In how many ways can 7 people sit around a round table if no two of the 3 people Pierre, Rosa, and Thomas can sit next to each other? (Seating arrangements which are rotations of each other are treated as the same. )

Answers

Answer 1

Answer:In so many ways because it's a round table

Explanation:

Answer 2

Answer:

144 seatings

Explanation:

After Pierre sits, we can place Rosa either two seats from Pierre (that is, with one seat between them) or three seats from Pierre. We tackle these two cases separately:

Case 1: Rosa is two seats from Pierre. There are 2 such seats. For either of these, there are then four empty seats in a row, and one empty seat between Rosa and Pierre. Thomas can sit in either of the middle two of the four empty seats in a row. So, there are 2*2 = 4 ways to seat Rosa and Thomas in this case. There are then 4 seats left, which the others can take in 4! = 24 ways. So, there are 4*24 = 96 seatings in this case.

Case 2: Rosa is three seats from Pierre (that is, there are 2 seats between them). There are 2 such seats. Thomas can't sit in either of the 2 seats directly between them, but after Rosa sits, there are 3 empty seats in a row still, and Thomas can only sit in the middle seat of these three. Once again, there are 4 empty seats remaining, and the 4 remaining people can sit in them in 4!= 24 ways. So, we have 2* 24 = 48 seatings in this case.

Putting our two cases together gives a total of 96+48 = 144 seatings.


Related Questions

Write one paragraph on something that has recently made you happy (also I'm in Grade 8 so I would really like it if you could write a paragraph about something an eighth grader would write about).

Answers

Answer:

My Vacation to the mountains

Explanation:

Many of the young ones of today's era undergo a serious amount of stress and anxiety which really upsets them. As one of them, I too was struggling to get balance with my mental and physical well-being. Observing my condition, my loving parents decided to take me on a break from the outside world. we went on a vacation...to the mountains! the area was completely isolated and beautiful. birds, animals, trees; everything was just so aligned with what was in my head. the little break consisted of a jolly little swim in an ice-cold river too. We went to small villages, exploring the people and their lifestyles. we tried to get along with a few cultures too which in my perspective, was successful. This small trip lasting for only 3-4 weeks made-up my whole year and it is the one thing that recently made me happier than ever.

Answer: So, my mom knows that I am enthusiastic about my games, so she surprised me with A gaming setup. I was really happy!! I told every single one of my friends and they were happy for me. The LED lights on my keyboard made it look cool!! I downloaded this new game that I wanted to try out. Its called Diablo IV, It's A bit of A scary game, but it's so cool!! I also watched A scary movie with my friends on Discord eating Popcorn. I really wanted to watch Megan, but I had to buy it, and I really did not feel like paying for anything else!! This made me really happy and  I gave thanks to my mom and as you know me and my friends celebrated with popcorn and scary movies.

Explanation: This is All have due to me being an 8th grader too.

Which of the following are physiological changes to the body that result from stress? Select all that apply.

Question 1 options:

issues with mood, anger, depression, irritability, lack of energy, concentration problems, anxiety and panic attacks


aches and pains, inflammation, tension, lowered bone density (propensity for osteoporosis), tightness in the shoulders and back


decreases blood pressure, slow heart beat, decreased risk of heart attack and stroke, and lower cholesterol


suppressed effectiveness of the immune system to battle and recover from illness. Leads to higher levels of inflammation in the body, which causes a variety of chronic health conditions


can cause peptic ulcer disease, IBD, IBS, food allergies, stomach cramps, reflux, nausea and weight fluctuations

Answers

Should be the fourth option, immune system suppression is a staple effect of stress on the body.
I think It’s the first one

Which of the following describes an outcome variable (dependent variable)?


A. the item or subject that the experiment is conducted on

B. a variable that changes in an experiment due to another factor

C. the variable that the experimenter is changing

D. any condition or event that could affect the outcome of an experiment

Answers

I’m pretty sure it’s B. A variable that changes in an experiment due to another factor. Please let me know if you get it right or not!
The answer should be B

plz help ,having a gap between the frisbee and the web of your thumb is critical for air flow


false


true

Answers

This is actually true
this answer is true.

Explain why each definition is important to Physical Education (PE) in your own words. Warm-Up Cool Down Respect Facilities Orientation Safety Diverse Etiquette Abilities Responsibilities

Answers

Warm-Up: to make sure you dont pull a muscle or anything while you exercise

Cool Down: after a workout its important to cool down so yuor body doesnt

overheat

Respect: having respect for the ppl around you and the equipment are both important to how your workout can go

Facilities: its important to have designated facilities to workout and exercise, so you dont have to clean every room, you can clean the few are designated for exercising

Orientation: having an orientation to the equipment is important so you dont misuse it and hurt yourself.  

