Attending Class The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state University
No. of Absensense, x 0 1 2 3 4 5 6 7 8 9
Final grade, y 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
A) Find the least-sqaures regresssion line treating number of absenses as the explanatory variable and final grade as a response variable.
B) Interpret the slope and y-intercept , if appropriate.
C) Predict the final grade for a student who misses five class periods and compute the residual. Is the final grade abover or below average for this number of absenses.
D) Draw a least-sqaures regression line on the scatter diagram of the data.
E) Would it be reasonable to to use the least-sqaures regression line to predict the final grade for a student who has missed 15 class periods? why or why not?

On solving the provided question, we can say that In lexicographic order, the following variation will be (5,6,7,4,3,2,1).

It is known as permuting the set in mathematics to rearrange the components of a set that is already ordered or, if the set is not already ordered, to place its members in a linear or sequential order. In this sense, "permutation" refers to the process of changing the linear order of an ordered set.It should be mentioned that a permutation is a mathematical concept that describes several potential arrangements of numbers or other objects.

The ascending numerical order is the lexicographic order when it comes to numbers. From left to right, the numbers are growing. The permutations of "1,2,3," for instance, are 123, 132, 213, 231, 312, and 321 in lexicographic order.

In lexicographic order, the following variation will be (5,6,7,4,3,2,1).

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If t is less than s and s is less than r then the relationship between the values t and r is - t is less than r.

We are given that-

t is less than s i.e. t < s

and

s is less than r i.e. s < r

Now, let us find the relationship between the values of t and r.

t < s and s < r

this implies that -  t < s < r

Hence, we get t < r.

Thus, we get that if t is less than s and s is less than r then the relationship between the values t and r is - t is less than r i.e. t < r.

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To answer this question, we first need to determine the objective and constraint equations.

The objective is to maximize the area of the rectangular garden, which is given by the equation $A = xy$.

The constraint is that the total cost of the fencing must not exceed $320. In other words, we have the equation $6x + 2(y+x) \le 320$.

To express the quantity to be maximized as a function of $x$, we can simply plug in the equation for the area of the rectangular garden into the objective equation. This gives us the function $f(x) = xy = x^2y$.

To find the optimal values of $x$ and $y$, we can use the method of Lagrange multipliers. Let $\lambda$ be the Lagrange multiplier. The Lagrange function is given by

$$L(x,y,\lambda) = x^2y + \lambda(6x + 2(y+x) - 320)$$

To find the optimal values of $x$ and $y$, we need to find the values of $x$ and $y$ that maximize $L(x,y,\lambda)$. To do this, we take the partial derivatives of $L(x,y,\lambda)$ with respect to $x$ and $y$ and set them equal to 0. This gives us the equations

$$\frac{\partial L}{\partial x} = 2xy + 6\lambda = 0 \quad \text{and} \quad \frac{\partial L}{\partial y} = x^2 + 2\lambda = 0$$

We can solve these equations simultaneously to find the optimal values of $x$ and $y$. First, we can solve for $y$ in the second equation to get

$$y = -\frac{x^2}{2\lambda}$$

Substituting this expression for $y$ into the first equation, we get

$$2x \left(-\frac{x^2}{2\lambda}\right) + 6\lambda = 0 \quad \Rightarrow \quad -x^3 + 12\lambda^2 = 0$$

Since $\lambda$ cannot be 0, we can divide both sides of this equation by $-12\lambda^2$ to get

$$x^3 = 12\lambda^2 \quad \Rightarrow \quad x = \sqrt[3]{12\lambda^2}$$

Substituting this expression for $x$ into the expression for $y$, we get

$$y = -\frac{\sqrt[3]{12\lambda^2}}{2\lambda}$$

Now we need to find the value of $\lambda$ that satisfies the constraint $6x + 2(y+x) \le 320$. Substituting the expressions for $x$ and $y$ into this equation, we get

$$6\sqrt[3]{12\lambda^2} + 2\left(-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + \sqrt[3]{12\lambda^2}\right) \le 320$$

