Given the following historical data, what is the simple three-period moving average forecast for period 6?
Period Demand
1 73
2 67
3 66
4 70
5 69
(Keep two decimal places in your answer)

The variable that can be used to represent the number of points scored before is x and the algebraic expression would be equal to (3x - 2).

Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

let the Number of points scored before = x

3 times the number of points scored before

= 3 × x

= 3x

Thus, two points fewer than 3 times the number of points scored before;

= 3x - 2

The examples of algebraic expression are:

2t - 5 + 3t

65x + y - 8y + 5x

In conclusion, the expression can be written as; 3x - 2

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The solution to the inequality 0 ≤ u² - 2u + 5 is all real numbers.

The solution of the inequality is calculated by applying the following method as shown below.

−u² ≤ −2u + 5

0 ≤ u² - 2u + 5

Now, to find the zeros of this quadratic equation, we can use the quadratic formula:

u = (-b ± √(b² - 4ac)) / 2a

where;

a = 1,

b = -2, and

c = 5.

u = (2 ± √(2² - (4 x 1 x 5)) / (2 x 1 )

u = (2 ± √(-16)) / 2

Since the square root of a negative number is not defined in real numbers, this means that the quadratic equation has no real zeros.

But we can still find the solution to the inequality by using the fact that a parabolic function y = ax² + bx + c is greater than or equal to 0 when it has x-intercepts that are both real and positive.

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Answer:

I believe it is about 3

Step-by-step explanation:

Go to y=2 then move across until you hit the line.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.

Mr. Hyper Chonder expects to receive a "Fit for Travel" evaluation with a probability of P(Fit) = 0.25 and an "Unfit for Travel" evaluation with a probability of P(Unfit) = 0.75. He believes that if the doctor finds that he will stay healthy, there is a P(Fit Healthy) = 0.8 chance of being evaluated as fit to travel and a P(Unfit Healthy) = 0.2 chance of being evaluated as unfit to travel. If the doctor finds that he will become sick, there is a P(Fit | Sick) = 0.4 chance of being evaluated as fit to travel and a P(Unfit | Sick) = 0.6 chance of being evaluated as unfit to travel.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he assigns a probability of P(Healthy | Fit) = 0.8 to staying healthy. If the doctor tells him that he is unfit for travel, he assigns a probability of P(Healthy | Unfit) = 0.2 to staying healthy and a probability of P(Sick | Unfit) = 0.8 to getting sick.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect a utility of 28 utils. If the doctor tells him that he is unfit for travel, he will not travel and expect a utility of 24 utils.

If the doctor tells Mr. Hyper Chonder that he is fit for travel, he will travel and expect 28 utils, and if the doctor tells him that he is unfit for travel, he will not travel and expect 24 utils.

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The point D on the graph shows that the rider has stopped moving.

What is a graph?

Graph is a line or curve of a line with represents the relation between two quantities.

There are two axis in graph each axis represents different quantity in a graph.

Two axis are X-axis and Y-axis. Generally quantity which increases gradually is kept on X-axis.

By using graph we can calculate many different things like in distance time graph if we calculate the area of the graph we can get the speed for that region.

Graph is a very helpful took as its a pectoral representation of data and we all know action speak louder than words so graphs can explain more information with less data.

Now for the given question:

In graph section D shows that bicycle rider has stopped because the distance of rider from its house is not increasing while the time increases due to of which this interval has a straight line.

Hence, rider has stopped moving at region D.

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The complete Question is:

The graph shows the position (distance from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval. Which of the following best explains how the graph shows that the rider stopped during time interval D?

Note that in the problem above, CL is 9m. This is resolved using the theorem of the Angle Bisector.

The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are separated by a line that bisects the opposing angle. It compares their lengths to the lengths of the other two sides of the triangle.

In geometry, the angle bisector is the ray, line, or segment that splits a given angle into two equal places.

Thus, given that, in ∆ABC, m∠C= 90° AL is an angle bisector m∠ABC = 30°, LB = 18 m,

CL is derived using the SOH principle; that is: Sine of the Angle = Opposite /Hypothenus

Sin 30° = CL/BL
⇒ 1/2 = CL/18

⇒ CL=9 m

Thus, the measure of CL is 9 m. See the attached image.

