Let HALF-CLIQUE = {H: H is a graph with n nodes having a clique with at least n/2 nodes}. Show that HALF-CLIQUE is NP-complete. Hint: Use the following reduction function to show CLIQUE p HALF-CLIQL7E. Given (G, k), f(G, k) = H where H is constructed from G and k in one of two ways. Let n be the number of nodes in G. If k < n/2, form H by adding (n-2k) new nodes to G and connecting each new node to every other node in H. If k n/2, form H by adding (2k-n) new nodes to G. The new nodes are isolated, i.e., they have no edges connected to them. Your solution should include steps showing: a. HALF-CLIQUE NP b. f is computable in polynomial time. c. (G, k) CLIQUE f(G, k) HALF-CLIQUE d. (G, k) CLIQUE f(G, k) HALF-CLIQUE e. HALF-CLIQUE is NP-complete

Answers

Answer 1

a. To show that HALF-CLIQUE is in NP, we need to demonstrate that given a graph H and a number m, we can verify in polynomial time whether H contains a clique with at least m nodes. This is possible by checking all subsets of nodes of size m in H and verifying if they form a complete subgraph.
b. To show that f is computable in polynomial time, we need to demonstrate that given a graph G and a number k, we can construct H in polynomial time. This is possible by following the steps in the reduction function, which involves adding nodes and edges to G based on the value of k and n.

c. To show that (G, k) is in CLIQUE if and only if f(G, k) is in HALF-CLIQUE, we need to demonstrate two things: first, if (G, k) is in CLIQUE, then f(G, k) is in HALF-CLIQUE. This follows directly from the construction of H, which ensures that if G has a clique with k nodes, then H has a clique with at least n/2 nodes. Second, if f(G, k) is in HALF-CLIQUE, then (G, k) is in CLIQUE. This follows from the fact that any clique of size n/2 or greater in H corresponds to a clique of size k or greater in G.
d. We have already shown (G, k) CLIQUE f(G, k) HALF-CLIQUE in part c.

e. To show that HALF-CLIQUE is NP-complete, we need to demonstrate that it is both in NP and NP-hard. We have already shown that it is in NP in part a. To show that it is NP-hard, we need to demonstrate that CLIQUE is polynomial-time reducible to HALF-CLIQUE. This follows directly from the reduction function f, which transforms any instance of CLIQUE into an instance of HALF-CLIQUE in polynomial time. Therefore, HALF-CLIQUE is NP-complete.

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Related Questions

At startup, Windows Server 2012 Core presents _______.

Answers

At startup, Windows Server 2012 Core presents a command window.

What is a Windows Server used for?

Windows Server is known to be a kind of a group of operating systems that is made by Microsoft that aids enterprise-level management, data storage, applications, and others.

The Command window is known to be that which gives a person  the information, it also gives instructions, and gives room for one  to be able to enter commands usually at the Command prompt.

Therefore, note that at startup, Windows Server 2012 Core presents a command window as it is the first thing that will come up.

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In which directory would a system administrator store scripts that should be run monthly by the cron daemon?

Answers

Answer: /etc/cron.monthly

Explanation:

Mary and Billy are moving away to college and both know in their hearts that they need to end their relationship. They move away with a mutual agreement to breakup and leave peacefully. What is this called

Answers

In the case of Mary and Billy, the above is called Negotiated farewell.

What is Negotiated farewell?

In the case of  Negotiated Farewell, one can say that couples are knonw to jointly create the story of the end to what we say their marriage.

Note that Negotiated Farewell is one that is made for emotionally immature or any kind of combative people. hence, In the case of Mary and Billy, the above is called Negotiated farewell.

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If a DBMS enforces a DELETE CASCADE option on the referential integrity constraint between SELLER and REALTOR in the HOMETOWN REALESTATE database, what will be the outcome after a user tries to delete the third record (R3, Cliff) from REALTOR

Answers

The outcome will be option b: ) CLIENT will have 6 records, AGENT will have 3 records.

What are client records?

Client record is known to be a form of a written composition of information that tells and documents the examination , diagnosis or others of a client.

