ill, both criminal justice and mental health staff must understand which issues drive recidivism in each specific patient and how best to approach these using shared and community resources. There is a lack of systematic assessment of crimogenic risk factors among mental health professionals; likewise, correctional officers have a poor understanding of mental health issues. As such, it is necessary for the two groups to collaborate and share their knowledge in order to devise programs which will be successful.

Antonio dose not have money to lend to Bassanio. What does he do?

At the beginning of the play, Bassanio approaches Antonio and asks him to fund his trip to Belmont. Bassanio explains to Antonio that he has wasted most of his money living beyond his means but has a plan to become rich. Bassanio tells Antonio that there is a wealthy unmarried woman named Portia living in Belmont who has inherited a large sum of money from her deceased father. Bassanio plans on traveling to Belmont and winning her hand in marriage. When Bassanio asks Antonio to fund his trip, Antonio explains to his friend that all of his money is tied up in his investments, which include the cargo on his merchant ships that are currently out at sea. In order for Antonio to get the money to fund Bassanio's trip to Belmont, he makes a deal with the Jewish moneylender, Shylock, who loans him three thousand ducats. As part of their deal, Antonio agrees that if he forfeits on the loan, he will give Shylock a pound of his flesh.

What are examples of structural grammar sentence analysis?

Examples of structural grammar applied to sentence analysis will show the syntax relationships between speech units that constitute the structure of each sentence. The smallest speech units that determine syntax relationships in language are phonemes and morphemes and words. Sentence element word classes and syntax relationships are designated by standard symbols used for structural grammar analysis. The two examples that follow the symbols (below) have limited detail since diagrams aren't supported by this format:
(Sb) is the symbol for sentence Subject. (P) is for sentence Predicate. (H) is for Head. (M) is for Modifier. (V) is for Verb. (C) is for Complement. (Sub) is for subordinate component. (D) is for Dependent component. These are additional standard symbols, Det: determiner; pres: present tense; Adj: adjective; Prn: pronoun; Aux: auxiliary verb.
ExamplesThe can has a broken tab.  The can (Sb) has a broken tab. (P)The (M) can (H) has (V) a broken tab. (D)... a broken (M) tab. (H)The (Det) can (Noun) has (Verb, pres) a (Det) broken (Adj) tab (Noun). I will tag the black horse.I (Sb) will tag the black horse. (P)I (H) will tag (V) the black horse. (D)... the black (M) horse. (H)I (Prn) will (Aux) tag (Verb, pres) the (Det) black (Adj) horse (Noun).
In structural grammar, phonemes are the smallest speech unit of language that determine word meaning: bit is a different thing from mit and kit because of the phonemes /b/ and /m/ and /k/, although all these words are in the noun word class. The verbs tap and tag can be changed to the noun word class tab (e.g., soda can tab) and tack by the substitution of the phonemes /b/ and /ck/, substituting for the phonemes /p/ or /g/. This change in word class results in a change in syntax relationships.
Morphemes are the smallest grammatical speech unit of language that determine meaning, word class and syntax relationship. For example, the morpheme free, of the adjective word class, can be changed to the noun word class by the addition of the morpheme -dom, a noun forming morpheme, forming the noun freedom.
Syntax relationships between speech words carry the meaning communicated by language. Structural grammar does not, however, consider semantic meaning a function of grammar. The word class and the syntax relationships between words can be changed by the addition, removal or substitution of phonemes and morphemes.
https://www.britannica.com/topic/morpheme

https://www.britannica.com/topic/phoneme

Which is bigger RNA or DNA?

DNA is bigger than RNA.
DNA stands for Deoxyribonucleic Acid, and RNA stands for Ribonucleic Acid. DNA is a double-strand helix with a long chain of nucleotides, whereas RNA is only a single-strand helix with a shorter chain of nucleotides. Thus, their shapes and appearance look quite different.
Another main difference between DNA and RNA is that DNA contains the sugar deoxyribose, whereas RNA contains the sugar ribose (this is apparent in their names). The ribose contained in RNA is considered "normal" because it contains an oxygen atoms that is attached to the carbon atoms. However, the deoxyribose in DNA is considered a different type of sugar because it lacks an oxygen atom.
Their bases are also slightly different; both DNA and RNA contain the bases adenine, guanine, and cytosine, but DNA's fourth base is thymine, and RNA's fourth base is uracil. 
 
https://www.ncbi.nlm.nih.gov/books/NBK26887/

How did the Slave Revolution in Haiti in 1804 motivate slave rebellions in the United States?

The Haitian slave rebellion in 1804 was part of the Haitian Revolution, which lasted from 1791-1804. This anti-colonial rebellion was successful, and had an impact on the institution of slavery in the Americas, especially the United States. The rebellion resulted in the founding of the free state of Haiti, in what was previously known as the French colony of Saint-Domingue. In 1804, the revolution ended with the massacre of much of the remaining white population.
This revolution had a significant impact on the Atlantic world, and as news of it traveled to the United States, many slaves or abolitionists in America were motivated to engage in similar rebellions with the purpose of freeing slaves of the United States. By seeing a successful slave revolt so close to the United States, it was clear that when united, the enslaved population could rise up against those that claimed authority over them.
There are several mass-slave rebellions often referenced in American history that took place in the nineteenth century after the rebellions in Haiti began, but prior to the abolition of slavery:

German Cost Uprising, 1811 – a slave driver named Charles Deslondes and 25 other slaves attacked the family and owner of the plantation they worked on in the Orleans area. The owner escaped, but the slaves used the plantation as a base for further rebellion. The rebels grew to great numbers, and after two days, many were imprisoned, killed, sold, or returned to their masters.

Nat Turner’s Rebellion, 1831 – a slave named Nathaniel Turner and 70 other slaves and free blacks attacked the homes and families of those who had enslaved them in Virginia. It is estimated approximately 60 white people were killed before the rebellion ended and Turner went into hiding. Turner was executed with many followers; many of the rebels were sold into other regions.