0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).
What is real numbers?
A real number in mathematics is a number that can be used to represent a continuous one-dimensional quantity, such as a length of time, temperature, or distance. In this context, continuous denotes that values may vary by arbitrary little amounts. An endless decimal expansion allows for a nearly universal representation of every real number.
The given equation is,
[tex]log_xa+log_ya=4log_x_ya[/tex]
Using the log rule: [tex]log_ab = \frac{ln b}{lna}[/tex]
⇒ [tex]\frac{lna}{lnx}+\frac{lna}{lny} = \frac{4lna}{lnxy}[/tex]
Multiply both sides by, [tex]\frac{lnxy}{lna}[/tex]
⇒ [tex]\frac{lnxy}{lnx}+\frac{lnxy}{lny} = 4[/tex], a ≠ e
Using log rule: [tex]ln(ab) = lna + lnb[/tex]
⇒
[tex]\frac{lnx+lny}{lnx} +\frac{lnx+lny}{lny} = 4\\ \frac{lnx}{lnx}+\frac{lny}{lnx}+ \frac{lnx}{lny}+\frac{lny}{lny} = 4\\1+\frac{lny}{lnx}+ \frac{lnx}{lny} +1=4\\\frac{lny}{lnx}+\frac{lnx}{lny}=2[/tex]
[tex]\frac{(lnx)^2+(lny)^2}{lnx(lny)} =2\\(lnx)^2+(lny)^2 = 2 lnx ln y\\(lnx)^2 - 2lnxlny+(lny)^2=0\\(lnx - lny)^2 = 0\\lnx - ln y = 0\\x = y[/tex]
Hence, 0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).
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the coordinate plane shows the outline of a town park. A bike path is to be constructed that runs directly through the park from point E to point G. What will be the length of the bike path to be nearest foot?
Applying the distance formula, the length of the bike path as shown in the coordinate plane is approximately 28 feet.
How to Find Distance on a Coordinate Plane?To find the distance between two points that are on a coordinate plane, the formula used is the distance formula which is given as:
d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Point G on the coordinate plane is at (20, 20), while point E is at (0, 0):
Therefore:
E (0, 0) = [tex](x_1, y_1)[/tex]
G (20, 20) = [tex](x_2, y_2)[/tex]
Plug in the values into the distance formula:
EG = √[(20 − 0)² + (20 − 0)²]
EG √[(20)² + (20)²]
EG = √(400 + 400)
EG = √800
EG ≈ 28 feet
The length of the bike path would be approximately 28 feet.
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Determine which of the following relations is a function.
The relation between the given function is X cannot repeat itself.
What is the function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of a varying quantity depends on another quantity.
We have given that the functions table.
We need to determine which relation is a function.
The relation between the function, that is;
X cannot repeat itself
Hence, the option C is correct.
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simplify a^4b^3/cd x c^2/a^4b^5
The solution for the given expression is a⁴b³/cd × c²/a⁴b⁵ = c/b²d.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given algebraic expression is as below,
a⁴b³/cd × c²/a⁴b⁵
It can be simplified by using the rules of exponent as follows,
a⁴b³/cd × c²/a⁴b⁵
= a⁴b³ c²/(cd × a⁴b⁵)
= b³ c²/b⁵cd
= c²/b²cd
= c/b²d
Hence, the given expression can be simplified as c/b²d.
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Kristen is investigating the opinions of students at her high school on the new school hours proposed by the school board. Which of the following is her population of interest?
All students at her high school
The population of interest in Kristen's investigation is the students at her high school.
What is meant by population of interest?The specific group of people or items that a researcher is researching in a given study is known as the population of interest. This group may be categorized according to factors like age, gender, employment, geography, or a particular health condition. The target audience for the study is the population of interest, and this demographic is generally the one to which the study's findings are applied. Identifying the population of interest is a crucial phase in the research process because it allows the researcher to focus on a specific group and develop meaningful findings that are applicable to that group.
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What are the 5 congruence theorems?.
The five rules of congruence theorem are described below.
Statement of congruence.The sign for congruence is ≅ and we compose △ABC≅△DEF. ∠A relates to ∠D, ∠B compares to ∠E, and ∠C relates to ∠F. Side Stomach muscle relates to DE,BC compares to EF, and AC relates to DF.