Based on the above scenario, The outcome will be option b: ) CLIENT will have 6 records, AGENT will have 3 records.

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Deploying an application across multiple __________________ can help build a robust architecture for an application that needs to have an up-time of at least 99.5

Answers

Deploying an application across multiple regions can help build a robust architecture for an application that needs to have an up-time of at least 99.5.

What is multi-region deployment?

The Multi-Region Infrastructure Deployment is known to be one that aids customers a lot to be able to easily control updates in regards to infrastructure needed for applications that are said to be deployed in all of primary and secondary Regions.

Hence, Deploying an application across multiple regions can help build a robust architecture for an application that needs to have an up-time of at least 99.5.

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Any two differences between second generation and third generation Write any generation computer.​

Answers

Answer:


The second generation computer is based on the transistor whereas the third generation computer is based on the integrated chip.

Explanation:

Write a short program that asks the user to enter a month & prints a message based on the month

Answers

Answer:

The Code:

def month(x):

    if (x==1):

        print ("January")

    if (x==2):

        print("February")

    if (x==3):

        print("March")

    if (x==4):

        print("April")

    if (x==5):

        print("May")

    if (x==6):

        print("June")

    if (x==7):

        print("July")

    if (x==8):

        print("August")

    if(x==9):

        print("September")

    if(x==10):

        print("October")

    if(x==11):

        print("November")

    if(x==12):

        print("December")

    if(x<1 or x>12):

        print("Wrong Input! Try again")

month = int(input("Enter the month number: "))

month(month)

Explanation:

The above program is written in the PYTHON programming language.

In this program, the user inputs the number of any month, showing the month name in the output. For example,

if user enters 1, month name = JANUARY

if user enters 5, month name = MAY

and if the user enters 13, then output = Wrong Input! try again

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Every time you call a method, the address to which the program should return at the completion of the method is stored in a memory location called the ____.

Answers

Answer:

Stack

Explanation:

Every time you call a method, the address to which the program should return at the completion of the method is stored in a memory location called the stack.

For a direct mapped cache design with a 32-bit address, the following bits of the address are used to access the cache. assume a write through cache policy.
tag index offset
31-10 9-5 4-0
1. what is the cache block size (in words)?
2. 151 how many entries does the cache have?
3. 151 cod $5.3> what is the ratio between total bits required for such a cache implementation over the data storage bits?
address
starting from power on, the following byte-addressed cache references are recorded.
0 4 1 132 232 160 3024 30 140 3100 180 2180
4. [10 how many blocks are replaced?
5. what is the hit ratio?
6. list the final state of the cache, with each valid entry represented as a record of sindex, tag, data>

Answers

From the information given, the cache block size is 32. See explanation below.

How do we arrive at the cache block size?

Where the offset is 5 bits, the block size is given as:

2⁵ = 32.

Hence, the total number of blocks in the cache is 32.

How many entries does the cache have?

Note that

Total cache size = No. of entries (No. of tag bits + data bits + valid bit)

Hence,

= 32 x (22+ 256 +1)

= 8, 928 bits

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The security team at an organization looks to protect highly confidential servers. Which method does the team propose when protecting the servers against explosives?

Answers

The method that the team propose in protecting the servers against explosives is Physical Security.

What are the Physical Security Considerations?

Physical security is known to be a key part as it acts in network security and tends to protect an organization and employees.

Note that   An organization's physical components is one that can have vulnerabilities that need to be mitigated by using appropriate physical security measures by:

The use of Building and grounds control Fire risks control, etc.

Hence, The method that the team propose in protecting the servers against explosives is Physical Security.

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connection failed while opening file within cryptographic module - mbedtls_ssl_handshake returned -9984 ( X509 - Certificate verification failed, e.g. CRL, CA or signature check failed )

Answers

The connection that failed while opening file within cryptographic module - mbedtls_ssl_handshake returned -9984 ( X509 - Certificate verification failed, e.g. CRL, CA or signature check failed is known to be a kind of a TLS hanshake failing with EC.

What are cryptographic products?

These are known to be Software, hardware or what we call the firmware that is made up of one or a lot of cryptographic functions.

