What is the infinitive form what is the gerund form?.

Answers

Answer 1

Walking, traveling, and voting are examples of gerunds, which are verb forms that end in "-ing" and are used as nouns. An infinitive is the base form of a verb that begins with "to" (to walk, to travel, and to vote).

What is the gerund?

A gerund is any of the various nonfinite verb forms that can be found across various languages; most often, but not always, one that also functions as a noun. It has qualities that distinguish it from nouns and verbs in English, including the ability to take a direct object and be modified by an adverb. Traditional grammar distinguishes between gerunds and present participles within the -ing forms, but more recent grammars, such as A Comprehensive Grammar of the EnglishLanguage and the Cambridge Grammar of the English

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Related Questions

What kind of poem is the disappointment?.

Answers

The poem "The Disappointment" is grouped with other male poems about "imperfect delight," in which a man's fault is a woman's beauty. Behn is more concerned with Cloris's irritation.

Poetry: What is it?

A poem employs rhyme, rhythm, and meter to convey feeling or to describe setting and plot. There are many different types of poetry, such as ballads, haiku, verse, and haiku. Even though shapes are not what define poems, they are used to identify them.

Which qualities define a poem as poetry?

A poem is a work of literature that makes imaginative word choices to convey ideas, emotions, or a story to the reader. A poet is a person who writes poetry. The words or phrases in many poems blend when they are read aloud.

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Which text would be the mot credible reource on thi topic?

an advertiement for lab afety equipment
the webite of a company that ell lab afety equipment
the reult of a tudy on lab afety equipment conducted by cientit
a blog pot of a high chool tudent that talk about lab afety equipment

Answers

c)The most credible resource on this topic would be the results of a study on lab safety equipment conducted by scientists.

This is because a study conducted by scientists is likely to be conducted in a controlled and unbiased manner, with proper methodology and data analysis. It is also likely to be peer-reviewed by other experts in the field, adding to its credibility.

On the other hand, an advertisement for lab safety equipment is likely to be biased towards promoting a certain product or brand, and a blog post by a high school student may not have the same level of expertise or experience with the topic.

A website of a company that sells lab safety equipment may provide useful information but it may not have credibility as a study conducted by scientists.

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Complete question:

Roquan is looking to buy new safety equipment for a chemistry lab. He wants to make sure the equipment has high safety ratings.

Which text would be the most credible resource on this topic?

an advertisement for lab safety equipment

the website of a company that sells lab safety equipment

the results of a study on lab safety equipment conducted by scientists

a blog post of a high school student that talks about lab safety equipment

The perpetrators are the people who participated in the killing.
O True
O False

Answers

Answer:

true

Explanation:

If this is relating to the holocaust then it is—- (True)

What is gerund and give 2 examples of the sentences?.

Answers

The subject or object of the phrase is a gerund, which is a noun. For instance, "I detest studying" or "Cooking is my favourite pleasure" (object).

What is a gerund and how are they used in sentences?

He made running a priority.) or the object of a preposition (such as "Besides running, he likes camping.") A gerund can also be the subject of the sentence.

Give two examples of a simple sentence.

The three fundamental components of a sentence—a subject, a verb, and a finished thought—are present in a simple sentence. The following are some illustrations of basic sentences: For the train, Joe waited. Subject is "Joe," and verb is "waited." The train arrived late.

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What is gerund in English grammar with examples PDF?.

Answers

A verb in the "-ing" form that is employed as a noun is called a gerund. It becomes the sentence's topic or object. Examples: On the weekends, I like to bake. (The subject is "baking," a gerund.) Studying is crucial.

Describe a gerund:

The noun form of a verb with the ending -ing is known as a gerund. Taking play, dancing, and eating as examples. Since they are accustomed to seeing that form as the continuous/progressive form of the verb (e.g., "she is eating," "they were dancing," etc.), pupils immediately find this puzzling.

A gerund is a -ing-ending verb that takes the form of a noun and is used as a verb. You may already be aware that a verb is a word that describes an action or a state of being.

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Summary!! Helppppp guysss

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The given passage is an article about Wendy Searle, who suddenly wondered about a solo expedition to the South Pole while arranging for a media campaign for the same by a military personnel team.


What is the summary of the given article on expedition?

