Explain why researchers formulate a null hypothesis in addition to a hypothesis when designing an experimental study.

Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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We have 19 students in a class.

We have to find how many different groups of 5 students can be selected from that class.

This is a combination of n=19 in r=5 and can be calculated as:

Answer: there are 11628 possible groups.

Answer:

\(\Large\boxed{\sf{x=-1, y=1}}\)

Step-by-step explanation:

Isolate the term of x and y from one side of the equation.

-x+6y=7= x=-7+6y

First, you have to substitute of x=-7+6y.

\(\Longrightarrow: \sf{6\left(-7+6y\right)+2y=-4}\)

Solve.

Use the distributive property.

Distributive property:

⇒ A(B+C)=AB+AC

⇒ A(B-C)=AB-AC

6(-7+6y)

Multiply expand.

6*-7=-42

6*6y=36y

-42+36y+2=-4

Add.

36y+2=38y

\(\Longrightarrow: \sf{-42+38y=-4}}\)

First, add by 42 from both sides.

-42+38y+42=-4+42

Solve.

38y=38

Divide by 38 from both sides.

38y/38=38/38

Solve.

38/38=1

For x=-7+6y

Substitute of y=1.

x=-7+6*1

Use the order of operations.

PEMDAS stands for:

-7+6*1

Do multiply.

6*1=6

-7+6

Add/subtract the numbers from left to right,

-7+6=-1

I hope this helps, let me know if you have any questions.

Answer:

\(x-6\)

Step-by-step explanation:

We can let the 'number' in the expression be equal to \(x\). Something 6 less than x would x minus 6, or \(x-6\).

Answer:

x-6

Step-by-step explanation:

Let the number be x

Less than means subtract from

x-6

The answer is A. Springsville has several different activities.

Answer:

21

Step-by-step explanation:

Set it up as 7/4 x 12/1.  Multiply the numerators and denominators.  That equals 84/4 which simplifies to 21.

The solid shapes are illustrations of volumes, and there are 1/27 cubic yards in 1 cubic foot

The given shapes are cubes.

So, the volume of each cube is:

V = l³

Where l represents the length of each cube

For the first cube with side length of 1 yard, the volume is:

V = (1 yd)³

Evaluate

V = 1 yd³

For the second cube with side length of 3 feet, the volume is:

V = (3 ft)³

Evaluate

V = 27 ft³

This means that:

1 yd³ = 27 ft³

Let the number of cubic yard in 1 cubic foot be x.

So, we have:

1 yd³ = 27 ft³

x yd³ = 1 ft³

Cross multiply

27 ft³ * x yd³ = 1 yd³ * 1 ft³

Cancel the units

27x = 1

Divide both sides by 27

\(x = \frac{1}{27}\)

Hence, there are 1/27 cubic yards in 1 cubic foot

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1- SHM stands for Simple Harmonic Motion.

In SHM, an object oscillates back and forth about an equilibrium position, with a motion that can be described by a sinusoidal function. The symbols commonly used in SHM are:

y: Displacement from the equilibrium position

t: Time

k: Spring constant or restoring force constant

m: Mass of the object

c₁ and c₂: Constants determined by initial conditions

2- Hooke's law relates the force exerted by a spring to the displacement of the object attached to it. It is represented by the second-order differential equation my" + ky = 0, where m is the mass of the object and k is the spring constant. The solution to this equation is given as y = c₁ cos(√(k/m) * t) + c₂ sin(√(k/m) * t). To determine the values of c₁ and c₂, initial conditions are needed.

3- If the initial conditions are y(0) = 0 and y'(0) = 0, which means the object starts at equilibrium with zero displacement and zero velocity, we can substitute these values into the solution equation and solve for c₁ and c₂. In this case, we find that c₁ = 0 and c₂ = 0.

4- To show that the sum of the solutions c₁ cos(w₀t) and c₂ sin(w₀t) is also a solution of the SHO (Simple Harmonic Oscillator) differential equation, we substitute the sum into the differential equation and demonstrate that it satisfies the equation. By taking the derivatives and substituting, we can show that the sum of the solutions satisfies the equation, thus confirming that it is also a solution.

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Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

\(15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0\)

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

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Answer:

A = 4 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 ( 4) (2)

A = 4 cm^2

Answer:

\(4 {cm}^{2} \)

Step-by-step explanation:

Formula for the area of a triangle= 1/2*base*height

\( \frac{1}{2} \times 4 \times 2 \\ = 4\)

\(therefore \: the \: area \: = 4 {cm}^{2} \)

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Given:

In triangle \(ABC, AB=9,BC=4,AC=7\).

