6 marks
2. As an engineer you inspect a 2, 500-foot sewer pipe and find that a 150-foot portion is
damaged. You get estimates for two different solutions. The first estimate is for
spot repair of the damaged portion at a cost of $375.00 per foot. The second estimate is
for relining the full length of the entire sewer pipe at a cost of $65.00 per foot. How much
could you save in immediate costs by choosing the lower estimate?

The length of the wire is 46.218 m and the volume of the wire is 7206.4 cm³.

To find the length of the wire, we need to calculate the circumference of the cylinder and multiply it by the number of times the wire is wrapped around it.

The circumference of the cylinder is the distance around the circular face, and can be calculated using the formula:

Circumference = π × diameter

where;

The diameter of the cylinder is 49 cm, so its circumference is:

Circumference = π × diameter = 3.14 × 49 cm = 154.06 cm

The wire is wrapped around the cylinder lengthwise, so the number of times it wraps around the cylinder is equal to the length of the cylinder divided by the diameter of the wire:

Number of wraps = Length of cylinder / Diameter of wire

The length of the cylinder is 24 cm, and the diameter of the wire is 8 mm, or 0.8 cm. So the number of wraps is:

Number of wraps = 24 cm / 0.8 cm = 30

Therefore, the length of the wire is:

Length of wire = Circumference of cylinder × Number of wraps

= 154.06 cm × 30

= 4621.8 cm or 46.218 m (to three decimal places)

To find the volume of the wire, we need to use the formula for the volume of a cylinder:

Volume of cylinder = π × (radius)² × height

Volume of wire = π × (0.4 cm)² × 4618.2 cm

= 7206.4 cm³ (to one decimal place)

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The complete question is below:

A copper wire of diameter 8mm is evenly wrapped over a cylinder of length 24cm and diameter 49cm find the length of the wire and the volume of the wire

Answer:

y=-21/10

Step-by-step explanation:

20y=-42

20y/20=-42/20

y=-42/20

y=-21/10

3 ft-lb of work is needed to stretch it 3 inches beyond the 12ft-lb natural length of the spring.

Here, the integral formula for work and springs should be set up first:

When we look at the integral work for the spring, we know that,

W = [tex]\int\limits^a_b {x} \, dx[/tex] kx dx = k [tex]\int\limits^a_b {x} \, dx[/tex]

we know that,

W = 12,

a = 0,

b = 1

therefore, when we substitute these values in the formula we get,

12 = k [x²/2]¹₀

12 = k (1/2 - 0)

24 = k

now, 3 inches = 1/4th foot = b

so when we substitute this value again with k in the formula we get,

W = [tex]\int\limits^3_0 24 {x} \, dx[/tex]

= 24x²/2

= 12(1/4)²

= 3 ft-lbs

Therefore, we know that when the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, 3 ft-lb is needed to stretch it 3 inches beyond its natural length.

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Answer:

3x3 (x+5) (x - 5)

Step-by-step explanation:

It can be concluded that 3¹⁵⁰ is the greater among them.

This question can be solved if we use the numerical factorization concepts

First, we do the factorization, looking for a number that is common between divisors 3 and 5

[tex]\begin{array}{r|l}\sf 100,150 & \sf 2\\\sf 50,75 & \sf 2\\\sf 25,75 & \sf 3\\\sf 25,25 & \sf 5\\\sf 5,5 & \sf 5\\\sf 1,1&\sf 1\end{array}[/tex]

With this, we can see that the number 25 is common between divisors 3 and 5.
It will be our main exponent, when factoring the exponents 100 and 150.