Wendy had never thought about crossing Antarctica five years ago . But she suddenly got curious about it while a media campaign with the military personnel team going for a South Pole expedition. Never having skied before or an expedition before, this is an extremely difficult feat for her. However, she skied 560km across Greenland ice sheet last year. Due to being underweight that the required weight to pull the pull, Searle has to train for 10 hours a day. Searle will have to ski 1130 km in 38 days, 23 hours and 5 minutes in this expedition. She is worried about no outside assistance or any contact with humans for her days in Antarctica and believes that losing even one day of training will lead to a decision of success and failure. Searle’s husband, a soldier and three teenage daughters and a son — are very supportive of her dream. Searle is not much worried about them in her absence as they are quite independent and quite often takes care and manages things for her. Searle wishes to be a role model for her children and show them that it is okay to pursue dreams passionately. Searle is struggling with fund raising for the expedition as she is experiencing some setbacks. She believes that being a female polar explorer makes it difficult for her to attract sponsorships. In an interaction with a TV agent she is told that there are not many audience who are interested in a woman’s expeditions. Searle believes her story can change this.

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Summary!! Helppppp guysss

What does Glaspell show the reader about the position of women in the early twentieth century community?.

Answers

Glaspell contends that despite the fact that women are just as intelligent as men, if not more so, they do not actively express their thoughts in society since men predominate.

What does Glaspell's play trifles say about what it is to be a woman?

In addition to highlighting the social standards of women at the period, Glaspell's play illustrates the gender imbalance that exists in the culture. Although women's responsibilities are devalued, she illustrates the women's loyalty to one another and stresses how they manage to thrive in a patriarchal culture. In the world of Trifles, which is ruled by men, social norms and constraints have virtually restricted women to the home and tied them to their husbands, leaving them with little autonomy or sense of self. Hale is making fun of Mrs. Wright for being more preoccupied with her preserve jars than her charge of murder. But whatever these women do or achieve is unimportant to the men.

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What is called the one line stanza 1 point?.

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With one line, a poem's stanza is referred to as a monostich. A poem's stanzas are collections of lines, and the space between them is referred to as a stanza break.

What makes anything a stanza?A stanza, which is an essential structural and organizational component of a poetic composition, is derived from the Italian term stanza, which means "chamber."A stanza is a collection of lines that are occasionally ordered in a particular pattern and typically (though not always) separated from the remainder of the poem by blank space.With one line, a poem's stanza is referred to as a monostich, with two, it is a couplet; with three, a tercet or triplet; and with four, a quatrain. Hexastich at six; heptastich at seven; and octave at eight.

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Why is it important to develop academic skills?.

Answers

These types of skills can boost your self-esteem, competence, and confidence.

Why is it important to develop academic skills/talents?

They can also lessen stress about tests and deadlines. You may be able to reduce the number of hours you spend studying by developing effective study skills, giving you more time for other activities.Academic skills are essential because they are actually intertwined with numerous other types of skills that are required in a variety of life areas. Skills like time management, organization, and good writing will make your daily life easier once you graduate.are the characteristics and learning strategies that improve your academic performance. They expose you to new ways of thinking, help you stay focused and motivated, and prepare you for your career. However, these abilities are more than just innate.Learning study skills will not only help you succeed in college but also in life.Having good study habits can boost your self-esteem, competence, and confidence. They can also lessen stress about tests and deadlines.We may be able to reduce the number of hours you spend studying by developing effective study skills, giving you more time for other activities.Having good study habits can help you learn and remember more.Students may feel that their work and effort are more valuable if they use effective study skills.

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Do haikus have to be about nature?.

Answers

Answer:

No, haikus do not have to be about nature. 

Explanation:

Haikus mostly have nature in them but they DON’T HAVE to be about nature they can portray many emotions such as love and sadness.

Decribe how the author of ""The Monkey’ Paw"" ued etting and the element of plot in a pecific way to build upene that led to the climax and the ambiguou (no clear reult) reolution

Answers

In "The Monkey's Paw," the author uses the setting and the element of the plot in a specific way to build suspense that leads to the climax and the ambiguous resolution.

The story is set in a small, isolated village in England, where the White family lives in a gloomy and decrepit old house. The setting of the story creates an eerie and foreboding atmosphere that sets the stage for the ominous events to come.

