Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).

Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created.

Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (3, 4), (4, 7), (8, 2), (3, 4).

The advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

In statistics, a simple random sample is a subset of persons taken from a larger set in which a subset of individuals is chosen randomly, all with the same probability.

It is a method of choosing a sample at random.

The outcomes of the observational study can be generalized to the population.

To construct a simple random sample, there are six steps: (a) defining the population; (b) picking your sample size; (c) listing the population; (d) assigning numbers to the units; (e) discovering random numbers, and (f) selecting your sample.

Therefore, the advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

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Correct question:
Which of the following is a benefit to using a random sample for an observational study?

a. The random sample allows for different treatments to be assigned.

b. A causal relationship can be determined.

c. The results of the observational study can be generalized to the population.

d. A random sample is the easiest method of data collection.

e. The distribution of the sample will match the distribution of the population.

The discounted price of an item did the price increased after the weekend by a fraction of 1/5.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. One-fifth is 20 percent of the total five parts of a number, and thus, the price increased by 1/5th after the weekend.

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The Maclaurin series expansion of f(x) = 1/(1-x)² is

1 + 2x + 6x² + 24x³ +......

The general expression for the Maclaurin series is given by the formula:

f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...

= ∑ f⁽ⁿ⁾ (0)xⁿ/n!

n= 0 to infinity

Specifying the convergence region completes the Maclaurin series formulation. Detailed five steps for determining the Maclaurin series of

f(x) = 1/(1-x)²

Step 1 : Find Derivatives for f(x)

f(x) = 1/(1-x)²

f'(x) = -2(1-x)⁽⁻²⁻¹⁾ (-1) = 2/(1-x)³

The second derivative of f(x) is the derivative of f''(x) :

f"(x) = 2(-3)(1-x)⁽⁻³⁻¹⁾(-1) = 6/(1-x)⁴

Differentiating again, f"'(x) = 6(-4)(1-x)⁽⁻⁴⁻¹⁾(-1)

= 24/(1-x)⁵

Thus, the nᵗʰ derivative is ,

f⁽ⁿ⁾(x) = (n+1)!/(1-x)⁽ⁿ⁻¹⁾

Step 2: Evaluate These Derivatives and f(x) at x=0 let x = 0 , f(0) = 1

f'(0) = 2 , f"(0) = 6 , ....... , f⁽ⁿ⁾(0) = (n+1)!

Step 3 : Now, the Sum of Products :

f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...

xf'(0) = 2x

x²f"(0) = 6x²

x³f"'(0) = 24 x³

----------------------------

xⁿf⁽ⁿ⁾(0)= (n+1)!

Thus, the Maclaurin series for ln(1 + x) is this:

f(x) = (1−x)⁻² = 1 + 2x + 6x² + 24x³ +......

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The value of the notation Δy from the points (-3,-5) and (0,10) is 15

The complete question is added at the end of this solution

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

Points = (-3,-5) and (0,10)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (-3,-5) and (0,10)

The notation Δy represents the change in the y values of the given points

This notation can be extended to calculate the slope of the points

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,-5) and (0,10)

Substitute the known values in the above equation

So, we have the following equation

Slope = (10 + 5)/(0 + 3)

Evaluate the sum

Slope = 15/3

The numerator represents Δy

i.e. Δy= 15

Evaluate the quotients

Slope = 5

Hence, the slope of the line is 5 and the value of the notation Δy is 15

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Complete question

Using the given points, determine Δy

Type a numerical answer in the space provided.

(-3,-5) and (0,10)

Answer:

(D)

Step-by-step explanation:

This is because if you have 3 angles, there is an infinite amount of possible triangles. For example, if you have a triangle with the angles 30 degrees, 60 degrees, and 90 degrees, you could have any triangle with side ratios of 1:[tex]\sqrt{3}[/tex]:2.

Answer: 250 grams/packet = 8 packets.

