Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Beth Left Right Andrew Left 8, 4 4, 5 Right 5, 4 6, 5
The only dominant strategy in this game is for to choose .
The outcome reflecting the unique Nash equilibrium in this game is as follows:
Andrew chooses and Beth chooses .

Answers

Answer 1

Answer:

Attached is the pictorial view of the solution

i)The only dominant strategy is BETH to choose RIGHT

ii) the outcome reflecting the unique Nash equilibrium in this game is as follows Andrew chooses LEFT and Beth chooses RIGHT

Explanation:

Andrew payoff = 6 when he chooses Right

Beth payoff = 5 when he chooses right

The given data

Beth :   Left ; 4,5. right ; 4,5

Andrew : Left ;  8,4. right ; 5,6

i)The only dominant strategy is BETH to choose RIGHT

ii) the outcome reflecting the unique Nash equilibrium in this game is as follows Andrew chooses LEFT and Beth chooses RIGHT

Solving For Dominant Strategies And The Nash Equilibrium Suppose Andrew And Beth Are Playing A Game In

Related Questions

A material has been loaded to a stress well below the proportional limit. At this point the stress is 257 MPa and the strain is 0.18 mm/mm. Assume the elastic region extends directly to zero (0 stress, 0 strain) from this point. Calculate Young's modulus for this material. Enter your answer in MPa to the nearest whole number.

Answers

To calculate Young's modulus for this material, we first need to understand the relationship between stress and strain in the elastic region. According to Hooke's Law, stress is proportional to strain within the elastic limit.

This means that we can use the following equation to calculate Young's modulus: Young's modulus (E) = stress/strain In this case, the stress is 257 MPa and the strain is 0.18 mm/mm. Therefore: E = 257 MPa / 0.18 mm/mm E = 1428.9 MPa Rounding to the nearest whole number, Young's modulus for this material is approximately 1429 MPa. It's worth noting that this calculation assumes that the elastic region extends directly to zero stress and zero strain from the given point. In reality, the elastic region may have a non-linear relationship between stress and strain, and the material may exhibit some degree of plastic deformation before reaching zero stress. However, this calculation provides a good estimate of Young's modulus for the given conditions.

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can the efficiency of a completely reversible heat engine be doubled by doubling the temperature of the energy source?

Answers

No, the efficiency of a completely reversible heat engine cannot be doubled by simply doubling the temperature of the energy source.

The efficiency of a reversible heat engine is given by the formula:
Efficiency = 1 - (Tc/Th)
where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
Doubling the temperature of the energy source (Th) will not double the efficiency because the relationship is not linear. However, increasing the temperature of the hot reservoir will generally improve the efficiency of the heat engine, but it will not be doubled.

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Which of the following is a Dashboard Scoreboard for alignment of the business where information is constantly flowing through the Tiers so immediate actions can be taken?

Answers

Answer:

What is a dashboard?

A dashboard is an information management tool used to track KPIs, metrics, and key data points that are relevant to your business, department, or a specific process. Dashboards aggregate and visualize data from multiple sources, such as databases, locally hosted files, and web services. Dashboards allow you to monitor your business performance by displaying historical trends, actionable data, and real-time information.

Dashboards actually take their name from automobile dashboards and they are used in much the same way. For the sake of an analogy, let’s look at a car. There may be hundreds of processes that impact the performance of your vehicle if you look under the hood. Your car’s dashboard summarizes this using visualizations so you can focus on what matters most: safely driving your vehicle.

For businesses, there are hundreds of processes that impact your performance if you look ‘under the hood’, so to speak. And with a wealth of data made available these days, managing and extracting value from it can be difficult. Simplifying data analysis and distribution through tools like dashboards is a way to help businesses rev their engines and make smarter, better, faster data-driven decisions.

And a well designed dashboard levels up your approach to information management. Everyone in the business, regardless of role, has questions about your company performance, whether it be campaign performance, new wins, or churn rate. Dashboards bring everyone (and your metrics) together in one place to answer these questions.

Explanation:

when servicing piston rods and pins it is important to always

Answers

Answer:

Pistons should be inspected and measured.