[tex]\begin{array}{cc}\sf 5^{100}&\sf 3^{150}\\\raisebox{5pt}{$\sf \Big(\big[5^{2}\big]^{2}\Big)^{25}$}&\raisebox{5pt}{$\sf \Big(\big[3^{2}\big]^{3}\Big)^{25}$}\\\raisebox{5pt}{$\sf \big(5^{4}\big)^{25}$}&\raisebox{5pt}{$\sf \big(3^{6}\big)^{25}$}\\\raisebox{5pt}{$\sf 625^{25}$}&\raisebox{5pt}{$\boxed{\bf729^{25}}$}\end{array}[/tex]

Since 729²⁵ > 625²⁵, it follows that 3¹⁵⁰ is the greater of the two

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If you have any question about this solution, you can ask me in the comments :)

Answer:

50

Step-by-step explanation:

To determine the total number of kilograms from 15 boxes, we need to know the weight of one box. Let's assume that one box contains 50 sachets (this is just an assumption, the actual number may vary). Then the weight of one sachet is 4 grams or 0.004 kilograms.

the weight of one box is:

50 sachets x 0.004 kg/sachet = 0.2 kg

the total weight of 15 boxes is:

15 boxes x 0.2 kg/box = 3 kg

the total weight of 15 boxes is 3 kilograms.

to determine whether the 15 boxes will be enough to last for a year, we need to know how many sachets a person uses in a day. Let's assume that a person uses one sachet per day.

then the total number of sachets used in a year is:

1 sachet/day x 365 days = 365 sachets

the total number of sachets in 15 boxes is:

15 boxes x 50 sachets/box = 750 sachets

since 750 sachets is greater than 365 sachets, 15 boxes will be enough to last for a year.

to determine the number of sachets that will make one box, we need to know the weight of one box and the weight of one sachet. Let's assume that one box weighs 0.2 kg and one sachet weighs 4 grams or 0.004 kg.

then the number of sachets in one box is:

number of sachets = weight of box / weight of one sachet

number of sachets = 0.2 kg / 0.004 kg

number of sachets = 50 sachets

therefore, one box contains 50 sachets.

The correct answer is D. The value of a in the equation of the second function is greater than 1.

A quadratic function is a type of function in algebra that can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants (coefficients) and x is the independent variable. The graph of a quadratic function is a parabola, which is a U-shaped curve.

The coefficient a determines whether the parabola opens upwards (if a > 0) or downwards (if a < 0). The point where the parabola changes direction is called the vertex, which is located at the point (-b/2a, f(-b/2a)).

The coefficient b determines the horizontal position of the vertex, and c determines the vertical position of the vertex.

We know that the parent quadratic function f(x) = x² is a U-shaped curve with its vertex at the origin (0,0).

If the graph of a second function g(x) = ax² intersects the graph of f(x) at exactly one point, then this point must be the vertex of g(x), since the vertex of f(x) is already fixed at the origin.

In order for g(x) to intersect f(x) at exactly one point, the vertex of g(x) must lie on the x-axis (since it cannot be above the x-axis, or else there would be two points of intersection). Therefore, the y-coordinate of the vertex of g(x) is 0.

The vertex of a quadratic function of the form ax² + bx + c has x-coordinate -b/2a and y-coordinate c - b²/4a. Since the y-coordinate must be 0 in this case, we have:

0 = c - b²/4a

Solving for c, we get:

c = b²/4a

Therefore, the vertex of g(x) is (0, b²/4a).

We can see from the graph that the vertex of g(x) is to the right of the origin, so its x-coordinate is positive. This means that the coefficient a must be positive, since otherwise the parabola would open downwards and the vertex would be below the x-axis.

We also know that the vertex of g(x) is above the x-axis, so its y-coordinate (which is b²/4a) must be positive. This means that b^2 and a have the same sign.

Putting this information together, we can conclude that:

If a > 0, then b²/4a > 0, which means that b² and a have the same sign. This means that the parabola opens upwards, and the vertex is above the x-axis. From the graph, we can see that this is the case, so we can eliminate options B and C.

If a < 1, then the parabola is narrower than the parent function f(x) = x², and the vertex is closer to the y-axis. This is not the case from the graph, so we can eliminate option A.

Therefore, the correct answer is D. The value of a in the equation of the second function is greater than 1.

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The complete question is:

We can conclude after answering the provided question that So the perimeter of TUJ4V is 35, but with the information provided, we cannot determine the perimeter of PQRS.

