Consider the following statement. For every integer m, 7m 4 is not divisible by 7. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order.

Answers

Answer 1

The constructed proof is given below.

Calculations and Parameters

Prove: f(M)= 7M +4 is not divisible by 7 for any integer M.

M=0 --> f(M) = 4 which is not divisible by 7.

M=1 --> f(M) = 11 which is not divisible by 7.

Suppose f(M) is not divisible by 7 for some positive integer M.

(this is the GIVEN induction hypothesis)

7(m+1)+4 = 7m+7+4 = 7m +4 + 7 = (7m+4)+7

dividing by 7, the quotient is [(7m+4)+7]/7

= (7m+4)/7 + 1

This is NOT divisible by 7 per induction hypothesis...

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Related Questions

Which of the following statements is NOT true about the consequences of alcohol

Answers

A statement which isn't true about the consequences of alcohol is: B. adolescents who drink alcohol are more likely to drop out of high school than their peers who don't drink.

What is an alcohol?

An alcohol is an organic chemical compound that's produced through the natural fermentation of sugars. Also, alcohol is the primary intoxicating constituent of all alcoholic drinks such as:

WineSpiritsBeer

Basically, some of the consequences of alcohol include the following:

Decreased ability to make a rational decision.Higher rate of accident in teenagers.It increases depressionHigher engagement in risky se-xual activity.

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Complete Question:

Which of the following statements is NOT true about the consequences of alcohol?

a. Drinking alcohol increases the likelihood of engaging in risky se-xual activity, such as unprotected sex.

b. Adolescents who drink alcohol are more likely to drop out of high school than their peers who don't drink.

c. Alcohol related crashes involving teenagers accounts for approximately 5,000 deaths per year in the US.

d. Students diagnosed with alcohol abuse are four times more likely to experience major depression.

Answer:

"adolescents who drink alcohol are more likely to drop out of high school than their peers who don't drink"

Explanation:

took the test got it right

Which of the following statements regarding the NREMT is correct

Answers

Answer:

I HAVE NO IDEA

Explanation: none

Having an awareness of the risks inherent in the particular road and traffic situation is one of the traits of a good driver

Answers

This is true. Having an awareness of the risks inherent in the particular road and traffic situation is one of the traits of a good driver.

Who is a good driver?

This is the person that has the necessary skills and requirements that can pass them off as good users of the road.

This is a person that has to be well aware of road principles, follows the law and is watchful of potential harms on the road. The ability to follow the laid down principle of the road is very important while a person is driving.

Certain actions and other forms of driving without the required training may pose as risks to the person driving and also to the other people that may be on the road. Hence in order to be a good driver, you should have  awareness of the risks inherent in the particular road and traffic situation.

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Consider the series Three-halves three-fourths StartFraction 3 Over 8 EndFraction StartFraction 3 Over 16 EndFraction ellipsis What expression defines Sn

Answers

The expression to find the sum of terms of the series is; Sₙ = 3(1 - ¹/₂ⁿ)

How to solve Geometric series?

We are given the series;

3/2 + 3/4 + 3/8 + 3/16 +.....

Formula for the nth term of a geometric series is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

From our given series;

a = ³/₂

r = (³/₄)/(³/₂) = ¹/₂

We know that Sum of GP when n < 1 is;

Sₙ = a(1 - rⁿ)/(1 - r)

Thus;

Sₙ = ³/₂(1 - ¹/₂ⁿ)/(1 - ¹/₂)

Sₙ = 3(1 - ¹/₂ⁿ)

Thus, the expression to find the sum of terms of the series is; Sₙ = 3(1 - ¹/₂ⁿ)

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Answer:

C i took the test

Explanation:

Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following.

