abe, bobby, charles, devin and edwin are the participants in a race. how many different $1$st-$2$nd-$3$rd place outcomes are possible if there are no ties? two different outcomes to include are bobby-devin-edwin and devin-bobby-edwin.

Answers

Answer 1

We apply permutation formula to the number of participants considering that there are no ties and find out that there are 60 different outcomes possible if there are no ties.

It is given to us that -

There are 5 participants - Abe, Bobby, Charles, Devin, and Edwin

We have to find out the number of different 1st - 2nd - 3rd place outcomes that are possible if there are no ties.

Considering that there should be no ties,

If we select one person, say Abe, then there are 4 different ways remaining for the second place in the race.

Similarly, assuming that Abe ranked 1st in the race and Bobby ranked 2nd in the race, there are 3 different ways remaining for the third place in the race.

Continuing like this, the 5 different participants can be ranked accordingly such that there are no ties.

For this situation, we have to find the permutation where -

Total number of objects (in this case, participants) = n = 5

and, total number of objects selected = r = 3

We know that the formula for permutation is -

[tex]P = \frac{n!}{(n-r)!}\\[/tex]

Substituting the values of 'n' and 'r' in the above equation, we have

[tex]P = \frac{n!}{(n-r)!}\\= > P = \frac{5!}{(5-3)!}\\= > P = 60[/tex]

Thus, by applying permutation formula, we find out that there are 60 different outcomes possible if there are no ties.

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Related Questions

When 1,250 superscript three-fourths is written in its simplest radical form, which value remains under the radical?10652.

Answers

The value under the radical is 8

what is power?

How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 82 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."

What is exponent and power?

Exponents and powers can be used to represent extremely large or extremely small numbers in a more straightforward way. To illustrate 3 x 3 x 3 x 3 in a straightforward manner, for instance, we could write it as 34, where 4 is the exponent and 3 is the base. It is said that the entire statement 34 has power.

Due to it,

1250^(3/4)

Having said that,

Since n is an integer number,

Greater than x is n.

actual number a

Therefore,

1250^(3/4)=5^(3) *((4)root(2)^3

1250^(3/4)=125 *((4)root(2)^3

Therefore, the value that is still below the radical is 8.

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What is the 3 phases of agile life cycle?.

Answers

The 3 phases of the agile life cycle:

The Continuous Delivery: Lean Life Cycle.

The Exploratory (Lean Startup) Life Cycle.

The Program Life Cycle for a Team of Teams.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The 3 phases of the agile life cycle:

The Continuous Delivery: Lean Life Cycle.

The Exploratory (Lean Startup) Life Cycle.

The Program Life Cycle for a Team of Teams.

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the drive time for a college student commuting between her dorm and her coop job is uniformly distributed between 20 and 45 minutes. the probability that she will get to work in 30 mins or less is

Answers

The probability that a college student will get to work in 30 mins or less is 0.4 or 40%.

What does uniformly distributed probability mean?

Uniform distribution refers to a type of probability distribution in which all outcomes are equally likely to occur.

According to the given question:

Since the time is uniformly distributed, every possible travel time has the same likelihood of occurring.

Lower boundary (L) = 20 minutes

Upper boundary (U) = 45 minutes

The probability that a student finishes her trip in 30 minutes or less is:

P (t ≤ 30) = (30 - L)/(U - L)

              = (30 - 20)/(45 - 20)

              = 10/25

              = 0.4 or 40%

The probability that she will get to work in 30 mins or less is 0.4 or 40%

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The registration fee for a used car is 0.8% of the sale price of $5,100. How much is the fee?

Answers

0.8% (5100)=40.80
So 40.80 is the fee


Can I get Brainly

Julie has a block of wood that has a height of 9 cm, a width 2 cm, and a length of 3 cm. What formula would Julie use to find the volume of this wooden block?

Answers

Answer:

V=HWL

54cm³

Step-by-step explanation:

V=HWL

∴V=9*2*3

V=54cm³

Find the point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8).

