the triangle with the vertices (4, 5, 1), (0, 8, 2), (4, 7, 8) is translated three units to the right along the y-axis. determine the coordinates of the translated triangle. (give your vertices in the same order as the original vertices.)

The equation of line passes through (-6,1) and has slope 6 will be y=6x+37.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that the line passes through (-6,1) and has a slope of 6,

The equation of line passes through (-6,1) and has slope 6 is found as,

y-y₁=m(x-x₁)

y-1=6(x-(-6)

y-1=6(x+6)

y-1=6x+36

y=6x+36+1

y=6x+37

Thus, the equation of line passes through (-6,1) and has slope 6 will be y=6x+37.

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Minimum value and maximum value attained at 36 and [tex]2\sqrt{648}[/tex] respectively.

Maxima and minima of a function are the largest and smallest value of the function respectively either within a given range or on the entire domain. Collectively they are also known as extrema of the function. The maxima and minima are the respective plurals of maximum and minimum of a function.

Given that f = [tex]x^{2}[/tex]+ [tex]y^{2}[/tex]

Let g = [tex]x^{4}[/tex] + [tex]y^{4}[/tex] = 1296

By Lagrange Multipliers:  grad(f) = λ grad(g)

or  <2x, 2y> = λ <4[tex]x^{3}[/tex], 4[tex]y^{3}[/tex]>

Equating like entries:

2x = 4λ[tex]x^{3}[/tex]=> x(2λ[tex]x^{2}[/tex] - 1) = 0

2y = 4λ[tex]y^{3}[/tex] => y(2λ[tex]y^{2}[/tex] - 1) = 0

Now there possible 3 cases :

(i) If x = 0, then   [tex]x^{4}[/tex] + 0 = 1296 => x = ±6.

(ii) If y = 0, then 0 + [tex]y^{4}[/tex]= 1296 => y = ±6

(iii) Otherwise, we have 2λ[tex]x^{2}[/tex] - 1 = 0 = 2λ[tex]y^{2}[/tex] - 1  => λ([tex]x^{2}[/tex] - [tex]y^{2}[/tex]) = 0.

If λ = 0, then both x = 0 and y = 0 and this is not possible since [tex]x^{4}[/tex]+ [tex]y^{4}[/tex]= 1296.

Otherwise,[tex]x^{2}[/tex] = [tex]y^{2}[/tex] ⇒ [tex]x^{4}[/tex] +  [tex]x^{4}[/tex] = 1296 => x = ± [tex]648^{1/4}[/tex]

(with x and y will have different signs)

Now we have following critical points (in lexicographic order):

(- [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex])

(- [tex]648^{1/4}[/tex],  648^(1/4))

(-6, 0)

(0, -6)

(0, 6)

(6, 0)

( [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex])

( [tex]648^{1/4}[/tex],  [tex]648^{1/4}[/tex])

Minimum value attained at f(±6, 0) = f(0, ±6) = 36

Maximum value attained at f(± [tex]648^{1/4}[/tex],  [tex]648^{1/4}[/tex]) = f(± [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex]) = [tex]2\sqrt{648}[/tex]

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The first term in both sequences f(n) = f(n - 1) + 4 and f(n)=3(5)^(n-1),  is -1.

What is a geometric sequence?

The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

We have,

f(n) = f(n - 1) + 4

And,

f(n) = 3(5)ⁿ⁻¹

f(1) = 3

Putting n=1

f(n) = f(n - 1) + 4

Now,

f(1) = f(1 - 1) + 4

3 = f(0) + 4

⇒ f(0) = 3 - 4 = -1

Here f(0)= -1

and  f(n) = 3(5)ⁿ⁻¹

Now,

f(1) = 3 × (5)¹⁻¹ = 3 × (5)⁰ = 3 × 1 = 3

f(1) = 3

Hence, the first term in both sequences is -1.