Answers

Please be rightly informed that the regression equation is:

Y = 1.3330 + 0.6667X

Complete question:

Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family home. A random sample of 10 homes yielded the following:

Number of Rooms Kilowatt-Hours

12 9

9 7

14 10

6 5

10. 8

8 6

10 8

10 10

5 4

7 7

X = Total x / n

= (12 + 9 + 14 + 6 + 10 + 8 + 10 + 10 + 5 + 7) / 10

= 9.1

Y = Total y / n

= (9 + 7 + 10 + 5 + 8 + 6 + 8 + 10 + 4 + 7) / 10

= 7.4

sX = ∑ √( X − X ¯ )² / n-1

= √66.9/10-1

= 2.7264

sY = ∑ √( Y − Y ¯ )² / n-1

= √36.4 / 10-1

= 2.0111

Correlation coefficient of X and Y

= ∑(X − X ¯ )(Y − Y ¯) / (n-1) SxSy

= 44.6 / (10-1)(2.7264)(2.0111)

= 0.9038

a Compute the regression in the equation

b. Determine the number of kilowatt-hours, in thousands, for a six-room house.(Round your answer to 3 decimal places.)

The complete solution to the question is attached to the images I sent.

So therefore, please be rightly informed that the regression equation is:

Y = 1.3330 + 0.6667X

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The Petters case was an example of which type of fraud

Answers

The Petters case was an example of the type of fraud called the Ponzi Scheme. This is further explained below.

What is Ponzi Scheme?

Generally, deception is when early investors are bribed with rapid returns on their money by later investors to believe in the success of a non-existent business.

In conclusion, The Petters affair is an example of a sort of investment scam known as a Ponzi Scheme.

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Choosing facility location has become more flexible for both companies and employees through the use of such as texting, teleconferencing, cell phones, and email.

Answers

Choosing facility location has become more flexible for both companies and employees through the use of information technology such as texting, teleconferencing, cell phones, and email.

What is information technology?

Information technology refers to all the digital channels that are used in communication. Today, many people use information technology in their interactions with others.

We use phones, tablets, and computers in our relations with people. Information technology is very good because it helps to enhance communication in the business and personal spheres.

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most people with dissasociatuve identity disorder exhibit high

Answers

Most people with dissociative identity disorder exhibit high hypnotic susceptibility and experienced a history of child abuse.

What is dissociative identity disorder?

Dissociative identity disorder (DID)  can be regarded as the mental health condition.

This mental disorder is associated with   multiple, distinct personalities. , ion this case, the  identities control a person's behavior at different times.

In this case, it can result to  memory loss as well as  delusions or depression and it should be noted that Most people with dissociative identity disorder exhibit high hypnotic susceptibility and experienced a history of child abuse.

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In the past two decades, the number of teenage pregnancies has

Answers

In the past two decades, the number of teenage pregnancies has dropped dramatically across all ethnic groups.

Why has teenage pregnancies has dropped dramatically across all ethnic groups?

The teenage pregnancies has dropped dramatically across all ethnic groups because of the education , there are alot of parents that are now educated to educate their children about danger of teenage pregnancies.

Also, there has been increased in protective measure by the government to reduce teenage pregnancies, hence, In the past two decades, the number of teenage pregnancies has dropped dramatically across all ethnic groups.

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in what form is the energy derived from carbohydrates stored in the body

Answers

The form in which energy derived from carbohydrates is stored in the body is:

Glycogen

In what form is emergy stored in the body?

The form in which energy is stored in the body is glycogen. Glycogen contains many glucose monomers that link up to form the polysaccharide glycogen.

This carbohydrate form is often stored in specific organs of the body. Some of these are the liver and the muscles.

When the body is in the fasting mood it utilizes the glycogen stored in these places to generate energy.

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Humans fit into the food pyramid as ________.

Answers

Humans fit into the food pyramid as tertiary consumer

What is food pyramid?

Food pyramid consist of many food web joined together.

Each food web consist of organisms in different energy group feeding directly on each other. The highest of the pyramid is Tertiary consumer.

Humans are tertiary consumer as they get their food by feeding on already available food.

Therefore, Humans fit into the food pyramid as tertiary consumer

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This architectural construction method consists of two uprights and a crossbeam.

Answers

The architectural construction method that consists of two uprights and a crossbeam is called post-and-lintel system

What are the building construction members?