A two-dimensional geometric shape's perimeter is the entire length of the borderline or outer edge. It is the total length of the shape's parties or edges. For example, the perimeter of a square is determined by dividing the lengths of all four edges of the square. Similarly, to calculate the outer wall of a rectangle, add the lengths of adjacent sides and then multiply by two because there are two different sets of adjacent sides.

To calculate the perimeter of PQRS, we must know the lengths of all four quadrilateral sides. However, we are only given one side's length, which is 12.

We know that TUJ4V has a perimeter of 35, so:

Circumference = 2x + 2y = 35

[tex]x + y = 17.5\\y = 15\\x + 15 = 17.5\\x = 2.5[/tex]

As a result, the length of each side of TUJ4V is as follows:

TU = JW = x = 2.5

TV = U4 = y = 15

The perimeter of TUJ4V is as follows:

2x + 2y = 2(2.5) + 2(15) = 35 Perimeter

So the perimeter of TUJ4V is 35, but with the information provided, we cannot determine the perimeter of PQRS.

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1. 4.167 radians does colton sweep out.

2. 238.1° degrees does colton sweep out.

3. 0.344 km is colton to the right of the center of the ski trail.

4. 0.139 km is colton above the center of the ski trail.

Question analysis Colton is skiing on a circular ski trail with a radius of 0.6 km.

Colton starts at the 3-o'clock position and travels 2.5 km in the counterclockwise direction.

There are four parts to this question: How many radians does Colton sweep out.

Radians refer to the distance covered by the object in circular motion around the circumference.

We can determine this using the formula:

θ = s / r

Where θ is the angle in radians, s is the length of the arc, and r is the radius of the circle.

Substituting the given values,θ = 2.5 km / 0.6 km= 4.167 radians.

Degrees does Colton sweep out:

We know that 180° = π radians

So, we can convert radians to degrees by multiplying it by

180° / πθ = 4.167 radians x (180° / π) ≈  238.1°

When Colton stops skiing, how many km is Colton to the right of the center of the ski trail.

The displacement of the skier from the center is the same as the horizontal distance.

We can use trigonometry to calculate this distance.

From the given position, we know that Colton has travelled 2.5 km along the circumference of the circle.

This is equivalent to the angle swept by Colton (4.167 radians) multiplied by the radius of the circle (0.6 km).Using trigonometry, we can determine the horizontal distance as:

d = r cos(θ)

Where d is the horizontal distance, r is the radius, and θ is the angle swept by Colton.

d = 0.6 km x cos(4.167)≈ 0.344 km.

When Colton stops skiing, how many km is Colton above the center of the ski trail?The vertical distance from the center of the circle can be calculated using trigonometry.

We can use the same method as above to calculate the vertical distance as:

v = r sin(θ)

Where v is the vertical distance, r is the radius, and θ is the angle swept by Colton.

v = 0.6 km x sin(4.167) ≈ 0.139 km

Colton sweeps out 4.167 radians ≈ 238.1°.

When Colton stops skiing, he is to the right of the center of the ski trail by ≈ 0.344 km.

When Colton stops skiing, he is above the center of the ski trail by ≈ 0.139 km.

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Sarah bought 5 first class tickets for 1030$ each and 9 coach tickets for 120$ each.

Let's use variables C and F to denote the quantity of coach and first class tickets purchased.

We may deduce from the problem:

C + F = 14 (because Sarah is one among the 14 persons) 

The overall cost of the tickets is as follows:

120C + 1030F = 6230

The first equation may be used to solve for one of the variables in terms of the other:

C = 14 - F

When we plug this into the second equation, we get:

120(14 - F) + 1030F = 6230

When we simplify this equation, we get:

1680 - 120F + 1030F = 6230

910F = 4550

F = 5

So Sarah purchased five first-class tickets. The first equation may be used to calculate the number of coach tickets:

C + 5 = 14

C = 9

As a result, Sarah purchased nine coach tickets.

