P/NP: VERTEX COVER, CLIQUE/INDEPENDENT SET
Consider the Clique problem restricted to graphs in which every vertex has degree at most 3. Call this problem Clique-3.
(a) (1) Show that Clique-3 is in NP.
(b) (3) Describe an O(|V |) time algorithm for solving Clique-3.

Answers

Answer 1

If we consider a clique problem restricted to graphs in which every vertex has a degree at most 3, (a) (1) Clique-3 is in NP. (b) (3) There is an O(|V|) time algorithm for solving Clique-3.

(a) (1) To show that Clique-3 is in NP, we need to demonstrate that given a solution, it can be verified in polynomial time. In the case of Clique-3, a solution would be a set of vertices that form a clique (a complete subgraph) in the input graph.

To verify this, we can simply check if all pairs of vertices in the solution set are connected by edges, which can be done in polynomial time. Therefore, Clique-3 is in NP.

(b) (3) An O(|V|) time algorithm for solving Clique-3 can be described as follows: Start with an empty set of vertices as the potential clique. Iterate through each vertex in the graph. For each vertex, check if it is connected to all the vertices already in the potential clique. If it is, add the vertex to the potential clique.

Continue this process until all vertices have been processed. The resulting set of vertices will form a maximum clique in the graph. Since we iterate through each vertex once and check its connections, the algorithm runs in O(|V|) time, where |V| represents the number of vertices in the graph.

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Related Questions

methods of reducing thr world's growing temperature​

Answers

Greenhouses require proper temperatures for optimal growth and production. Temperatures that are too high or too low will reduce photosynthesis, which is the ability of the plant to make food for itself and fuel growth. Controlling temperature with environmental control computers is the most accurate, especially with larger growing operations.

Properly size your HVAC system.Have enough heating and cooling capacity for your greenhouses.  Install horizontal air flow (HAF) fans. Use shade curtains during high-light and high-temperature months.Measure temperature correctly. Try to locate environmental control sensors closer to the crop and in the center of the zone.we must improve our ways of traveling between places, either with the use of bicycles or the use of vehicles and electric trains in order to avoid the use of gasoline vehicles in order to reduce emissions from carbon.

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Reuse bottles, plastic containers, and other items bought at the grocery store. Reusing water bottles, yogurt cups, bread ties, and other items is being conscious about what is already out there. It will lessen having to purchase other items that would fulfill the same function. Try to use disposable products into some other form. Just don’t throw them away.

You can recycle almost anything for e.g., paper, bottles, aluminum foils, cans, newspapers. Recycling of these unwanted things is a great earth saving tip. By recycling, you can help in reducing landfills.

Reduce Waste

Landfills are the major contributor of methane and other greenhouse gases. When the waste is burnt, it releases toxic gases in the atmosphere, which results in global warming. Reusing and recycling old items can significantly reduce your carbon footprint as it takes far less energy to recycle old items than to produce items from scratch.

Upcycle your Furniture
Upcycle tables, furniture, and other outdated items to keep landfills clean. Consider using recycled materials like pallets or repurposing your old furniture instead of buying new ones.

Bring your own Shopping Bags
Plastic bags are destructive to the environment. They take hundreds of years to break down, contaminate soil and waterways, and cause widespread marine animal deaths. Cities and states around the country have enacted plastic-bag bans or charges on single-use bags to combat the problem. Switch to reusable bags and use them consistently to contribute.

Replace Regular Incandescent Light Bulb

Replace regular incandescent light bulb with compact fluorescent light (CFL) bulbs. They consume 70% less energy than ordinary bulbs and have a longer lifetime.

What is the current temperature in buffalo new york?

Answers

The current temperature in Buffalo, New York, EE.UU is 3 ° C or 37 °F

Climate of Buffalo, New York

In Buffalo, the summers are hot and partly cloudy and the winters are freezing, snowy and mostly cloudy. During the course of the year, the temperature generally ranges from -7°C to 26°C and rarely drops below -15°C or rises above 30°C.

The temperate season lasts for 3.7 months, from May 29 to September 20, with an average daily high temperature above 70°F. The warmest month of the year in Buffalo is July, with an average high of 26°C and low of 18°C.