Step-by-step explanation:

To find the number of 250g packets of biscuits that can be made from 2kg of biscuits, we need to first convert the weight of the biscuits to the same unit of measurement. Since 1 kilogram is equal to 1000 grams, 2kg of biscuits is equal to 2000 grams. Therefore, the number of 250g packets of biscuits that can be made from 2kg of biscuits is 2000 grams / 250 grams/packet = 8 packets.

Step-by-step explanation:

1 kg = 1000 g

as k stands for "kilo" meaning 1000.

250 g fit therefore 4 times into 1 kg.

and then 2×4 = 8 times into 2×1 = 2 kg.

so, there can be 8 250 g packets made from 2 kg.

Here the missing component in this study is control group.

A control group is a group of participants used to compare different groups in a test or experiment. Consists of participants who did not receive an experimental treatment. Some experiments use multiple control groups to collect more information and improve the accuracy of the results. For example, many medical studies include positive, negative, and placebo control groups to better understand the effectiveness of a treatment or drug.

Given the circumstances, the energy drink company claims that its products boost memory in students. To back up its claims, the company publishes an ad claiming that eight out of 10 people (randomly selected across the country) who tried the product reported improved memory.

But they didn't compose a control group to compare the results for test.

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The complete question is as follows:

An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a

A) control group

B) sample group

C) population

D) test group

Answer:

A. Control Group

Plato

The solution to the equation are x=a

The given equation is sin (2x) = a and 0 < x < pi/2

Sin(2x) = sin x, 0≤x≤2п  ........................... (eq. 1)

Using the trigonometrical formula,

sin(2x) = sin xcosx

Let us subtract the formula from equation 1

2sinxcosx = sinx

Therefore, 2sinxcosx-sinx = 0

Let us remove common terms to get

sinx(2cox-1)=0

Now, sinx=0

x= 0, [tex]\pi[/tex], [tex]2\pi[/tex]

Also, 2cos x =1

This means that cos x = 1/2

By implication, x=cos⁻¹(1/2)

That is to say that x= [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

In conclusion, the value of [tex]\pi[/tex] is a as a single integer

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The probability of getting exactly 4 heads is 0.26

A loaded coin has 0.48 probability of coming up heads

0.52 probability of coming up tails.

coin is flipped 7 times

let's assume n = 7.

The seven flips of the coin are separate from one another, so what happens on one flip is unaffected by the outcomes of the other tosses.

When calculating the likelihood that two events will occur simultaneously, we must multiply the probabilities of events 1 and 2, presuming that event 1 occurred.

Tosses never affect one another, so the "assuming event 1 happened" part is no longer necessary because it has no effect on the probability. As a result, we just need to multiply the chances for each toss. This supposition is essential. We would have needed to know exactly how tosses are dependent on one another if they were interdependent.

Typically, we would have [tex](n! /(r!)*(n - r)!)*p^r*(1-p)^(n-r)[/tex] is the probability of getting r heads out of n, without taking into account the order.

probability of getting exactly 4 heads r = 4.

out of 7 flipping n =7.

7!/(4!*3!)   = 35

(0.48)^4 = 0.05308416

(0.52)^3 = 0.140608

35*0.05308416*0.140608 = 0.26124201492 = 0.26

so the probability of getting exactly 4 heads is 0.26.

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The given pair of equations has no solution.

Two equations can be solved through three different methods:

Let's use the elimination method in this question

                         20x - 4y = 11      .....(I)

                          10x - 2y = 6      .....(II)

Multiply (II) by 2

                          20x - 4y = 11      .....(I)

                          20x - 4y = 6      .....(II)

Now, subtracting equations (I) and (II) we will get no solution.

It is possible for the two lines to be parallel and not intersect. In this situation, we cannot identify a shared point between the two, and as a result, the system of the two equations representing the two lines cannot provide a solution!

This question is incomplete. The correct question is

Consider the two equations and solve for x and y.

                          20x - 4y = 11    

                          10x - 2y = 6  

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Let a be the area of smaller pentagon. Then area of the smaller pentagon is a=8 [tex]in^{2}[/tex] .

