Read these sentences and answer the question that follows:

Frank Lloyd Wright was an American architect.
Frank Lloyd Wright designed hundreds of buildings.
American Institute of Architects recognized Frank Lloyd Wright as the greatest American architect of all time.

Which of these best combines the ideas in the group of sentences above to make an interesting sentence? (5 points)

Frank Lloyd Wright, who designed hundreds of buildings and was recognized by the American Institute of Architects as the greatest American architect of all time.
Frank Lloyd Wright, an American architect who designed hundreds of buildings, was recognized by the American Institute of Architects as the greatest American architect of all time.
Frank Lloyd Wright was an American architect who designed hundreds of buildings and who was recognized by the American Institute of Architects as the greatest American architect of all time.
The American architect, Frank Lloyd Wright, the designer of hundreds of buildings, who was recognized by the American Institute of Architects, was the greatest American architect of all time.

Answers

Answer 1

The option that best combines the ideas in the group of sentences is B, "Frank Lloyd Wright, an American architect who designed hundreds of buildings, was..."

How to combine the sentences

First, we need to understand that all sentences are about the same person, Frank Lloyd Wright. Therefore, when we combine them, there is no need to mention this name more than once. To avoid repeating Wright's name, we can use the relative pronoun "who" whenever necessary.

Second, we need to see where Wright is the subject of the sentence and where he is the object. When we combine the sentences into one, we must change the sentence where Wright is the object into the passive voice:

Sentence 1: Subject.Sentence 2: Subject.Sentence 3: Object. - This sentence must be changed into the passive voice.

Using the information above to combine the sentences, we will see that option B is the correct answer: "Frank Lloyd Wright, an American architect who designed hundreds of buildings, was recognized by the American Institute of Architects as the greatest American architect of all time."

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Answer 2

Answer:

Frank Lloyd Wright, an American architect who designed hundreds of buildings, was recognized by the American Institute of Architects as the greatest American architect of all time.

Explanation:


Related Questions

William is writing a research question to drive his study about the difference between the USDA's recommendations regarding the consumption of dairy products and current research on the subject.

Which question is most effective for guiding William's research?

A.
How does the USDA work with researchers to update their recommendations to the public regarding dairy product consumption?
B.
Who does the USDA consult in the research community when considering whether to change their guidelines concerning dairy product consumption?
C.
Why do the USDA’s current recommendations regarding the consumption of dairy products contradict current research findings?
D.
How often does the USDA apply current research findings to update their guidelines concerning the consumption of dairy products?

Answers

The question is most effective for guiding William's research is why do the USDA’s current recommendations regarding the consumption of dairy products contradict current research finding.

What is research question?

Research question are asked to help guide research, this are question to answer when doing research and the results of the research help answer the question.

Therefore,

The question is most effective for guiding William's research is why do the USDA’s current recommendations regarding the consumption of dairy products contradict current research finding.

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Answer:

C.

Why do the USDA’s current recommendations regarding the consumption of dairy products contradict current research findings?

Explanation:

Just did it

Choose the correct chronological order of the time periods. 1 fall of the roman empire /\ 2 Gregory I becomes pope /\ 3 height of the medieval period /\ 4 Fall of the roman empire

Answers

The correct chronological order is as follows:

Fall of the Western Roman Empire.

The Western Roman Empire fell in in 476 AD.

Gregory I becomes pope.

Gregory I becomes pope in 590 AD.

Height of the medieval period.

The medieval period peaked around 1000 - 1300 AD, or 1150 AD if you take the mean.

Fall of the Eastern Roman Empire.

The Eastern Roman Empire, or the Byzantine Empire, fell at 1453.

~

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https://brainly.com/question/20369245?referrer=searchResults - The result of moving the capitol to Byzantine, away from Rome.

I reproached the wall; I replied to the yells of him who clamoured . What due the wyd clamoured likely mean in the sentence?

Answers

Answer:

Can you ask that again?? this really didn't make sense.

Explanation:

How does Alexander Hamilton’s letter support the way in which Lin-Manuel Miranda characterizes him in “Alexander Hamilton”?

Answers

Alexander Hamilton’s letter supported the way in which Lin-Manuel Miranda characterizes him in “Alexander Hamilton as it provides information about his Latin American experience.

Who is Alexander Hamilton?