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By using the concept of probability, it can be calculated that

a)  P(X [tex]\leq[/tex] 1) = 0.25

b) P(0.5 [tex]\leq[/tex] X [tex]\leq[/tex] 1)  = 0.1875

c) P(X > 1.5) = 0.4375

d) Median = 1.414

e) F'(X) = 0.5x , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2

           0, otherwise

f) E(X) = 1.33

g) V(X) = 0.2311, SD(X) = 0.4807

h)  E(h(X)) = 2

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

The cdf is

f(x) = [tex]\left \{ {\frac{x^2}{4}},{ 0 \leq x \leq 2} \atop {1, x=2}} \right.[/tex]

Now,

a) P(X [tex]\leq[/tex] 1) = [tex]\frac{1^2}{4} = 0.25[/tex]

b) P(0.5 [tex]\leq[/tex] X [tex]\leq[/tex] 1)

= [tex]\frac{1^2}{4} - \frac{0.5^2}{4}\\\\\frac{3}{16}\\\\0.1875[/tex]

c) P(X > 1.5) = 1 - P(X [tex]\leq[/tex] 1.5)

                      [tex]1 - \frac{1.5^2}{4}[/tex]

                       0.4375

d) Let [tex]\mu[/tex] be the median

P(x [tex]\leq \mu[/tex]) = 0.5

[tex]\frac{\mu^2}{4} = 0.5[/tex]

[tex]\mu^2 = 0.5 \times 4 =2\\\mu = \sqrt{2}\\\mu = 1.414[/tex]

e) F'(x) =

[tex]\frac{2x}{4}, 0 \leq x \leq 2\\0, otherwise[/tex]

F'(X) = 0.5x , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2

           0, otherwise

f) E(x) =

[tex]\int_0^2 x \times 0.5 xdx\\=0.5 \times \frac{x^3}{3} |_0^2 \\=0.5 \times \frac{2^3}{3}\\=\frac{4}{3}\\=1.33[/tex]

g) V(X) = E([tex]X^2[/tex]) -[tex](E(X))^2[/tex]

    E(X^2) =

                   [tex]\int_0^2x^2(0.5x)dx \\0.5 \times \frac{x^4}{4}|_0^2\\2[/tex]

[tex]V(X) = 2 - (1.33)^2[/tex]

V(X) = 0.2311

SD(X) = [tex]\sqrt{0.2311} = 0.4807[/tex]

h) h(X) = [tex]X^2[/tex]

   E(h(X)) = [tex]\int_0^2X^2({0.5X)dx[/tex]

               = [tex]0.5 \frac{x^4}{4}|_0^2[/tex]

               = [tex]0.5 \times \frac{2^4}{4}[/tex]

               = 2

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13x = 39 can be used in place of the equation 3x + 5y = 59.

Only D(0,2) falls on the line, as can be seen. Another way to check is to plug the values of the points' x and y coordinates into the equation 2x3y=6, which, as can be seen, only has one solution (0, 2).

An assignment of values to the variables x1, x2,..., xn such that each of the equations is satisfied is the definition of a solution of a linear system. The solution set is the collection of all conceivable solutions.

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Using the given formula, the sum of S(n) for the arithmetic series is 565.5.

In the given question we have to find the sum S(n) for the arithmetic series

The given formula is S(n)=n/2 {a(1)+a(n)}

The given values are a(1)=12, a(n)=75,n=13

We just have to put values in given formula

S(n)=n/2 {a(1)+a(n)}

S(n)=13/2 (12+75)

S(n)=6.5*87

S(n)=565.5

Hence, the sum of S(n) for the arithmetic series described is 565.5.

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The number of students in 2001 is 150.4 thousand and the number of students in 2018 is 467.5 thousand

In the year 2001

The function in the question is given as

y = 123.1(1.069)ˣ

Where

x is the number of years from 1998 through 2013

So, the value of x in 2001 is

x = 2001 - 1998

This gives

x = 3

Replace x with 3 in the equation y = 123.1(1.069)ˣ

So, we have the following

y = 123.1(1.069)³

Evaluate the expression on the right-hand side

y = 150.4

In the year 2018

The value of x in 2018 is

x = 2018 - 1998

This gives

x = 20

Replace x with 20 in the equation y = 123.1(1.069)ˣ

y = 123.1(1.069)²⁰

Evaluate the expression on the right-hand side

y = 467.5

Hence, there are about 467.5 thousand students in 2018 is

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There are 4²⁴ possible ways to complete the multiple-choice test consisting of 24 questions, with each question having four possible answers.