The element of the plot is used to create a sense of rising tension and foreboding. The story follows the White family as they are given a monkey's paw with the power to grant three wishes. The father, Mr. White, uses the first wish to wish for money, which leads to the tragic death of their son. This event creates a sense of unease and foreboding as the reader wonders what will happen when the two remaining wishes are used.

As the story progresses, the tension builds as the characters make their second wish and the events that follow, leading to the climax of the story where the reader is left in suspense about the outcome, and the reader is left with an ambiguous resolution. The reader is left with a feeling of unease as the story does not provide a clear result. The ambiguous resolution adds to the eerie and foreboding atmosphere and leaves the reader with a sense of uncertainty about what has occurred and what will happen next.

In summary, the author of "The Monkey's Paw" uses the setting and the element of the plot in a specific way to build suspense that leads to the climax and the ambiguous resolution. The setting creates an eerie and foreboding atmosphere, the plot creates a sense of rising tension and foreboding, and the ambiguous resolution adds to the eerie and foreboding atmosphere and leaves the reader with a sense of uncertainty.

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How does the author make connections between her many ideas on love? does she repeat any of these ideas?​

Answers

I am sorry I cannot answer your question as you didn't specify which author and which text you're referring to. It is important to provide the author's name and the title of the book to give a specific answer. If you provide me the specific information, I'll be happy to assist you.

What are the 10 examples of preposition in a sentence?.

Answers

On the chair, he sat, The refrigerator has some milk, She was under the table, hiding, Off the counter, the cat leaped. Barry crossed the bridge by car are the 10 examples of preposition in a sentence.

What do you mean by preposition?

Adpositions, a class of words that consists of prepositions and postpositions, are used to convey spatial or temporal links or denote different semantic responsibilities. the noun phrase that a preposition or postposition usually joins with is Its complement, or occasionally object.

Examples of preposition are:

Matilde misplaced her ring on the shore.Anthony is the owner of the book.By the tree, they were seated.

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3
1. Recommended D
certain nutrient.
Determined
Daily
O Delivered
Discharge
Amount/Allowance is how much you should be getting of a

Answers

The Recommended Dietary Allowance (RDA) is a set of guidelines, developed by the Food and Nutrition Board of the Institute of Medicine that specify the daily recommended amount of essential nutrients needed to meet the nutritional needs of healthy individuals.

The RDA serves as a baseline for individuals to determine their daily nutrient needs. It is important to note that the RDA is not a one-size-fits-all solution and that individual nutrient needs may vary based on factors such as age, gender, weight, and activity level. However, following the RDA can help ensure that individuals are getting the essential nutrients they need to maintain good health..

One is recommended to consult a healthcare professional before making significant changes to their diet, as the Recommended Dietary Allowance may not be appropriate for individuals with specific health conditions or dietary restrictions. The RDA serves as a helpful guide for individuals looking to make informed decisions about their daily nutrient intake.

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What are the themes of Ode on a Grecian Urn?.

Answers

Themes. The ideas of beauty, romanticism, and the immortality of art are all present in Keats' "Ode on a Grecian Urn." The longevity of art is the poem's central theme.

What is the subject matter of the quiz "Ode to a Grecian Urn"?

Theme: Appreciation of the eternal perfection of art and understanding of the fleeting nature of time. Throughout the paintings on the urn, art and beauty are preserved in time as a sign of everlasting perfection.

In his poem "Ode on a Grecian Urn," Keats addresses the issue of life and art.

The conflict between art and life is captured by Keats' use of the theme of immortality in Ode on a Grecian Urn because "once [the poet] has imaginatively grasped the eternal beauty of the model and the material through which the urn's sculptor worked, the problem of their actual existence completely vanishes."

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What is the Birdcage based on?.

Answers

The 1978 French film La Cage aux Folles served as the inspiration for the film Birdcage.

The film Birdcage features, among other things, Nathan Lane having pitch-perfect fits of laughter, Hank Azaria dancing in cutoffs, and Robin Williams playing the straight guy (no pun intended). It may also rank among the funniest films ever produced.

The narrative of nightclub owner Armand Goldman and his partner and featured performer, Albert, is told in the film The Birdcage. When their son Val returns home to announce his impending marriage, the couple's life are completely turned upside down. The problem is that Val wants Armand and Albert to pretend to be gay in order to win over Kevin and Louise Keeley, the ultra-conservative Republican senator's daughter, who is the mother of Barbara, Val's future bride.