The cold season lasts for 3.3 months, from December 5 to March 13, with an average daily high temperature below 5°C. The coldest month of the year in Buffalo is January, with an average minimum temperature of -6°C and a maximum of -0°C.

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How should
government weigh the
tensions between
political expression and
national security
concerns?

Answers

Balancing political expression and national security concerns can be a challenging task for governments because on the one hand, political expression is a fundamental right that is protected by many countries' constitutions and international human rights conventions and on the other hand, national security is a critical concern that governments must prioritize to protect their citizens and prevent violence or other harmful actions.

How can Government Weigh the Tension between Political Expression and National Security?

To weigh these tensions between political expression and national security, governments must first establish clear and objective criteria for determining when political expression becomes a threat to national security. This could include a range of factors, such as the likelihood of violence or the potential impact on critical infrastructure or public safety.

Once these criteria have been established, governments should carefully consider the specific circumstances in which political expression may pose a risk to national security. This could involve evaluating the nature and content of the political expression, the context in which it is occurring, and the likelihood that it may lead to violence or other harmful actions.

Overall, the key to balancing political expression and national security concerns is to establish clear and objective criteria, carefully consider the specific circumstances in which these tensions arise, and take steps to protect individuals' rights while also safeguarding national security.

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How are Muslims in the United States given the freedom to pray five times a day?
A)The U.S. Constitution
B)The Bill of Rights
C)The Magna Carta
D)The Preamble to the Constitution

Answers

Answer:

The Bill of Rights

Explanation:

The 1st Amendment of the Bill of Rights gives citizens of the United States the freedom to practice their religion.

Which of the following pieces of legislation enabled remote deposit capture?
Select one:
a. Federal Reserve Act
b. Financial Services Modernization Act
c. Check Clearing for the 21st Century Act
d. Interstate Banking Branching and Efficiency Act

Answers

Remote Deposit Capture (RDC) is a way to deposit funds from a check into a bank account, using an imaging system. It enables banks and credit unions to scan checks and transmit the check images to the bank, avoiding the need to physically deliver the paper check.

The Check Clearing for the 21st Century Act, or Check 21 Act, is the piece of legislation that enabled remote deposit capture. The law was enacted in 2004 to update the process of check clearing for the modern age. It allows banks to create “substitute checks” from electronic images of original paper checks that can be used in place of the original. This means that banks can transmit electronic check images to each other and not have to physically transport paper checks, which can save time and money. Hence, the correct option is "Check Clearing for the 21st Century Act."

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What body of water is considered a crossroads for its location and cultural diffusion between Europe, Asia and Africa

Answers

Answer:

Constantinople

Explanation:

Constantinople was considered a crossroads for trade because there were goods coming from three different continents, Europe, Asia and Africa.

The largest mountain range in Europe is the __________. A. Alps B. Pyrenees C. Apennines D. Mt. Vesuvius

Answers

Answer:

A. Alps

Explanation:

search it on google.

Answer:

Alps

Explanation:

The American system of limited government in which the people are the ultimate source of government is called a?

Answers

It’s a popular sovereignty

What was war of crime about

Answers

Answer:

A war crime is an act that constitutes a serious violation of the laws of war that gives rise to individual criminal responsibility.

Explanation:

Answer:

A war crime is an act that constitutes a serious violation of the laws of war that gives rise to individual criminal responsibility. An example of crimes would be intentionally killing civilians or prisoners, torturing, destroying civilian property, taking hostages, performing a perfidy, raping, using child soldiers, pillaging, declaring that no quarter will be given, and seriously violating the principles of distinction, proportionality, and military necessity.

Explanation:

Name three problems caused when an area is depopulated.​

Answers

1. Less jobs/money
2. Pest/weed invasions
3. Reduction of biodiversity

Answer:

A decrease in birth rate

High level of emigration

Low level of export

eula is willing to speak-up when she feels like she has a point to make and is defending a cause she believes in. eula will score high on:

Answers

Eula will score high on argumentativeness.

What is the focus of argumentativeness?

Argumentativeness is characterized as an usually stable trait that predisposes people to advocate their own ideas while concurrently disputing the opinions of others in communication circumstances.

What distinguishes verbal aggressiveness from argumentativeness?