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The vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given a triangle DEF which is being dilated by a dilation factor of (2,M) we need to find the vertices of the image,

The vertices before dilation are D(2, -1), E(-1, 1) and F(-1, -1)

Since, the dilation factor is (2,M), so the new vertices are,

D'(2×2, -1×M)

D'(4, -M)

E'(-1×2, 1×M)

E'(-2, M)

F'(-1×2, -1×M)

F'(-2, -M)

Hence, the vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

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The expression for r and h are 9 and x⁸ respectively.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The volume of a cone is 27πx⁸.

We know, The volume of a cone is (1/3)πr²h.

Therefore,  (1/3)πr²h = 27πx⁸.

r²h = 81x⁸.

h = x⁸ and r² = 81 ⇒ r = 9

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first off let's find the slope of M

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-2)}}} \implies \cfrac{1 +8}{1 +2} \implies \cfrac{ 9 }{ 3 } \implies \text{\LARGE 3}[/tex]

now, any line that intersects M will have a different slope than M, and since they're both lines and going to infinity, they will intersect at some point, so let's check those points for their slope, who is different than M's

[tex]\boxed{A}\qquad (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ 3 }{ 1 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{B}\qquad (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{14}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-2)}}} \implies \cfrac{14 +1}{3 +2} \implies \cfrac{ 15 }{ 5 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{C}\qquad (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-20}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-20}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{2}}} \implies \cfrac{ -21 }{ -7 } \implies 3 ~~ \bigotimes \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{D}\qquad (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{6 +2}{2 +3} \implies \cfrac{ 8 }{ 5 } ~~ \textit{\LARGE \checkmark}[/tex]

The trigonometry ratios are tan(∅) = 2/3√10 and

csc(∅) = 7√10/20

From the question, we have the following parameters that can be used in our computation:

0°≤ ∅ ≤ 180°

Also, we have

cos(∅) = -3/7

The tangent is calculated as

tan(∅) = √[1/cos²(∅) - 1]

Substitute the known values in the above equation, so, we have the following representation

tan(∅) = √[1/(-3/7)² - 1]

So, we have

tan(∅) = √[49/9 - 1]

This gives

tan(∅) = √40/9

So, we have

tan(∅) = 2/3√10

Also, we have

cos²(∅) + sin²(∅) = 1

So, we have

(-3/7)² + sin²(∅) = 1

Evaluate

sin²(∅) = 1 - (-3/7)²

sin²(∅) = 1 - (9/49)

sin²(∅) = 40/49

Take the inverse of both sides

csc²(∅) = 49/40

So, we have

csc(∅) = 7/(2√10)

Rationalize

csc(∅) = 7√10/20

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The mean of the given data set is 59.83.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a given set of observations.

The given data set is:-

George Bush

64

Bill Clinton

46

George W. Bush

54

Barack Obama

47

Donald Trump

70

Joe Biden

78

The mean of the data set is calculated as:-

Mean = ( 64 + 46 + 54 + 47 + 70 + 78 ) / 6

Mean = 359 / 6

Mean = 59.83

Hence, the mean of the data set is 59.83.

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A dynamic array is an array with a big improvement: automatic resizing.

How does dynamic array works?

A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.

A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.

Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.

Initial Values:

n = 2

arr[0] = [ ]

arr[1] = [ ]

Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5]

arr[1] = [ ]

Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]

arr[0] = [5]

arr[1] = [7 ]

Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5, 3]

arr[1] = [7 ]

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The equations 5y+25= 5*(y+4) are not equivalent.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+9. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=5 and b=9.

Algebraic expressions or linear equations are considered equivalent when they are equal.

For solving this question, you should:

    1 .Expression y+4y= y(1+4)

       2+4*2=2*5

       2+8=10

       10=10

     The equations are equivalent.

  2. Expression y+y+y= 3y

       2+2+2=3*2

       6=6

     The equations are equivalent.

 3. Expression 5y+25= 5*(y+4)

       5*2+25=5*(2+4)

      10+25=5*(6)

       35≠30

     The equations are not equivalent.

4. Expression 2*(y+2)=2y+4

       2*(2+2)=2*2+4

      2*4=4+4

        8=8

     The equations are equivalent.