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Answer:

ANSWER: -5,2.55

Step-by-step explanation:

I got it right

Answer:

System A: C)infinite answers

System B: B)special answer (x,y)=(3,1)

Step-by-step explanation:

System A:

if we find sum of same variables, we get 5x-5x-y+y=-2+2, it means 0=0 so, this system has infinite answers.

System B:

same thing applied here,

x-x+4y+4y=7+1

8y=8

y=1

so,

x+4*1=x+4=7

x=3

The height at a time of 15.3 seconds ≈ 729.2562 feet.

Finding the best-fit equation for a set of data with a parabola-like form is the goal of quadratic regression.

Making a scatter plot is the first stage in the regression process. You should generally consider a quadratic equation as the best fit for your data if your scatter plot has a "U" shape, either concave up (like the letter U) or concave down (). You can have only a portion of a quadratic "U" shape, like a quarter or a third.

The general form of the quadratic regression equation is y = A + Bx + Cx²

The quadratic regression formula is given as follows;

[tex]B=\frac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'}-(S_{xx'})^2}\\\\\\C=\frac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'}-(S_{xx'})^2}\\\\\\A=y'-Bx'-Cx^2\\\\[/tex]

Solving using an online quadratic regression calculator, gives;

A = 2.5643259\

B = 246.6374865

C = -15.41986006

Substituting gives;

y = 2.5643259 + 246.6374865·x -15.41986006·x²

When time, x = 15.3, we have;

y = 2.5643259 + 246.6374865×15.3 -15.41986006×15.3²≈ 729.2562 feet

The height at a time of 15.3 seconds ≈ 729.2562 feet.

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Answer:

The intersection of sets L and M has 13 numbers.

It is used to calculate the probabilities of random variables being less than or equal to a specific value

The Kaplan-Meier estimator is used to estimate the survival function from right-censored data.What is the Kaplan-Meier estimator?The Kaplan-Meier estimator is a non-parametric statistic that estimates the survival function from right-censored data. It is frequently utilized in clinical research and other fields of study where the time-to-event outcome is crucial to the analysis.What is the probability density function of a continuous random variable?The probability density function (PDF) of a continuous random variable is a function that specifies the probability distribution of that random variable. It provides the likelihood of observing a particular value within a particular interval of values.What is a continuous random variable?A continuous random variable is a type of random variable that can take on any numerical value in a given range of values. It can be any value on a continuous range of values rather than just taking on certain values.What is the cumulative distribution function?The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value. It is used to calculate the probabilities of random variables being less than or equal to a specific value.

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Area of a circle = pi x r²

So taking pi as 22/7,

Area=707.14cm²

The probability of selecting all four bulbs of the same color is approximately 0.0061.

To calculate the probability that all four bulbs are of the same color, we need to consider the following cases,

1) The probability of selecting the first blue bulb is 3/12 (since there are 3 blue bulbs out of 12 total bulbs). After one blue bulb has been selected, there are 2 blue bulbs left out of 11 total bulbs, so the probability of selecting a second blue bulb is 2/11. Similarly, the probability of selecting the third blue bulb is 1/10, and the probability of selecting the fourth blue bulb is 0/9 (since there are no more blue bulbs left). Therefore, the probability of selecting all four blue bulbs is:

(3/12) × (2/11) × (1/10) × (0/9) = 0

2) Using the same logic as in Case 1, the probability of selecting all four green bulbs is:

(4/12) × (3/11) × (2/10) × (1/9) = 1/495

3) The probability of selecting all four red bulbs is:

(5/12) × (4/11) × (3/10) × (2/9) = 2/495

Therefore, the total probability of selecting all four bulbs of the same color is the sum of the probabilities from Cases 2 and 3

1/495 + 2/495 = 3/495

Simplifying this fraction, we get:

3/495 = 1/165

= 0.0061

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Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar when compounded daily.

The interest that is accrued on both the principle and any prior interest is known as compound interest. This implies that the interest received in succeeding periods rises as the interest is added to the principle. Compound interest is a crucial idea in personal finance that may be utilised in calculations for both savings and loans.