The architectural construction method that consists of two uprights and a crossbeam is called post-and-lintel system. This is because in building construction, a system in which two upright members, the posts, hold up a third member, the lintel, laid horizontally across their top surfaces.

The post-and-lintel system is a simple method of construction involving the use of vertical and horizontal elements. The verticals support the horizontals, creating one Storey of a building. Additional verticals can be placed atop the horizontals to create structures with more than one level.

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identify a characteristic of the data that is ignored by the regression line

Answers

There is a significant point that has a significant impact on the graph of the regression line, which is a feature of the data that is disregarded by the regression line. This is one of the characteristics of the data that is ignored by the regression line.

This is further explained below.

What is a regression line?

Generally, A regression line is an estimate of the line that depicts the real, but unknown, linear connection between the two variables. This line is drawn using the method of linear regression. When trying to forecast (or make an estimate of) the value of the response variable based on the value of the explanatory variable, the equation of the regression line may be utilized.

In conclusion, Data that is overlooked by regression lines has an important point that has a significant impact on how the graph looks.

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what my mother and i don't talk about pdf free

Answers

The inference about the story is that Leslie Jamison writes about trying to discover who her perfect mother was before ever becoming a mom.

How to illustrate the information?

As an undergraduate, Michele Filgate started writing an essay about being abused by her stepfather and it took her more than a decade to realize that she was actually trying to write about how this affected her relationship with her mother.

When it was published, the essay went viral, shared on social media by Anne Lamott, and many others. This then gave Filgate an idea, and the resulting anthology offers a candid look at our relationships with our mothers.

Leslie Jamison writes about trying to discover who her seemingly perfect mother was before ever becoming a mom.

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Complete question:

What inference can be deducted from the story titled "what my mother and i don't talk about"?

Casey is looking for a free, open-source RDBMS for his company. Which of the following best meets these requirements

Answers

A free open-source RDBMS  that best meets the needs of Casey is the PostgreSQL.

What is an open source database?

An Open source data base is available to be freely copied and modified to meet specific needs. The following are the types of open-source RDBMS; MariaDB, Db2 Express-C, SQLite, CUBRID, Firebird, Oracle Database XE etc. The database makes the management of the company information to be seamless. This is why many companies, not just the tech companies are heading towards the development of excellent databases.

A free open-source RDBMS  that best meets the needs of Casey is the PostgreSQL. This is the kind of database that would meet the specifications of the company.

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一亩 We mailed you a notice informing you of the action we intend to take on your case.

Answers

The above notice is known as NOID. This means a "Notice of Intent to Deny". This is usually issued to a person who is seeking legal immigration in to the US that their petition will not be granted in the way that they have presented it.

What else does the NOID state?

The NOID is also instructional in that it tell the recipient the instructions or steps that they must take after the receipt of the notice.

What is USCIS?

The above is an acronym for: U.S. Citizenship and Immigration Services.

This is the name of the body in the United States of America that is in charge of lawful immigration in to the US.

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Full Question:

Notice explaining USCIS action is mailed. We mailed you a notice informing you of the action we intend to take on your case. Please follow the instructions in the notice and submit any requested materials.

What does this mean?

what percentage of people are hermaphrodites

Answers

The percentage of the people who are referred to as hermaphrodites in existence is 1.7% which is regarded as a small part of the overall population in the world.

Who is a Hermaphrodite?

These refers to an individuals which has both types of reproductive organs present in their body. They are also able to produce gametes which are related to the male and female gender. An example of organisms which are hermaphrodites include earthworms, snails etc.

They have a few population of which some have clinically identifiable variations in their system and could be of natural or an abnormal feature. This therefore enables them to have both male and female characteristics present in their body system hence, there is usually difficulty in gender identification of the species in general.

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Rank the different types of bank accounts according to their liquidity.

Answers

The Rank of the different types of bank accounts according to their liquidity from Highest liquidity to Lowest liquidity are:

Checking AccountSavings Account Certificate of Deposit (CD)

What liquidity means in business?

Liquidity is known to be a company's ability to be able to raise cash if it is said to be in dine need of  it.