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The average per diem cost in Nairobi is $417.806.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Given that, 86.65% of the per diem costs in Nairobi, Kenya, are less than $449, and if the standard deviation of per diem costs is $36.

z=(x-μ)/σ

z= standard score

x= raw observed data point

μ= population mean

σ= population standard deviation.

Here, 0.8665 =(449-μ)/36

0.8665×36=449-μ

31.194=449-μ

μ=449-31.194

μ=$417.806

Therefore, the average per diem cost in Nairobi is $417.806.

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The expression can be factored as:

(16x^3 - 20x^2 + 28x - 35) = 4x(4x^2 - 5x + 7) = 4x(x - 1)(4x - 7)

Answer:

I think it is 4.5 length
area= 20.25

Step-by-step explanation:

Step 1: I square rooted 324 to get 18

Step 2: I divided that number by 2 twice to get 4.5
18/2 = 9/2 = 4.5
multiply 4.5 by 4.5 to get 20.25!


Hope this is correct!

By using trigonometry formula, The value of variable y is 63.6396103.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

Given that, the angle is 45°.

the height is 45.

from the formula Sin A = height/ hypotenuse

⇒ Sin45° = 45/ y

⇒ y = 45 / Sin45°

⇒ y = 45 / 0.7071067

⇒ y = 63.6396103

The value of variable y is 63.6396103.

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The set is {0, 1, 2, 3, 5, 6, 8}. and the truth set is {0, 1, 2, 3, 5}

From the question, we have the following parameters that can be used in our computation:

ID = 01238586

So, the roster notation for the set is

{0, 1, 2, 3, 5, 6, 8}.

We have:

The statement is x ∈ S, (x prime) ∨ (x + 1 ∈ S)

This means that

Using the above as a guide, we have the following:

So, the truth set is {0, 1, 2, 3, 5}

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The probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.

The formula used to calculate the probability of a group of five students being selected from a group of 12 nominees is C(12,5) which is equal to 792. This can be calculated using the formula n!/(r!(n-r)!), where n is the number of nominees (12) and r is the number of students in the group (5).

To calculate C(12,5), first calculate 12!/5!7!. This is equal to 12x11x10x9x8/5x4x3x2x1, which is equal to 11,664. Then divide 11,664 by 7! (7x6x5x4x3x2x1) which is equal to 5040. This is equal to 2.32, which is the probability of selecting a group of five students from a group of 12 nominees.

Therefore, the probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.

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The statement -

"If there is {b} ounces of water in a bottle, than (b + 5) would represent the amount of water left in the bottle after you drink 5 ounces" in option 2, cannot be represented with the help of the function given.

An function in mathematics defines a relationship between one variable (the independent variable, {x})  and another variable (the dependent variable, {y}). Example -

y = f{x} = ax + b

Given is a function as -

y{b} = b + 5

The statement that cannot be represented with the help of this function is  given below -

Therefore, the statement "If there is {b} ounces of water in a bottle, than (b + 5) would represent the amount of water left in the bottle after you drink 5 ounces" cannot be represented with the help of the function given.

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The solution set of the inequality is shown in the graph as the set of all points to the left of the line x = -5. This represents the solution set for the inequality x < -5. So correct option is F.

An inequality is a mathematical statement that represents a relationship between two values or expressions. It is used to express that one value is greater than, less than, or equal to another value. Inequalities are written using symbols such as ">", "<", "≥", or "≤". For example, the statement "x < 10" represents the inequality that the value of x is less than 10. Inequalities are used in many areas of mathematics, including algebra, geometry, and calculus, to model real-world situations and solve problems. They are also used in many scientific and engineering fields, such as economics, physics, and engineering, to model and analyze complex systems and relationships.

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Any field if is also a vector space over itself, with the field addition used as vector addition, and the field multiplication used as scalar multiplication is True.

A set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars is referred to as a vector space (also known as a linear space). Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field.

If V and W are both sub spaces of the vector space U, then their intersection is also a subspace of U.

According to the definition of a subspace, we can say that {0} belongs to both V and W.

So, {0} will also belong to the intersection of V and W.

That is, {0} ∈ V ∩ W.

Now, let a, b are scalars and v, w∈ V ∩ W.

So, we get

v, w ∈ V  and  v, w ∈ W.