To find:

The measure of angle C.

Solution:

We have, \(AB=9,BC=4,AC=7\). It means \(c=9,a=4,b=7\).

According to the law of cosines:

\(cos C=\dfrac{a^2+b^2-c^2}{2ab}\)

\(cos C=\dfrac{4^2+7^2-9^2}{2(4)(7)}\)

\(cos C=\dfrac{16+49-81}{56}\)

\(cos C=\dfrac{-16}{56}\)

Taking cos inverse on both sides, we get

\(C=cos^{-1} \dfrac{-16}{56}\)

\(C=106.60155\)

\(C\approx 106.6\)

Therefore, the correct option is C.

Answer:

6x +3

Step-by-step explanation:

Perimeter of a triangle is the sum of all the length of its sides. Since a triangle as 3 sides, add the 3 lengths together.

Perimeter of triangle= 2x -6 +x +8 +3x +1

Bringing all the x terms together and constants together:

Perimeter of triangle= 2x +x +3x -6 +8 +1

Simplify:

Perimeter of triangle= 6x +3

Answer:

rate = change in height / change in time

rate = (8 - 2) / (9 - 3)

rate = 6 / 6

rate = 1

y = 1w + b

2 = 1(3) + b

2 = 3 + b

-1 = b                  Not sure how a plant starts out at -1 feet!

y = w - 1

Check:

9 - 1

8

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

The purchase price of the new car if the sales tax is $3500 is $50000

Let the amount of sales tax be A and the purchase price be p

If the amount of sales tax is directly proportional to the purchase price, this is expressed as:

S = kp

If S = $1750 and p = $25000, the;

k = S/p

k = 1750/25000

k = 175/2500

If the sales tax is $3500, the purchase price will be given as:

S = kp
3500 = 175/2500 p

175p = 3500*2500
175p = 8750000

p = 8750000/175

p = 50000

Hence the purchase price of the new car if the sales tax is $3500 is $50000

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The volume and the T.S.A of the hemisphere is a 226.38π and 147π.

According to the statement

we have to find the volume and the surface area of the given hemisphere.

So, For this purpose, we know that the

A hemisphere may be a 3D geometric shape that's 1/2 a sphere with one side flat and also the other side as a circular bowl.

Then from the given information,

The radius is 7 cm then

We know that the

The volume of a hemisphere = (2/3)πr^3 cubic units.

volume of a hemisphere = (2/3)πr^3

volume of a hemisphere = (2/3)π7^3

volume of a hemisphere = 226.38π

And the

The total extent of a hemisphere = 3πr^2 square units

total expanse of a hemisphere = 3πr^2

total extent of a hemisphere = 3π7^2

total extent of a hemisphere = 147π

So, The volume and the T.S.A of the hemisphere is a 226.38π and 147π.

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Answer:

1680 ways

Step-by-step explanation:

Permutation has to do with arrangement

If a contractor builds homes of 8 different models and presently has 4 lots to build on, the number of ways he can arrange his homes is expressed as;

8P4 = 8!/(8-4)!

8P4 = 8!/4!

8P4 = 8*7*6*5*4!/4!

8P4 = 8*7*6*5

8P4 = 1680

Hence the can arrange his homes 1680 ways

If actual production totals 8,000 units, the flexible budget would still show fixed costs of $3.00 per unit. The fixed costs per unit remain the same regardless of the actual production volume.

The static budget was developed based on an expected volume of 7,000 units, with fixed costs amounting to $3.00 per unit.

However, even if the actual production totals 8,000 units, the fixed costs per unit would remain unchanged at $3.00.

This is because fixed costs are not affected by changes in production volume within the relevant range.

The fixed costs represent the expenses that do not vary with the level of production and remain constant regardless of the actual volume of units produced.

Therefore, the flexible budget would still show fixed costs of $3.00 per unit when the actual production is 8,000 units.

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A seam or edge is an obvious line where the foundation starts or stops. This term refers to a clear boundary or distinction between two areas or surfaces, such as when applying makeup.

A seam or edge is an obvious line where the foundation starts or stops. These lines indicate the boundary of where foundation makeup should be applied or where it should end. It is important to blend the foundation seamlessly into the skin to avoid any noticeable lines or streaks. Additionally, applying a primer beforehand can help smooth out the skin's texture and create a more even base for foundation application. By taking the time to properly blend and apply foundation, you can achieve a flawless, natural-looking complexion.
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Answer: x=11

Step-by-step explanation:

I got this by 126-49=77. Then I divided 77 by 7 and got 11.