Answers

The point, M, that is midway between P=(5,−8,−6) and Q=(-7,-2,-8) is

M = (-1, -5, -7)

How to find the midway

In geometry, the midpoint formula is an equation that determines the separation between two known coordinate locations at their halfway point.

The midway between the points P and Q is calculated using the method

Mid point = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)

Applying the method to the given points gives

P = (5, −8, −6) and Q = (-7, -2, -8)

M = ((5 + -7)/2, (-8 + -2)/2, (-6 + -8)/2)

M = (-1, -5, -7)

The coordinates of point M (-1, -5, -7) is the mid way between point  P=(5,−8,−6) and Q=(-7,-2,-8).

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What are the 5 examples of linear equation?.

Answers

The required five equation of linear equation are given below.

What is linear equation?

A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the incline and b is the y-catch. At times, the above is known as a "direct condition of two factors," where y and x are the factors.

According to question:

Five examples of linear equation,

1) 2x – 3 = 0

2) 2y = 8

3) m + 1 = 0

4) x/2 = 3

5) x + y = 2

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What is the central angle called?.

Answers

The central angle states the property of the center of the circle, So It is called the central angle.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

Hence,

The central angle states the property of the center of the circle, So It is called the central angle.

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Paul and Brian win some money and share it in the ratio 3:4. Paul gets £30. How much did Brian get?

Answers

Answer:

£10

Step-by-step explanation:

3:4 is equal to 3/4 (three-quarters)

Paul gets 75%, and Brian gets 25%.

Paul gets £30.  30 is 3/4 of what number?

75/100 × x = 30

Multiply both sides by 100 and divide both sides by 75

x = 30 × 100/75

x = 30 x 1.33333333333

x= 40

£30 is 75% of £40

30/40 x 100 = 75%

10/40 x 100 = 25%

Brian gets £10

Penny works 43 hours at an hourly rate of $8.50. She was paid time
and a half for the overtime. What were her total wages?

Answers

Answer: $548.25

Step-by-step explanation: 43 x $8.50 = 365.5 x 1.5 = $548.25

What is the monthly finance charge if the average daily balance is $30, the daily periodic rate is 0.07%, and the number of days in the cycle is 30? a. 21¢ b. 63¢ c. 90¢

Answers

The monthly finance charge is 63 cents.

Here we have to find the monthly finance charge.

The given data:

Average daily balance = $30

The daily periodic rate = 0.07%

The number of days in a cycle is 30.

The formula to find the finance charge:

Finance charge = APR balance × number of days in billing cycle / 365

As it is given a daily periodic rate this means that:

APR / 365 = 0.07%

                = 0.0007

Hence, putting the value in the formula we have:

Finance charge = 0.0007 × 30 × 30

                         = 0.63

As we know that $1 = 100 cents

So finance charge = 0.63 × 100

                               = 63 cents

Therefore the finance charge is 63 cents.

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What is specialized language?.

Answers

Specialized language is language that is distinctive and pertinent to a particular industry.

Define the term specialized language?

Language that is relevant to and distinctive of an industry is referred to as specialised language.

A language that uses specialised terms and particular terminologies to distinguish itself from general language is referred to as specialised language.When used correctly for the audience, specialised terms can make literature easier to grasp.Any in-group or specialised language for use by small groups of people with similar interests is referred to as "jargon."According to Durham University researchers, the ability to express oneself uniquely through language necessitates the creation and flexible use of signals by people.

They contend that it could only have occurred with the emergence of specific psychological skills, explaining why language is only found in humans.

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TRUE/FALSE. if new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants.

Answers

If new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is false.

What is statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given,

We need to check whether if new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is true or false.

The given statement is false because Primary data collection is a process of collecting original data, directly from the source.

Hence, if new data will be collected (i.e., primary data collection), the researcher can easily recruit an adequate number of participants is false.

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7.3.3: basic class definition. define the missing method. licensenum is created as: (100000 * customid) licenseyear, where customid is a method parameter. sample output with inputs 2014 777:

Answers

Program in java ,

public int createLicenseNum(int customID){

      licenseNum = (100000 * customID) + licenseYear;  

      return (licenseNum);     }

createLicenseNum method takes customID as its parameter. The formula function :

licenseNum = (100000 * customID) + licenseYear;

100000  is multiplied to the customID and  the result is added  to the licenseYear and is assignedlicenseNum.

