Shivering and vasoconstriction would be signaled to cause a: A. increase in pH. B. decrease in temperature. C. decrease in pH. D. increase in temperature.

Answers

Answer 1

Answer:D

Explanation: shivering occurs when someone is cold and vasoconstriction is when the blood vessels close to the skin and the veins closer to the skin surface constrict as a result of dat air doesn’t enter the body

Answer 2

Vasoconstriction is the narrowing of the blood vessels that hinders blood flow. Vasoconstriction and shivering will lead to an increase in the temperature through thermoregulation. Thus, option d is correct.

What is thermoregulation?

Thermoregulation is the maintenance and balancing of the temperature and heat in the body. They are regulated by many factors including shivering and vasoconstriction.

During the vasoconstriction, the blood vessels close to the skin surface close and the body shivers as a result of cold or decreased temperature. This signals the body to increase the temperature so that shivering can be stopped.

Therefore, vasoconstriction and shivering signal the body to increase the temperature.

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Related Questions

When a volcano erupts, tiny particles from which of Earth's spheres are released into the air?
atmosphere
biosphere
geosphere
hydrosphere

Answers

The geosphere :) that’s where the earth’s mantle and crust is which is where the volcanoes are. So, when they erupt pieces of them are released from the level which they came from (aka the geosphere) hope that helps!

When a volcano erupts, tiny particles from the geosphere are released into the air. So, the correct option is C.

What is Volcano?

A volcano is a geological formation on the surface of the Earth that develops as magma and volcanic ash build up. During an eruption, lava, ash, and gas can escape through a crater or vent that is generally shaped like a mountain.

Explosive or non-explosive eruptions can have a large negative impact on the environment, causing ash fall, landslides, and lava flows, among other things. Tiny geosphere-derived particles are discharged into the atmosphere during volcanic eruptions.

All areas of volcanism contain compound volcanoes, but these volcanic structures are most common at plate convergence zones, where one tectonic plate plunges beneath another towards the earth's mantle.

Therefore, the correct option is C.

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Which of the following is true of living things that have prokaryotic cells when compared to living things that have eukaryotic cells?
They have many types of organelles.
They are types of plants.
O They are always larger than eukaryotic organisms.
They are always unicellular.

Answers

Answer:

the answer is the last one, they are always unicellular

Explanation:

In human body where is liver located

Answers

The liver is your largest internal organ. About the size of a football, it's located mainly in the upper right portion of your abdomen — beneath the diaphragm and above your stomach — but a small portion extends into the upper left quadrant.

Answer:

The liver is located in the upper right-hand portion of the abdominal cavity, beneath the diaphragm, and on top of the stomach, right kidney, and intestines. Shaped like a cone, the liver is a dark reddish-brown organ that weighs about 3 pounds.

Explanation:

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Earthquakes sometimes occur when
. Some underwater earthquakes shake the ocean floor and cause large sea waves that destroy property and threaten lives. Such a sea wave is called
.

Answers

Answer:

A Tsunami

Explanation:

Answer:

Earthquakes sometimes occur when a divergent boundary abruptly reverses roles to become a convergent boundary. Some underwater eartquakes shake the ocean floor and cause large sea waves that destroy property and threaten lives. Such a sea wave is called a tsunami.

Explanation:

PLATO

3. What are the consequences of felling of trees?​

Answers

Answer:

The loss of trees and other vegetation can cause climate change, desertification, soil erosion, fewer crops, flooding, increased greenhouse gases in the atmosphere, and a host of problems for indigenous people.

Explanation:

A newborn that is SGA would be at risk for which of the following complications?

I. Diabetes
II. Obesity
III. Shoulder Dystocia
IV. Heart Disease

Answers

A newborn that is SGA would be at risk for suffering from Diabetes or Hypoglycemia (Option I).

What is diabetes?

Diabetes is a disease where the individual cannot control the levels of glucose in the blood.

A newborn that is Small for Gestational Age (SGA) shows an increased risk of suffering from Hypoglycemia due to the lack of control of glucose in blood.

In conclusion, A newborn that is SGA would be at risk for suffering Hypoglycemia (Option I).

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the cell wall in plants is made of CHITIN. Correct and rewrite the following

Answers

Answer:

See below

Explanation:

The correct statements can be two. Either:

1) The cell wall of plants is made up of cellulose

2) The cell wall of fungi is made up of chitin.