A pentagon is a 2D polygon with five sides and five angles. The word "pentagon" is created by combining the Greek words "penta" (which means "five") and "gon," which means "angles."

The President and the Secretary of Defense have exercised global command and control over the nation's armed forces from the Pentagon. Since its construction, the Pentagon has served as a national and international emblem. It is, above all, a metaphor for American strength and influence, with all the positive and negative connotations that entails.

Similar figures' surfaces have an area that is proportional to the square of their sides.

The ratio of the sides is on the left, and the ratio of their areas is on the right, therefore we may write this as a proportion.

Keep in mind that the ratio of the sides is squared because we are working with areas.

[tex]\frac{side_{1} ^{2} }{side_{2} ^{2} } =\frac{area_{1} }{area_{2} }[/tex]

Let area a smaller pentagon is a

[tex]\frac{7^{2} }{2^{2} }=\frac{98}{a}[/tex]

a=[tex]\frac{98*4}{49}[/tex]

a= 8 [tex]in^{2}[/tex]

So the area of the smaller pentagon is 8 [tex]in^{2}[/tex]

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The probability that Steph Curry makes the first 2 free throws and misses the last throw is 81/1000

Let A be the event that Steph Curry makes the free throw.

Let B be the event that Stech Curry does not make the free throw.

According to the problem,

P(A) = 90%

= 9/10

Since B is the complement of A,

P(B) = 1 - P(A)

= 1/10

Hee, Steph Curry gets 3 free throws. Hence, the probability that he makes the first 2 throws while he misses the third one is

P(A) X P(A) X P(B)

= 9/10 X 9/10 X 1/10

= 81/1000

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Step-by-step explanation:

the volume of a pyramid is

base area × inner height / 3

we have the base area : 7×7 = 49 in²

so, we need to get the inner height h.

fit this we need to get the outer height l.

the surface area is

base area (49 in²) + 4×side triangle area = 185 in².

one of these 4 side triangle area is

baseline (7 in) × l / 2

so, we have a surface area

49 + 4×7×l/2 = 185

49 + 2×7×l = 185

49 + 14×l = 185

14×l = 136

l = 136/14 = 68/7 = 9.714285714... in

h we get now via Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.

l² = h² + 3.5²

94.36734694... = h² + 12.25

h² = 94.36734694... - 12.25 = 82.11734694...

h = 9.061862222... in

so, the volume of the pyramid is

49 × 9.061862222... / 3 = 148.0104163... in³ ≈

≈ 148.01 in³

Amrit's income is £27434.16.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let the Bethan's income be x

Amrit's income is 32% more than Bethan's income.

So, Amrit's income=x+32%

Amrit and Bethan's combined income is £54868.

According to given question we have

x+x+32%=£54868

2x+32/100=£54868

2x=54868-0.32

2x=54867.68

x=27433.84

Bethan's income=£ 27433.84

Amrit's income

=x+32%

=£ 27433.84+0.32

=£27434.16

Therefore,  Amrit's income is £27434.16.

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In equilateral triangle ABC, the length of side A is equal to the side B and side C.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees.

Here,

The length of side A of an equilateral triangle ABC is equal to the lengths of sides B and C.

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The shape will be rectangular.

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely. A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.The uniform distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a probability p = 0.50 and would be depicted by a line from the y-axis at 0.50.

From the definition of a uniform probability distribution, since it has a constant probability across a given interval, then it has a rectangular shape. Note also that another term for the uniform probability distribution is the rectangular distribution. Therefore, the correct answer is c.

Thus, option (c) will be the correct option.

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The area is 0.25

What is a tangent line?

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.  A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.