The compound interest is given by the formula:

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

For Elijah substituting the values we have:

[tex]A = $94,000(1 + 0.04125/4)^{(4*7)} = $129,852.94[/tex]

For Kayden substituting the values we have:

[tex]A = $94,000(1 + 0.0425/365)^{(365*7)} = $130,963.39[/tex]

The difference between the two amounts is:

$130,963.39 - $129,852.94 = $1,110.45

Therefore, Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar.

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Answer:$1286 when rounded. Got it right

Step-by-step explanation:

The rate οf pοwer drainage per hοur is 13.32 watts per hοur οr 13.32 Wh (watt-hοurs) per hοur.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο calculate the rate οf pοwer drainage per hοur, we need tο knοw the pοwer cοnsumptiοn οf the cell phοne. Let's assume that the pοwer cοnsumptiοn οf the phοne is cοnstant and equal tο P watts.

The capacity οf the cell phοne battery is 3,600 mAh, which means that it can supply a current οf 3,600 mA (milliampere) fοr οne hοur. Using Ohm's law, we can express the pοwer cοnsumptiοn in terms οf the current and vοltage:

P = I × V

where I is the current and V is the vοltage.

The vοltage οf a typical cell phοne battery is arοund 3.7 vοlts. Therefοre, the current drawn by the phοne is:

I = 3,600 mA = 3.6 A

t = 1 hοur

The pοwer cοnsumptiοn οf the phοne is:

P = I × V = 3.6 A × 3.7 V = 13.32 W

Hence, the rate οf pοwer drainage per hοur is 13.32 watts per hοur οr 13.32 Wh (watt-hοurs) per hοur.

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The rope would be about 4,285,082.98 feet high above the ground.

Answer: The circumference of the earth is 24,902 miles. We have to add 3 ft of rope and keep its circular shape. We must determine how high the rope would be from the ground.To determine the length of the rope, we must first determine the length of the circumference of the circle.Circumference of the circle = πd = π * 8000 miles = 25132 miles (taking radius of earth as 4000 miles).1 mile is 5280 feet, which implies that the distance around the circle is 25132 * 5280 = 132712960 feet.

The length of the rope will be equal to the distance around the circle, plus 3 feet.Length of the rope = 132712963 feet.Now, to determine how high the rope would be from the ground, we need to use the Pythagorean theorem.Height of the rope = √(length of the rope² - radius of earth²) = √(132712963² - 4000²) = √17602394294769 = 4,285,082.98 feet (approx.)The rope would be about 4,285,082.98 feet high above the ground.

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Answer:

its Value is 50 degree.

Step-by-step explanation:

Because It is vertically opposite angle.

Jon's parents invested $300 for his college tuition in a savings account when he was born. The account pays 5% simple interest every year. Consequently, if no additional money was invested, the account would be worth $570 after 18 years.

To answer the problem, we must employ the basic interest formula:

Principle x Interest Rate x Time = Simple Interest

where:

Principal = the initial amount invested

Interest Rate = the yearly interest rate expressed in decimal form.

Time = the amount of years the money has been invested for.

The principal in this scenario is $300, the interest rate is 5% (0.05 as a decimal), and the term is 18 years. Thus we may enter the following values into the formula:

Simple Interest = $300 x 0.05 x 18 = $270

As a result, after 18 years, the total money in the account would be:

Total amount = Principal + Simple Interest

=$300 + $270 = $570

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Answer: A,

Step-by-step explanation:

it will be -170 feet after 8 min

Answer: [tex]a=\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

the answer is 17

Step-by-step explanation:

you get this by adding all numbers together 5+7+5+7+10=34 you then to make the total and devide it by 2 to get the median

34/2=17

Answer:

option C is correct

Step-by-step explanation:

Ratio of boys to girls is15:10

=3:2

Therefore , the solution of the given problem of percentage comes out to be this amount to the closest dollar, we get $1,042.

A number or measure that is represented as a proportion of 100 is known as a "a%" in statistics. Additionally, the terms "pct," "pct," and "pc" are not commonly used. However, it is commonly denoted by the symbol "%". There are no dimensions; the percentage total is flat. Since a percentage's numerator is almost always 100, percentages are actually integers. To indicate that a number is a percentage, either the percentage symbol (%).