Answer:

chintin is the chemical components of the cell walls of fungi

A cell has a 5\%5%5, percent salt concentration. It is placed into a solution with a 0.5\%0.5%0, point, 5, percent salt concentration. What will happen to the cell?

Answers

The question is not clear, so the clear question is as follows:

A cell has a 5 percent salt concentration. It is placed into a solution with a 0.5 percent salt concentration. What will happen to the cell?

Answer:

Cell will get swelled and burst

Explanation:

When a cell is placed in a solution with less concentration, then the solvent particles move from lower concentration to higher concentration through a semipermeable membrane and the process s called osmosis.

In this case also, the cell has higher concentration and the solution has less, so water will move into the animal cell, causing it to swell and burst after some time.

Hence, the correct asnwer is "Cell will get swelled and burst".

Answer:

Water will move into the cell, causing it to swell.

Explanation:

The cell has higher concentration of solute and a lower concentration of water than the solution it is placed in. This means that water will move into the cell, causing it to swell and ultimately burst.

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A researcher wants to introduce the human gene encoding tissue plasminogen activator (used to dissolve blood clots) into a mammal so that the protein will be secreted into the milk of the mammary gland. For the researcher to succeed, the gene should be:

Answers

Answer:

In the given case, for the researcher to succeed, there is a need to place the gene next to the promoter sequence, which gets expressed in the mammary cells. The sequences of DNA, which illustrate that where the transcription of a gene by the RNA polymerase initiates is known as the promoter. These sequences are generally situated at the 5 prime terminals of the initiation site of transcription or are situated directly upstream.

How does the design of your experiment control for outside factors that may affect the results?​

Answers

Answer:

It separate the inner environment from the outer environment.

Explanation:

The design provides the separation of the inner environment from the outer environment which is responsible to control the outside factors which directly affects the results of the experiment. The design provides control environment which is required for the experiment. In this control environment, the environmental factors will not affect the results of the experiment.

Question What was the ratio of tall to short plants in the F2 generation of Mendel's experiments? A. 3:1 B. 2:1 O C. 1:1 D. 6:1 ​

Answers

Answer:

A

Explanation:

Answer: 3:1

Explanation:

i got it right on the test

what are the different types of waste? and what are the methods used in biodegrable waste managment​

Answers

Answer:

liquid waste , solid waste,harzadious waste,recyclable rubbish and organic waste

help pls, just need this part on the top

Answers

Answer:

Concentration Gradient

Explanation:

This means that it will move from a region where it's in lower conc to a region of higher conc

concentration gradient


State one reason why soil organisms need air

Answers

Answer:

To release plants nutrition's to soil .

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Which of the following describes the most likely way in which two water molecules will interact?

A. A covalent bond will form between the hydrogen of one water molecule and the oxygen of the other water molecule.

B. An ionic bond will form between the oxygens in each water molecule.

C. A metallic bond will form between the hydrogens in each water molecule.

D. A hydrogen bond will form between the hydrogen atom of one water molecule and the oxygen atom of the other water molecule.

Answers

Answer:

D. A hydrogen bond will form between the hydrogen atom of one water molecule and the oxygen atom of the other water molecule.

Explanation:

The most likely way in which two water molecules will interact is a hydrogen bond will form between the hydrogen atom of one water molecule and the oxygen atom of the other water molecule. Therefore, option (D) is the required answer.

List out the names of some
plants that grow in your village.
Which parts of it are used as
food?​

Answers

Answer:

Explanation:

The plants grown in my place are -  rice, groundnut, sugarcane, grapes, mulberry, castor, ragi etc.

Parts of it used as food

rice - seed

groundnut - seed

sugarcane - stem

grape - fruit

Mulberry - fruit

Castor - seed

ragi - filler millet

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what the parts of Earth's biosphere

Answers

Answer:

lithosphere, atmosphere and hydrosphere.

Explanation:

Answer:

the hydrosphere

the atmosphere

the lithosphere

Explanation:

The hydrosphere is all waters on the Earth's surface, such as lakes and seas, and sometimes including water over the Earth's surface, such as clouds.

The atmosphere is the Earth's layer of gases, commonly known as air, that is retained by Earth's gravity.

The lithosphere is the rigid part of the earth, consisting of the crust and upper mantle.