Safety: if you're not safe around the equipment, that could be a life-threatening situation, saftey is important to your own health

Diverse: all workouts are diverse. there are many that can tailor to just one need, or you can do multiple just for the heck of it.

Ettiqutte: having good ettiqurte fo those around you is vital for the best workout possible. if you're not nice to those aroun you, they wont be nice back and your workout is gonna suck

Abilities: you need to know your abilities so you overwork yourself and pull a muscle, drop something on yourself, or strain too hard and hurt yourself internally.

Responsibilities: if you know your responsibilities, you can have a healthy and safe workout. some of your responsibilities might be, cleaning up equipment after you use it, picking up your swaety towels and putting them where they need to go, or simply picking up your water bottle.

HOPE THIS HELPS!!!! (lemme know if it doesnt)

Warm-up and cool downs are very important because they allow the students to stretch their muscles and they help prevent injuries. Cool downs are important because they allow time for the students to rest. Respect for facilities is also important because students need to respect the building and equipment they use during PE to ensure their safety and to allow other students the opportunity to use the facilities in the future. Orientation and Safety is very important because orientation allows you to get to know your environment and safety helps you be safe in your environment to prevent injuries. Diverse Etiquette is important because people should respect others no matter how different they are. So just be respectful to everyone. Abilities and responsibilities are also very important because you need to learn new abilities in PE. Like how to do a push-up or how to run a mile. Responsibilities are important because you need to be responsible when playing with others and be responsible with equipment in the gym itself.

Highlight details that show how Alice feels. "If that there King was to wake," added Tweedledum, "you'd go out – bang! – just like a candle!" "I shouldn't!" Alice exclaimed indignantly. . . . "Well, it's no use YOUR talking about waking him," said Tweedledum, "when you're only one of the things in his dream. You know very well you're not real." "I AM real!" said Alice and began to cry. —Through the Looking Glass, Lewis Carroll What inference can be made using these details? Alice is frustrated by Tweedledum’s logic. Alice wants to wake the king. Alice realizes that she is not real. Alice understands Tweedledum’s logic.

Answers

Answer:

Alice exclaimed indignantly,  Alice began to cry.

Explanation:

Answer:

"Alice is frustrated by Tweedledum’s logic."

Explanation:

Highlight details that show how Alice feels. "If that there King was to wake," added Tweedledum, "you'd go out – bang! – just like a candle!" "I shouldn't!" Alice exclaimed indignantly. . . . "Well, it's no use YOUR talking about waking him," said Tweedledum, "when you're only one of the things in his dream. You know very well you're not real." "I AM real!" said Alice and began to cry. —Through the Looking Glass, Lewis Carroll What inference can be made using these details? Alice is frustrated by Tweedledum’s logic. Alice wants to wake the king. Alice realizes that she is not real. Alice understands Tweedledum’s logic.

I hope this helps :)

Neeeeeed help on this one

Neeeeeed help on this one

Answers

When burned tobacco creates more than 7,000 chemicals. AT LEAST 70 are known to cause cancer
The answer issssssssssssssss 70

people keep telling me being lesbian will make me go to hell is that true?

Answers

Answer:

No, it isn’t.

Explanation:

They don’t support lesbians people.

Answer:  NOOOO

Explanation:

Some people are just inconsiderate and if they could just be a little more thoughtful of others the world might be even just a little bit better. You will not go to hell for a feeling towards other people. These are the same people that think the earth is flat. Please don’t listen to them.

can pets get coronavirus, can they sense coronavirus explain

Answers

Answer:

Animals don't appear to play a significant role in spreading the virus that causes CO.VID-19 . There is no evidence that viruses can spread to people or other animals from a pet's skin, fur or hair.

Explanation:

but to me i think cov.id-19 came from animals in china and i believe pets can sense anything

Pets probably won’t be able to spread coronavirus easily but they might be able to sense it. Pets like dogs are able to sense more things than we even realize

help please!!!!!!!!!!!!!!!!!!!!!!!

help please!!!!!!!!!!!!!!!!!!!!!!!

Answers

Explanation:

13

19

-3

8

9

10

y= 15

ur welcome

The answer to this is y=15

What is a calorie? Empty calories, give examples.

Answers

Answer:

A calorie is a unit of energy.

"In human nutrition, the term empty calories applies to foods and beverages composed primarily or solely of sugar, fats or oils, or alcohol-containing beverages. These supply food energy but little to no other nutrition in the way of vitamins, minerals, protein, fiber, or essential fatty acids."- Wikipedia

Answer:

The calorie is a unit of energy defined as the amount of heat needed to raise a quantity of water by one degree of temperature. There are two versions of the unit in use, which has led to some confusion.

Explanation:

I got it from google.

How does squatting help your overall health and well-being? How do you feel before stretching? How do you feel after stretching?