Since V and W are sub spaces of V and W, so we get

av + bw ∈ V  and  av + bw ∈ W.

Therefore, av + bw ∈ V ∩ W.

Thus, V ∩ W is also a subspace of U.

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A kilometer is the largest unit.

In the International System of Units, a kilometer represents one mile (SI). The symbol for it is km. Km is typically used to describe a location's or a piece of land's distance. It is possible to measure length and distance in kilometers or "km." The measurement unit "kilometer," which is also used to measure geographic distances, is comparable to the measurement unit "mile." Kilometers are a common measurement unit for length and distance in many nations. 1000 meters make up one kilometer.

the distance between two points along an object's longest side or length; often used to describe a specific component of an object: a length of rope; the boat is 20 feet long.

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Using Factorization, The solution of the algebraic fraction is [tex]\frac{10}{p-4}[/tex].

Due to the fact that they have polynomials on both sides of the equality sign, algebraic equations are also known as polynomials. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of algebraic equations.

Numbers are factored using formulas for factorization. Decomposing an entity into the result of another entity or factors that, when multiplied together, produce the original number is known as factorization. Simple factorization formulas are used in factorization procedures to simplify algebraic or quadratic equations. Instead of expanding parentheses, expressions are expressed as the sum of their constituent parts. Each equation may have factors that are algebraic expressions, variables, or .

[tex]\frac{p - 8}{8 p²-12p+32} \div \frac{1}{10}[/tex]

first we factorize the denominator and using invert Endo to the other fraction.

[tex]\frac{p - 8}{8 p²-12p+32} \times \frac{10}{1}\\\frac{p - 8}{(p - 8)(p - 4)} \times 10[/tex]

= [tex]\frac{10}{p-4}[/tex]

Hence the simplified fraction is [tex]\frac{10}{p-4}[/tex]

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Answer:Multiply 3 times twelve and add one. You will get 37 inches tall. He needs to be 42 inches tall. subtract 42 - 37 and you will get 5. William needs to be five inches taller.

Step-by-step explanation:

An addition inequality to find the how much taller William to ride the coaster is, Height of William + x ≥ 42.

Inequality can be defined relation that compares two numbers or other mathematical expressions in an unequal way.

We are Given, Riders should be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.

Therefore,

The inequality which may be used to calculate how much taller William has to be in order to ride the coaster.

Height of William + x ≥ 42

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Answer:

yes, it is a funtion

Step-by-step explanation:

we can rewrite the equation as,

y = 14/5 - 7x/5

there us only one value of y for every real no of x

The relation 7x = 14 - 5y is a function.

To determine whether the relation 7x = 14 - 5y represents a function, we need to check if each value of x corresponds to a unique value of y.

First, let's isolate y in terms of x:

7x = 14 - 5y

Subtract 14 from both sides:

7x - 14 = -5y

Divide by -5:

(7x - 14) / -5 = y

Simplifying further:

y = (-7x + 14) / 5

Since we have found a formula for y in terms of x, this relation represents a function.

For each value of x, there is a unique corresponding value of y based on the equation y = (-7x + 14) / 5.

Therefore, the relation 7x = 14 - 5y is a function.

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The arc lengths of the given circles are 8π/3, 14π/3 and 4π

Arc length is the distance between two points along a section of a curve.

Given are circles, with radii 4, 3 and 3 units, we need to find the arc length of each,

Since, angles are in radian, convert them into degree by multiply them by π/180°

1) radius = 2π/3 × 180°/π

= 120°

2) radius = 7π/6 × 180°/π

= 210°

3) radius = 4π/3 × 180°/π

= 240°

Arc length = θ/360° × 2π × radius, where θ is the central angle,

1) Arc length = 120°/360° × 2π × 4

= 8π/3

2) Arc length = 210°/360° × 2π × 3

= 14π/3

3) Arc length = 240°/360° × 2π × 3

= 4π

Hence, the arc lengths of the given circles are 8π/3, 14π/3 and 4π

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The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

[tex]0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70[/tex]

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

[tex]s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }[/tex]

Where [tex]X_{mean}[/tex] is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate [tex](X - X_{mean})^2[/tex]for each data point and sum up the values:

[tex](0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36[/tex]

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

[tex]\sqrt{1.31} = 1.15[/tex]

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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