When the CreateLicenseNum function is invoked it computes and returns the value of licenseNum as:

licenseNum = (100000 * customID) + licenseYear;

                    = (100000 * 777) + 2014

                    = 77700000 + 2014

licenseNum = 77702014                                                                                                        

Output is:

Dog license: 77702014      

   

Function call JAVA:

public class CallDogLicense {

public static void main(String[] args) {

DogLicense dog1 = new DogLicense();

dog1.setYear(2014);

dog1.createLicenseNum(777);

System.out.println("Dog license: " + dog1.getLicenseNum()); //calls getLicenseNum to get the computed licenceNum value

return; } }

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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?

PLEASE HELP!!!!!!!!!

Answers

Answer:

The answer you are looking for would be 60% off.

Step-by-step explanation:

On a calculator, set up this equation:

0.60 x 49.99 = 29.994, rounded is $30.00

(Do this with all answer choices, just replace 0.60 with 0.70, 0.40 and so on).

But, 60% would be the answer.

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using the digits $1$, $2$, $3$, $4$, $5$, how many even three-digit numbers less than $500$ can be formed if each digit can be used more than once?

Answers

The number of three-digit numbers less than $500 that cab be formed is 90.

How to form three digit numbers numbers from a set?

The formation of the numbers involves the permutation of the first three even digits. Also, permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear.

The sequence include the following:  $1$, $2$, $3$, $4$, $5$,

The number must be less than $500$.

In order to find the number of even digits numbers to be fixed, we select the even numbers.

So, the number of possible arrangements = [tex]6_{P_{2} }[/tex]

[tex]\frac{6!}{(6-2)!}[/tex]

=[tex]\frac{6*5*4*3*2*1}{4*3*2*1}[/tex]

6*5

=30

Similarly, fixing the units digit as 4

The number pf possible arrangements =    [tex]6_{P_{2} }[/tex]

=6*5=30

Fixing the unit digit as 6

The number of arrangements possible is [tex]6_{P_{2} }[/tex]

5*6 = 30

Therefore three-digit even numbers  that can be formed is:

30+30+30=90

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If ADEF=AJAM, which statement will always be true?

Answers

The first statement is always true.

If m ∠m = 64° then m ∠F = 64°.

What is isomorphic triangles?

If there is an isomorphism connecting the vertices of P and Q, and that isomorphism has the property that three vertices of P form a triangle in Tp if and only if the mapping of the three vertices in Q, then the triangulations of two simple polygons, Tp and Tq, are said to be isomorphic (or occasionally compatible).

Given: ΔDEF ≅ ΔJAM

As the triangles are isomorphic that means that each angle of the triangle are same.

⇒ ∠D = ∠J

∠E = ∠A

∠F = ∠M

Hence, If m ∠m = 64° then m ∠F = 64° is true.

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Find -1 1/8 - 3/4.
First write the expression with a common denominator
-1 1/8 - 3/4 = -1 1/8 - ?/8

Answers

The value of the unknown is 6

What is fraction?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

the expression -1 1/8 - 3/4 = -1 1/8 - ?/8 shows that

-3/4=-?/8

the LCM of the denominator of two fractions is 8

multiply both sides by 8

-3/4×8=-?/8×8

therefore,. -? = -3×2

?= 6

Therefore the value if the unknown is 6

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The fraction is expressed with a common denominator as - 15/ 8

What is a fraction?

A fraction is simply described as the part of a whole, element or number.

There are several types of fractions, which includes;

Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractions

From the information given, we have  the fractions;

-1 1/8 - 3/4.

Convert the mixed fraction to improper fraction

- 9/ 8 - 3/4

Find the Lowest common multiple

-9 - 6  /8

Subtract the numerators

-15/ 8

Hence, the value of the expression is -15/8

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Can you use a right triangle to represent the distance between any two points on the coordinate plane?.

Answers

Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.

We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:

( 3, 4 ) and ( − 2, 1 )

We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.