Answers

Answer:

Stretching has been shown to activate your parasympathetic nervous system. When this system is activated, it can result in a feeling of calmness and relaxation.

Stretching helps you relax your body and muscles so you feel relaxed and regenerated afterwards.

What are factors that influence your risk of non-communicable diseases?
options:
a) Heredity

b) Environment

c) Catching them from someone else

d) Both A and B

Answers

If i am not mistaken it is just A.

I’m pretty sure it’s A

Match each of the terms with the best identifying phrase.
can someone HELP ME LIKE FR THIS TIME

Match each of the terms with the best identifying phrase.can someone HELP ME LIKE FR THIS TIME

Answers

Answer:

1 f

2-I

3 c

4 e

5 a

6 j

7G

9 d

10 b

Answer:

1.f

2.J

3.C

4.E

5.a

6.I

7.g

8.h

9.d

10.b

Explanation:

Food labels contain a lot of important information consumers can use to make wise food choices. You learned what type of information is found on the food label, now it is time to get creative. You will create a food label for a brand new food or beverage product. Your product should be original, creative, and school appropriate.

Your food label should contain the following:

Creative, catchy product name (describes the food/beverage)
Picture of the food product
The Nutrition Facts (numbers and amounts can be made up)
Product ingredients
A Health Claim (low-fat, 100% of your daily Vitamin C, etc.)

Answers

food label should contain the picture of the food product, product ingredients, and a health claim

is it true that humen have 5 scenes

Answers

If you mean humans have 5 senses (taste touch hear smell see) YES

Answer:

Humans have 5 senses

Explanation:

Touch Smell vision hearing Touch

Fun fact
Bananas are curved because they grow towards the sun.

I don’t know, I’m bored, okay?

Answers

Answer: They curve towards the sun

Explanation:

Bananas are curved so they can retrieve sunlight. Bananas go through a process called 'negative geotropism'. I bet you're asking yourself how bananas could ever be negative. What it means is that bananas grow away from the ground, instead of growing towards it, hence the 'negative' geotropism.

Answer: bananas are so good

Which of the following is not a suggestion for eating healthy while out at a restaurant?
A. Get dressings and sauce on the side in order to monitor their use to just enough
B. Select foods that are grilled, boiled, or roasted rather than fried
C. Order an appetizer rather than an entree
D. Order heart-healthy selections

Answers

Answer:  my bad a

Explanation:

I’m thinking its A
Because B,C, and D are sort of eating healthy

Select all that apply.

In the lungs, blood _____.

picks up oxygen
drops off oxygen
drops off carbon dioxide
picks up carbon dioxide

Answers

Answer:

picks up oxygen & drops off carbon dioxide

Explanation:

the lungs pick up the oxygen to take it to the cells of the body where it is needed for metabolism. the carbon dioxide produced from ur metabolism is carried back into the lungs to be exhaled.

hope this helps!

Answer:

picks up oxygen

Explanation:

Red blood cells pick up oxygen in the lungs. Blood travels away from the heart and lungs through the arteries.

HELP ME PLS I WILL GIVE BRAINLIEST

HELP ME PLS I WILL GIVE BRAINLIEST

Answers

1. Enzymes
Explanation: Digestive enzymes play a key role in breaking down the food you eat. These proteins speed up chemical reactions that turn nutrients into substances that your digestive tract can absorb.

2. Epiglottis
Explanation: The epiglottis is a flap of tissue that sits beneath the tongue at the back of the throat. Its main function is to close over the windpipe (trachea) while you're eating to prevent food entering your airway.
1- enzymes
2-epiglottis

Question 4 (1 point)
Treatment with antibiotics is effective against bacterial infections, but they do not work against viruses, fungi, and protozoa.
True
False
Question 5 (1 point)
Many noncommunicable diseases are chronic illnesses that usually heal once they go into remission.
True
False
Question 6 (1 point)
Making healthy lifestyle choices and forming healthy habits now can reduce your risk of developing cancer later in life.
True
False
Question 7 (1 point)
Asthma and chronic obstructive pulmonary disease cannot be cured, but medications can help manage the conditions and symptoms.
True
False

Answers

Answer:

1.True

2.False

3.True

4.True

Explanation:

True.

Antibiotics are effective against bacterial infections but do not work against viruses, fungi, and protozoa. These different types of microorganisms require specific treatments, and antibiotics are specifically designed to target bacteria.

False.

Many noncommunicable diseases are chronic illnesses, meaning they persist over a long period of time. While some noncommunicable diseases may go into remission, it is not true that they usually heal once they go into remission. Remission refers to a period when the symptoms of a disease are reduced or disappear, but the underlying condition may still be present and require ongoing management.

True.

Making healthy lifestyle choices and forming healthy habits can indeed reduce the risk of developing cancer later in life. Factors such as maintaining a balanced diet, engaging in regular physical activity, avoiding tobacco and excessive alcohol consumption, protecting oneself from harmful environmental exposures, and getting recommended screenings and vaccinations can all contribute to reducing the risk of cancer.

