is the same conclusion necessarily true if n is even or if a is odd? give a proof or a counterexamples in each case
Answers
In the following question, "if n is even or if a is odd," the conclusion that a and b have the same parity is still "true."
is the same conclusion necessarily true if n is even or if a is odd When n is even or if a is odd, is the same conclusion necessarily true, yes. There are two cases to consider here:
Case 1: When n is even When n is even, then n = 2k for some positive integer k.
Substituting n = 2k in the equation given,
we get:a^(2k) - b^(2k) = (a^k - b^k)(a^k + b^k)
Since a^(2k) and b^(2k) are both perfect squares, it follows that (a^k - b^k)(a^k + b^k) must also be a perfect square.
This means that a^k - b^k and a^k + b^k are both perfect squares.
We can now use the same argument as in the previous
case to conclude that a and b must have the same parity.
Case 2: When a is odd When a is odd, then a = 2k + 1 for some integer k. Substituting a = 2k + 1 in the equation given,
we get:(2k + 1)^n - b^n = (2k + 1 - b)(1 + (2k + 1) + ... + (2k + 1)^(n - 1))The second factor on the right-hand side is a sum of odd terms and hence must be odd. It follows that (2k + 1)^n - b^n must also be odd.
But the only way this is possible is if b is odd as well. Therefore, if n is even or if a is odd, the conclusion that a and b have the same parity is still true.
For more such questions on parity
https://brainly.com/question/13138872
#SPJ11
Related Questions
Female CEOs In 1990, there were 3 women among the CEOs of Fortune 500 companies. In 2009, this number had risen to 15 women.
(Source: H. Ibarra and Hansen, M., Women CEOs: Why So Few?, The Conversation-Harvard Business Review, Dec 21, 2009)
a. What was the change in the number of Fortune 500 women CEOs between 1990 and 2009?
b. What was the percentage change in the number of Fortune 500 women CEOs between 1990 and 2009?
Answers
Answer:
a. The change in the number of Fortune 500 women CEOs between 1990 and 2009 can be calculated by subtracting the number of women CEOs in 1990 from the number of women CEOs in 2009. In 1990, there were 3 women among the CEOs of Fortune 500 companies, and in 2009, this number had risen to 15 women. Therefore, the change in the number of Fortune 500 women CEOs between 1990 and 2009 was:
15 - 3 = 12
So, there was an increase of 12 Fortune 500 women CEOs between 1990 and 2009.
b. The percentage change in the number of Fortune 500 women CEOs between 1990 and 2009 can be calculated by dividing the change in the number of women CEOs by the original number of women CEOs in 1990 and then multiplying by 100 to express the result as a percentage. Using the values calculated above, we get:
Percentage change = (Change in number of women CEOs / Original number of women CEOs) * 100 Percentage change = (12 / 3) * 100 Percentage change = 400%
So, there was a 400% increase in the number of Fortune 500 women CEOs between 1990 and 2009.
Explanation:
The change in the number of women CEOs of Fortune 500 companies between 1990 and 2009 was 12. The percentage change during this period was a 400% increase.
Explanation:The subject of this question is Business. In 1990, there were 3 women among the CEOs of Fortune 500 companies, while in 2009, this number had risen to 15 women. The change in the number of Fortune 500 women CEOs between 1990 and 2009 was an increase of 12.
The percentage change in the number of Fortune 500 women CEOs between 1990 and 2009 can be calculated using the formula:
Percentage Change = (New Value - Old Value) / Old Value * 100.
In this case, the percentage change would be ((15 - 3) / 3) * 100 = 400%.
https://brainly.com/question/33936680
#SPJ2
At the time of the Age of Exploration, who were the first people to inhabit Canada? Vikings Celts Inuit Indians
Answers
Answer:
The Spanish were among the first Europeans to explore the New World and the first to settle in what is now the United States. By 1650, however, England had established a dominant presence on the Atlantic coast. The first colony was founded at Jamestown, Virginia, in 1607.
Follow me please
Mark brainliest
What is the formation of the executive according to the Constitution of Nepal?
Answers
The executive power of Kingdom of Nepal is, consistent to the Constitution and law, unconditional within the Council of Ministers.
Read the bolded sentence in the passage. advise a gr. 12 learner on how to find
a balance between the new-found freedom and responsible behaviour.
3x2 (6)
Answers
It is crucial to develop a balance between freedom and responsibility to one's parents and academics. A student can keep their balance in a number unexpected ways.