Note that a cryptographic product is one that is made up of a kind of cryptographic module and they also help to implements security functions (such as cryptographic algorithms),

Therefore, based on the above, The connection that failed while opening file within cryptographic module - mbedtls_ssl_handshake returned -9984 ( X509 - Certificate verification failed, e.g. CRL, CA or signature check failed is known to be a kind of a TLS hanshake failing with EC.

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find_cow(name, cows) Given a name and a Python list of Cow objects, return the Cow object with the specified name. If no such Cow object can be found, return None.

Answers

Using the computational knowledge in python it is possible to write a code that Given a name and a Python list of Cow objects

Writting the code in python:

def load_cows(filename):

     cow_dict = dict()

   f = open(filename, 'r')

   for line in f:

       line_data = line.split(',')

       cow_dict[line_data[0]] = int(line_data[1])

   return cow_dict

def greedy_cow_transport(cows, limit=10):

      trips = []

   cowsCopy = cows.copy()

   sortedCows = sorted(cowsCopy.items(), key=lambda x: x[1], reverse = True)

   while sum(cowsCopy.values()) > 0:

       ship = []

       total = 0

       for cow, value in sortedCows:

           if cowsCopy[cow] != 0 and value + total <= limit:

               ship.append(cow)

               total += value

               cowsCopy[cow] = 0

       trips.append(ship)

   return trips

def brute_force_cow_transport(cows,limit=10):

    trips = []

    possibilities = []

   for i in power_list:

       ship = []

       for j in i:

           ship_weights = []

           for k in j:

               ship_weights.append(cows[k])

               #print(ship_weights)

           ship.append(sum(ship_weights))

           #print(ship)

       if all(d <= limit for d in ship):

           possibilities.append(i)

     pruned_possibilities = []

   for k in possibilities:

       if k not in pruned_possibilities:

           pruned_possibilities.append(k)

   # now find the minimum list length:

   min_list_len = min(map(len, pruned_possibilities))

   for l in pruned_possibilities:

       if len(l) == min_list_len:

           return l

     

def compare_cow_transport_algorithms():

      greedy_start = time.time()

   greedy_results = greedy_cow_transport(cows, limit = 10)

   greedy_end = time.time()

   print('Greedy Algorithm time:', greedy_end -greedy_start)

   brute_force_start = time.time()

   brute_force_results = brute_force_cow_transport(cows, limit = 10)

   brute_force_end = time.time()

   print('Brute force time:', brute_force_end - brute_force_start)

   print('Greedy Algorithm results:', greedy_results)

   print('Number of trips returned by Greedy Algorithm:', len(greedy_results))

   print('Brute Force Algorithm results:', brute_force_results)

   print('Number of trips returned by Brute Force Algorithm:', len(brute_force_results))

   

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Choose the term that matches each definition.

: increasing capacity by adding nodes or units


: increasing capacity by upgrading individual resources to be more powerful

Horizontal Scaling
Vertical Scaling

Answers

Horizontal Scaling is the act of increasing capacity by adding nodes or units while increasing capacity by upgrading individual resources to be more powerful is called Vertical Scaling.

What is vertical and horizontal scalability?

Horizontal scaling is known to be the act of  adding more nodes while vertical scaling is a term that connote the act of adding a lot of power to one's current machines.

Therefore, Horizontal Scaling is the act of increasing capacity by adding nodes or units while increasing capacity by upgrading individual resources to be more powerful is called Vertical Scaling.

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Which epolicy orchestrator component gathers the events from the managed systems and uploads them to the epo server?

Answers

The policy orchestrator component that gathers the events from the managed systems and uploads them to the epo server is mcAfee agent.

Which ePolicy orchestrator component  is enforced?

The McAfee Agent can be described as the one that is distributed component of McAfee ePolicy Orchestrator (McAfee ePO).

It helps in downloads and enforcement of policies and it executes client-side tasks.

To find  find  McAfee agent, one can follow these steps:

View McAfee Agent Status MonitorOn the managed system,  select McAfee Agent Status Monitor. Save Contents to Desktop to save the contents of the McAfee Agent log to a file.

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What are the nuclear codes?