True.

Asthma and chronic obstructive pulmonary disease (COPD) are chronic respiratory conditions that cannot be cured. However, medications and management strategies can help control and alleviate the symptoms associated with these conditions, allowing individuals to lead relatively normal lives with appropriate treatment and lifestyle adjustments.

true
false
true
true

All living things have four basic needs to live and function. List these four needs. Sample Response: All living things require water, air, food, and a place to live in order to survive.______________ What did you include in your response? Check all that apply. Living things require water. Living things require air. Living things require food. Living things require a place to live.

Answers

Answer:

food water shelter and air.

Explanation:

Air because all living things require air to survive

What should you do with a spoon that you have used for tasting food?​

Answers

Answer: If you use a silverware spoon, either wash it right away or put it in the dishwasher and if you use a plastic spoon, throw it in the trash right away.

Explanation: Stirring or mixing food that is still cooking or almost done cooking after tasting with the spoon can cause cross contamination.

Answer: wash it with soap and then use it again if needed. (Sponge, not hand)

The sentence below from the section "2. So Does Your Heart" helps prove the claim that changes in gravity dramatically affect the cardiovascular system over time.

Without gravity, however, the heart and blood vessels change – and the longer the flight, the more severe the changes.

Which sentence from the article provides further support for the claim?

The sentence below from the section "2. So Does Your Heart" helps prove the claim that changes in gravity

Answers

I know what you said you do not
A helps support the claim best

How are hormone levels regulated?

Answers

Answer:

The endocrine system is a tightly regulated system that keeps the hormones and their effects at just the right level. One way this is achieved is through 'feedback loops'. The release of hormones is regulated by other hormones, proteins or neuronal signals. The released hormone then has its effect on other organs.

Explanation:

Answer:

Consume antioxidants such as orange juice, lemon and blueberry.

To raise levels of DHEA, include fish in your diet such as salmon, tuna and mackerel, at the least three times a week.

Increases the consumption of vitamin A, B, D and folic acid.

Question 3 (1 point)
Storing chemicals in original containers in a locked area and wearing protective equipment when using chemicals can prevent injury.
True
False
Question 4 (1 point)
Putting a fire blanket over flames will remove the heat of a fire, which causes it to stop burning.
True
False
Question 5 (1 point)
Testing smoke detectors monthly and changing smoke detector batteries yearly is important when conducting a fire safety inspection.
True
False
Question 6 (1 point)
Emergency supplies should be stored in a locked cabinet so they are out of children’s reach.
True
False

Answers

Answer: All are true

Explanation: I learned this when I was in HOSA, PE, and Health Class. Trust me

Hope this helps

--Wavey

True false. True false true

Between 2018 and 2019, describe the change in the % of obesity ratings using the maps provided. Note three major changes. (3-4 complete sentences).

Between 2018 and 2019, describe the change in the % of obesity ratings using the maps provided. Note
Between 2018 and 2019, describe the change in the % of obesity ratings using the maps provided. Note
Between 2018 and 2019, describe the change in the % of obesity ratings using the maps provided. Note

Answers

Answer:

This should get you started it should be a little easier from here.

The Percent has obviously gone up. The red is showing the most growth within the chart.

You could say how the percentage of the places colour coded orange have increased and the countries colour coded purple have decreased :)

What does it mean if your laying down on your knees and then it starts to hurt when getting up?

Answers

Probably because u have been like that for a couple of hours and then u stand up and it hurts a lot

Answer:

Osteoarthritis (OA) If you experience inner knee pain while putting pressure on your joint, such as when walking up and down stairs or sitting down in a chair, you may have OA. Because this pressure causes the pain, your symptoms may get more severe as the day goes on.

What is the sub-group of AA that helps young people come together to share their experiences of having been affected by someone else’s drinking?
Answer:

Answers

The sub-group of AA that helps young people come together to share their experiences of having been affected by someone else's drinking is called “Alateen.”

Answer:

The sub-group of AA that helps young people come together to share their experiences of having been affected by someone else's drinking is called Al-Anon. Al-Anon is a 12-step program for people who have been affected by someone else's drinking, including children, spouses, partners, parents, and friends. Al-Anon meetings are held all over the world, and they are free to attend.

Al-Anon is based on the idea that alcoholism is a family disease, and that everyone in the family is affected by the alcoholic's drinking. Al-Anon meetings provide a safe space for people to share their experiences, feelings, and fears about alcoholism. Meetings also provide information about alcoholism and how to cope with its effects.

Explanation:

what is sperm (sexual cell) and what is it used for?

Answers

They are male reproductive cells made to fertilize the female’s egg
Sperm is used to fertilized a females egg to have kids
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