It should be noted that Alexander Hamilton was an American revolutionary statesman as founding father.

Alexander Hamilton’s letter supported the way in which Lin-Manuel Miranda characterizes him in “Alexander Hamilton as it provides information about his Latin American experience.

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in which location would you most likely find a print source?

Answers

Answer:

C

Explanation:

C at store magazine rack

In this excerpt, the Dillingham Youngs are described as a couple that
.

Answers

In this excerpt, the Dillingham Youngs is described as a couple that follows a daily routine.

Who are the characters in the story "The gift of the Magi"?

There are three famous characters through which the whole story surrounds. They are Della Dillingham Young, her husband Jim Dillingham Young, and Madame Sofronie who is the minor character in the story.

The options under this question are:

enjoys fancy mealsfollows daily routineenjoys living in the citypractices religion

This story features a young husband and wife and their scrabble to purchase Christmas gifts for each other with very little money. According to the excerpt of the story "The gift of the Magi" both of them are described as a couple that has a certain daily routine.

Thus, the correct option for this question is B, i.e. follows daily routines.

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Read the rough-draft paragraph.

Since popcorn is a whole grain, it is high in dietary fiber, which helps in the regulation and maintenance of the digestive system. To maximize the healthful benefits of eating popcorn, be sure to only munch on either air-popped popcorn or kernels that have been popped using little oil. In addition to providing dietary fiber, popcorn is also a source of antioxidants. This means that like fruits and vegetables, popcorn contains compounds that can reduce or prevent certain cancers. So, not only is popcorn a tasty treat, it is also a nutritional powerhouse.

Which topic sentence should be added to this body paragraph?

Foods loaded with fiber have been known to lower the risk of heart disease.
Recent studies prove that popcorn is one of the healthiest snack choices.
Antioxidants are sought after by many health-conscious people.
Air-popping and microwaving are two methods of preparing popcorn.

Answers

The answer choice which represents a possible topic sentence for the body paragraph is; Recent studies prove that popcorn is one of the healthiest snack choices.

Which topic sentence should be added to this body paragraph?

The body paragraph while discussing the dietary fiber content of popcorn also indicates that popcorn is a rich source of antioxidants. Hence, a suitable topic sentence would be; Recent studies prove that popcorn is one of the healthiest snack choices.

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After reading a passage, what might be a good way to make sure you understand what you have read?
a.
reread the passage until you understand
c.
locate key words
b.
share with someone
d.
create a graphic organizer in an easy reference format

Answers

Answer:

d.

create a graphic organizer in an easy reference format

Explanation:

It will be in easy reference format so you can look at it when you need it


1. The queen knew that she would be the only pretty woman at the party.

Answers

In the given sentence, the queen knew that she would be the only pretty woman at the party signifies the part of speech i.e. adjective.

What does part of speech mean?

Part of speech may be defined as a conventional class of terms differentiated according to the kind of idea represented and the operation performed in a sentence. There are eight types of parts of speech.

The complete question is: Identify the part of speech in the sentence "The queen knew that she would be the only pretty woman at the party".

The word pretty in the given sentence classified it as an adjective form of parts of speech. But, it should be kept in mind that in a different context the same word is classified under adverb, verb, and sometimes a noun.

Therefore, it is well described above.

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In your opinion, did Whitman's use of free verse in "Song of Myself" help him to connect with his readers? Give reasons for your answers. Your response should be at least 150 words.

Answers

Answer:

yes I do believe that Whitman's use of free verse in "Song of Myself," helped him to better connect with his readers. Whitman's use of free verse enables him to talk to his readers in a new way that is not constricted by rhyme or meter parameters. Also, his use of language sounds more like spoken language and helps readers to not only understand what he is saying, but also to better connect with the complex and emotional themes that Whitman was discussing in "Song of Myself." More than one hundred fifty years later, the themes he uses in "Song of Myself," as well as his exciting use of language still speaks to a new audience in a new generation, which shows how well thought out and carefully pieced together his poetry was, and I believe that the use of free verse aided significantly in Whitman's ability to make the poem into exactly what he wanted it to be.

Yes, I believe Whitman's use of free verse in "Song of Myself" helped him connect with his readers better. Whitman's use of free verse allows him to communicate with his readers in a way that is not limited by rhyme or meter parameters.