Five rules of congruence theorem:Side-Side-Side(SSS):Corresponding sides of two triangles are equal, then triangles are congruent.
Side-Angle-Sid(SAS):Corresponding two sides and one angle are equal, then triangles are congruent.
Angle-Side- Angle(ASA):One side and two angles are equal, then triangles are congruent.
Angle-Angle-Side(AAS):Corresponding conductive two angles and one side are equal, then triangles are congruent.
Right angle- Hypotenuse-Side(RHS): assuming the hypotenuse and side of one right-calculated triangle are equivalent to the hypotenuse and the comparing side of another right-calculated triangle, the two triangles are consistent.
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What is a function give 4 examples?.
Answer:
a function is like f(X)=2x+6 where X can be anything , you just substitute in the number u have been given
Step-by-step explanation:
other examples could include
f(X)=X+1
or they can start with
g(X)=3x+7
h(X)=4-3x
and there are inverse functions witch can be found be rearranging the function
example if substituteing a function
if
f(X)= 2x+1
f(3)=2(3)+1
f(3)=6+1=7
Hope this helps
The density curve for a continuous random variable x has which of the following properties
a. the probability of any event is the area under the density curve and above the values of X that make up the event
b. the total are under the density curve for X must be exactly 1
c. the probability of any event of the form x= constant is 0
d. all of the above
Out of the choices provided, the density curve for a continuous and a random variable ''x'' has all the properties, which have been listed above. Therefore, the option D holds true.
A density curve can be referred to or considered as the smooth curve, which is used for the purpose of representation of shape of a variable's distribution, which is easily identified through the properties that it contains. A density curve can be used for the purpose of graphical representation, such as a histogram.
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If Lisa is x years old now, how old will she be in 10 years. (Represent the answers in terms of x) this question makes zero sense to me
If the is lets say 5 years old, in 2 years, she will be 5 + 2 = 7 years old, and in 10 years 5 + 10 = 15 years old
so age in the future is the present age + how many years from now she will be
in this example the present age is 5 years old , if you replace that 5 with an x, the age in 10 years will be x + 10
A painter leans a 10 ft ladder against a building. The base of the ladder is 7 ft from the building. To the nearest foot, how high on the building does the ladder reach?.
The nearest foot, on the building does the ladder reach is 7.1 ft
Because of Pythagorean Theorem.
Since the ladder is leaning against a building it makes 10ft the hypotenuse, (c).
Additionally, they give you one of the bases = 7ft, (a)
So in order to find the other base you must plug in what you already know.
= [tex]10^{2} = 7^{2} + b^{2}[/tex]
Which equals to 100= 49 + [tex]b^{2}[/tex]
Then you have to subtract 49 on both sides ending up with
[tex]b^{2}[/tex] = 51.
Then you have to square root on both sides and we will get [tex]\sqrt{51}[/tex].
Which is around 7.1 ft.
Hence the answer is the nearest foot, on the building does the ladder reach is 7.1 ft
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What do you call a triangle that has less than 90 angle?.
Answer:
A triangle in which each angle is less than 90 degrees is called an acute angled triangle.
Step-by-step explanation:
employees of a firm receive annual reviews. in a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating. if 3 employees in this department are randomly selected to complete a form for an internal study of the firm, find the probability that the following occurs. (enter your probabilities as fractions.)
The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.
In the given question,
In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.
So total number of employees = 5+14+1 = 20
If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.
The following occurs given below:
(a) We have to find the probability of all 3 selected were rated excellent.
5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:
selection of 3 employees from 5 employees = [tex]^5C_{3}[/tex]
Using, [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5!}{3!(5-3)!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5!}{3!2!}[/tex]
selection of 3 employees from 5 employees = [tex]\frac{5\times4\times3!}{3!\times2\times1}[/tex]
selection of 3 employees from 5 employees = 5×2
selection of 3 employees from 5 employees = 10
Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140
Probability of 3 employees who got excellent rating
P(E) = 10/1140
P(E) = 1/114
(b) We have to find the probability of one from each category was selected.