We have 24 questions with each having 4 possible outcomes. If we had a question, then we would have 4 ways of answering question 1 and for each of the four answers in question 1, we would have four ways of answering question 2. So, we have 4² ways of answering the questions.

Like this, we have 24 questions. There are four ways to choose an answer to each question. By counting principle, we multiply the number of choices at each step and then we have -

= 4×4×4×4...= 4²⁴ ways to complete the test

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We can see two clusters (a group of values that stick together):

Please attach the picture (dot plot or other graph or figure) next time.

Firm X is least likely to capture gains from the innovation when end users have inelastic demand for the product.

When the demand is inelastic for the product, firm X will be least likely to capture the gains, because the firm will not able to adjust prices for any added production cost.

Production costs allude to the costs an organization causes by assembling an item or offering support that produces income for the organization. Production costs can incorporate various costs, for example, work, unrefined components, consumable assembling supplies, and generally above.

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Yes because (50)(0.25) and (50)(1 - 0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample portions.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

25% = 0.25

Then (50)(0.25) > 10 and also (50)(1 - 0.25) > 10.

Hence, we can use the normal distribution to model the distribution of sample portions.

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The process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition is shown below:

A polynomial is the quotient (with or without a remainder). multiplying this polynomial by the polynomial's divisor We get a polynomial with updated exponents and coefficients, so it's closed under multiplication.

A polynomial is defined as an equation composed of variables, constants, and exponents that are joined together using mathematical operations such as addition, subtraction, multiplication, and division.

If no remainder exists, the dividend is equal to the quotient multiplied by the divisor.

The quotient and divisor, as well as their product, the dividend, are both polynomials.

If there is a residual, it is added to the product of the quotient and divisor.

The polynomial dividend is the sum of the remainder and the product of the quotient and divisor.

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Answer: The input is the x variable and the output is the y variable, so the equation is y=0 which is just a line on the x axis

**the thicker line in the picture is what the line should look like.

Answer:

0.375 miles on each side.

Step-by-step explanation:

Since a square is equal on each side, and has 4 sides, we can take 1.5 miles and divide it by 4:

1.5 divided by 4 = 0.375 miles per side

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

[tex]\dfrac{3}{8}\;\;\sf miles[/tex]

Step-by-step explanation:

A square is a quadrilateral (4-sided shape) with sides of equal length.

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, the perimeter of a square is four times its side length.

Given:

[tex]\begin{aligned}\textsf{Perimeter of a square}&=4s\\\\\implies 1\frac{1}{2}&=4s\\\\\dfrac{3}{2}&=4s\\\\s&=\dfrac{3}{2} \div 4\\\\s&=\dfrac{3}{2} \times \dfrac{1}{4}\\\\s&=\dfrac{3 \times 1}{2\times4}\\\\s&=\dfrac{3}{8}\; \sf miles \end{aligned}[/tex]

Therefore, the side length of a square field with a perimeter of 1 and 1/2 miles is 3/8 miles.

The inequality that can be used to find p is 7p -12 < 45.

What is a Triangle?

A triangle is a polygon with three sides, three angles, and three vertices.

The perimeter of the given triangle is at most 45 centimeters.

The perimeter of a triangle is equal to the sum of all sides.

The sides given is 3p-6 , 3p-6 ,p

So,

3p-6 +3p-6 +p < 45

7p -12 < 45

Hence the answer is, the inequality that can be used to find p is 7p -12 < 45.

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Three years ago , mine age was 6 years

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Let my present age be x

Age of mine , 20 years ago = x - 20

Age of mine , 10 years ago = x - 10

According to question,

(x - 20) = 13(x - 10)

⇒ x - 20 = 13x - 130

⇒ 13x - x = 130 - 20

⇒ 12x = 110

⇒ x = 110/12

⇒ x = 9.17

Age of mine , theree years ago = x - 3

= 9.17 - 3

= 6.17

≈ 6

Therefore, three years ago , mine age was 6 years

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CD makes approximate 10.9 resolutions to make as it spins to a stop.