Answers

Answer:

Nuclear codes allow the president to prove the individual is authorized to order the launch.

Explanation:

Hope this helps!

If not, I am sorry.

Joe is examining the logs for his web server and discovers that a user sent input to a web application that contained the string WAITFOR. What type of attack was the user likely attempting

Answers

SQL Injection Attack

Given five positive integers, find the minimum and maximum values that can be calculated by summing exactly four of the five integers. Then print the respective minimum and maximum values as a single line of two space-separated long integers.

Answers

Using the knowledge in computational language in JAVA it is possible to write a code that  print the respective minimum and maximum values as a single line

Writting the code in JAVA:

import java.io.*;

import java.util.*;

import java.text.*;

import java.math.*;

import java.util.regex.*;

public class Solution {

   public static void main(String[] args) {

       Scanner in = new Scanner(System.in);

       long sum = 0;

       long max = Long.MIN_VALUE;

       long min = Long.MAX_VALUE;

       for (int i = 0; i < 5; i++){

           long n = in.nextLong();

           sum += n;

           max = Math.max(max, n);

           min = Math.min(min, n);

       }

       System.out.println((sum - max) + " " + (sum - min));

   }

}

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You need a(n) _____ to play an mp3 audio file on a desktop or laptop computer

Answers

You need a stand alone player to play an mp3 audio file on a desktop or laptop computer.

What is a stand alone player?

The standalone player is known to be a device that gives room for a person or is one that allows a Blender game to be able to run without one trying to load the Blender system.

Note that in the above, You need a stand alone player to play an mp3 audio file on a desktop or laptop computer.

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________ is installed in special, read-only memory in devices like printers or communication devices.

Answers

A firmware is installed in special, read-only memory in devices like printers or communication devices.

What is firmware and give example?

Firmware is known to be a kind of software that makes or produce the basic machine instructions that gives room for the hardware to act and be able to communicate with other kinds of software that is said to be running on a device.

Note that Firmware makes low-level control in for a lot of device's hardware and its example is microcontroller which is said to be an aspect of the microprocessor that informs the microprocessor the right actions to take.

Hence A firmware is installed in special, read-only memory in devices like printers or communication devices is the right answer.

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What is the purpose of installing updates on your computer?

Answers

The purpose of adding updates to your computer are as follows:

Making sure your computer hardware can run the newest software programsEnsuring the built-in virus protection software is up to dateRemoving bugs and glitches from your operating systemAllowing your computer to run as fast as possible

Every time a user enters a different web page url into a browser, the same web page appears. what will help in this situation?atask managerbfirewallcanti-malwareddevice manager

Answers

Every time a user enters a different web page url into a browser, the same web page appears. the issue that can help is the use of firewall.

What is firewall and how it works?

The term firewall is known to be that which helps protect a person's network from attackers.

Note that A firewall shields one's network because it work in a 24/7 filter window, and this is one that often works by scanning the data that tries to enter your network and hinder anything that may act or looks suspicious from getting through.

Hence, in the case above, Every time a user enters a different web page url into a browser, the same web page appears. the issue that can help is the use of firewall.

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In order to prevent ports that are serving network hosts from being considered as best paths, what should be enabled to block bpdus?

Answers

In order to prevent ports that are serving network hosts from being considered as best paths, BPDU guard should be enabled to block bpdus.

What are BPDU used for?

A bridge protocol data unit (BPDU) is known to be a kind of a data message that is known to be often  transmitted in a local area network to be able to know or find loops in that given network topologies.

Hence, in the case above, In order to prevent ports that are serving network hosts from being considered as best paths, BPDU guard should be enabled to block bpdus.

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. In order to prevent ports that are serving network hosts from being considered as best paths, what should be enabled to block BPDUs?

a. BPDU filter

b. BPDU guard

c. root guard

d. BPDU drop

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What are the three different types of hard drives? Briefly describe each, and list the possible configurations and device files for each type. Describe RAID level 5. What are the advantages of using RAID level 5 over other types of RAID?

Answers

The three different types of hard drives are:

SATASSD NVMe

What is the SATA drive?