Verbal aggression is the propensity to criticize another person's perception of themselves. Argumentativeness is the propensity to identify problems and zealously support a viewpoint.

What sort of communication is argumentative?

While all argumentation is assertive, not all assertiveness is argumentative, hence argumentative communication is regarded as a subset of assertiveness. Argumentative persons promote their positions on contentious matters and verbally criticize the divergent viewpoints of others.

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Follow Jaysuels on twitch

Answers

Answer:

f4f my twotter is The Kid D but i might change it to qt dee

Explanation:

All of these are major functions of governments EXCEPT

A) Maintaining private property
B) Keeping the population in order
C) Providing services for citizens
D) Providing security for the people

Answers

Answer:

Keeping the population in order

All of the options listed are major functions of governments, except for Maintaining private property. Option A is the correct answer.

While governments play a role in establishing and enforcing laws to protect private property rights, it is not necessarily a major function of governments. The primary responsibility lies in ensuring the overall well-being and welfare of its citizens. Option A is the correct answer.

Governments have the responsibility to maintain law and order within a society. This includes enforcing laws, resolving conflicts, and ensuring public safety. This function is essential for maintaining social stability and ensuring the peaceful coexistence of individuals within a society. They are responsible for providing various services and infrastructure to meet the needs of their citizens. This includes services such as education, healthcare, transportation, and public utilities. By providing these services, governments aim to enhance the quality of life and promote the well-being of their citizens. One of the primary functions of governments is to ensure the security and protection of their citizens. This includes maintaining armed forces and law enforcement agencies to defend the nation against external threats and maintain internal security.

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Segregation can be voluntary or involuntary. True or False?

Answers

Segregation was not done at one's will. It was enforced by law. Therefore the answer is false. (I'm sorry if I am wrong I haven't dug much into this subject lol)

The canadian government helps preserve the use of french by requiring all official documents to be written in both english and french. the provincial government of the canadian province of quebec has implemented further regulations that require that signs have french letters larger than english letters. why is the size of letters important?

Answers

An official requirement for all documents to be written in both English and French languages by the Canadian government helps in preservation of the French language. Furthering this purpose, the Canadian Provincial government of Quebec requires the French letters to be larger than English ones. This is because the size of the letters has a crucial role in the preservation and promotion of the language.

The following reasons can be attributed to this -

In the public signage (signs, posters, displays etc.), it is natural for the larger font to attract more attention towards it. Hence, the French language will command general curiosity and interest from the audience or the viewers of the signs.This kindled interest among people will in turn drive them to attempt to learn more about the French language to quench their curiosity, thus leading to popularization of the language.Also, the French letters, being bigger in size, will have more and prior visibility compared to the English part. This too can have a two -fold psychological impact. At first, it shall facilitate efficient reading for the people who know French, giving them a slightly upper hand. As for those who are unable to understand, will have to see the smaller English version. This will establish the need to learn and use French in their minds while also subconsciously establishing the French language as superior to English.

Thus, having French letters written in larger size is going to dramatically support the government's agenda of preserving and promoting French.

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I need a quick essay about the issue of government,equality,independence and rights in 4 paragraphs. Please help you’ll get as much points!!

Answers

The Declaration of Independence and the Promise of Liberty and Equality for All

In the aftermath of the Seven Years’ War (1756–1763), the British government enacted a series of new laws, including new taxes, to be applied to its colonies in North America. Because the colonists had no direct representation in the British government, many protested the legality of these laws. They then began a serious public conversation about the nature and origin of their rights. Many believed that rights are grounded in nature—that is, in human nature, or natural law—and are therefore applicable to all humankind and higher than any laws made by human authority. The idea that rights derive from human nature has deep roots in western political thinking and was embraced by many thinkers of the Enlightenment, particularly the English political philosopher John Locke. This view of natural rights was invoked by the North American colonists as they explained and justified their revolution against British rule in the Declaration of Independence. In this way, the Declaration of Independence did much more than formally announce the colonists’ separation from Great Britain: it was also a tightly compressed philosophical argument that clearly articulated equality as the fundamental moral fact of human nature. According to the Declaration, this inherent equality, along with natural rights, formed the basis and limits of a just government. The principles of equality, liberty, and justice served as the foundation of the new nation and are therefore referred to as Founding principles.

dissadvantage of mussunderstandung and conflict

Answers

SOMEONE PLEASE HELP THIS QUESTION IS DUE AT 10:50 AND ITS CURRENTLY 10:32

SOMEONE PLEASE HELP THIS QUESTION IS DUE AT 10:50 AND ITS CURRENTLY 10:32

Answers

Using only these supplies, the question can Michelle investigate with an experiment is Does a tablet charge faster with a two-foot-long charging cable or a five-foot-long charging cable? The correct option is b.