Who was Whitman?

Walter Whitman Jr. was a poet, essayist, and journalist from the United States. He was a humanist who participated in the transition between transcendentalism and realism, incorporating both perspectives in his works.

His use of language sounds more like spoken language, which helps readers not only understand what he is saying, but also connect with the complex and emotional themes discussed by Whitman in "Song of Myself."

More than one hundred fifty years later, the themes he uses in "Song of Myself," as well as his exciting use of language still speaks to a new audience in a new generation, which shows how well thought out and carefully pieced together his poetry was.

Therefore, I believe that the use of free verse aided significantly in Whitman's ability to make the poem into exactly what he wanted it to be.

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Which line from Edgar Allan Poe's "Annabel Lee" contains alliteration?
Annabel Lee
by Edgar Allan Poe
It was many and many a year ago,
In a kingdom by the sea,
That a maiden there lived whom you may know
By the name of Annabel Lee;
And this maiden she lived with no other thought
Than to love and be loved by me.
/was a child and she was a child,
In this kingdom by the sea.
But we loved with a love that was more than love-
I and my Annabel Lee-
With a love that the winged seraphs of Heaven
Coveted her and me.
And this was the reason that, long ago.
In this kingdom by the sea,
A wind blew out of a chnud, chilling
My beautiful Annabel te
So that her highborn kinsmen came
And bore her away from me.
To shut her up in a sepulchre
In this kingdom by the sea.
The angels, not half so happy in Heaven,
Went envying her and me-
Yes!-that was the reason (as all men know,
In this kingdom by the sea)
That the wind came out of the cloud by night,
Chilling and killing my Annabel Lee.

Answers

Answer:

bsbsbajqajjs

What is the purpose of monologue?
O to quickly share a speaker's thoughts without other characters hearing
O to disclose a speaker's thoughts quietly to the audience
O to express a speaker's innermost thoughts only to themselves without other characters engaging or responding to
their words
• to reveal their thoughts and emotions to the audience and characters through a moving speech that builds to a
climax

Answers

The purpose of monologue is to reveal their thoughts and emotions to the audience and characters through a moving speech that builds to a climax.

What is monologue?

Monologue is defined as a type of speech that is performed by a character in a play before the audience which is usually extended.

The main reason for this speech is to reveal one's thoughts and emotions usually through moving speech that builds to a climax.

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Answer:

D. to reveal their thoughts and emotions to the audience and characters through a moving speech that builds to a climax

Which rhetorical appeal does Murray use MOST effectively (logos, pathos, or ethos)? Give at least one example from the essay to prove your answer.

Answers

The author of the article uses pathos which is a rhetorical appeal to emotions.

What is the rhetorical appeal?

Rhetorical appeals refer to the qualities of an argument that make it truly persuasive.

The author of the article majorly uses pathos as a rhetorical appeal to the emotions.

Murray resorts to the descriptive and figurative language, powerful connotative words like emotional diction with a number of rhetorical questions and phrases.

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in the first question in Beowulf, which part is most clearly the rising action

Answers

In the first section of this story, the rising action is the attack of Grendel on Heorot.

What is the rising action?

This refers to events in a story that later lead to the main conflict or the climax of the story.

What is the rising action in Bewoulf?

In this story, the rising action is the first time Gredel attacks the people. This is because this event is the one that leads to the main conflict between Bewoulf and the monster and therefore this event triggers the climax or conflict of this story.

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3 4 ASSESS YOURSELF Fill in the blanks choosing correct word from bracket. 1. There are lots of here. (shop, shops) 2. These are really slow. (bus, buses) How many does he have? (wife, wives) 4. The of horses are very strong. (hoof, hooves) 5. These over there run very fast. (calf, calves) 6. I like to swim if the ___________ aren't too big. (wave, waves) 7. She always brings lots of_________ with her. (toy, toys) 8. I fill my three with water. (bucket, buckets) 9. These are from the next village. (sheep, sheeps) 10. Her_________ are very smooth. (hair, hairs) 11. How many of chalks do you have? (piece, pieces) 3.​

Answers

Answer:

1. shops, buses, wives, hooves, calves, waves, toys, buckets, sheeps, hair, pieces

Explanation:

Answer:

answers highlighted in green

adapted excerpt from Cats: Their Points and Characteristics
by W. Gordon Stables

“Are cats to be trusted?”