Simplifying, we get

$$-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + 10\sqrt[3]{12\lambda^2} \le 320$$

Dividing both sides by $10\sqrt[3]{12\lambda^

Answer: Radius or Diameter

Step-by-step explanation: The formula for circumference is diameter times pi. Since radius is half of diameter, you could still easily find the circumference. You could also find it with area, but that involves multiple formulas and a lot of math. I hope this helped :)

Answer:

Step-by-step explanation:

(a)

The sample space is

{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}

(b)

i  {(2,2), (4,4), (2,4), 4,2)}

ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}

iii {(1,1)}

iv {3,4), (4,3)}

v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}

vi {(1,1), (2,2), (3,3), (4,4)}

vii  {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}

viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}

The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.

As given in the question,

Total number of squares present = 2

Side length of the bigger square = 16 units

Side length of the smaller square = 14 units

Area of the bigger square = ( side length )²

                                           = ( 16 )²

                                           = 256 square units

Area of the smaller square = ( side length )²

                                           = ( 14 )²

                                           = 196 square units

Here favorable outcome is represented by small square and total outcome is represented by bigger square

Probability that the given dart hit the area between the square is

= 196 / 256

= 49/64

= 0.765625

≈ 0.7656

Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.

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The Equation of parabola  ( y + 8 )² = 12( x - 2 )

In math, what is a parabola?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.

                 All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.

Given,

Directrix is known as x=a Directrix=a=3 Equation of parabola

(Y-y1)²= 4a(X-x1)

Vertex (X1,Y1) = (2,-8)

Directrix=a=3

Equation of parabola

       ( y - y₁ )² = 4a( x - x₁)

        ( y - ( -8))² = 4 * 3(x - 2 )

          ( y + 8 )² = 12( x - 2 )

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Answer:

  14.7

Step-by-step explanation:

You want the side opposite the 60° angle in a right triangle with hypotenuse 17.

The sine relation is ...

  Sin = Opposite/Hypotenuse

Solving for the opposite side gives ...

  Opposite = Hypotenuse × Sin

  x = 17·sin(60°) ≈ 14.7

The missing side is about 14.7.

The number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.

Taylor’s inequality:

If Rn( x ) = 0

Rn(x)=0

Rn​(x)=0.

The given function is eˣ

Thus, all the derivatives of eˣ is eˣ itself.

Suppose that, the nth derivative of eˣ is eˣ

To estimate the value of [tex]e^{0.1}[/tex] substitute the value of x as 0.1.

Note that Taylor series is called Maclaurin series when a=0.

Usually, Maclaurin series will starts with n=2.

Increase the value of n until the reminder is less than 0.00001.

By Taylor’s inequality,

If | [tex]f^{n}[/tex](0.1) | = [tex]e^{0.1}[/tex]≤ M then | Rₙ(x) |≤[tex]\frac{M}{(n+1)!}[/tex] [tex]|0.1-0|^{n+1}[/tex]

Substitute the value of n as 2. Then,

[tex]|R2(x)|[/tex]≤[tex]\frac{M}{(2+1)!} |0.1-0|^{2+1}[/tex]

≤ [tex]\frac{e^{0.1}}{3!} |0.1|^{3}[/tex]

≤ [tex]\frac{e^{0.1}}{6} 0.001[/tex]

≤ 0.00018

Since [tex]|R2(x)|[/tex] ≥ choose the value of n as 3. Then,

[tex]|R3(x)|[/tex] ≤[tex]\frac{M}{(3+1)!} |0.1-0|^{3+1}[/tex]

≤ [tex]\frac{e^{0.1}}{4!} |0.1|^{4}[/tex]

≤ [tex]\frac{e^{0.1}}{24} 0.0001[/tex]

≤ 0.0000046

Therefore, [tex]|R3(x)|[/tex] ≤ 0.00001

That is, n=3 satisfies the inequality.