A charging cable for a smartphone or other portable device. The cable has a device connector on one end and plugs into the socket of a USB charger on the other (Mini USB, Micro USB, Apple dock connector, etc.).

Your smartphone and tablet will use cables and ports that are either micro-USB and USB-C on one end and USB-A on the other. You can learn more about the USB type that your device employs. Some cables that come via older models will only have the plug and not the USB-A connector. These plugs are typically much lower in amperage.

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What three British laws did most Patriots (Rebels) feel violated their rights as British citizens?

Answers

The three British laws that most Patriots (Rebels) feel violated their rights as British citizens were taxation without consent, quartering soldiers in citizens' homes, and denying colonists the right to a trial.

As Britain attempted to maintain control over the colonies through taxes and regulations, calls for independence spread throughout the 13 colonies. Patriots were colonists who supported independence from Great Britain. Patriots were mostly supported in the colonies of New England.

Patriots believed that recent British laws enacted on American colonies were unjust and infringed on their rights. Many Patriots came from the middle and lower classes, lived in the New England Colonies in rural areas and worked as fishermen and farmers. Patriots desired independence from the Crown and were willing to use violence if necessary.

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what does the conflict in ephesus teach us about the way christ's kingdom advances in the present age

Answers

Paul's address to the Ephesian elders in Acts 20:17-38 teaches us that a minister's primary duty is to faithfully preach the gospel and protect their flock from false teachers.

Paul emphasized that his ministry was not motivated by worldly power or gain, but by a sincere desire to serve God and build up the church. He also reminded them of their duty to protect the church from false teachers who may try to lead them astray.

Paul also stresses the importance of humility and integrity in ministry, reminding the elders that they should be examples of godliness and holiness in all their actions. He urged them to be vigilant and to guard their flock from such false teachings. This passage teaches us that a minister's responsibility is to remain faithful to the gospel, to guard the flock from false teachers, and to serve the church with integrity and humility.

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Which of the following are the results of the action of sodium-potassium pumps in a neuron? (select all that apply)
A. There is a buildup of K+ ions inside the cell.
B. A concentration gradient of K+ ions is created.
C. Na+ ions get pumped out of the cell at the same rate at which K+ ions are pumped in.
D. The concentration of Na+ ions increases within the cell and generates electrostatic pressure.

Answers

The results of the action of sodium-potassium pumps in a neuron are as follows:a) There is a buildup of K+ ions inside the cell.b) A concentration gradient of K+ ions is created.c) Na+ ions get pumped out of the cell at the same rate at which K+ ions are pumped in.

Neurons, or nerve cells, are specialized cells that transmit messages or signals to and from the brain and the rest of the body. Na+/K+ ATPases, also known as sodium-potassium pumps, are present in all neurons to maintain ion concentrations inside and outside the cells. Sodium-potassium pumps function to transport three Na+ ions out of the cell while simultaneously transporting two K+ ions into the cell to maintain the cell's negative resting potential.As a result of the action of sodium-potassium pumps in a neuron, a concentration gradient of K+ ions is generated. Na+ ions get pumped out of the cell at the same rate at which K+ ions are pumped in. A buildup of K+ ions inside the cell is also observed. As a result of this pumping, the concentration of Na+ ions within the cell decreases while the concentration of K+ ions increases.

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what would be most characteristic of a non-life-threatening allergic reaction

Answers

A moderate allergic reaction, also known as a non-life-threatening allergic reaction, is characterized by localized symptoms that do not jeopardize a person's health.

