Brendon is building a clubhouse where 1 inch on the plans is equivalent to 8 inches on the actual clubhouse.

If the clubhouse is to be 126 inches wide, what will the width be on the plans?

Round answer to the nearest hundredth if necessary.

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 2)² = 3²

(x + 3)² + (y - 2)² = 9.

By dilating with a scale factor of 2, we have:

(x + 3)² + (y - 2)² = (9 × 2)

(x + 3)² + (y - 2)² = 18

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By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]

So that is an equivalent equation.

We also can keep rewritting this to get:

[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]

The correct options are B and C.

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As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a) where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°. Plugging those values into the formula, we get d = 300 * tan(15°) = 517.4 feet. Rounding this to the nearest whole number, we get 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a). This equation is derived from the Pythagorean Theorem, where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°, so we can plug these values into the equation. When we do this, we get d = 300 * tan(15°) = 517.4 feet. As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

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There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.

Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:

Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.

Using a spreadsheet, we get r = 0.80.

Using the formula: df = n - 2.

The sample size (n) is 10, so df = 10 - 2 = 8.

Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).

For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.

Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.

Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.

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The width of the soccer field in the drawing is 116 inches if the ratio is 2 inches to 1 yard

If 2 inches on the drawing represents 1 yard in reality, then 1 inch on the drawing represents 1/2 yard in reality.

So, to find the width of the soccer field in the drawing, we can use the following proportion:

1 inch on drawing / (1/2) yard in reality = x inches on drawing / 58 yards in reality

Simplifying this proportion, we get:

x inches on drawing = (1 inch on drawing / (1/2) yard in reality) * 58 yards in reality

x inches on drawing = 2 * 58

x inches on drawing = 116

Therefore, the width of the soccer field in the drawing is 116 inches.

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Answer:

5

Step-by-step explanation:

this is wrong

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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The five in 35.76 is 100 times bigger than the five in 26.95.

Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.

To compare them we need to compare the place value in which each five is.

To compare them, just write the numbers but replacing all the other values by zeros:

35.76 = 05.00 = 5

26.95 = 00.05 = 0.05

Now take the quotient of these two, we will get:

5/0.05 = 100

Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.

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Hence the value of c = 4 in [3,5] for Rolles theorem.

Rolle's Principle

If a function f is defined in the closed interval [a, b] in a manner that meets the requirements listed below.

The interval [a, b] is closed and the function f is continuous.

ii) On the open interval, the function f can be differentiated (a, b)

iii) If f (a) = f (b), then at least one value of x exists; in this case, let's assume that this value is c, which is situated between a and b, i.e. (a c b), in such a way that f'(c) = 0.

There exists a point x = c in (a, b) such that f'(c) = 0 if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

let f(x)=x²-8x+12 in [3,5]

i) f(x) is continuous in closed interval [3,5] because f(x) is algebraic function.

ii) f(x) is differentiable in the open interval (3,5) since the algebraic function is differentiable.

now f(3)=3²-8*3+12

f(3)= 9-24+12

f(3)= -3

f(5) = 25-40+12

f(5)= - 3

f(3) = f(5)

f'(x)= 2x-8

x=c ,c in [3,5]

f'(c)= 2c-8

2c-8=0

c=4

Hence the value of c = 4 in [3,5] for Rolles theorem.

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Answer:

  (a)  Figure 3

  (b)  66.2 meters per second

Step-by-step explanation:

You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.

The fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.

The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.

The speed is estimated by the equation of the curve of best fit as ...

  y = 0.6x² +2.1x +11

A slight rearrangement can make this easier to evaluate:

  y = (0.6x +2.1)x +11

For x=8, the value of y is ...

  y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2

The predicted speed at 8 seconds is 66.2 meters per second.

The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.

Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.

They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.

center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation

corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position

dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.

scale factor (of a dilation): in a dilation, the constant  rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the  matching point on thepre-image

similar polygons: B.two or  further polygons in which corresponding angles are  harmonious and the lengths of corresponding sides are in proportion.

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The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.

A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.

The standard form of linear equation is given as:

y = mx + b

The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.

While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.

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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.

What is linear function?

In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.

1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.

2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.

3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.

In this case, if we let d = y and g = x, we get:

y = (x-28)7/11

This can be simplified as:

y = 7/11 * x - 196/11

So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.

4. This is a non-linear function since it includes a variable raised to a power (r³).

5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.

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Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

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Answer:

Start off with the 20ft sides

20x2 =40ft

40ft + 8ft = 48ft

Now we need to find the perimeter of the half circle.

Since we know the diameter of the half circle is 8ft, we can use the following formula: Diameter x Pi = Circumference

Plug in:

8ft x 3.14159 = 25.132ft

25.132 /2 gives us the perimeter of the half circle

25.132 / 2 = 12.566

Rounded = 12.57 ft

48 ft + 12.57 ft =  60.57 feet perimeter.

The perimeter of the given solution is 76.56 feet.