So, by adding the 4 terms (when n=0,1,2,and 3) of the Maclaurin series, it

is possible to estimate the value of [tex]e^{0.1}[/tex] to within 0.00001.

Thus, the number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.

The number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.

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The range of the data set { 6.2 , 9.1 , 2.9 , 1.6 ,9.3 , 5.5 , 8.3 } is 7.7 .

Given :

the range of the data set {6.2,9.1,2.9,1.6,9.3,5.5,8.3}

Enter your answer as a decimal, rounded to the nearest tenth .

Range :

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.

Range = highest value - lowest value

Arrange in ascending order = { 1.6 , 2.9 , 5.5 , 6.2 , 8.3 , 9.1 , 9.3 }

Here highest value = 9.3

Lowest value = 1.6

Range = 9.3 - 1.6

= 7.7

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The equation of the area is 308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)

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

Area = 308

The formula used to calculate area

Area = S.A of the bottom + S.A of the top - 2 * Overlap

Using the given figure, we have

S.A of the top = 6 * (5 * 5)

S.A of the bottom = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2)

Overlap = 2 * (5 * 5)

So, we have

308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)

Hence, the equation is (b)

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The magnitude of the vector having the initial point P and the terminal point Q is 17.

What is magnitude ?

Simply said, "distance or amount" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.

Given: p (- 3,2) , q (5,17)

vector  = (17-2)i + (5+3)j

= 15i + 8j

Magnitude = [tex]\sqrt{(15^{2}+8^{2} ) }[/tex]

magnitude =17

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By analyzing the question, we find that there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

A permutation is an arrangement of a set of items in a specific order. Permutations are typically denoted using the notation "P" followed by the number of items being permuted and the number of items being chosen at a time.

The formula for calculating permutations is as follows:

P(n,r) = n! / (n-r)!

where:

P(n,r) is the number of permutations of r items from a set of n items.

n! is the factorial of n, which is the product of all positive integers less than or equal to n.

There are five fashion models and three remaining outfits, which means there are 5 ways to choose the model who wears the first outfit, 4 ways to choose the model who wears the second outfit, and 3 ways to choose the model who wears the third outfit. Therefore, there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

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In the given triangle, length of AC = 12.3 units

α= 45⁰ and θ = 45⁰

Using Pythagoras theorem,

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]

[tex]AC^{2}[/tex] = 9 + 144

AC = 12.37

Now, to find the angles:

AC is the diagonal.

Then AD=BC and AB=CD

And ∠ABC=∠BCA=∠CDA=∠DAB=90⁰

In ΔABC and ΔADC

∠ABC=∠ADC (Angle of rectangle)

AB=DC (Opposite side of rectangle)

AC=AC (Common side)

∴ΔABC≅ΔADC

∴∠ACD=∠ACB

∵∠ACD+∠ACB=90⁰ ..........[Angle ACB is the angle of rectangle]

∴2∠ACD=90⁰

⇒∠ACD=45⁰

⇒θ = 45⁰

similarly, α = 45⁰

Pythagoras theorem:

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

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The solution of the inequality 42 > g + 27 is 25 > g  and the graph of the inequality has been plotted on a number line

The given inequality is

42 > g + 27

The inequality is the mathematical statement that shows the relationship between two expression with and inequality sign. The inequality maybe less than, less than or equal, greater than, greater than or equal etc. The equal sign will not be a part of inequality

Th given inequality is

42 > g + 27

Subtract both side of the inequality by 27

42 - 27 > g + 27 - 27

25 > g

Plot the inequality in number line

Therefore, the solution is 25 > g and the inequality has been plotted on the number line

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true census  is most likely to be based on a census There are many benefits to choosing a portion of the population selected to represent the population.

• Reducing the cost and time needed to conduct research. Researchers will save more time and money analyzing sample than the whole population.  

• Reducing resource deployment. The manpower needed to analyze a sample is less than the manpower needed to analyze the whole population.  

• Increasing data accuracy. Data taken from the sample will be more accurate than data taken from the whole population because the sample is more willing to join the research.  