A question like this, which to kitty is a most momentous one, affecting not only her comfort and happiness, but her standing as a social pet and her very existence itself, cannot be treated lightly in a work like mine. My own opinion is, and always has been, that if cats are properly fed and cared for, they will do anything rather than steal. However, I was not content with providing just my own experience in this volume, since some might say my cats have been exceptional. Instead, I placed cats in court, as it were, and given them a long, fair, and impartial trial. For several months, I have summoned evidence for and against cats’ honesty from people all throughout Great Britain and Ireland.

Based on the information my participants provided, the verdict is as follows: “cats are not as a rule thieves, but in fact, quite the reverse.” In most cases, when properly treated, cats are to be trusted.

Which sentence in the writer’s essay should be revised to include an in-text citation?

While many might disagree, I believe cats are the best pet of all. Some insist that dogs are better companions because they are more reliable and well-behaved. However, cats don’t necessarily deserve their negative reputation. Based on a survey of cat owners throughout Great Britain and Ireland, most cats do not steal food if the humans around them take good care of them.

Answers

The sentence in the writer’s essay that should be revised to include an in-text citation is However, cats don’t necessarily deserve their negative reputation.

What is an excerpt?

An excerpt refer to words , Statements, ideas or phrases that is extracted from a literature which has meaning.

Therefore, The sentence in the writer’s essay that should be revised to include an in-text citation is However, cats don’t necessarily deserve their negative reputation.

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a piece of reasoning in the text

suggesting how a specific example relates to the broader argument

Grammatically correct the sentence Learned how to download the correct internet browser

Answers

The grammatical correct sentence is, 'Learn how to download the correct internet browser'.

What is grammatical errors?

Grammatical errors, are the errors in English, is the wrong use of grammar when writing a sentence.

For example, wrong use of tense, or preposition or adverb, etc.

Thus, the grammatical correct sentence is, 'Learn how to download the correct internet browser'.

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what do max and sarai have in common commonlit( the night oak street burned down)

Answers

The inference shows that the thing that Max and Sarai had in common was that they both witnessed how their house got burnt.

What is an inference?

An inference simply means the conclusion that can be deduced based on the information given in a story.

In this case, the inference shows that the thing that Max and Sarai had in common was that they both witnessed how their house got burnt. This was a result of the power outage and loss of cell phone signals.

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I didn't tell him the

Answers

Answer:

you didn't tell him the what??

Explanation:

What does Odysseus tell Penelope and why is it ironic?

Answers

You would need to be more specific for a good answer. But I’ll take a shot in the dark and say you are talking about when Odysseus tells her he must leave again after just arriving in Ithaca. It’s ironic because the whole book was about getting home, and showed how much Odysseus missed his home, just for him to leave as soon as he arrived.

Select the correct answer.
Which set of words best describes the woman's character?
A.
energetic, attractive, friendly
B.
worried, shy, intimidated
C.
independent, eccentric, nervous
D.
lonely, languid, desperate

Answers

Answer

A! I think its A cus the other ones dont seem right..

Explanation:

Good morning guys how are you please help me this question

Answers

1. E
2. A
3. G
4. D
5. B
6. F
7. C

Pretty certain that’s right.

WILL MARK BRAINLIEST AND 50 POINTS!!
Can somebody write an essay for me for Writing an Essay to Compare the Presentation of Ideas across Genres
Here's the prompt
Award-winning author Sonia Nazario is best known for her Pulitzer Prize–winning biography Enrique’s Journey. The book brings to life the very real and dangerous journey of a Honduran boy fleeing his home in hopes of finding his mother in America. In addition to the biography, Nazario has written countless articles informing readers of the dangers children like Enrique face. While the biography and the articles serve the same purpose and present the same ideas, they do so in different ways. You will be comparing and contrasting how Nazario informs her audience through a biography and an editorial. You may access the editorial here and the biography here.

Write a comparative essay in which you compare and contrast the way Sonia Nazario presents similar ideas in a biography and an editorial. Support your comparison with well-chosen, relevant, and sufficient evidence from both texts. Apply MLA guidelines to properly cite the evidence used in your essay. Be sure your essay uses formal and objective language.

Answers

The biography Enrique's Journey tells how this one boy made his journey to America.