Only ------ percent of the food eaten is turned into its own body. ​

Answers

Answer:

10%

Explanation:

there is a the rule that only 10% of the energy is transferred from one trophic level to the other.

this means that only 10% of the food an organism eats  is passed onto the next organism. eg only 10% of the energy in a plant is transferred to a rabbit that eats the plant. After that if  a wolf eats the rabbit only 10% of the energy of food will pass on to the wolf.

Which of the following California animals is found in both marshlands and grasslands?

Answers

Answer:

pronghorn antelope.giant kangaroo rats.gophers.mule deer.

¿En qué momento se produce la hinchazón del tejido?

Answers

Answer:

Es el agrandamiento de órganos, piel u otras partes del cuerpo, causado por la acumulación de líquidos en los tejidos. La presencia de líquido extra puede llevar a un aumento rápido de peso durante un período corto (de días a semanas).

Match each hormone to its function
•luteinizing hormone
•testosterone
•oxytocin
•follicle-stimulating hormone
•estrogen
•gonadotropin-releasing hormone

Answers

Answer: Stimulates the contraction of the uterus during childbirth - OXYTOCIN

Stimulates sperm production and growth of ovarian follicles - FOLLICLE STIMULATING HORMONE

Initiates the Secretion of leutinizing hormone and follicle stimulating hormone - GONADOTROPIN RELEASING HORMONE

Initiates the development of secondary sex characteristics in females - ESTROGEN

Initiates the development of secondary sex characteristics in males - TESTOSTERONE

Initiates cell production of testosterone and estradiol by cells in the gonads - LUTEINIZING HORMONE.

The correct match for hormone and their functions are- 1- Oxytocin, 2- follicle-stimulating hormone, 3- a gonadotropin-releasing hormone, 4- estrogen, 5- testosterone, and 6- luteinizing hormone.

Oxytocin is a naturally occurring hormone that plays a vital role in the reproductive system of both men and women, including labor, delivery, and breastfeeding, as well as in human behavior.

FSH is produced by the pituitary, which is a small gland just below the brain. The pituitary plays a vital role in the development and regulation of sexual function.

Gonadotropin-releasing hormone stimulates the brain’s pituitary gland to produce and release the hormones LH and FSH.

Estrogen is a family of hormones that play a vital role in the reproductive and sexual development of women.

Testosterone is a male sex hormone. It is responsible for spermatogenesis and fertility in males.

Luteinizing hormones (LH) are hormones in the body that stimulate the reproductive system. Luteinizing hormone stimulates ovulation and stimulates the production of the hormones needed for pregnancy

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Which of the following is the best definition of alternative energy? A. Energy sources that can be used in place of fossil fuels. B. Energy sources that can be used in place of coal. C. Energy sources that can be used in place of wind energy. D. Energy sources that can be used in place of hydroelectric energy.

Answers

Answer:

My answer is D.

Energy sources that can be used i. place of hydroelectric energy.

The best definition of alternative energy is energy that can be used in place of fossil fuels. The correct option is A.

What is alternative energy?

Alternative energy is that energies are used in the place of the conventional form of energy. These energies are renewable and eco-friendly.

The burning of coal and fossil fuel produces lots of greenhouse gases, so the best alternative energy is the one that replaces it.

Thus, the correct option is A. Energy sources can be used in place of fossil fuels.

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why does people have sex?

Answers

Answer:

for the continuation of species.. further it's as needy as a person take the meal

Explanation:

It's can be counted as a daily need of people as we take the meal

People have sex for either pleasure or reproduction, it can be used for passion or something else.

Some people take advantage of this though, which can lead to jail

In your own words, describe the role of the scientific method in scientific investigation.

Answers

The role of the scientific method would be to test your hypothesis

The scientific method serves as a structured framework for conducting scientific investigations.

How does the scientific method shape investigative processes?

The scientific method involves a series of steps, starting with observation and formulation of a research question. Researchers then formulate hypotheses, educated guesses about the outcomes of their experiments.

These hypotheses are tested through carefully designed experiments, allowing for the collection of empirical data. The collected data is then analyzed to draw meaningful conclusions. The scientific method promotes objectivity, consistency, and reproducibility in research, enabling scientists to build upon existing knowledge and refine their understanding of the natural world.