One candidate selected from excellent category = [tex]^5C_{1}[/tex] = 5
One candidate selected from marginal category = [tex]^1C_{1}[/tex] = 1
One candidate selected from good category = [tex]^{14}C_{1}[/tex] = 14
Selection of 3 employees from 20 employees= [tex]^{20}C_{3}[/tex] = 1140
The probabilty of one from each category = (5*1*14)/1140
The probabilty of one from each category = 70/1140
The probabilty of one from each category = 7/117
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For what value of the variable doe the following expreion make ene: quare root of (-5x)^3
take any negative value of x suppose x= -1,-2 ....etc then it makes sence and it is valid cube
What are types of expressions?
There are three kinds of expressions: An arithmetic expression evaluates to a single arithmetic value. A character expression evaluates to a single value of type character. A logical or relational expression evaluates to a single logical value.
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the angle of depression is measured from the top of a 43 ft tower to a reference point on the ground. its value is found to be 63 degrees. how far is the base of the tower from the point on the ground
The required distance between point on the ground and foot of the tower.
What is the angle of depression?On the off potential for success that an individual has and peers down at an item, the angle of depression is the point between the level view and the item. Geometry can be utilized to take care of issues that utilization a point of rise or sorrow.
According to given data in the question:Height of the tower = 43 ft
And angle of depression = 63 degree
we know that
tan(theta) = P/B
P is height of tower, B distance between tower and point on the ground.
tan(63)= 43/B
B = 43/tan(63)
B = 43/1.96 = 21.93 = 22 ft approx.
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An equation for a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is:.
The equation of a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is: P(t) = -1/3 + 1
Given:
p(t) = 3t + 4
point (3,1)
To find this out, we must use the slope perpendicular to 3
perpendicular slopes are the slope's reciprocal's negative, which in this case it is -1/3
to find the line with the points (3,1), we simply use the equation y = -1/3x + b and then plug them in
1 = -1/3(3) + b
1 = -1 + b
b = 2
the y intercept is 2 and so we can write the equation like this:
P(t) = -1/3t + 2
Hence we get the required equation of a line.
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What do all agile framework have in common TCS?.
The agile frameworks that have in common are:
Self-organized teams can better adapt to business requirements with a lightweight strategy.
All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.
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 agile frameworks that have in common are:
Self-organized teams can better adapt to business requirements with a lightweight strategy. All agile frameworks use iterative and incremental development and have a set, defined iteration duration. They also all take a lightweight approach that enables self-organized teams to better adapt to business needs. It's a term for methods used in software development.
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How do you find the leading coefficient of a graphed polynomial?.
A polynomial is a function with two or more terms that have positive integer exponents. The terms can be constants and/or have variables. They are separated by either addition or subtraction signs.
fundamental coefficients are the numbers written in front of the variable with the maximum important exponent. just like ordinary coefficients, they may be fine, terrible, real, or imaginary further to whole numbers, fractions, or decimals. for instance, inside the equation [tex]-7x^4[/tex] +[tex]2x^(3-11)[/tex], the very satisfactory exponent is four.
The degree of the polynomial is the best strength of the variable that takes location in the polynomial. the number one time period is the time period containing the very high-quality energy of the variable: the term with the very wonderful degree.
In a polynomial, the principal term is the term with the very first-rate electricity of x. for instance, the principal term of 7+x−3x² is −3x². the principal coefficient of a polynomial is the coefficient of the primary term. within the above instance, the primary coefficient is −3.
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Alicia has a collision deductible of $500 and a bodily injury liability coverage limit of $50,000. She hits another driver and injures them severely. The case goes to trial and there is a verdict to compensate the injured person for $40,000. How much does alicia have to pay? how much does her insurance pay?.
Alicia have to pay $10,000 and her insurance will pay $10,500.
What is limit of coverage in insurance?
This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.
Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.
And there is a verdict to compensate the injured person for $40,000
Therefore Alicia have to pay
$50,000-$40,000 = $10,000
And her insurance will pay
$10,000 + $500 = $10,500
Hence Alicia have to pay $10,000 and her insurance will pay $10,500.
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What is a prime number Class 8?.
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself.
In the given question we have to explain about the prime number.
Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.
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If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?dPdt=200Answer A: d cap p over d t is equal to 200AdPdt=200tAnswer B: d cap p over d t is equal to 200 tBdPdt=100t2Answer C: d cap p over d t is equal to 100 t squaredCdPdt=200PAnswer D: d cap p over d t is equal to 200 cap pDdPdt=100P2
If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is [tex]\frac{dP}{dt}=200[/tex]
The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.
dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable
According to the question,
Size of population at t time = P(t)
Also given ,The differential equations have a linear growth in the size of the population.