• Creating an intensive and exhaustive data. The data taken from a sample will be more intensive and exhaustive because the respondents are minimum.  

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Answer:

19.8

Step-by-step explanation:

19.83 rounded to the nearest tenth is 19.8.

Answer:

26 units

Step-by-step explanation:

First he goes from home to the video store.

home (-2,3) --> video store (4,3)

There is no change in his y distance, so the distance he travels is only the change in x.

distance from home to video store = 4 - (-2) = 6 units

Then he goes from the video store to the grocery store

video store (4,3) --> grocery store (4,-4)

There is no change in his x distance, so the distance he travels is only the change in y.

distance from video store to the grocery store = 3 - (-4) = 7 units

Then he goes from the grocery store to the fast snacks

grocery store (4,-4) --> fast snacks (-2,-4)

There is no change in his y distance, so the distance he travels is only the change in x.

distance from the grocery store to the fast snacks = 4 - (-2) = 6 units

Finally he goes from the fast snack store to his house

fast snacks (2,-4) --> house (2,3)

There is no change in his x distance, so the distance he travels is only the change in y.

distance from the fast snacks to his house = 3 - (-4) = 7 units

therefore the total distance he traveled is 6 units + 7 units + 7 units + 6 units = 26 units

I hope this helps!

The statement that is a good definition is D. Parallel lines are lines that do not intersect.

A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.

Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.

Therefore, based on the information, the correct option is D

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The 3-year Weighted Moving Average (WMA) for predicting the amount of sports equipment sales in 2022 is 1.7.

A Weighted Moving Average gives more weight to recent data and less weight to historical data. This is accomplished by multiplying the price of each bar by a weighting factor. WMA will track prices more precisely than a related Simple Moving Average due to its unique formula. A Weighted Moving Average (WMA) is a sort of moving average that prioritizes recent data over historical data. A moving average is a technical indicator that displays how the price has moved on average over a given time period.

Here,

weights=0.5, 0.3, and 0.2

(0.5×1+0.3×2+0.2×3) / (0.5+0.3+0.2) = 1.7

The 3-year Weighted Moving Average (WMA) to predict the number of sports equipment that will be sold in 2022 is 1.7.

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The amount of Little phone company is $230.8 and of Big phone company is $246.5. Little Phone Company is cheaper. The correct option is B.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Big phone Company charges a connection fee of $200 and $0.15 per minute. Little phone Company charges a connection fee of $175 and $0.18 per minute.

The cost for both companies for time 310 minutes will be calculated as,

Cbc= 0.15t + 200

Cbc = ( 0.15 x 310) + 200

Cbc = $246.5

The cost of little company,

Clc = 0.18t + 175

Clc = ( 0.18 x 310 ) + 175

Clp = $230.8

From the above costs, it is observed that the Little Phone Company is cheaper.

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The different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour include 11 cups of 1/4 or 3.67 cups of 3/4.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.

The combination will be:.

= 2 3/4 ÷ 1/4.

= 11

The second combination will be:

= 2 3/4 ÷ 3/4

= 3.67

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A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

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Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

As per the given standard deviation, the Lana hypothesis is not equal to 25 point and the alternative hypothesis is greater.

The term standard deviation refers the measure of how dispersed the data is in relation to the mean.

Here we have given that the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection.

And we need to find if  the mean social marginality scores are not the same for all four age groups

While we looking into the given the alternate hypothesis for this problem is μ greater than 115 point.

And here we have to find the test statistics which are equal to x, power, minus μ, divided by 10 point.

And the bar is 125 points in the x bar and 25.2 points in the me.

Then it can be written as,

=> x² = 125.2

Where as 1.5 and sigma equal to 30 and then equal to 25.

Now, we have to do the Minus 115 and then divided into 30 by root 5 and 25 by root.

Then we will get it as 1.70

Now we have to simplify it.

Which is, is that greater than 1.70, which is equal to 1 minus p p, is less than 1.70, which is equal to 1 minus 0.9554, which is equal to 0.0446.