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You experimentally apply a toxin to a muscle and find that it does not contract when you electrically stimulate the motor neuron leading to it. You know that this toxin blocks acetylcholine receptors. Therefore, you suspect that the stimulation of contraction is failing because: Group of answer choices

Answers

The question provided is not complete as it lacks the group of choices, however the group of choices are given as follows:

A. A contraction fails to occur because an action potential is not generated in the muscle cell.

B. A contraction fails to occur because this toxin directly prevents ion release from intracellular stores.

C. A contraction fails to occur because neurotransmitter release by the motor neuron is blocked at the neuromuscular junction.

D. A contraction fails to occur because this toxin prevents cross bridge formation and thereby directly prevents contraction.

E. C and D are both true

Answer:

The correct answer is option A : A contraction fails to occur because an action potential is not generated in the muscle cell.

Explanation:

A muscle contraction takes place when action potential bring to muscles by nerves, which is traveled with the help of motor neuron and imitated the muscle contraction.

Acetylcholine or Ach is a chemical messenger to bring the nerve impulses between a nerve and a muscle. If the receptor is block with applying toxin muscle will not contract as ACh will not be able to propagate the nerve impulse to the muscle so there will be no action potential.

The correct answer is option A : A contraction fails to occur because an action potential is not generated in the muscle cell.

PEOPLE IF YOU DONT KNOW THE ANSWER DONT EVEN TRY TO SAY '' I WISH I CAN HELP DUT IDK THE ANSWER" Write true if the statement is true or false if the statement is false. _____ 1. Earth’s diameter is longer through the poles than through the equator. _____ 2. Earth’s magnetic field extends several thousands of kilometers into space. _____ 3. Earth’s axis of rotation passes through the north and south poles. _____ 4. One complete rotation of Earth requires a little more than 24 hours. _____ 5. A swinging pendulum appears to change direction because of Earth’s revolution. _____ 6. Earth’s speed of rotation is greatest at the equator. _____ 7. Earth has seasons because its orbit around the sun is elliptical. _____ 8. Earth travels about 150 million kilometers during one revolution. _____ 9. Earth revolves around the sun at a constant speed. _____ 10. Earth’s axis is tilted 23 ½ degrees relative to a line drawn perpendicular to the equator.

Answers

Answer: 1. Earth’s diameter is longer through the poles than through the equator. False 2. Earth’s magnetic field extends several thousands of kilometers into space. True 3. Earth’s axis of rotation passes through the north and south poles. False 4. One complete rotation of Earth requires a little more than 24 hours. False 5. A swinging pendulum appears to change direction because of Earth’s revolution. False 6. Earth’s speed of rotation is greatest at the equator. True 7. Earth has seasons because its orbit around the sun is elliptical. False 8. Earth travels about 150 million kilometers during one revolution. False 9. Earth revolves around the sun at a constant speed. False 10. Earth’s axis is tilted 23 ½ degrees relative to a line drawn perpendicular to the equator. True

Explanation:

What does the formula below represent? CO2 + H20 → C6 H12 06+02

Answers

Answer:

Photosynthesis

Explanation:



Watch the video “Teen Stress.” Now, imagine that a friend confides in you that he is going to the doctor because he feels that stress might be affecting his blood pressure. He wants you to help him develop a list of questions to ask the doctor. Come up with five questions for your friend to ask about stress and blood pressure.

Answers

Answer:

questions:

Should I or can I eat salty foods?

Do I have to check my pressure immediately?

Do I have to follow a balanced diet?

Is it good to do physical activity?

Do I have to worry about the signs of eye flickering and headache?

Explanation:

Blood pressure is regulated by endogenous mechanisms, although these sometimes fail and it is necessary to take drugs to reduce high blood pressure, an example of which is beta-blockers.

Blood pressure is also regulated by diets based on low sodium consumption, necessary calories and with great contributions of nutrients since cardiac or cardiovascular health is also essential in the face of possible formation of atheroma plaques.

The increase in blood pressure with the appearance of atheroma plaques is very common, and it is also the two most frequent causes of AMI (acute myocardial infarction)

Answer:

1)How much does blood pressure rise because of stress?

2)Are there techniques that I can use to cope with stress?

3)Do these techniques help to reduce blood pressure?

4)Is exercise helpful in reducing blood pressure caused by stress?

5)Would medication help my condition?