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What is the Elgin Marbles debate?.

Answers

Answer:

arguments about the legality (or alleged illegality)

Explanation:

Over the past decades, the Greek government has made a series of requests for the return of these objects. These repatriation demands include arguments about the legality (or alleged illegality) of the original sale of the works to Lord Elgin during a period of Ottoman control over Greece.

What do you call to the tools methods and styles of the author to express and give more meaning to his or her writing?.

Answers

Literary devices are a range of writing strategies that may be utilized to help you express yourself and your emotions in a somewhat more original way, therefore making your work and the world you create pop off the page.

What distinguishes literarily from literally?

The difference between "actually" and "literally" is that the former refers to more in-depth facts acquired through books or literature, whilst the latter is just a metaphor for the literal or face-value perception of anything being stated.

What are the 4 types of literature?

There are four main categories of literary works: poetry, theater, fiction, and creative nonfiction. While each genre has certain distinguishing characteristics, these are more of the author's conventions or tools than official rules.

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What evidence do Mrs Hale and Mrs Peters uncover?.

Answers

When Mrs. Peters Hale finds a dead canary in Mrs. Wright's sewing basket, she understands that Mrs. Wright (Minnie Foster) murdered her husband in Trifles.

Briefly describe the conflict in Trifles.

In Trifles, the hypocrisy and institutionalized prejudice of a male-dominated society are dramatized, and it is also discussed the perils that women who submit to such systems face. Trifles is a drama about the difficulties between women and society and about how they metaphorically flee from oppression.

The first dispute in the narrative demonstrates how social and professional circles in our culture exclude women. The idea of the roles that society expects women to play as homemakers is expressed in this dispute. "Trifles," the name of the drama, refers to how men perceive women. Susan Glaspell uses language throughout the play to demonstrate how men view women, which is insulting, as well as to illustrate the dangers for women who submit to such systems.

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What is the most important skill needed for academic success?.

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Time management is the most important skill needed for academic success for a student.

What is time management?The process of planning and exercising conscious control over the amount of time spent on particular activities, particularly to improve effectiveness, efficiency, and productivity is known as time management. Due to the limited amount of time, it places numerous demands on a person's work, social life, family, hobbies, personal interests, and commitments. Time management can be aided by a variety of skills, tools, and techniques used to manage time when completing specific tasks, projects, and goals in accordance with a due date.[1] Effective time management gives the individual "choice" to spend or manage activities at their own time and expediency. At first, the term "time management" only applied to activities at work or in business, but over time, it came to include activities at home as well. A system for managing time is a planned combination of procedures, instruments, strategies, and methods. Because it determines the duration and scope of a project, time management is typically a requirement for project management.Setting priorities, the related process of reducing time spent on non-priorities, and putting goals into action are the major themes emerging from the literature on time management. The advantages of time management are as follows:focus increasesthings get doneno confusiondeadlines completed on timemulti-tasking etc.

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which water should you use for the water bath during the recrystallization?

Answers

The solution is placed in an ice-water bath to further reduce the temperature and allow additional crystals to form. Ice water should you use for the water bath during the recrystallization.

When recrystallizing, you should use cold water for the water bath while chilling the recrystallization. Depending on a compound's solubility, recrystallization is a physical method for removing impurities. Heating the substance to dissolve the chemical with impurities in a solvent mixture completes the procedure. In chemistry, recrystallization is a technique for separating apart chemicals.

The desired compound or the impurities can be extracted from the solution after a compound and impurities combination has been dissolved in an appropriate solvent, leaving the other behind. The crystals that develop when the chemical precipitates give it its name. The natural creation of larger ice crystals at the expense of smaller ones is also referred to as recrystallization.

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What are the most effective presentation strategies?.

Answers

Not every suggestion will result in a compelling presentation. First, keep an eye contact and a grin when speaking. Use of gestures and facial emotions is tip number two. The third tip is to stay focused. Be assured.

What do the seven Cs of presentation mean?

The seven Cs are completeness, courtesy, accuracy, and summation accuracy.

What does a good presentation skill look like?

An effective presentation should have a solid subject, align with the aim, best suit the audience, and be well-organized.

The presentation's delivery is the phase of the process that matters the most. The actual labour is in delivering the presentation to the audience while making eye contact with them. Being a live, in-person process, there will be a great deal of human emotion involved. For the presenter, it may be extremely stressful. While giving the presentation, the following considerations should be made.