1) Discipline - devise a schedule that separates time for studying from other fun pursuits. You will be disciplined and succeed in life if you adhere to the schedule.
2) Improved focus through higher concentration leads to better results in all activities. Yoga can be practiced for concentration if you have trouble focusing.
3) Time - Give everything time. In order to retain excellent mental and emotional health, going out with friends is just as crucial as studying.
4) Maintain a positive attitude- Doing so will help you move forward, accomplish all outstanding duties, and prevent stress.
To know more about freedom:
https://brainly.com/question/4077647
#SPJ4
Virtually all drugs that are used to treat psychopathology work by influencing: neurotransmitters electrical conductivity of neurons brain structure neuronal structure
Answers
Drugs used to treat psychopathology influence neurotransmitters, which are the body's chemical messengers.
What is the function of neurotransmitters?They are molecules of the nervous system responsible for transmitting messages between neurons and to the muscles, being converted into chemical signals, causing different responses in the receptors, influencing behaviors and emotions.
Therefore, drugs used to treat psychopathology influence the response of neurotransmitters such as serotonin and dopamine, associated with feelings of happiness and pleasure.
Find out more about neurotransmitters here:
https://brainly.com/question/26387085
After discrimination training, an organism’s operant responding is determined by…
The excitation to respond produced by the S+
The inhibition to respond produced by the S-
The excitation produced by the S- and the inhibition produced by the S+
The excitation produced by the S+ and the inhibition produced by the S-
Answers
After discrimination training, an organism's operant responding is determined by the excitation produced by the S+ and the inhibition produced by the S-.
Discrimination training involves teaching an organism to respond to one stimulus (S+) but not to another (S-). The S+ is associated with a positive consequence, such as food or praise, while the S- is associated with a negative consequence, such as a loud noise or punishment. Through repeated exposure to these stimuli and consequences, the organism learns to discriminate between them and adjust their behavior accordingly. As a result, the S+ elicits an excitatory response and the S- elicits an inhibitory response, ultimately determining the organism's operant responding.
To learn more about discrimination, visit:
https://brainly.com/question/29553191
#SPJ11
A double-blind procedure is used in an effort to reduce the likelihood that _____ of condition will influence the results; therefore, both the participants and the administrators of treatments are unaware of which treatments are being provided.
Answers
A double-blind procedure is used in an effort to reduce the likelihood that bias of condition will influence the results; therefore, both the participants and the administrators of treatments are unaware of which treatments are being provided.
A double-blind procedure is a research method in which neither the participant nor the administrator is aware of who is receiving the treatment being studied. Double-blind research is considered the gold standard in research since it eliminates experimental bias, resulting in reliable results.
The significance of a double-blind procedure is that it eliminates the potential for bias in research. When researchers or experimenters are aware of which group is receiving a particular treatment, they may unintentionally act in ways that influence the outcome of the study, resulting in experimental bias.
Double-blind research is considered the gold standard in research since it eliminates experimental bias, resulting in reliable results.
To know more about administrators visit:
https://brainly.com/question/32491945
#SPJ11
If you were asked to redesign the one dollar coin, who would you put on the coin and why.
Answers
Answer: I would put Pocahontas on the one dollar coin
Explanation:
She helped the Jamestown settlement
Determine whether the item was or was not a direct result of the French and Indian war sever years war
Answers
Following are the items that happened or not happened as a result of the French and Indian War or Seven Years War:
Direct Result
Proclamation of 1763
Whiskey Tax
Alien & Sedition Acts
NOT a Direct Result
Tea Act
Sugar Act
What was Seven Years War?The Austrian Habsburgs tried to reclaim Silesia, which Prussia's Frederick the Great had stolen from them, and this led to the Seven Years' War. Fighting for control of North America and India in the context of Great Britain and France's overseas colonies also contributed to the conflict.
The ratification of the treaties of Hubertusburg and Paris marked the end of the Seven Years' War. By signing the Treaty of Paris, France gave up all of its claims to Canada and ceded Louisiana to Spain, while giving Upper Canada, Spanish Florida, and a number of other French overseas assets to Britain.
Learn more about Seven Years War from here:
https://brainly.com/question/904638
#SPJ1
prejudice is an action; discrimination is an attitude. TRUE/FALSE
Answers
The given statement "prejudice is an action; discrimination is an attitude" is false because prejudice and discrimination are both concepts related to attitudes and actions, but their definitions are not accurately reflected in the statement provided.
Prejudice refers to preconceived opinions, attitudes, or beliefs held by individuals or groups about others based on their perceived membership in a particular social category (e.g., race, gender, religion). It involves forming judgments or stereotypes about others without sufficient evidence or knowledge.