6)Are there any other risk factors for high blood pressure?

Explanation:

Answer from plato.

What protective items should you wear when using benedicts solution?

Answers

Answer:

Hey there!

You should wear gloves and safety goggles when using benedicts solution.

Let me know if this helps :)

If Sammi had more time or better resources, how could she improve her model to eliminate some of the weaknesses?

Answers

Answer:

She could use more materials to replicate the entire digestive system instead of the small intestine only. Maybe use some better material than cardboard to represent the villi lining. She could also use more capillaries to make it more realistic.

Explanation:

answer for plato activity, your welcome :)

Answer: She may utilize additional materials to duplicate the full digestive system instead of the small intestine only. Maybe use some better material than cardboard to represent the villi lining. She could also use more capillaries to make it more realistic.

Explanation:

Other Questions
I NEED ALGEBRA HELP! Can you solve a system of equations using the substitution by solving one equation for x or y and then using the substitution method? x + 6y = 6 and 7x - 5y = -5 Hi Mathies, Help with this vectors excercise pls. Givan that OA (segment) = 13x+7y , OB = 5x+12y and CO = -15+12y write down each of the following vectors in its simplest form a) BA = 8x+ 5y (l got it, i ve done it) b) AC= ?? i cant find vector AC thanks in advance Select the word that doesn't belong:a. El vestidob. El collarC. El anillod. La pulsera(Please help) Solve each of the following exponential equations using common bases:1.) 4^(3x+5)=8^(4x-3)2.) 9^(2x+3)=(1/27)^(3x+1)3.) 4^(x+6)8^(x-9)=64 What is the value of x? 10) Juan is writing a report on Italian food. He finds a book titled "Foods of the World." He opens toChapter 2 on page 12 and reads the word "Spain" in large letters. Further down on the page, he reads theword "Northern Spain" in smaller letters. Page 12 of Juan's bookOA) Has no text features.OB) Has a diagram but no other text features.OC) Has the table of contents only.OD) Has a heading and a subheading.Save Amber lives in New York, "the city that never sleeps," so she feels she has a great deal of freedom and choice. However, sociologists argue that this freedom prevents city dwellers from developing intimate personal relationships or community, a situation that is often referred to as Group of answer choices Gen-Fast Shoes wants to expand internationally and is deciding if its line of tennis shoes can be sold at a high price in Europe. One way for Gen-Fast Shoes to assess this is to determine whether these types of shoes in the foreign market offer customers greater.a. cost.b. exports.c. value.d. competition.e. production. Debt financing has one important advantage that the early Modigliani and Miller (MM) propositions ignored: the interest on business debt is tax deductible. This benefit means that the amount of taxes that a business is required to pay will be reduced by a phenomenon called an interest tax shield, which is a function of the amount of debt in the firm's capital structure and its tax rate. In contrast, the dividends that a corporation pays on its common and preferred shares are not tax deductible. Consider the case of Green Llama Foodstuffs, Inc.: At the beginning of the year, Blue Chipmunk Foodstuffs, Inc. had an unlevered value of $8,500,000. It pays federal and state taxes at the marginal rate of 40%, and currently has $2,500,000 in debt capital in its capital structure.According to MM Proposition I with taxes, Green Llama Foodstuffs is allowed to recognize a tax shield of ___________, and the levered value of the firm is: a. $7,100,000 b. $12,500,000 c. $9,900,000 d. $4,500,000 Normally, the buyer's offer in a commercial transaction takes the form of:____________. 1. a phone call with the parties directly speaking with each other. 2. a personal letter. 3. a purchase order. 4. an acknowledgment form. 1. How________ is it from here to the nearest supermarket? - Its about 500 meters.A. far B. long C. difficult D. nice2. My English teacher, Mr. Nam, often drives his car________ on the way to school.A. careful B. caring C. carefully D. careless3. When I was at primary school. My father________ me to school every day.A. takes B. is taking C. used to take D. is used to taking4. There________ a stadium in the town but now there isn't.A. use to be B. was used to C. is used to D. used to be5. She didnt use to ________in the hospital.A. work B. working C. to work D. worked6. Did you________ to the cinema when you lived in London?A. used to go B. were used to go C. use to go D. were used to going7. We go to the _______to watch a film.A. stadium B. hospital C. restaurant D. cinema8. The traffic light turns______, you should stop your vehicle.A. pink B. red