[tex]$$\begin{aligned}& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3-2 x\right] \\& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3\right]-\frac{\mathrm{d}}{\mathrm{d} x}[2 x] \quad \text { Sum } / \text { Rest rule } \\& f^{\prime}(x)=3 x^{3-1}-2 \quad \text { Power rule } \\& f^{\prime}(x)=3 x^2-2 \\&\end{aligned}$$[/tex]

Now finding tangent for a=-1,

[tex]\begin{aligned}& y=f^{\prime}(a)(x-a)+f(a) \\& y=f^{\prime}(-1)(x+1)+f(-1) \\& y=\left(3(-1)^2-2\right)(x+1)+(-1)^3-2(-1) \\& \mathbf{y}=\mathbf{x}+\mathbf{2}\end{aligned}$$[/tex]

For the first area,

[tex]$$\begin{aligned}& A_1: \int_{-2}^{-\sqrt{2}} x+2 d x=\frac{1}{2} x^2+\left.2 x\right|_{-2} ^{-\sqrt{2}} \\& A_1=\frac{1}{2}(-\sqrt{2})^2+2(-\sqrt{2})-\left(\frac{1}{2}(-2)^2+2(-2)\right) \\& A_1=\mathbf{3}-\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{1}} \approx \mathbf{0 . 1 7 1 5 7 2 8 7 6} \ldots\end{aligned}$$[/tex]

For the second area,

[tex]$$\begin{aligned}& A_2: \int_{-\sqrt{2}}^{-1} x+2-\left(x^3-2 x\right) d x=-\frac{1}{4} x^4+\frac{3}{2} x^2+\left.2 x\right|_{-\sqrt{2}} ^{-1} \\& A_2=-\frac{1}{4}(-1)^4+\frac{3}{2}(-1)^2+2(-1)-\left(-\frac{1}{4}(-\sqrt{2})^4+\frac{3}{2}(-\sqrt{2})^2+2(-\sqrt{2})\right) \\& A_2=-\frac{\mathbf{1 1}}{\mathbf{4}}+\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{2}} \approx \mathbf{0 . 0 7 8 4 2 7 1 2 4} \ldots .\end{aligned}$$[/tex]

Hence, required area is

[tex]$$\begin{aligned}& A=A_1+A_2 \\& A=3-2 \sqrt{2}-\frac{11}{4}+2 \sqrt{2} \\& \mathbf{A}=\frac{\mathbf{1}}{\mathbf{4}}=\mathbf{0 . 2 5}\end{aligned}$$[/tex]

The area is 0.25

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Answer: 12 miles

Step-by-step explanation:

Let y represent the cost and x represent the number of miles!

y = 1.25x + 3

Now put the $18 in for y

18= 1.25x + 3

15 = 1.25x

x = 12 miles

Answer:

Step-by-step explanation:

We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:

18 = 1.25x + 3

15 = 1.25x (subtracted 3 from both sides)

12 = x (divided each side by 1.25)

So, the trip was 12 miles

y=3 is the equation of a horizontal line that passes through the point (9, 3)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If a line passes through a point (x₁, y₁) and has a slope of m, then the

equation of the line is given by (y-y₁) = m(x-x₁).  

Because the question states the line is horizontal, the slope is zero, or m=0.

Plugging the information into the slope equation gives:

(y-(3)) = 0(x-(9)).

y-3= 0

y= 3.

Hence, y=3 is the equation of a horizontal line that passes through the point (9, 3).

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The number of applicants that were not accepted are calculated to be 1260.

The number of applicants that were not accepted can be determined as follows;

Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;

360 × 9 / 2 = 3240 / 2 = 1620

Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.

The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;

Applicants not accepted = 1620 - 360

Applicants not accepted = 1260

Therefore 1260 applicants were not accepted by the program.

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AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

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Answer:

$8 per pound

Step-by-step explanation:

16/2 = 8

Answer: $8

Step-by-step explanation:

16 divided by 2 = $8 per pound

Answer:

The answer is : 9345.

Step-by-step explanation:

N/A

 y = 3/8x + 1/4 is equation of linear equation .

What in mathematics is a linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. with m the slope and b the y-intercept as the single constant and a first-order (linear) term.

                   The aforementioned is occasionally referred to as a "linear equation of two variables," where y and x are the variables.