We need to find the perimeter of the figure by splitting the figure into a rectangle and a semi-circle. The radius for the semi-circle is found by dividing the diameter by 2, Radius = 8 ÷ 2 = 4.

Therefore, the formula for finding the Perimeter of the given rectangle is  

P = 2( l+b )

P = 2( 20 + 8)

P = 56 feet.

now, the formula for the circumference of a semi-circle is

C = [tex]\pi[/tex]r + 2r

C = 3.14( 4) + 2 (4)

C = 20.56 feet.

Therefore, the perimeter of the given figure is

The perimeter of  the rectangle + circumference of the Semi-circle

= 56 + 20.56

= 76.56 feet

Therefore, the perimeter of the given solution is 76.56 feet.

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Answer:

the first answer is correct

Step-by-step explanation:

y=118x=118

Answer:37

Step-by-step explanation:

<UYW=<UYV+<VYW=36+2x=110

2x=110-36=74

x=74/2=37

Step-by-step explanation:

For x;

[tex]{ \tt{ \tan( \theta) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( 60 \degree) = \frac{x}{5} }} \\ \\ { \tt{x = 5 \tan(60 \degree) }} \\ \\ { \tt{x = 5 \sqrt{3} }}[/tex]

For y;

[tex] { \tt{\cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{cos(60 \degree) = \frac{5}{y} }} \\ \\ { \tt{y = 5 \cos(60 \degree) }} \\ \\ { \tt{y = 2.5}}[/tex]

Answer:

Step-by-step explanation:

To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.

First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:

PV = PMT x [(1 - (1 / (1 + r)n)) / r]

where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06

Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:

PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)

where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97

So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:

R153,094.97 - R141,798.06 = R11,296.91

So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.

The correct coordinates of the center of dilation are (2.8, 3.8).

What is dilation?

In geometry, dilation is a transformation that changes the size of an object. When a figure is dilated, each point of the original figure is moved away from or toward the center of dilation.

Dylan's claim is incorrect because the center of dilation is not necessarily located on the line segment PP'.

To find the center of dilation, we need to locate the image point of a known point after dilation.

Let's consider a point Q on the same line as PP', but on the other side of P', such that PQ = 1 unit. After dilation with a scale factor of 4, the image of Q will be on the line passing through P and P'. Let's denote this image point by Q'.

Since PQ : P'Q' = 1 : 4, the distance from P to Q' is 4 units. Similarly, since PP' : PQ' = 1 : 5, the distance from P to Q' is 5 times the distance from P to P'. Thus, the distance from P to P' is 1 unit and the distance from P to Q' is 5 units.

Therefore, the center of dilation is located on the line passing through P and Q', and is 4 units away from P and 1 unit away from Q'.

Using the midpoint formula, we can find the coordinates of the center of dilation:

[tex]x &= \frac{1}{2}(4.8 + 0.8)[/tex]

[tex]&= 2.8[/tex]

[tex]y &= \frac{1}{2}(3.2 + 4.4)[/tex]

[tex]&= 3.8[/tex]

Thus, the correct coordinates of the center of dilation are (2.8, 3.8).

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Answer:

If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.

The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

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the account balance after 12 years of continuous compounding at 7% annual interest, assuming no additional deposits or withdrawals are made, would be $32,447.44.

The formula for continuous compounding is:

A = P[tex]e^(rt)[/tex]

where:

A = the final amount

P = the principal amount (initial investment)

e = the mathematical constant approximately equal to 2.71828

r = the annual interest rate

t = the time in years

Plugging in the given values, we get:

A = 14000[tex]e^(0.0712)[/tex]

A = 14000*[tex]e^0.84[/tex]

A = 14000*2.31796

A = $32,447.44

Compound interest is a type of interest that is calculated not only on the initial principal amount, but also on the accumulated interest from previous periods. In other words, interest is added to the principal amount, and then interest is calculated on the new total amount.

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The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

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AFE triangle,

FE= 6cos60

    = 3

dc= 3

ae= 6sin60

   = 3*squareroot3

Area= 1/2(10+4)*3*squareroot3

       = 7*3*squareroot3

        = 21*squareroot3

        = 21*1.73

         = 36.33square units

The product is decreased by a factor of 16.

What is a factor?

In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.

Let's say we have two numbers, A and B, and we want to find the product of A and B.

The product of A and B is AB.

If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.

So the new product of A/2 and B/8 is:

(A/2)(B/8) = AB/16

Therefore, the product is decreased by a factor of 16.

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The option that describes the null and alternative hypothesis, test statistic and conclusion will be B. test statistic = -1.5625 and the conclusion is to reject the null hypothesis.

In statistical hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference or relationship between two or more variables. It represents the default position that there is no effect or change, or that any observed effect is due to chance.

The alternative hypothesis (H1), on the other hand, represents the opposite of the null hypothesis. It states that there is a significant difference or relationship between the variables being tested. The alternative hypothesis is typically what the researcher is trying to prove or support with their study.

The test statistic will be:

= (116 - 121) / 16(✓1/50 + 1/50)

= -1.5625

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