So, The degree of the variable must be one. And the equation of the population will be quadratic.
Therefore , dP/dt = 200 tells us the rate change of population with respect to time.
A derivative of linear function is constant .
Hence , option B is correct.
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1) how does the fuel consumption of a car change as its speed increases? here are data for a british ford escort. speed is measured in kilometers per hour, and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled.
The way fuel consumption of a car change as its speed increases represents a relationship that is curved with higher at extremes when scatter plot is constructed. It shows fuel efficiency is high at moderate speeds.
What is scatter plot?
A scatter plot is a type of mathematical diagram using Cartesian coordinates to demonstrate values for typically two variables for a set of data.
Main body:
In the given case, the scatter plot shows a relationship between the speeds of a car and fuel consumption.
The curved relationship which is high on extreme and low in the middle. As the car speed increases from 10km/h to 60 km/h, the fuel consumption decreases. As the car speed increases from 60km/h to 150khm/h, the fuel consumption increases. Hence, the fuel consumption is lowest at 60km/h and its generally low for moderate speeds – 40 km/hr to 100 km/h. It can be deduced that fuel efficiency (which pertains to how well a vehicle uses fuel) is high for moderate speeds.
Hence, at moderate speeds best performance is achieved.
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you start driving west for 3 miles, turn right, and drive north for another 13 miles. at the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]\sqrt{178}[/tex] or 13.3 rounded to the nearest tenth
Step-by-step explanation:
A tree casts a 217 centimeter shadow. A person next to the tree casts a 57 centimeter shadow. If the person is 161 centimeters tall, how tall is the tree to the nearest centimeter?
The height of the tree to the nearest centimeter is 613 centimeters
What is proportion?A proportion can be described as an equation having two ratios set equal to each other.
It is also seen as the mathematical comparison of two elements, numbers of ratios.
From the information given, we have that;
The tree casts a shadow of 217 centimetersThe person is 161 centimeters tall and casts a shadow of 57 centimetersIf 57 centimeters = 161 centimeters
Then 217 centimeters = x
cross multiply
x = 161(217)/57
multiply the values
x = 34, 937/57
x = 613 centimeters
Hence, the value is 613 centimeters
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a descriptive measure of a population characteristic is best described as a: a. parameter. b. sample statistic. c. frequency distribution.
Answer:
a. parameter
Step-by-step explanation:
A parameter is any descriptive measure of a population characteristic.
the environmental protection agency is concerned with the problem of setting criteria for the amounts of certain toxic chemicals to be allowed in freshwater lakes and rivers. a common measure of toxicity for any pollutant is the concentration of the pollutant that will kill half of the test species in a given amount of time (usually 96 hours for fish species). this measure is called lc50 (lethal concentration killing 50% of the test species). in many studies, the values contained in the natural logarithm of lc50 measurements are normally distributed, and, hence, the analysis is based on ln(lc50) data. studies of the effects of copper on a certain species of fish (say, species a) show the variance of ln(lc50) measurements to be around 0.6 with concentration measurements in milligrams per liter. suppose that the effects of copper on a second species of fish (say, species b) show the variance of ln(lc50) measurements to be 0.2. if the population means of ln(lc50) for the two species are equal, find the probability that, with random samples of seven measurements from each species, the sample mean for species a exceeds the sample mean for species b by at least 1 unit. (round your answer to four decimal places.)
The probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999
1) Using by the central limiting theorem:
We know the formula for the z-score for the normal distribution is given by:
z = (x - μ) /( ρ√n)
Follows normal distribution with mean 0 and the variance of 1.
Where
x is the sample mean,
μ is the population mean,
ρ denotes population standard deviation
n = sample size
The required probability is
P(z < 0.5/[0.4/√ 10])
= P(z < 3.95)
P = 0.9999
Therefore the probability that, with random samples of seven measurements the sample mean for species a and b by at least 1 unit is 0.9999 .
Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.
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A function f is defined for all real numbers and has the following three properties: f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)=5f(3)=21f(a+b)−f(a)=kab+2b 2 for all real numbers a and b where k is a fixed real number independent of a and b. (a) Use a=1 and b=2 to find k. (b) Find f^{\prime}(3)f ′(3) (c) Find f^{\prime}(x)f (x) for all real x.