Hence, The Rank of the different types of bank accounts according to their liquidity from Highest liquidity to Lowest liquidity are:

Checking AccountSavings Account Certificate of Deposit (CD)

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A company that makes mirrors sends their slightly flawed products to a discount store. This week, the company sent four mirrors to the discount store. Each mirror is approximately rectangular, with both lengths the same and both widths the same.

Answers

Based on the given dimensions, a mirror which is the closest to being rectangular is: mirror 4.

What is a diagonal?

The diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

Mathematically, the length of diagonals of a rectangle can be calculated by using this formula:

d = √(l² + w²)

Where:

d is the diagonal of a rectangle.l is the length of a rectangle.w is the width of a rectangle.

For mirror 4, we have:

d = √(16² + 18²)

d = √580

d = 24.08 inches.

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Complete Question:

A company that makes mirrors sends their slightly flawed products to a discount store. This week, the company sent four mirrors to the discount store. Each mirror is approximately rectangular, with both lengths the same and both widths the same.

Mirror 1

length: 16 inches

width: 18 inches

diagonal: 25 inches

Mirror 2

length: 16 inches

width: 18 inches

diagonal: 26 inches

Mirror 3

length: 16 inches

width: 18 inches

diagonal: 23 feet

Mirror 4

length: 16 inches

width: 18 inches

diagonal: 24 inches

Based on these dimensions, which mirror is the closest to rectangular?

Mirror 1

Mirror 2

Mirror 3

Mirror 4

Match the correct graph to the function.

Answers

There is no picture attached.

Whole potatoes were coated with olive oil and salt, baked in-house and stored in a cooler for several days. What must be included on the label for the baked potatoes

Answers

On the labels should be included the date that food should be discarded.

What is a food label?

A food label is an informative piece that indicates specific features of processed foods.

The expiration date of food is fundamental to avoid intoxication and/or food-borne contamination.

In conclusion, on the labels should be included the date that food should be discarded.

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because stalin feared western capitalist expansion, he

Answers

Because Stalin feared Western capitalist expansion, he refused to allow free elections in Eastern Europe.

What is Capitalism?

This refers to the economic system where businesses are allowed to thrive in a free market system with the main aim of making a profit.

Hence, we can see that based on the difference in ideology between America and the Soviet Union; capitalism and communism, Joseph Stalin refused to allow free elections in Eastern Europe for a fear of capitalist expansion.

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Which of the following protocols would secure a tunnel for credential exchange using port 636?

Answers

The protocols that  would secure a tunnel for credential exchange using port 636 is Lightweight Directory Access Protocol Secure (LDAPS).  

What is LDAPS?

Lightweight Directory Access Protocol Secure (LDAPS) is known to be a protocol that uses a PKI certificate to  be able to secure LDAP connections over the network and it often uses TCP port 636.

Hence, The protocols that  would secure a tunnel for credential exchange using port 636 is Lightweight Directory Access Protocol Secure (LDAPS).  

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In spinal motion restriction of the adult, which action demonstrates correct stabilization technique

Answers

In spinal motion restriction of the adult, to maintain the client's nose and umbilicus aligned at all times demonstrates the correct stabilization technique.

What is spinal motion restriction?

Spinal motion restriction is a strategy used to maintain spine alignment during spinal injury.

This technique is fundamental to avoiding severe spinal injury after accidents or traumatic situations.

In conclusion, in spinal motion restriction of the adult, to maintain the client's nose and umbilicus aligned at all times demonstrates the correct stabilization technique.

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Match each white blood cell with its description.

Answers

The correct description of the white blood cells are as follows:

Neutrophil - Phagocytizes small particles; first-responders at infection siteMonocyte - Phagocytizes large particles in tissuesLymphocyte - Provides immunityBasophil - Releases histamine and heparinEosinophil - Moderates allergic reactions; defends against parasitic worm infections

What are white blood cells?

White blood cells also known as leukocytes are special cells white are found in the blood and whose function is the immune system of the body.

White blood cells are named the because they lack hemoglobin found in the red blood cells, and as such are not red in color like the red blood cells.