Here we have to determine the number of rotations N ,the CD spun before it comes to a stop. We first need to express the initial angular velocity ω , in terms of rad/s by applying the conversion factor ω = 2πf × 1/60 min/s where f = 500 rpm.

Then we apply the equation for the angular displacement of the CD upon coming to a stop,

Ф=  (ωi²-ωf²)/2α , We have the final angular velocity of ωf = 0 rad/s and an angular acceleration of α = 20.1 rad/s² Now we proceed with finding Φ.

Ф=  (ωi²-ωf²)/2α

  = {(2Πf×1/60min/s)² - ωf²}/2α

  = {(2π(500 rpm) × 1/60 min/s) -0 rad/s}/2(20.1 rad/s²)

  ≈ 68.19792... rad

Now we divide the answer by 2π to find the answer ,N, or

N =   Ф/2π

N =   (68.19792... rad)/2ππ

N  ≈ 10.9 revolutions

So, CD makes approximate 10.9 revolutions to make it stop.

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From the given array and by division, we can say that; No, it would not be possible for the students to use 24 paper squares to make quilts with 5 rows of paper squares.

We are told that the students want to use 24 paper squares to make quilts with 5 rows of paper squares.

To get the number of possible rows they can make from this, what we need to do is to divide the number of required rows by the number of paper squares to the maximum number of paper squares for each row. Thus;

24/5 = 4.8

Thus, since it is 4.8 , it means that they would not have enough for five rows.

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x = I9I

or:

x = I-9I

so:

x = 9 or -9

The property used in the equation is called Distributive property.

The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.

Given an equation, 4 x (5 + 6) = (4 x 5) + (4 x 6)

The property used in this equation is distributive property.

a(b+c) = (a*b)+(a*c)

Hence, The property used in the equation is called Distributive property.

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Binary is a base-2 number system that represents numbers using the states 0 and 1. It is also possible to refer to it as a true state and a false state. The process for creating a binary number is the same as for creating a regular decimal number.

Negative numbers can be expressed in a variety of ways. Magnitude of the sign is one method. In this technique, the sign is indicated using one bit. Typically, mathematical numbers consist of a sign and a value. While the value denotes the size of the number, the sign shows whether it is positive (+) or negative (-).

Negative binary numbers can be represented in a signed binary number system using the one's complement method. Positive numbers continue to be unchanged in one's complement.

Hence we get the required answer.

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Answer:

1 and 0

Step-by-step explanation:

Answer:

29/30

Step-by-step explanation:

29/30 as a percentage is %96.67 which is more than 90%

The principle that individuals will be given only the level of access that is appropriate for their specific job role or function is called Principle of Least Privilege (PoLP)

The IT team will frequently need to re-grant credentials so that users may accomplish certain tasks when businesses choose to revoke all administrative capabilities from business users. For instance, many commercial off-the-shelf (COTS) apps and legacy programmes used in enterprise IT systems need privileges to function. The IT staff needs to restore local administrator access to business users so they can utilise these approved and necessary programmes.

As privileges are rarely removed once they have been granted again, organisations may find that many of their users eventually have local administrator rights once more.A user is only provided the minimal levels of access - or permissions - required to carry out his or her job functions under the principle of least privilege (PoLP), which is a notion in information security. It is widely regarded as a best practise in cybersecurity and is a crucial step in safeguarding privileged access to highly valuable data and assets. Beyond human access, least privilege applies.

Applications, systems, and linked devices that require rights or permissions to carry out a necessary operation can all use the paradigm. Least privilege enforcement makes sure the machine tool only has the minimal access required. A mechanism to centrally store and secure privileged credentials is necessary for least privilege enforcement, combined with adaptable policies that can balance cybersecurity and compliance needs with operational and end-user needs.

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Cost of Case of Juice: 20

Cost of Case of Water: 15

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Here, we let

cost of a case of juice = x

cost of a case of water = y

6x + 1y = 135...(1)

4x + 2y = 110.....(2)

Now, we multiply equation (1) by 2 and equation (2) by 1 and we get

12x + 2y = 270

4x + 2y = 110

Now, we subtract equation (1) from equation (2) and we get

8x = 160

x = 20

and y = 15

Hence, the Cost of a Case of Juice: 20

Cost of Case of Water: 15

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The exponential growth formula for bacteria growth is P(t) = 8600 [tex](2)^(t/5)[/tex].