                 There are three main types of linear equations: point-slope form, standard form, and slope-intercept form.

3/2x -4y+1=0

  -4y = -3/2x - 1

    y = 3/8x + 1/4

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The complete question is -

Which equation is equivalent to 3/2x -4y+1=0

The area of the ring between these two circles if the radius of the larger and the smaller circle is 10 and 6 is 200.96.

Given:

two circles have the same center $c.$

the larger circle has radius $10$

and the smaller circle has radius $6.$

we are asked to determine the  the area of the ring between these two circles.

⇒ Area of the ring =  Area of larger circle - area of smaller circle

⇒ Area of circle = πr²

⇒ Area of larger circle  = π(10)²

= 100π

⇒ Area of small circle = π(6)²

= 36π

Area of the ring =  Area of larger circle - area of smaller circle

Area of the ring = 100π - 36π

= 64π

= 200.96

Hence the area of the ring is 200.96

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Answer:

1)

Step-by-step explanation:

[tex] {(x - 5)}^{2} = 38[/tex]

The required step solving the equation using Completing the square method is (x - 5)² = 38.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the Equation: x² - 10x-13 = 0

Now, half the coefficient of x and add and subtract the square of the half of the coefficient of x.

So, x² - 10x-13 = 0

x² - 10x-13 -5² + 5² = 0

(x - 5)² - 25 - 13 = 0

(x-5)² -38= 0

(x - 5)² = 38

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Total 36 storage locations are allocated by the statement declare [tex]a[4,9][/tex] as integer.

The statement declare [tex]A[4,9][/tex] as integer allocates 4 × 9 = 36 storage locations for the array A. Each storage location is capable of holding a single integer value.

In this statement, the array A is declared with two dimensions, 4 and 9. The first dimension, 4, represents the number of rows in the array, and the second dimension, 9, represents the number of columns. This means that the array A has a total of 4 rows and 9 columns, for a total of 4 × 9 = 36 storage locations.

Here's an example of how the array A might be structured in memory:[tex]A[0,0] \ A[0,1] \ A[0,2] \ A[0,3] \ A[0,4] \ A[0,5] \ A[0,6] \ A[0,7] \ A[0,8]\\A[1,0] \ A[1,1] \ A[1,2] \ A[1,3] \ A[1,4] \ A[1,5] \ A[1,6] \ A[1,7] \ A[1,8]\\A[2,0] \ A[2,1] \ A[2,2] \ A[2,3] \ A[2,4] \ A[2,5] \ A[2,6]\ A[2,7] \ A[2,8]\\A[3,0] \ A[3,1] \ A[3,2] \ A[3,3] \ A[3,4] \ A[3,5] \ A[3,6] \ A[3,7] \ A[3,8][/tex]

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The area of the triangle given in this problem is of:

A = 84 cm².

The area of a triangle of base b and height h is given by the multiplication of these two dimensions divided by two, which is equivalent to the multiplication of these measures by 0.5, hence:

Area = 0.5 x base x height.

For the triangle given at the end of the answer, these dimensions are given as follows:

Then the area of the triangle is obtained by the multiplication as follows:

Area = 0.5 x 8 x 21 = 4 x 21 = 84 cm².

The triangle from which we calculate the area is given by the image shown at the end of the answer.

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Null Hypothesis that is, the average errors for two processes differ significantly.

Two options being the same is the null hypothesis in inferential statistics. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

Always indicate the "null hypothesis" with an equal sign, and the alternative with a less-than, greater-than, or not equal sign. The researcher is looking for evidence that the two methods/processes produce different average errors since this alternative statement contains the not equal to symbol.

Hence, the correct pair of “null and alternative” hypotheses is given by,

[tex]Null Hypothesis(H0): UA = UB versus\\ H1: UA \neq UB; that is, the average .errors. for .two .processes .differ .significantly.[/tex]

[tex]"H0: UA = UB H1: UA \neq UB"[/tex]

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