C. yellow D. green9. The film is too _______to show to children.A. violence B. violent C. violently D. interested10. He was _______ that Tom couldnt come to his party.A. disappoint B. disappointedly C. disappointed D. disappointing11. A film that shows actual events is called a _______A. horror B. thriller C. comedy D. documentary12. I love traveling by______ because I can see the whole city from above the sky.A. bus B. boat C. train D. airplane13. How far is ______ from you school to the bus stop?A. that B. it C. this D. there14. The Beatles is my favorite musical band. I love all their______A. performing B. performance C. performed D. perform15. The film is _______ a beautiful princess.A. on B. about C. in D. up16. How ______is this festival held? - It is held every two years.A. long B. far C. often D. much17. ______did the package come from?- Hanoi.A. When B. Where C. Which D. Who18. ______ money does your mother earn? - About $300 a month.A. How much B. Where C. Which D. How many19. ______ is it to the supermarket? - About five hundred meters.A. How much B. How far C. How long D. How often20. ______ do you like that festival? Because it is an interesting thing of Vietnamese cultureA. What B. How C. When D. Why21. _______ does it take you to walk to school?A. How much B. How far C. How long D. How often22. I am interested reading books.A. on B. of C. in D. by23. Lan: Could I borrow your calculator? - Pike:_______.A. Yes, you could. B. Yes, you can. C. Yes, you do. D. Yes, you will.24. My home is far______ the cinema.A. at B. from C. after D. for25. The people who watch a film are called _______.A. directors B. actors C. characters D. audiences26. We are not allowed to ride motorbike without wearing a _______.A. helmet B. mask C. watch D. ring27. Solar energy, air and water are _______.A. renewable B. limited C. restricted D. narrow28. Although nuclear power is clean and plentiful, it is not _______A. dangerous B. unsafe C. safe D. renewed29. Solar energy can be changed into _______.A. electricity B. electric C. electrician D. electrical30. I _______ for you at this time next week.A. will waiting B. will be waiting C. will be waited D. will be wait31. What _______at 2 p.m tomorrow?A. will you be doing B. will you doC. you will be doing D. you will do32. This table_______ to another room this weekend.A. will be moving B. will moving C. will move D. will be moved33. He enjoys ______a horse when he has free time. A. riding B. flying C. pedaling D. driving34. This is her bag and that is______A. I B. me C.my D. mine35. She didnt phone you, _______? A. did she B. didnt she C. does she D. doesnt she36. Youve won the competition, _______?A. have you B. has he C. havent you D. hasnt he37. The ring belongs to my mother. The ring is_____.A. his B. hers C. her D. she38. The_____ of the world is growing at a dangerous rate.A. populous B. popular C. population D. populate39. September has _____days than October.A. less B. fewer C. more D. few40. A hydro power station _______in this area next month.A. will be built B. will build C. will be building D. will built write 2 paragraphs explaining this poem.must include- explain what poetic devices are used and why they are used.- what/which poems this poem is referenced too and why - explain the meaning of this poem- background information on what would help someone understand the poem Please answer this, getting very frustrated. write about a time when you or someone you know was lost. short paragraph Kevin made a business trip of 312.5 miles. He averages 60 mph for the first part of the trip and 55 mph for the second part. If the trip took a 5.5 hours how long did he travel at each rate a piece of paper is 5.5 x 10^-4 inches thick. If jennifer has 35 such pieces,how thick is the whole stack? Write your answer in standard form. how many years will it take for a sum of money to double at 10% compounded annually The history of China, from xia dynasty, nearly 4100 years of history; From China's first unified dynasty qin dynasty, about 2241 years. Prehistoric times have seruice, revered as the father. About 2070 BC, the xia dynasty; In shang dynasty of China's earliest known mature text - oracle; The further development of the western zhou dynasty when the society, the spring and autumn period and the warring states period when productivity, schools of thought contend. In 221 BC, qin shi huang established the first centralized feudal state in Chinese history - the qin dynasty; When the western han dynasty and han dynasty and further consolidate and develop the unified situation, basic finalize the design of Chinese characters. The three jin and the northern and southern dynasties, China into separate regime. I wish I _________stay longer, Maryam said to Lan at the end of the week.A.canB.willC.couldD.may Match each function name with its equation.