What is exponential growth?

     Exponential growth is a pattern of data that exhibits a greater increase over time, resulting in an exponential curve. Exponential is also a mathematical term meaning "with exponents". For example, if you raise a number to the 10th power, the number increases exponentially. Exponential growth is growth that increases at a constant rate.

Here given take Initial number of bacteria = 8600. rate of growth = 2.

It doubles every year. Then doubling time = 5 hours.

Now population growth after t years,

P(t) = Po [tex](2)^(t/5)[/tex]

=> P(t) = 8600 [tex](2)^(t/5)[/tex]

Therefore exponential growth formula is P(t) = 8600 [tex](2)^(t/5)[/tex].

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The length of the rectangle is 12 units long.

A rectangle is a geometric figure with equal opposite sides.

The angle between two consecutive sides is 90 degrees.

Area of ​​rectangle = length x width. Perimeter of rectangle = 2 (length + width).

let's assume,

length = l, width = w

Given the,

The length of the rectangle is 3 times the width

l = 3w

The difference in length and width is 8 feet

l-b = 8

According to equations 1 and 2

3w - w = 8

2w = 8

w = 4

Substitute into expression 1

l = 3(4)

l = 12 units.

So the rectangle is 12 units long.

your question is incomplete, but most probably the full question was

The length of a rectangle is 3 times the width. The difference between the length and the width is 8 feet. Determine the rectangle's length

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The value of

From the figure

2a = 60 degrees ( Corresponding angles are equal )

a = 60 / 2

a = 30 degrees

4c + 60 = 180  degrees ( Sum of angles on a straight line is 180 degrees)

4c = 120

c  = 30 degrees

f = 4c  ( Corresponding angles are equal )

f = 4 × 30

f = 120 degrees

3b + 60 = 180 degrees ( Sum of angles on a straight line is 180 degrees)

3b = 120

b = 40 degrees

f + d = 180 degrees ( Sum of angles on a straight line is 180 degrees)

120 + d = 180

d = 60 degrees

d + e = 180 degrees ( Sum of angles on a straight line is 180 degrees)

60 + e = 180

e = 120 degrees

Hence, the value of

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The test statistic has a value of -633.6915 if a sample mean of 10 bottles was chosen, and the average number of ounces was 12.005.

As stated. Sample mean is 10.

12.005 people on average.

0.01 is the standard deviation.

The test statistic's value is -633.6915 when calculated using the formula:

T = mean - average population / s/root n

= 10-12.005 / 0.01/3.16

= -2.005 /0.0031

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Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

Given that,

We have to find perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

We know that

Let us take a triangle ABC and draw an altitude CD

Being an isosceles triangle

In ΔACD and ΔCDB

CD=CD (common )

CA=CB ( equal opposite sides)

∠ A=∠ B (the angle between the opposing sides is also equal)

Triangle ACD and triangle CDB are congruent

So , AD=DB by CPCT

So, its true

Therefore, Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.

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The mean of the first 10 whole numbers is 4.5.

What is mean?

A amount that includes a price intermediate between those of the acute members of some set is known as mean.

Main body:

In this question we have to find the mean of the first 10 whole numbers. Whole numbers are all non-negative integers which start from 0. Now the mean of the first 10 whole numbers will be the mean of numbers from 0 to 9, as the count of numbers from 0-9 is 10. Use this concept to reach the answer.

Mean of numbers is equal to the sum of the numbers divided by the count of the numbers that is

Mean = sum of numbers/ total numbers          …………………….. (1)

To find the mean of the first 10 whole numbers, we will find the sum of numbers from 0 to 9 as 0-9 are the first 10 whole numbers.

So, the sum of the first 10 whole numbers is 0+1+2+3+4+5+6+7+8+9=45.

Now putting the values in equation (1) we get, mean = 45/10 = 4.5

Hence, the mean of the first 10 whole numbers is 4.5.

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