Discrimination, on the other hand, refers to actions or behaviors that treat individuals or groups unfairly or differentially based on their perceived social category. It is the act of acting upon prejudiced attitudes or beliefs by treating individuals or groups unequally or denying them certain rights, opportunities, or privileges.
Therefore, prejudice is an attitude or belief, while discrimination is the action that stems from those attitudes or beliefs.
To know more about prejudice:
https://brainly.com/question/31431721
#SPJ11
How does the act of alexander disguising her gender advance the plot? cite evidence from the text to support your answer.
Answers
Some slaves in the tale had to dissimulate and run from their owners. The Rising Action, which is Alexander's attempt to conceal her gender, moves the plot along.
What is the plot?The story's principal conflict—survival during their escape and emigration to a new country—was sparked by a scenario in which Alexander assumed a false identity. The story's suspense was increased.
It should be noted that Alexander ultimately benefited from keeping her name a secret because she was one of those who were herself traveling to Nova Scotia when the crisis was finally resolved.
Learn more about Alexander at:
https://brainly.com/question/25136542
#SPJ1
(T/F) based on research, identify the statements about married people as either
Answers
Based on research, it is true that married individuals tend to live longer than their single counterparts, which is statement (a). Married women also report more emotional satisfaction than single women, which is statement (b).
However, it is false that married people experience increased mental illness compared to single people, which is statement (c). In fact, studies have shown that single people are at higher risk for developing mental health problems. It is also false that married men suffer from more drinking problems than single men, which is statement (d). Studies suggest that single men actually have higher rates of alcohol use disorders. Finally, it is false that married individuals experience less life satisfaction than single individuals, which is statement (e). Overall, research suggests that marriage can provide numerous benefits for individuals, such as increased social support and improved physical and emotional well-being.
Learn more about disorders :
https://brainly.com/question/30004431
#SPJ4
The complete question is :
Based on research, identify the statements about married people as either true or false.
(a)Married men and women live longer than their single counterparts.
(b)Married women report more emotional satisfaction than single women do.
(c)Married people experience increased mental illness compared to single people.
(d)Married men suffer from more drinking problems than single men do.
(e)Married individuals experience less life satisfaction than single individuals do.
Moral Science
Mention the 10 factors that help us achieve excellence
i) ____________________________________________
ii) ____________________________________________
iii) ____________________________________________
iv) ____________________________________________
v) _____________________________________________
vi) ____________________________________________
vii) ____________________________________________
viii) ____________________________________________
ix) ____________________________________________
x) _____________________________________________
Answers
Answer:
Have the hunger for excellenceBelieve that you can do itBuild concrete strategy & plansBenchmark against the bestLearn from the bestDo not limit yourselfGo all out; Work really hardFocus your effortsBe adaptableNever give upWhich societies gained the most as a result of mangol period? Which societies gained the least?
Answers
Answer:
The societies which gained during the Mongol period were those who were actively involved in trading due to the Mongol reopening of the Silk Road trading routes between China and Europe which allowed exchange of goods and services which made them richer along the trade paths including Western Africa, East Asia and Europe.
The societies which were negatively impacted by the Mongol period were those who resisted its expansion into Western europe, East Asia. The Mongol empire had a strong and sophisticated army which were able to carry out deadly and tactical attacks.
Answer these question in a complete sentences and no links:)
1.What usually happens as the human population increases?
2. Why do rain forests often suffer the most from human impacts?
3.What are two ways humans can help the environment?
Answers
2. Humans damage wildlife habitat in the rainforests, causing animals and plants to be homeless
3. recycle, reduce amount of waste, reuse the same containers, bottles, using less plastic
which best explains the mesopotamian practice of placing ziggurats at the center of their city-states?which best explains the mesopotamian practice of placing ziggurats at the center of their city-states?the stepped architecture was designed to designate different levels of social hierarchy.it looked best there.leaders valued religion and wanted a prominent place to pay tribute to local gods.mesopotamians believed that demons could not reach the center of a circle, so they put the ziggurat as close to the center as possible.
Answers
The best explanation for the Mesopotamian practice of placing ziggurats at the center of their city-states is that leaders valued religion and wanted a prominent place to pay tribute to local gods. Option (d)
Ziggurats were massive stepped pyramids that served as religious centers and were believed to be the dwelling places of the gods. As such, they were considered to be the most important structures in Mesopotamian cities. Placing them at the center of city-states allowed for easy access for citizens to make offerings and participate in religious ceremonies.