The white blood cells found in the blood are of various types which includes:

NeutrophilsMonocytesLymphocytesBasophilsEosinophils

The various forms of the white blood cells play various roles in the immune system such as; phagocytosis of foreign particles, release of histamine and heparin, as well as being involved in allergic reactions of the body.

In conclusion, the white blood cells are special cells which play important role in maintaining the immune system of the body.

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Note that the complete question is given below:

Match each white blood cell with its description.

Neutrophil

Phagocytizes small particles; first-responders at infection site

Monocyte

Phagocytizes large particles in tissues

Lymphocyte

Provides immunity

Basophil

Releases histamine and heparin

Eosinophil

Moderates allergic reactions; defends against parasitic worm infections

The primary function of a scuba regulator is to:

Answers

The primary function of a scuba regulator is to reduce high-pressure air in the scuba cylinder to surrounding pressure.

What is a Scuba?

This is a type of underwater diving where breathing equipment are used due to lack of air supply.

The scuba regulator makes breathing under water easier as a result of it reducing high-pressure air to ambient pressure.

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minor blows to the head never lead to long-term brain injury

Answers

Minor blows to the head never lead to long-term brain injury: False.

What is a brain?

A brain can be defined as a delicate internal organ of soft-nerve tissue that is primarily found within the skull of vertebrates, and it's mainly responsible for the coordination of nervous activities, sensation and intellect in living organisms.

Based on medical information and records, the brain comprises two (2) sides which are able to communicate through the corpus callosum and they include:

Symmetrical left hemispheresSymmetrical right hemispheres

In conclusion, it is very important to note that both minor and major blows to the head can lead to long-term brain injury in living organisms.

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Categorize each statement as true or false. The SI V-Scope is a virtual microscope program which simulates the use of a compound light microscope.

Answers

The SI V-Scope is indeed a virtual microscope program that can stimulate the use of a compound light microscope so this is TRUE.

What is a SI V-Scope?

The SI V-Scope stands for a Science Interactive and then Virtual scope which is used simulate the way that a compound light microscope works.

These microscopes are very useful because they help people who don't have a physical microscope to access microscopes wherever they are.

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which priority teaching intervention would the nurse include in the care plan for a client who has insomnia

Answers

The teaching intervention that the nurse would have to include would be to give the patient prescribed insomnia during dinner.

What is insomnia?

Insomnia is the term that is used to refer to the fact that a person is having issues with sleeping.

This may be due to underlying issues with health or with mental health. The patient can be helped by giving them prescribed pills that may help them to sleep.

In other to help the person that is suffering from this condition,  A nurse would help them through the use of prescribed pills. The issue is that there are usually a lot of side effects when it comes to the use of pills to treat insomnia in a person.

Another way is through the use of sleep therapy to get them to readjust their sleep pattern. If this condition persists, it could be a cause for alarm for the patient.

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2) Use the Kspa expressions for CuS and ZnS to calculate the pH where you might be able to precipitate as much Cu2 as possible while leaving the Zn2 in solution, and find what concentration of copper would be left. Assume the initial concentration of both ions is 0.075M.

Answers

The pH where you might be able to precipitate as much Cu2 as possible will be any value that is less than 5.85.

How to illustrate the information?

The solubility product of salt is defined as the product of molar concentrations of ions in a saturated solution of it.

An ion will be precipitated if the ionic product exceeds the solubility product of the cation. In the case of Cu and Zn, the solubility product is greater for Zinc than Copper.

Also Cu will be precipitated in an acidic medium while Zn is precipitated in an alkaline medium. We have for CuS, K= S2 so S = 2.4495*10-8. For ZnS, S = 0.1414. So the lower the pH higher will be the amount of CuS precipitated.

If we are starting with 0.075M CuS and ZnS solution it will have 0.075 moles each of Cu2+, Zn2+, and S2. Since the anion concentration can be equated to POH, POH for Cus and Zns are 14.096 and 5.85.

The maximum precipitation will take place is any value which is less than 5.85.

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