This was said to be Introduced in the year 2003, SATA (or Serial Advanced Technology Attachment) is known to be a kind of a default interface that was made for a lot of desktop and laptop hard drives.

Hence, The three different types of hard drives are:

SATASSD NVMe

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Simple statistics looks catalog 3.15 LAB: Simple statistics Given 4 floating-point numbers. Use a string formatting expression with conversion specifiers to output their product and the average as integers (rounded, then as floating point numbers Output each rounded integer using the following print (1.0).tornat (your_value)) Output each floating point value with three digits after the decimal point, which can be achieved as follows print(1.3).format(your value)) Ex If the input is 3.3 10. 5.0 the output is 20722 2071. 7. 125 ACTIVITY 3151 LAB Simple statistics 0/10 main.py 1 2 - Floatinet()) - Floatinus Fotout Flatirot)

Answers

Based on the given instructions:

1. you must set the display format for all values: %0.2f

2. use f-string in this format: f"{}" and add your value in {}

3. int: convert float to integer and round: round up the number

The given code

num1 = float(input())

num2 = float(input())

num3 = float(input())

average = (num1+num2+num3) / 3

your_value = num1*num2*num3

print('%0.0f %0.0f %0.2f %0.2f' % (int(average), int(your_value), average, your_value))

# or:

print(f"{int(average)} {int(your_value)} {round(average,2)} {round(your_value,2)}")

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In this program you will draw some ASCII art using System.out.println(). Write a program that outputs exactly this drawing. ()_____ // O)___ // ) // _____/

Answers

This is known as ASCII Art. The program that give the above output is given below.

What is the program that give the above output?

The codes that resort to the above output are given below:


public class ASCIIArt{

public static void main(String[] args) {

System.out.println(" /)___");

System.out.println(" / o|___");

System.out.println(" / )");

System.out.println("/ )___/");

}

}

What is ASCII Art?

The 95 readable characters from the total of 128 established by the ASCII Standard from 1963 and ASCII compliant character sets with proprietary extra characters make up ASCII art, a visual design style that leverages computers for display (beyond the 128 characters of standard 7-bit ASCII).

The phrase is also figuratively used to describe all forms of text-based visual art. Any text editor may be used to make ASCII graphics, which is frequently used with free-form languages.

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Full Question:

See attached image.

When you group together related variables, the group is referred to as a(n) ____ of variables

Answers

Answer:

Array of variables

Explanation:

This occurs when you group together related variables

"necessarily is the mother of computer " justify this statement with respect to the evolution of computer.​

Answers

Explanation:

Computers in the form of personal desktop computers, laptops and tablets have become such an important part of everyday living that it can be difficult to remember a time when they did not exist. In reality, computers as they are known and used today are still relatively new. Although computers have technically been in use since the abacus approximately 5000 years ago,

If a few bits in an hdd sector or nvm page are corrupted, the controller can recover the correct values using ecc only if:___.

Answers

If a few bits in an hdd sector or nvm page are corrupted, the controller can recover the correct values using ecc only if option D) number of bits corrupted is low irrespective of where the corruption occurs in the sector/page.

Do hard drives have sectors?

In computer disk storage, a sector is known to be a kind of a subdivision that is made up of a track that can be seen on a magnetic disk or what we call the optical disc.

Note that Each sector is one that saves a fixed amount of what we call the user-accessible data.

Note that  the sector is seen as the smallest physical storage unit that can be found on the disk, and also on most file systems and thus when  a few bits in an hdd sector or nvm page are corrupted, the controller can recover the correct values using ecc only if option D) number of bits corrupted is low irrespective of where the corruption occurs in the sector/page.

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See full question below

If a few bits in an HDD sector or NVM page are corrupted, the controller can recover the correct values using ECC only if

A) the bit corruption is limited to the data portion of the sector/page.

B) the bit corruption hasn't occurred in the ECC of the sector/page.

C) the bit corruption hasn't occurred in the ECC or the header of the sector/page.

D) number of bits corrupted is low irrespective of where the corruption occurs in the sector/page.

Javascript and java are really just two slightly different names for the same language.
a) True
b) False

Answers

Answer:

False

Explanation:

JavaScript is language used along with html documents.