Additionally, the central placement of the ziggurat would have emphasized the importance of religion in the daily lives of Mesopotamians.
Learn more about ziggurats
https://brainly.com/question/2515747
#SPJ4
Full Question: Which of the following best explains the Mesopotamian practice of placing ziggurats at the center of their city-states:
a) The stepped architecture was designed to designate different levels of social hierarchy.
b) It looked best there.
c) Leaders valued religion and wanted a prominent place to pay tribute to local gods.
d) Mesopotamians believed that demons could not reach the center of a circle, so they put the ziggurat as close to the center as possible.
what is eco- tourism ?
why do people travel ?
Answers
Answer:
Ecotourism is a form of tourism involving visiting fragile, pristine, and relatively undisturbed natural areas, intended as a low-impact and often small scale alternative to standard commercial
Explanation:
.because They want to experience something unfamiliar and leave with new skills or knowledge. ... People may travel to learn something specific: a new language, a new cuisine, aspects of a different culture, or a deeper appreciation of faith or spirituality.
Which is the most credible source for a biographical essay on the deeds of Joan of Arc?
a book about Joan of Arc published in 1980
a .net website about Joan of Arc that does not list an author
a wiki site on Joan of Arc's political role, updated in 2019
a 2019 encyclopedia article on Joan of Arc's military role
Answers
Answer:
A
Explanation:
Answer:
The answer is "D"
Explanation:
Which of the following are among the primary considerations when determining the mode in which a firm enters a foreign market
Answers
Rely on strategic alliances or joint ventures are among the primary considerations when determining the mode in which a firm enters a foreign market.
What does starting a new business mean?Those businesses that are in the first stages of creation and growth are generally referred to as new ventures or entrepreneurial ventures. They frequently are in the process of building their customer base and releasing their first goods or services to the market.
What kinds of businesses are there?The three most prevalent varieties of venture capital companies are angel investors, seed investors, and growth investors. Wealthy people who invest their own money in businesses are known as angel investors.
To know more about Venture visit:
https://brainly.com/question/28462236
#SPJ4
Can someone explain to me what liberalism means but can you explain it saying it with your own words?
Answers
Answer:
Liberalism is pretty much willing to respect another person's statement and accepting their opinions from one's own.
Explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
people who have an integrating conflict style are least likely to have which big five trait? t
Answers
Conscientiousness, openness, extraversion, neuroticism, and agreeableness are the Big Five Dimensions.
- Everyone possesses some degree of each of these traits; nevertheless, the particular combination of how highly some traits are rated and how poorly others are rated results in the distinctive feature we refer to as personality.
- Understanding someone's personality can help us predict how they will likely act and feel in a range of scenarios. Each of us has a distinctive personality that sets us apart from other people. The personalities of various employees should be understood in order to manage conflict efficiently. Having this knowledge is helpful for matching people with organizations and jobs.
To know more Big Five Dimensions, kindly click on the link below :
https://brainly.com/question/28499865?referrer=searchResults
#SPJ4
70 POINTS ONLY ANSWER IF YOU KNOW IT PLEASE What did the Maya believe about the world?
A)It is round.
B)It is cyclical.
C)It moves around the moon.
D)It was made by the Christian God.
Answers
Answer:
B. It is cyclical.
Explanation:
Most beliefs back then were either Christianity, Judaism, Islam, Buddhism Shintoism, Daoism, Sikhism, Muism/Sinisme/Shingyo, Cao Dai or Hinduism. Mayan, Hinduism, Shintoism, Daoism and Buddhism believe in a cyclical lifestyle.
The answer isn't A,B or D because they thought the earth was flat, weren't astronauts and believed in Mayan Gods.
<3 Enjoy,
Dea
The Maya believe about the world is cyclical. Thus, option D is correct.
What is a Maya?The Maya produced some of the best pottery, horticulture, astronomy, chronology, and arithmetic ever, and they also left behind an astounding amount of beautiful structures and meaningful artwork.
The ancient Maya had a concept of periods and believed in cyclical patterns of production and death. They adhered to the pagan mythology philosophy. The idea of animus is the conviction that every creature, region, and the thing has a unique spiritual value or mind.
The Maya consider the world to be eternal. occurring as a full set of occurrences that frequently occur in the exact order or for a fairly frequent length of time. Therefore, option D is the correct option.