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State your conclusion about Bill's exact binomial test in a complete sentence. That is, explain why you choose to reject the null or why you choose to fail to reject the null. Fail to reject the null hypothesis, because the p-value is not small (it's more than 10%). Fail to reject the null hypothesis, because the p-value is small (it's less than 2%). Reject the null hypothesis because the p-value is not small (it's more than 10%). Reject the null hypothesis because the p-value is small (it's less than 1%). Then confront Bill about his cheating, or play with someone else.

Answers

Reject the null hypothesis, because the P-value is small (it's less than 1%) then confront Bill about his cheating play with someone else.

Fail to reject the null hypotheses, because the P-value is not small (it's more them 10%).

One of the most generally utilized p-values is 0.05. If the determined p-values end up being under 0.05, the invalid speculation is viewed as bogus, or invalidated (subsequently the name invalid theory). What's more, on the off chance that the worth is more prominent than 0.05, the invalid speculation is viewed as obvious.

That p-value is the likelihood that we'll obtain similar outcomes as the invalid speculation, and in our model, the edge for that likelihood is 0.05. So if the determined p-value is under 0.05, it really intends that there's exceptionally less probability that we'll come by similar outcomes as the invalid speculation. Also, in the event that the p-value is more than 0.05, the likelihood of obtaining similar outcomes as invalid speculation is exceptionally high, so we can believe the invalid speculation to be valid.

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a statistical relationship between two variables is considered statistically significant if it is stronger than what percent of relationships we'd expect to see by chance.

Answers

The statistical relationship between two variables is stronger than 95% of the relationships we would expect to see just by chance.

Statistical relationship:

Statistical relationship defines that  if a change in one variable (X) results in a systematic increase in another (Y).

Given,

A statistical relationship between two variables is considered statistically significant.

Here we need to find if it is stronger than what percent of relationships we'd expect to see by chance.

While we looking into the given question we know that the statistical relationship is stronger then the percent of relationships we'd expect to see by chance is 95%.

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What is the complex number in the form a bi?.

Answers

A complex number is represented as a + bi, where a denotes the real part and bi denotes the imaginary part, to represent it in standard form.

How to find the value of i ?

Its value is fixed which is  √-1

A complex number is, for instance, 5 + 2 i. The same is true for 3+4i.

Consequently, a complex number is a straightforward illustration of the addition of two integers, namely a real number and an imaginary number. There are two distinct halves to it: one is entirely real, and the other is fantastical.

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The table given shows the length, in feet, of dolphins at an aquarium.
3 15 30 19 11 18 17 12
Are there any outliers in the data?
There is an outlier at 3 feet.
There is an outlier at 30 feet.
There are outliers at 3 and 30 feet.
There are no outliers.

Answers

Answer:

......................................................d

There are two outliers in the given data and they are 3 and 30. Hence, option C is correct.

What is the arithmetic sequence?

Two definitions are given for an arithmetic sequence. A "series where the variances in between every two succeeding terms are the same" is what it is. Each term in an algebraic expression is created by multiplying its previous term by a specified integer (either positive, negative, or zero).

As per the given information in the question,

The length of dolphins is given as:

3, 15, 30, 19, 11, 18, 17, 12

As we can see in this data every length is somewhere close to 20 but lengths 3 and 30 are not similar to others.

So, these two are outliers.

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How do you calculate obtuse value?.

Answers

Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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how many inflection points can a (a) quadratic polynomial have? (b) cubic polynomial have? (c) polynomial of degree n have?

Answers

The number of inflection points can a quadratic polynomial and a cubic polynomial have is zero and one respectively.

For the points of inflection,

We know that the roots of second derivatives give the inflection points of a function,

For inflection point , f(x)'' = 0

(a) For quadratic, there will be f(x)'' independent of x, So, there will be no point of inflection.

(b) For cubic, there is a second derivative have a linear function, So, only one point of inflection.

Any degree polynomial, it has (n-2) points of inflection, where n is the degree of the polynomial.