Foods, drugs, bug bites, and environmental variables might cause these reactions. Itching, redness, and minor swelling at the exposure site are the most frequent signs of a non-life-threatening allergic reaction. It can also cause a rash, hives, or welts. Nasal congestion, sneezing, and itchy, watery eyes may occur. These symptoms normally create discomfort but don't affect breathing. Systemic symptoms including trouble breathing, throat constriction, or a sudden drop in blood pressure are rare in non-life-threatening allergic responses. However, symptoms should be monitored and medical treatment sought if they intensify or if there is any doubt about the reaction's severity.

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What is part of an effective introduction?

a piece of evidence to support the claim
an interesting quote or fact about the topic
a reason the reader should agree with the writer
an explanation of how the reader can help

Answers

Answer:

an interesting quote or fact about the topic

Explanation:

An effective introduction is done by writing about the general idea of the essay topic, this helps the reader have a better understanding of what the paper is gonna be about, and what ideas will be discuss throughout the body of the essay.

50 points!!!!!!!
What was the network of abolitionists and safe houses that helped people escape slavery called?

A) the Underground Railroad
B) the slave codes
C) the manumission society
D) the antebellum period choose letter

Answers

Answer:

A: the Underground Railroad

Explanation:

Answer:

The underground railroad

Explanation:

Slavery was a key concern in US before 1960Many unbearable assaults were happened over the slaves who are usually blacks .They were migrated from Africa and Asia .

Give two examples of information that a cartographer could display on a thematic map.

Answers

Answer: Common examples are maps of demographic data such as population density. When designing a thematic map, cartographers must balance a number of factors in order to effectively represent the data.

Explanation:

unions tend to have all of the following effects on pay except

Answers

unions tend to have all of the following effects on pay except reducing overall wages.

Unions generally have significant effects on pay and working conditions for their members. However, there is one effect that is not typically associated with unions in regard to pay. To clarify, unions tend to have the following effects on pay:

- Reducing overall wages for union members

The primary objective of unions is to protect and improve the working conditions, benefits, and wages of their members. They achieve this through collective bargaining, where they negotiate contracts with employers to establish fair wages, hours, and working conditions. As a result, unions usually have a positive impact on wages, leading to higher salaries for union members compared to non-union workers.

Some of the positive effects of unions on pay include:

1. Increased wages: Union members typically earn more than non-union workers, as unions negotiate for higher salaries on behalf of their members.

2. Pay equity: Unions help to ensure equal pay for equal work, reducing wage disparities between different groups of workers.

3. Benefits and protections: In addition to higher wages, unions often negotiate for better benefits, such as health insurance, retirement plans, and paid leave, which can indirectly improve a worker's overall compensation package.

4. Wage standards: Unions can set industry-wide wage standards, helping to raise the pay of non-union workers as well.

To summarize, unions tend to have various positive effects on pay for their members, with the exception of reducing overall wages. Instead, unions work to increase wages, promote pay equity, and secure better benefits and protections for their members.

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Scientists have discovered a new planet. The planet is in a solar system whose star is similar in size to the sun and is about as far from the star as Venus is from the sun. The planet is similar in size to Earth, and its atmosphere is similar in thickness to Earth’s atmosphere. The atmosphere is composed almost entirely of carbon dioxide and methane.

In three to five sentences, make a hypothesis about the temperature on the planet’s surface. Explain your answer using information about the planet’s location and atmosphere.

Answers

There is a new planet other than the discovered planet known in the solar system. There is a planet whose star is similar in size to the sun. There is no planet that is similar to the planet earth in the solar system. The new planet is hotter than the closest planet to the sun.

The research have shown that a new planet has been discovered and its star shares similar size with that of the sun. Considering its location, it is believed that the temperature in the newly discovered planet will be cooler or better still moderate as its atmosphere is similar in thickness to Earth’s atmosphere.

The said planet could be said to be habitable as it shares similar atmospheric carbon dioxide with that of the earth.

What is a hypothesis?

A hypothesis is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories.

Therefore, the correct answer is as given above.

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what specific challenge did Floridians face during the Great Depression

Answers

Unemployment rates were rising

Explain five ways through which the rights of an individual can be violated​

Answers

Human rights are violated in a great number of ways. Genocide, war crimes, crimes against humanity, aggression, sexual abuse,and many other ways

Joe Biden is the main cause of this too(thought you should know)

The Battle of Palmito Ranch took place CLOSEST to which of the events on this timeline? A: Ft. Sumter Attacked B: Battle of Atlanta ends C: Lee Surrenders to Grant D: Battle of Gettysburg ends

Answers

Answer:

A ft sumter attack

Explanation:

i took the test in usatest prep

The Battle of Palmito Ranch took place closest to Sumter Attacked . The appropriate response is option A.