Learn more about Maya , here:
https://brainly.com/question/1952923
#SPJ6
general ideas or understandings that can be used to group together objects, events, qualities, or abstractions that are similar in some way are referred to as a. concepts. b. beliefs. c. perceptions. d. theories.
Answers
General ideas or understandings that can be used to group together objects, events, qualities, or abstractions that are similar in some way are referred to as concepts Option (a).
Concepts are general ideas or understandings that can be used to group together objects, events, qualities, or abstractions that are similar in some way. They are mental representations that allow individuals to understand and categorize the world around them. Concepts are formed through experiences and observations, and they can be refined and updated as new information is acquired.
Beliefs are ideas or opinions that a person holds to be true, and they can be based on personal experiences, cultural or social influences, or other factors. Beliefs are subjective and may not be based on empirical evidence.
Perceptions refer to the way in which individuals interpret and make sense of sensory information from the environment. Perceptions can be influenced by factors such as attention, motivation, and expectations.
Learn more about Concepts
https://brainly.com/question/16185615
#SPJ4
What changes do you think needed to be made to the Articles of Confederation in order to have an effective government?
Answers
Answer:
The power to tax the states by the Federal government.
Explanation:
The articles of confederations provided the states government with somewhat stronger power compared to the central government. This made the central government had very little power to stop the states in case any of them did something that causing problems for other states.
On top of that, the central government also experience difficulties in obtaining funding to pay for proposed programs that created on national scale.
To fix it, Federal government need to possess the power to tax the states. This will allow the federal government to obtain the necessary budget to fund government programs and impose punishment to the states that were causing problems.
would it be legal for congress to allow a territory of the united states to become a full state on the condition that it choose a new governor? why or why not?
Answers
Answer:
No, it would not be legal, based on a Supreme Court decision that held that Congress cannot compromise the independence of a State and its ability to manage its own internal affairs.
Explanation:
Jefferson chose his personal secretary to lead the expedition, a man named Meriwether Lewis. Lewis chose a friend from the army named William Clark to be his co-leader. Together Lewis and Clark put together a band of explorers that would come to be called the Corps of Discovery. The Corps included soldiers, translators and one slave named York. The Corps set off on May 14, 1804, from a camp near St. Louis. They traveled by canoe up the Missouri River, which was tough. The men used sails, poles, oars and sometimes towed the boats with ropes that they pulled from shore. Later they had to physically carry the boats across land, a process called portaging. As they traveled, Clark navigated and made hand-drawn maps. Lewis studied flora and fauna—or plants and animals—made drawings, took samples and recorded notes. Which of the following best describes the trip up the Missouri River?
Answers
The Corps of Discovery had a difficult time travelling up the Missouri River in their canoes because they had to use a variety of techniques, including sails, poles, and ropes hauled from shore.
Why was it so difficult to cross the Missouri River?Due to the heat, injuries, insects, and the hazardous Missouri River itself, with its strong current and numerous snags, travel up the river was challenging and laborious.
Who crossed the Missouri River upstream?About 18 miles from the fledgling community of St. Louis, Missouri, at the Missouri River's mouth. Louis, Meriwether Lewis, William Clark, and their crew of 40 men—collectively known as the Corps of Discovery—launched their pirogues and keelboats on May 14, 1804.
To know more about Missouri River visit:-
https://brainly.com/question/11260945
#SPJ1
Nepalis a multicultural country .justify the statement
Answers
Answer:
Nepal is a multicultural country because here people from different cultural Live and have different cultural backgrounds. Althrough they have different cultures they live together forming a society helping each other. They never disrespect each other cultures but they involve themselves in other cultures.
Name the countries that became Communist during cold war
Answers
Who was the author of prometheus bound, and often tried to find reasons for laws in the universe?.
Answers
Aeschylus was the author of Prometheus bound, and often tried to find reasons for laws in the universe.
Greek dramatist Aeschylus is frequently cited as the originator or father of tragedy. The other two Greek tragedians- Sophocles and Euripides wrote plays that have since been preserved, but Aeschylus was one of the key players in the Western world's development of drama. Aeschylus explored how the gods impacted the lives of ordinary mortals. He was greatly interested in the presence of the divine, the road to moral purity and the essence of justice.
Aeschylus is also widely recognized for penning the Greek tragedy- Prometheus Bound. The play shows how Prometheus' hamartia of sympathy for others made him lose his status as a revered god and finally become a tragic hero.
To read about Sophocles see:
https://brainly.com/question/1623911
#SPJ4
_____ is framing the outlines of the future activities in order to attain the desired goals.
a. planning
b. organising
c. controlling
d. evalution