Here,

a. The formula: can be used to calculate the weekly payment.

=> P = (Ar(1+r)ⁿ) / ((1+r)^n - 1)

A = 9900, r = 0.06/12, and n = 48 in this instance (since there are 4 years or 48 months in total).

Substituting these numbers into the formula, we get:

=> P = (99000.005(1+0.005)⁴⁸) / ((1+0.005)⁴⁸ - 1) ≈ $227.88

Therefore, the monthly payment is roughly $227.88.

=> Overall = P*n = $227.88 * 48 = $10,942.24

We arrive at $10,942 by rounding this sum to the closest dollar.

c. The total interest paid over the course of the loan's four-year term is equivalent to the total amount repaid less the loan balance:

Total interest equals the total sum less A, or $10,942 minus $9,900, or $1,042.

Rounding this amount to the closest dollar, we get $1,042.

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Answer:

SA = 56π cm²

Step-by-step explanation:

the surface area (SA) is calculated as

SA = area of 2 circular ends + area of curved surface

     = 2πr² + 2πrh ( r is the radius and h the height )

here r = 4 and h = 3 , then

SA = 2π × 4² + 2π × 4 × 3

    = 2π × 16 + 2π × 12

    = 32π + 24π

   = 56π cm²

The conditional probabilities are are (a) P(A/B) = 0.69   b) P(A/B) = 31/100

You should recall that Probability is the chance that a given event will occur; the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes;

The conditional probability P(A|B) is calculated using:

P(A/B)

P(A/B) = P( A and B) / P(B)

P(A/B) = (18/26 * 8/26)/ 8/26

P(A/B) = (0.69 * 0.31)/ 0.31

P(A/B) = 0.69

P(A/B) = 69/100

b)  Using the same formula

P(B/A) = P( B and A) / P(A)

P(A/B) = (8/26 * 18/26) / 18/26

P(A/B) = (0.31 * 0.69)/0.69

P(A/B) = 0.31

P(A/B) = 31/100

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a) The null and alternative hypothesis are

H₀ : μ₁ − μ₂ = 0

H₁ : μ₁ − μ₂<0

b) The test statistic value, tₒ = -1.3748.

c) At α = 0.05, the result is not significant.

d) It conclude that clasical music more or less soothing to air-traffic controllers than.

e) The p- value> α = 0.05, conclusion is that

no relationship in nature between type of music and irritability.

f) Other statistical methods for computing ,

The t-test for difference of two means : As we are required to conclude if the means' difference from two independent samples is indifferent or not, through a very small sample size, hence we will consider the t-test statistic. The test statistic:

t = ( x₁-bar - x₂-bar )/(√s₁²/n₁ - s₂²/n₂)

For classical:

x₁ = 14.69

s₁² = 8.4

n₁ = 6

For modern:

x₁ = 17.20

s₂² = 11. 6

n₂ = 6

(a)We set up:

H₀ : μ₁ − μ₂ = 0

H₁ : μ₁ − μ₂<0

(b) The test statistic is:

t = ( 14.69 - 17.20)/√(8.4/6 - 11.2/6)

= -2.51/√(8.4/6 - 11.2/6)

= -1.3748

c) The degree of freedom, df = 6 + 6- 2 = 10

Using the t-table, The p-value for t = -1.3748 and df = 10, α = 0.05 is equals to the 0.099606. Significance level, α = 0.05

As p-value (=0.099606) > α (=0.05), result is insignificant.

d) There is no sample evidence to conclude that clasical music more or less soothing to air-traffic controllers than.

e) As p-value (=0.099606) > α

Conclusion: Null hypothesis can't be rejected. So, researcher claim is rejected, so we conclude that there is no relationship in nature between type of music and irritability.

d = difference between means/√S²(pool)

= 2.52/√10 = 0.80

This is a moderate to large effect.

r² = t²/( t₀² + df) = (-1.3748)²/(-1.3748 + 10)

= 0.16

Hence, required value are obtained.

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