Java is a full-fledged programming language that handles applications.

Anonymity on the internet has lowered the cost of rudely confronting people. what has happened to the supply of rude confrontations?

Answers

The thing that has happened to the supply of rude confrontations is that  The supply has increased, shifting down and to the right.

What supply means in economics?

Supply in economics is known to be seen as the full amount of a given product or service that a given  supplier is known to offers to consumers at a specific point in time and a given price level.

Hence, The thing that has happened to the supply of rude confrontations is that  The supply has increased, shifting down and to the right because Anonymity on the internet has lowered the cost of rudely confronting people.

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Anonymity on the Internet has lowered the cost of rudely confronting people. What has happened to the supply of rude confrontations? a) The supply has decreased, shifting up and to the left. b) The supply has increased, shifting up and to the left. C) The supply has decreased, shifting down and to the right. d) The supply has increased, shifting down and to the right. Question 46 (1 point) Figure: Supply Shift Saved Price $100-

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Apply a solid line border, using the default line color, to the Pie chart legend. pair of bean-shaped organs located between the peritoneum and the back muscles a patient who is breathing on his own has a fenestrated trach tube with a cuff. which precaution must the nurse instruct the student about when caring for this patient? How many grams of H2 are needed to react with 3.15 g of N2 (r^4-3r^3+6r-18)/(r-3) Synthetic Division I really need help with this question x + 2/3 =9/10 Have vehicles gotten more fuel-efficient over the years? between 1960 and 1999 the size and shape of automobiles in the united states has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline. Year, t 1960 1970 1980 1990 1995 1997 1998 1999 gallons consumed per passenger car 668 760 576 520 530 538 544 552 determine the average rate of change, in gallons of gas per year, from 1960 and 1999 and then determine what the result means in this situation. A. 0. 33gal/year; the average fuel consumption per year of a passenger car in the u. S. Decreased by a third of a gallon per year. B. 0. 33 gal/year; the average fuel consumption per year of a passenger car in the u. S. Increased by a third of a gallon per year. C. 2. 97 gal/year; the average fuel consumption per year of a passenger car in the u. S. Increased by nearly 3 gal/year. D. -2. 97 gal/year; the average fuel consumption per year of a passenger car in the u. S. Decreased by nearly 3 gal/year. QuestionIsabella and Penelope are both draining their backyard swimming pools. Isabellas pool holds 1,700 gallons and she is draining the water at a rate of 2.4 gallons per minute. Penelopes pool holds 1,350 gallons and she is draining the water at a rate of 1.6 gallons per minute. How long will it take to have the same amount of water in both pools? how many minutes? The aim of the Federal Home Loan Bank Act was to *O encourage new constructionO make it easier for banks to foreclose on farms and homesO prevent farmers and homeowners from losing their propertyO increase the value of homes and farms What types of cooling systems do EVs and HEVs have? The overview of ethical codes and methods for handling ethical issues or conflicts with a code of ethics is called the _____.PLEASE HELP I HAVE BARELY ANY TIMEResponsesA. statement of purposeB. appendixC. preambleD. abstract How do you find the end behavior of a graph with Asymptotes? What 4 European countries were involved in colonization in the New World? Which of Newton's Laws explain why the table moves at 0.25 m/s/s when you push on it Initially, Michel and Asaro found plutonium with the iridium in the KT boundary. Which importantfeature of science proved they were incorrect?peer-reviewreplicationhypotheses developmentnew observations In Iagos last speech the audience learns of another reason for Iagos hatred of Othello. What is it? Put the correct verb ending on each stem.1. Yo habl2. T mir3. Usted regres4. l ense5. Ella trabaj6. Nosotros contest7. Ustedes escuch8. Ellos tom9. Ellas estudi 5. Why would a measurement be reported as 18.0 mL instead of 18 mL? What are two advantages to rating attributes as a way to measure performance? Matching vocabularyJobOccupationCareer1.a chosen field of work in which youadvance over time2. a broad category of work3. paid work that gives you experiencea relationship in which someonewho is more experienced guidessomeone who has less experience4.