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What academic skills do you need?.

Answers

Research is one of the most crucial academic skills because it serves as the cornerstone of all academic endeavours.

What makes academic talents necessary?

Academic skills are essential since they actually overlap with many other kinds of talents that are required in many different facets of life. After you graduate, abilities like time management, organisation, and effective writing will simplify your daily tasks.

Reading, spelling, written expression, and math are examples of subjects where basic academic talents are those that lay the groundwork for more advanced intellectual abilities, such as the synthesis and application of knowledge. There are three categories of skills: self-management, functional, and specialised knowledge. Functional skills are innate aptitudes or capabilities that are refined through practise and education.

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Where did Elie live before he was deported?.

Answers

In 1928, Elie Stein was born in the Romanian village of Sighet. He was sent to the German prison and forced labor camps throughout World War II together with my family and other local Jews.

For what is Elie renowned?

One of the most well-known Holocaust survivors, Elie Wiesel (1928–2016), was also a renowned novelist and an advocate for human rights. His debut novel, Night, which has since become the classic of Nazi literature, details his experience as a youngster in Auschwitz.

Would be Elie Tahari a high-end company?

Elie Tahari's in-depth knowledge of fashion designing has given him a special place in the premium market for even more than 40 years. The globally recognized brand is present on all five continents.

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What is the irony used in the poem?.

Answers

Susan Glaspell's play "Trifles" depicts feminist stereotypes, or gender representations from a time when women had less power.

In what ways do male and female characters in the play Trifles differ from one another?

The play Trifles is about the differences between men and women in how they find and think about murder evidence. The male characters in the play look for the murder evidence in places and big things like a gun or rope in the kitchen of the house.

What is the predominant theme when considering gender roles in Trifles?

Social Discrimination Against Women The play depicts a world governed by rigid gender roles in which men work and women stay home alone. However, the division of labor that exists between men's and women's spheres goes beyond that.

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the silence between us chapters 1-7 summary quick!! it was due yesterday and i’m already gonna get points taken off!!

Answers

In chapters 1-7 of The Silence Between Us, main character Maya moves to Colorado with her deaf parents and starts attending a hearing high school. She struggles to fit in and feels isolated from her peers. She eventually meets two other deaf students, Joaquin and Paxton. She begins to learn sign language from them and finally feels like she belongs somewhere.

What is Isolated?
Isolated refers to a state of being separated or detached from others. It can refer to physical separation, such as when a person is alone in a room, or to emotional separation, such as when a person feels disconnected from the people around them.

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What is a traditional sonnet about?.

Answers

Sir Thomas Wyatt and Henry Howard introduced a 14-line poem with a varied rhyme pattern from Italy to England. The sonnet, which is literally a "small song," typically reflects on a single emotion.

What guidelines apply to a classical sonnet?

A sonnet is a 14-line poetry that reflects on a particular subject or notion. A "volta," or turn, frequently needs to be taken before the problem is solved. Iambic pentameter and the rhyme scheme ABAB CDCD EFEF GG are both used in Shakespearean sonnets, but don't worry too much about that.

What distinguishes a traditional poem?

Poetry in the traditional style adheres to a particular poetic structure, such as rhyme schemes or meter patterns.

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What is the climax or the turning point of the story Trifles?.

Answers

The pivotal moment, or climax, of a play, takes place when the conflict starts to be resolved, which is the most dramatic part of the narrative.

What is the story Trifles's summary?

Susan Glaspell wrote a one-act drama titled Trifles. The piece explores what happened after farmer John Wright was strangulated and killed. Glaspell played the role of Mrs. Hale during the play's initial run at the Wharf Theater in Provincetown, Massachusetts, in 1916.

The drama was partially based on the 1900 murder of Iowa farmer John Hossack, who died from axe wounds received while lying in bed. Later, his wife Margaret Hossack was put on trial and found guilty, though the decision was ultimately reversed on a technicality. As a reporter for the Des Moines Daily News, Glaspell covered the murder of Hossack and the subsequent trial.

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What happens at the end of the life you save may be your own?.

Answers

He tries to out run a storm  in his car paying that the storm wash away the slime from the earth at the end of "The Life You Save May Be Your Own,"

Who is Mr Shiftlet?