What is Battle of Palmito Ranch?

Some people believe that the Battle of Palmito Ranch, often referred to it as the Battle of Palmito Hill, was the last combat action of the American Civil War.

Because it was the final land battle of the American Civil War, the Texas battle of Palmito Ranch is notable. It is unclear why Union soldiers kept attacking after the war was over since both Union and Confederate leaders were informed that Confederate General Robert E. Lee had submitted.

As the final significant conflict between Union and Confederate soldiers, the Battle of Palmito Ranch is said to have occurred. Given that the Battle of Columbus in April 1865 is largely regarded as the final conflict of the Civil War, the conflict is typically referred to as a post-Civil War conflict.

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simple interest on a $198,562 mortgage at 3.99%? a binding minimum wage tends to a. cause a labor surplus. b. cause unemployment. c. have the greatest impact in the market for teenage labor. d. all of the above are correct. Question 1: Derive average and marginal cost curves from the total cost curve.Question 2: Derive long-run average and marginal cost curves from the short-run average and marginal cost curves respectively.Question 3: What is the necessary condition for producer equilibrium by using iso-quant and iso-cost curves and also draw the diagram. What is the benefit to doing epidemiological studies?A.) Patients do not have to unwillingly be exposed to harmful substancesB.) Patients are never exposed to harmful substances Kristen is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?All students at her high school Use your bicycle to go to the market near your home. Come back to your home by using a different path. Measure and note down the time in seconds and distance in meters, from home to market, and from market to home. Calculate your speed for approach and return. what is a question that is easier to answer using a stem-and-leaf plot than a dot plot? A company owes $15,000 to the bank as of November 30. The company is preparing a cash budget for December and anticipates $30,000 in cash receipts and $34,500 in cash disbursements during December. The expected cash balance on November 30 is $12,000. The company has an agreement with its bank to maintain a cash balance of at least $9,000. To maintain the $9,000 minimum balance, during December must : A. Borrow $4,500, B. Borrow $1,500, C. Repay $1,500, D. Repay $7,500 7. Does the boiling temperature ever exceed 100 C during steam distillation? Explain. 8. Can steam distillation of ethanol be done using a mixture of ethanol and water? Why or why not? 11. Should steam distillation be considered as a method of isolation and purification of an organic liquid that has a vapor pressure of 760 torr at 46 C? Steve pushes a crate 20 m across a level floor at a constant speed with a force of 200 N, this time on a frictionless floor. The velocity of the crate is in the direction of the force Steve is applying to the crate. What is the net work done on the crate Which of the following equations has a slope of -2 and passes through the point (3,-4)? A thin glass slide (n = 1.53) that is 0.470 m thick and surrounded by air is illuminated by a monochromatic electromagnetic wave. The wave is incident along the normal to the slide.Please show step by step work please and thanks!Part AWhat is the lowest frequency of the wave that will produce an intensified reflected wave?Express your answer in hertz to three significant figures.Part BWhat is the lowest frequency of the wave that will produce a cancelled reflected wave? HELP ME PLEASE I WILL GIVE BRAINLIEST!!!Unique selling propositions are designed to make a companys product stand out in the crowd. Lets say a certain company builds a USP for its over-the-counter allergy medicine as the only solution for those pet allergies. Other medications may work just as well for pet allergies, but this company positions itself as the only medication for this problem. Is it unethical for a company to present itself this way? Or, is it just another way to advertise? how can sonar best be used to monitor the hydrosphere "I only regret I have but one life to lose for my country," was said by: Find an equation for (-8,1) parallel to x-4y=4 When Walter left the Dietrichson house after the insurance papers were signed, what happened? In a ________, employees operate remotely from each other and from their managers. Over what interval is the function in this graph constant?OA. -3x2B. -4sxs-2OC. -2x3OD. -5x5 Which math expreion mean the um of an unknown number and 15 A. 15. X B. X 15 C. X - 15 D. 15 divided x