How to depict the essay?

The biography was that he lived and had to try to survive, just to have a better life. He scratched to get to America and at one point, on a train, he was introduced him to other bad people. Nazario claims that when he was deported, he always stuck with one of these members to protect himself from any attacks.

The editorial, also written by Nazario, mostly shows objective facts obtained from studies, not just one perspective as it tells how almost 7,000 children were picked up by Immigration officers three years before the article was written.

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Read the dialogue between Romeo and Mercutio found in Act I, scene iv of Romeo and Juliet.

Romeo: Give me a torch: I am not for this ambling;
Being but heavy, I will bear the light.

Mercutio: Nay, gentle Romeo, we must have you dance.

Romeo: Not I, believe me: you have dancing shoes
With nimble soles; I have a soul of lead
So stakes me to the ground I cannot move.

Based on these lines, which statement is true?

Romeo is unhappy, and Mercutio is upbeat.
Romeo is upbeat, and Mercutio is unhappy.
Romeo is nervous, and Mercutio is brave.
Romeo is brave, and Mercutio is nervous.

Answers

We can actually deduce here that based on the given lines above, the statement that is true is: Romeo is unhappy, and Mercutio is upbeat.

What is Romeo and Juliet?

Romeo and Juliet is a play that was authored by William Shakespeare. The play reveals how Romeo and Juliet fell in love with each other even when their families were at rancour.

We see that the given lines show that Romeo is unhappy here. Romeo stated that he is not for this ambling and wasn't in the mood to dance.

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Answer: B)  Romeo is upbeat, and Mercutio is unhappy.

Explanation:

Hope this helps!

Mark me brainliest!

Pls and TY!

PLEASE HELP LAST DAY OF SCHOOL!!! ~100 Points~

Thermometer Pills Tracy Wilson 1 Over the past ten years, more than two dozen athletes have died from the medical condition known as heatstroke. Heatstroke occurs when the body’s internal temperature becomes so elevated that its cooling system begins shutting down. Who is most at risk? Surprisingly, it is younger athletes. Often, they either do not recognize or ignore the warning signs until it’s too late. To make matters worse, children’s bodies are much less efficient than adults at cooling themselves. A promising new product hopes to end the all too common heatstroke trend. It is called a thermometer pill. 2 While it doesn’t look much different from the average vitamin capsule, the work it does inside the body is truly amazing. Once ingested, these capsules send an internal body temperature reading to a portable device that is not much bigger than an iPhone. A coach or professional trainer monitors the device during practices or events held when temperatures and heat indexes are particularly high. If an athlete’s body temperature reaches a dangerous level, the monitor immediately transmits an alert. The player is then rushed indoors and placed in an ice bath to rapidly decrease his or her body temperature. This is important, since internal organs can begin shutting down at 105 degrees Fahrenheit. 3 While these tiny lifesavers have proven to be effective, they are quite expensive. On average the cost is $50.00 per pill. However, many parents of young athletes say that it is a small price to pay for the peace of mind it gives them on a hot, sultry day.

Read the passage on the left to answer the following questions: 14) The word however is used in paragraph 3 to show A) that the price of the pills is outrageous. B) that the pills are not a good idea for young athletes. C) that some parents will not buy the pills because of the expense. D) that some parents will buy the thermometer pills in spite of the expense

Answers

Answer:

D.

Explanation:

The parents will buy the pills to keep their child safe.

our hamburgers (be)so tasty!

Answers

Answer:

our hamburgers are so tasty!

"Our hamburgers are so tasty!" The verb "are" is the correct form of "to be" to complete the sentence.

In this sentence, the subject "our hamburgers" is plural, referring to more than one hamburger. When the subject is plural, the corresponding form of "to be" is "are." The use of "are" indicates that the hamburgers possess the quality of being tasty.

This sentence expresses a positive statement about the deliciousness of the hamburgers. Proper subject-verb agreement is essential in English grammar to ensure that the sentence is clear and grammatically correct. In this case, "are" matches the plural subject "our hamburgers" to create a coherent and accurate sentence.