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A veterinarian uses weights in kilograms to figure out what dosages of medicines to prescribe for animals. For every 10 kilograms, there are 22 pounds. Calculate this animal’s weight in kilograms and explain your reasoning.
Fido the Labrador weighs 88 pounds.

Answers

The required weight of fido the labrador is 40 kilogram.

What is relation between kilogram and pound?

kilogram is the fundamental unit used to measure weight ans pound is used in UK to measure weight of any object.

As we have given in 10 kilogram, there are 22 pounds. So, one kilogram is equal to 2.2 pound.

According to given data in the question:

We have to find the weight of fido the labrador in kilogram

here,weight in pound is 88

we know that one pound contain 1/2.2 kilogram

So, weight of 88 pound in kilogram = (88)1/2.2

weight in kilogram = 40 kilograms.

Hence, the required answer is 40 kilogram.

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Stan and Talia each went to see a movie. Both movies started at 7:15.

Stan's movie ended at 9:40.

Talia's movie ended at 10:10.



Part A
Use the drop-down menus to complete the sentence about the length of Stan's movie.

Stan's movie lasted
Choose...
hours and
Choose...
minutes.

Part B
Use the drop-down menus to complete the sentence that compares the length of the two movies.

Talia's movie lasted
Choose...
hours and
Choose...
minutes longer than Stan's movie.

Answers

The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

What are the length of the movies?

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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the velocity function (in meters per second) for a particle moving along a line is grven by u(t) : 2t-4, for 0 ( t < 6 (in seconds). what is the total distance traveied by the particle during this interval of tim

Answers

Hence, the total distance traveled by the particle is 16 meters

The velocity function  for a particle moving along a line is given by u(t): 2t-4, for 0 < t < 6 (in seconds)

[tex]Distance(D) = \int\limits^a_b {u(t)} \, dt[/tex]

[tex]Distance(D) = \int\limits^6_0 {(2t-4)} \, dt[/tex]

In this time period velocity will be zero

So, u(t) = 0

2t-4=0

at t=2 seconds, velocity will be zero.

So,

[tex]Distance(D) = |\int\limits^2_0 {(2t-4)} \, dt| +| \int\limits^6_2 {(2t-4)} \, dt|[/tex]

[tex]Distance (D) = |[t^2-4t]\right\{{{2}\atop{0}}\right.|+|[t^2-4t]\right\{{{6}\atop{4}}\right.|[/tex]

[tex]Distance (D) = |[2^{2}-8-0+0]| + |[6^{2} -24-4^{2} +16]|[/tex]

[tex]Distance (D) = |4-8|+|36-24-16+16|[/tex]

[tex]Distance (D) = 4+12[/tex]

[tex]Distance (D) = 16 meters[/tex]

Hence, the total distance traveled by the particle is 16 meters

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when prove that all positive integers less than 4 are prime numbers by showing that 1, 2 and 3 are prime numbers, which of the following kinds of proof are we using?
Proof by contradiction
Trivial proof
Proof by induction
Exhaustive proof

Answers

To prove that all positive integers less than 4 are prime numbers, we will use the method of exhaustive proof.

Proof by contradiction is a method that establishes the the validity of a proposition, by assuming the proposition to be false leads to a contradiction.

Trivial Proof implies that if q is true then p → q is true regardless of the

truth value of p.

Proof by Induction is a method for proving that a statement P(n) is true for every natural number n

Finally, Proof by exhaustion, also known as proof by cases, is a method of proof in which the statement to be proved is split into a finite number of cases, and each type is then checked to see if the proposition in question holds.

Here, as we can see, by definition, exhaustive proof will be most appropriate as we can easily split the statement into 3 cases, taking the integers 1, 2 and 3 in each.

Thus, we will use Exhaustive Proof.

Learn more about proofs here-

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Given vectors u = (-8,-5) and
v = (-1, -2), find the sum u + v and write
the result in component form.

Answers

Answer:

u + v = < - 9, - 7 >

Step-by-step explanation:

to sum u and v add the corresponding x and y components of the 2 vectors

u + v

= < - 8, - 5 > + < - 1, - 2 >

= < - 8 - 1, - 5 - 2 >

= < - 9, - 7 >

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