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The rate at which the slope of the line is changing with respect to time is dθ/dt.

The rate at which the slope of a line is changing with respect to time is a concept in calculus that is known as the derivative. The derivative measures the rate of change of a function with respect to one of its variables. In this case, we are looking at the rate of change of the slope of the line with respect to time. The slope of a line is determined by the angle, theta, between the line and the positive x-axis. Therefore, the rate of change of the slope of the line with respect to time is equal to the rate of change of the angle, theta, with respect to time. This can be expressed as dθ/dt, where dθ represents the change in theta and dt represents the change in time. Therefore, the expression which gives the rate at which the slope of the line is changing with respect to time is dθ/dt.

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The volume of the given cylinder is V = 1809.56 in³ and the volume of the NBA basketball is V = 448.92 in³.

The formula for the volume of a cylinder is V = π × r² × h cubic units.

Where the radius of the cylinder is represented by 'r' and the height of the cylinder is represented by 'h'.

The formula for the volume of the sphere is V = 4/3 × π × r³ cubic units.

Where the radius of the sphere is represented by 'r'.

The given cylinder has a diameter is of 16 inches and a height of 9 inches.

I.e., d = 2r = 16 in and h = 9 in

Then the volume of the cylinder is

V = π × (d/2)² × h

  = π × (16/2)² × 9

  = π × 64 × 9

  = 1809.56 in³

The shape of the NBA basketball is a sphere. The given sphere has a diameter of 9.5 inches.

I.e., d = 2r = 9.5 in

Then the volume of the sphere is

V = 4/3 × π × (d/2)³

  = 4/3 × π × (9.5/2)³

  = 4/3 × π × (4.75)³

  = 4/3 × π × 107.172

  = 448.92 in³

Therefore, the volume of the cylinder and the basketball are 1809.56 in³ and 448.92 in³ respectively.

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The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2) = 9 + 4√2

What is composite function?

Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.

Given:

u(x) = x^2 + 3

w(x) = √x+2

We have to find (w о u)(2) and (u о w)(2).

First to find (w о u)(x)

(w о u) = w(u(x))

           = w(x^2 + 3)

(w о u) = √(x^2 + 3) + 2

⇒ (w о u)(2) = √(2^2 + 3) + 2

   (w о u)(2) = √7 + 2

Now to find (u о w).

(u о w)(x) = u(w(x))

= u(√x+2)

= (√x+2)^2 + 3

= x + 4√x + 4 + 3

(u о w)(x) = x +  4√x + 7

⇒ (u о w)(2)  = 2 + 4√2 + 7

   (u о w)(2)  = 9 + 4√2

Hence,

The values of composite functions are,

(w о u)(2) = √7 + 2

(u о w)(2)  = 9 + 4√2

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The conclusion of the hypothesis test is;

B: Reject H₀. At the 10% significance level, the data provides sufficient evidence to conclude that the mean time is less than 9 minutes.

We are given;

Null Hypothesis; H₀: μ = 9;

Alternative Hypothesis; Hₐ: μ < 9

Significance level; α = 0.1

The critical value; z_0.1 = 1.28

Test statistic; z = -4.5

Now, the rejection rule here is that if the test statistic is below the critical value, we reject the null hypothesis at the significance level.

In this case, the the test statistic is less than the critical value and as such we reject the null hypothesis and conclude that the data provides sufficient evidence to conclude that the mean time is less than 9 minutes

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The simplified form of the expression is 123/20 x - 228

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

three 7/5 X +4-232 -5/4 X

Rewrite the above expression properly

So, we have the following representation

37/5 x + 4 - 232 - 5/4 x

Collect the like terms in the above expression

So, we have the following representation

37/5 x - 5/4 x + 4 - 232

Evaluate the like terms in the above expression

So, we have the following representation

123/20 x + 4 - 232

Solving further, we have

123/20 x - 228

Hence, the solution is  123/20 x - 228

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