The solutions of given function;
(a) k = -12
(b) f'(3) = 0
(c) f'(x) = 0
Given info,
A function f is defined for all real numbers and has the following three properties:
[tex]f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)\\[/tex]
for all real numbers a and b where k is a fixed real number independent of a and b.
To find,
(a) Use a = 1 and b = 2 to find k.
[tex]f(a+b)-f(a)=k a b+2 b^{2}f(1)[/tex]
f(1 + 2) - f(1) = k(1 * 2) + 2 * 2² * f(1)
f(3) - f(1) = 2k + f(1) * 8
21 - 5 = 2k + 8 * 5
16 = 2k + 40
-2k = 24
k = -12
(b) Find f'(3).
f(3) = 21
f'(3) = d/dx(21) = 0
(c) Find f'(x) for all real x.
f'(x) = 0
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a six-sided die is rolled three times. the probability of observing a 1 three times in a row is . a. .037 b. .004629 c. .3 d. .16
The correct option b. 0.004629 for the probability of observing a 1 three times in a row.
Explain the meaning of the term probability?Mathematics' branch of probability studies the likelihood of a random event occurring. In mathematics, probability is used to determine how likely an event is to occur. Only the numbers 0 and 1 can be used to express probability, which can also be expressed as a percentage.Probability of an event = (Number of favorable events) / (total number of event).
P(B) = (Event B) / (total number of event).
The number of times the dice are rolled has no bearing on the outcome of the roll.
The likelihood of receiving 1 is 1/6.
The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.
Receiving 1 three times in succession has a probability;
= 1/6 x 1/6 x 1/6
= 1/216.
As a result, there is a 0.463% chance that you'll get 1 three times in a row.
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Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given families of curves orthogonal trajectories of each other? That is, is every curve in one family orthogonal to every curve in the other family? x^2 + y^2 = ax
x^2 + y^2 = by
Yes, the given curves are orthogonal.
What is orthogonal trajectory?In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.
Given equation is,
x²+y²=ax
Differentiating,
2x+2yy'=a
y' = (a-2x)/2y = m1
Again,
x²+y²=by
Differentiating,
2x+2yy'=by'
y' = -2x/(2y-b) = m2
For both curves are orthogonal, we have
m1*m2 = -1
(a-2x)/2y*-2x/(2y-b) = -1
-2ax+4x² = -4y²+2yb
4(x²+y²) = 2ax+2yb
Since, ax = (x²+y²)
by = (x²+y²)
Then,
4(x²+y²) = 2(x²+y²) +2(x²+y²)
4(x²+y²) = 4(x²+y²) (true)
Hence, the above response is appropriate.
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Marshall is writing an equivalent equation to solve for x. what should be his next step? 5 x 4 y = 8. 5 x 4 y minus 4 y = 8 minus 4 y. 5 x = 8 minus 4 y. add 5x to both sides of the equation. subtract 5x from both sides of the equation. multiply both sides of the equation by 5. divide both sides of the equation by 5.
The next step of marshall should be divide both sides of the equation by 5.
Given:
Marshall is writing an equivalent equation to solve for x. what should be his next step.
5 + 4 y = 8.
5+4y-4y = 8-4y
5x = 8 - 4y
To solve for x:
The correct step is:
divide by 5 on both sides
5x/5 = 8-4y / 5
x = 8/5 - 4y/5
x = 1/5(8-4y).
Therefore The next step of marshall should be divide both sides of the equation by 5.
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assume that adults have iq scores that are normally distributed with a mean of and a standard deviation . find the probability that a randomly selected adult has an iq less than .
the probability that a randomly selected when the IQ is lower than 136 is 0.9641
Given that
The mean is 100
The standard deviation is 20
We need to find out the probability when the IQ is lower than 136
So,
z value equivalent to 136 = (136 - 100) ÷ 20 = 1.8
Now
p (z < 1.8) = 0.9641
hence, the probability when the IQ is lower than 136 is 0.9641
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R Markdown is a file format for making dynamic documents with R. What are the benefits of creating this kind of document? Select all that apply.
Multiple Choice Question. Please Choose The Correct Options A
Perform calculations for analysis more efficiently
B
Generate a report with executable code chunks
C
Save, organize, and document code
D
Create a record of your cleaning process
An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.
It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.
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