Tom Shiftlet, a one-armed wanderer who appears in Flannery O'Connor's short story "The Life You Save May Be Your Own," agrees to wed Crater's daughter in exchange for a car.

Who is Flannery O connor?

Mary Flannery O'Connor is an American novelist, short story author, and essayist. She also wrote 31 short stories, two novels, and a tonne of reviews and commentary. The best way to describe O'Connor's writing is to term it "Southern Gothic," a literary subgenre that often takes place in the southern United States and depicts wounded and disturbed characters in dark situations. She analyses morality and religion in her writing, typically showing the terrible ways in which they collide and interact.

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What is gerund in English grammar with examples PDF?.

Answers

A gerund is formed by adding -ing to the base form of a verb. Example, play + ing = playing.

How do you form gerunds, how does it differ from infinitives and what are the types?

Nouns can be substituted in sentences for infinitives and gerunds. A gerund is a verb's present participle (-ing) form, which includes actions like singing, dancing, and sprinting.

Infinitive = to + the root form of the verb, such as to run, sing, or dance.

The Six Gerund-Use ways:

- Gerund as the sentence's topic.

- Subject complement for a gerund.

- Gerund serving as the transitive verb's object.

- Gerund as prepositional object

- Infinitive replaced with gerund.

10 examples of gerunds are:

Since she was five years old, Sharon has loved swimming in the water.

This time, apologizing to me is insufficient.

Having to get up early won't bother me at all.

Being married will not make me happy.

Looking after many dogs keeps Susan busy.

I can't stand Tom's speaking German.

After taking a bath, I felt fine.

Biking is my newest hobby.

Olivia spends her free time running.

Olivia even dreams about painting contests.

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andro co. has a $10 million note payable that is due three months after year end. the note payable was refinanced when long-term bonds were issued one month after year end for $11 million What type of function is Y =- 2x 3?. Please help me with all Ill mark you brainly Companies are interested in the demographics of those who listen and call in to the radio programs they sponsor. Suppose that only 20% of listeners phoning into a morning talk show are male.a. If the station takes a random sample of 200 callers, what is the probability that the sample proportion of males will be at least 0.30?b. The station management wonders if adding a male host to the program will increase the proportion of callers who are male. After adding the male host, the station records selects a random sample of 200 callers and finds that 30% are male. Does this provide convincing evidence to suggest that the proportion of male callers has increased from 20%? Explain. Solve for x...............[tex]\bf 4x+6=14[/tex] Why do you think Canada has such an abundance of natural resources? a nurse is reading a journal article about care of the woman with pelvic organ prolapse. the nurse would expect to find information related to which disorder? select all that apply. Evaluate this expression for the given values of x and y 2x^2 - y x=3 y=8 QUICK FAST PLEASE HURRY What should you regularly do in order to stay grounded in reality when it comes to your career planning and goal setting?regularly measure the outcome of your career effortsregularly ask your boss for a raiseregularly journal all of your feelings about your careerregularly ask your parents how they think you are doing at your jobANSWER ASAP help please i need to finish in 30 minutes "a business that makes nothing but money is a poor kind of business" elaborate Which of the following correctly describes the life span in the study of human development?It ends once an individual enters late adulthood.It involves growth and changeIt occurs throughout life.It focuses on old age the majority of employees view their leaders and colleagues blank in the post-trust era. multiple choice question. What was widespread in the North even though segregation was not legal? One of the important features of the _____ environment is the existence of protections for consumers that emerged during the 1960s to increase the influence, power, and rights of consumers in dealing with institutions. How would having too much sample in the melting point tube most likely affect a melting point measurement? The melting point will be lower than expected. The sample will thermally decompose.The melting point range will be broader than expected. The melting point range will be narrower than expected. based on the setup below, which of the following statements is true? (assume the car starts at rest and there is no friction.) If me.hernandez turns in a late order for 1 turkey sandwich What are the 6 components of health List and describe?. elena is proving the pythagorean theorem. she knows the goal is to prove that in a right triangle. so far she has: in a right triangle the altitude that intersects the hypotenuse decomposes the triangle into 2 smaller right triangles. these triangles are similar to the large triangle by the angle-angle triangle similarity theorem since each smaller triangle shares one angle with the larger triangle and has a right angle. similar triangles have proportional side lengths, so and . i can rewrite those equations to get and . therefore . . .