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------------The given question is incomplete, the complete question is:

"Complete the sentence with the correct verb for(to be)

- Our hamburgers_(be) so tasty!"------------

In which situation is it most important to display text using large letters when
giving a speech?
A. When presenting remotely
B. When presenting in a classroom to a group of friends
C. When presenting with little access to technology
D. When presenting in a large room to a large audience

Answers

Answer:

D, A, and maybe C

Explanation:

Ram said to me,"where are you going now."into indirect speech

Answers

Answer:

the ram asked where i was going then

Why does Henry David Thoreau think imprisonment is ineffective?
O A. Because governments can only lock a person up physically, not
mentally
O B. Because prisoners tend to train one another on how to commit
crimes
O
C. Because prisons only serve to make prisoners hate the
government more
O D. Because prisoners know that governments don't have true
authority to lock them up

Answers

The answer it’s a since being imprisoned only affects the body not the mind

Which sentence should appear first in an effective summary of Part 2 of "The Adventure of the Blue Carbuncle"? The owner of the hat, Henry Baker, pays a visit to Holmes after spotting the advertisement in the newspaper. Holmes and Watson learn from the innkeeper the goose was purchased from a market in Covent Garden. Holmes and Watson visit the innkeeper who sold the goose to Baker. Holmes and Watson set out to find the salesperson at Covent Garden.

Answers

The sentence that should appear first in an effective summary of Part 2 of "The Adventure of the Blue Carbuncle" is A. The owner of the hat, Henry Baker, pays a visit to Holmes after spotting the advertisement in the newspaper.

What is summary?

It should be noted that summary simply means a concise information about a particular happening or event

In this case, the sentence that should appear first in an effective summary of Part 2 of "The Adventure of the Blue Carbuncle" is that the owner of the hat, Henry Baker, pays a visit to Holmes after spotting the advertisement in the newspaper. This is important for the text sequence.

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Answer:The sentence that should appear first in an effective summary of Part 2 of "The Adventure of the Blue Carbuncle" is A. The owner of the hat, Henry Baker, pays a visit to Holmes after spotting the advertisement in the newspaper.

Explanation:

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What is the common ratio for this geometric sequence?16, 8, 4, 2, ... How is a warm-up different from a cooldown? How are a warm-up and a cooldown similar? Answer please quick What is the value of n?38 Using the information in the table, calculate the number of formula units in a 62.2 g sample of aluminum sulfide (Al2S3) When did those around Socrates begin to cry? a. when he made his prayer c. when they saw him drink the poison b. when he actually died d. they did not cry Please select the best answer from the choices provided A B C D What are the options for video playback in a PowerPoint presentation? Check all that apply. looping the video adjusting the volume trimming and adding fades starting the file automatically rerecording sections of the file rewinding the file automatically You also learn what it takes to make money: a lot of effort.What is the verb in this sentence?O a. youO b. moneyO c. effortO d.learn A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak? Determine the value of "a" for which g(h(a)) = 13 Find the midpoint of A and B where A has coordinates (8, 2)and B has coordinates (3,8). solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb Which two sentences support the inference that Maria is hardworking?Select the correct text in the passage.Maria carried the heavy basket of beans shed collected and, rather than rest, walked briskly to the peach trees. There, she joined her husband, Ethan, and younger sons, Lee and Sam. Together, they picked fruit as the temperature rose and foreboding thunderclouds formed. A half an hour had passed when a clap of thunder disrupted their quiet activity. Heavy raindrops pelted them, so they headed for the house. The clouds then poured down their bounty of rain. Lee and Sam sprinted to the travel trailer with their dog, Oscar, while Ethan and Maria sought shelter inside the house.Maria lifted the canning pot onto the stove to boil water, and Ethan stood nearby slicing peaches and humming a tune. Thunder gave an encore, and in their bare feet, Maria and Ethan could sense its vibrations through the floorboards.Submit Bill Clinton became the second president in U.S. history to be Can someone say happy birthday to me do it for how every many point this question is gonna give yoouuu whats the theme of the gift of the magi please help if u know :D Which statement from the passage is an opinion?A poor peasant woman bore many sons.One of them was born a fool.He was neglected and left to shift for himself as best he could.All day long he worked on a large patch of sandy soil. Your mortgage is a 30-year fixed at 8% on $150,000. you are considering refinancing at 3.5% fixed for 30 years. the bank charges you 1.5% of your debt in closing fees. approximately how long will it take you to recoup the closing fees from the reduced loan payment amount? Is b=2a+10 equal to 4a+2b=10