Based on the speed of the Great White Shark in kilometers per hour, the meters per hour that the Great White Shark swims at top speed is 40,000 meters per hour

A kilometer per hour is equivalent to 999.999 meters per hour or 1,000 meters per hour approximately.

This means that if a Great White Shark swims at 40 kilometers per hour at its top speed, in meters per hour this is:
= 40 x 999.999

= 39,999.60 meters per hour

= 40,000 meters per hour

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Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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Answer: \(4a^4+4b^4-8a^3b+8ab^3-13a^2b^2\)

Step-by-step explanation:

\(4(a^2-b^2)^2-8ab(a^2-b^2)-5a^2b^2\)

First, solve the square binomial.

\(4((a^2)^2-2(a^2)(b^2)+(b^2)^2)-8ab(a^2-b^2)-5a^2b^2\)

\(4(a^4-2a^2b^2+b^4)-8ab(a^2-b^2)-5a^2b^2\)

Now, distribute the 4 and 8ab respectively.

\(4a^4-8a^2b^2+4b^4-8a^3b+8ab^3-5a^2b^2\)

Combine like terms. (I'll group them so that you can see them more clearly)

\(4a^4+4b^4-8a^3b+8ab^3+(-8a^2b^2-5a^2b^2)\)

\(4a^4+4b^4-8a^3b+8ab^3+(-13a^2b^2)\)

\(4a^4+4b^4-8a^3b+8ab^3-13a^2b^2\)

Answer:

(2a²-2b²+a²b²)(2a²-2b²-5a²b²)

Step-by-step explanation:

4(a²-b²)²-8ab(a²-b²)-5a²b²

Let's replace 2(a²-b²)= m and a²b²=n for simplicity

then we have

Now we can replace m and n with initial values:

The number of "same" types of 2x3 matrices in reduced row echelon form, option (c) 4.

To determine the number of "same" types of 2x3 matrices in reduced row echelon form, we need to consider the possible configurations of the leading entries (pivot positions) in the matrix.

Since we have a 2x3 matrix, there can be at most two leading entries, one in each row. The possible configurations of the leading entries are as follows:

No leading entries (both rows contain only zeros): This is a valid configuration and counts as one type.

Considering the valid configurations, there are a total of 4 "same" types of 2x3 matrices in reduced row echelon form.

Therefore, the answer is c. 4.

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9.022 hours time it will take to make all the cable

given

A company must construct 32.9 kilometers of cable for a customer.

The cable-making machine can produce 4.5 kilometers of cable.

each hour.

The company is working on the cable while the customer adds 8 kilometers to the order.

customer add 8km to the order

equation : 32.9 + 8 = 4.5x

    40.9 = 4.5x

   x = 40.9/4.5

   x = 9.022

9.022 hours time it will take to make all the cable.

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The statement ''If a test is run and p = 0.0356, then we can reject H0 at alpha = 0.05'' is true because p is 0.0356 is less than alpha is 0.05, we can reject the null hypothesis.

If the p-value (probability value) is less than the chosen level of significance, alpha (0.05 in this case), then we reject the null hypothesis (H0).

In this scenario, since p = 0.0356 is less than alpha = 0.05, we can reject the null hypothesis.

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the regression equation y = 5x + 23 is true.

The number 23 represents the fixed or baseline number of people attending the picnic, regardless of the number of flyers used to advertise it (x).

what is regression?

Regression in mathematics refers to a statistical analysis method used to model the relationship between variables. It aims to find the best-fitting mathematical function that describes the relationship between a dependent variable (also known as the response variable) and one or more independent variables (also known as predictor variables or features).

The purpose of regression analysis is to estimate the parameters of the mathematical function that minimize the difference between the predicted values and the actual observed values of the dependent variable. This allows us to make predictions or draw inferences about the relationship between variables based on the available data.

There are different types of regression analysis, including linear regression, polynomial regression, multiple regression, logistic regression, and more. Each type is suited for different types of relationships between variables and has its own assumptions and techniques for parameter estimation.

Regression analysis is widely used in various fields, such as economics, finance, social sciences, engineering, and machine learning, to analyze and understand the relationship between variables, make predictions, and inform decision-making processes.

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