Explanation:

Instructions: For each problem, identify the appropriate test statistic to be use (t test or z-test). Then compute z or t value.
1) A teacher claims that the mean score of students in his class is greater than 82 with a standard deviation of 20. If a sample of 81 students was selected with a mean score of 90 then check if there is enough evidence to support this claim at a 0.05 significance level.
2) An online medicine shop claims that the mean delivery time for medicines is less than 120 minutes with a standard deviation of 30 minutes. Is there enough evidence to support this claim at a 0.05 significance level if 49 orders were examined with a mean of 100 minutes?
3) An English teacher wanted to test whether the mean reading speed of students is 550 words per minute. A sample of 12 students revealed a sample mean of 540 words per minute with a standard deviation of 5 words per minute . At 0.05 significance level, is the reading speed different from 550 words per minute?

Answers

The sample of 81 students was selected with a mean score of 90, this illustrates an example of a right tailed one sample z test.

How to illustrate the sample?

From the information given, the teacher claims that the mean score of students in his class is greater than 82 with a standard deviation of 20. In this case, the right tailed one sample z test is used.

The z value will be:

= (90 - 82)/20/✓81

= 3.6

Since 3.6 > 1.645, the null hypothesis will be rejected as there's enough evidence to support the teacher's claim.

When an online medicine shop claims that the mean delivery time for medicines is less than 120 minutes with a standard deviation of 30 minutes, the left tailed one sample test is used.

The z value will be:

= (100 - 120)/(30/✓49)

= -4.66

The null hypothesis is rejected as there is enough evidence to support the claim of the medicine shop.

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which of these is a characteristic of and application A it manages communication with the hardware. B it maintains the user interface. C it is essential to the computer's operation. D it helps the user perform an activity they want to do

Answers

Answer:

The answer is D

Explanation:

The characteristic of an application is it helps the user perform an activity they want to do. The correct option is D.

What is an application?

An application program is a computer program that is designed to perform a specific activity that is not related to the operation of the computer itself and is typically utilized by end users. Examples include word processors, media players, and accounting software.

The different types of applications: are web, native, cross-platform, hybrid, etc. Scalability, portability, robustness, and agility are four fundamental features and functionalities that modern applications must have. Scalability: Today, we require apps that can scale to millions of people worldwide on demand.

Therefore, the correct option is D, it helps the user perform an activity they want to do.

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what is "self" typically used for in a python method within a class?

Answers

In Python, "self" is used as a reference to the instance of the class. It is the first parameter of a method within a class and represents the object that the method is being called on.

"Self" is a convention in Python that represents the instance of the class. It allows accessing the attributes and methods of the class within its own methods. When a method is called on an object, the object itself is automatically passed as the first argument to the method, which is typically named "self." This parameter enables the method to operate on the specific instance of the class and manipulate its state. By using "self," you can access and modify instance variables and call other methods of the class. It helps in maintaining encapsulation and ensures that each instance of the class can have its own unique data and behavior.

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The coaster moves up the first hill by a long ____________.
Select one:

a.
chain

b.
rope

c.
belt

Answers

The answer would be rope.

Answer:

B.) rope

Explanation:

hopes this help

the following questions need to answered please and thank you

the following questions need to answered please and thank you

Answers

Answer:

Can't see, clearly photo then you can get your answer quickly

Explanation:

2 points) what is the eeg frequency in each section? trace 1 sectionsfrequency (hz)trace 2 sectionsfrequency (hz) left, 0-1sleft, 0-1s left, 1-2sleft, 1-2s left, 2-3sleft, 2-3s right, 0-1sright, 0-1s right, 1-2sright, 1-2s right, 2-3sright, 2-3s

Answers

The waveforms delta (0.5 to 4Hz), theta (4 to 7Hz), alpha (8 to 12Hz), sigma (12 to 16Hz), and beta are among the most frequently researched waveforms (13 to 30Hz).

What are the EEG's frequency ranges?

EEG frequency patterns can be divided into four categories: beta (14–30 Hz), alpha (8–13 Hz), theta (4–7 Hz), and delta (1-3 Hz). In general, when the frequency drops, the EEG's amplitude rises. Each of the four EEG frequencies corresponds to a distinct degree of cerebral cortex arousal.

How can you determine an EEG's frequency?

The frequency is then calculated by taking I and dividing it by the duration, which in this case results in a 5Hz wave. the amount of analogue millimetres in a second.

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A 1.5 m x1.5 m square footing is supported by a soil deposit that contains a 16.5 m thick saturated clay layer followed by the bedrock. The clay has μs = 0.50 and Es = 5,000 kN/m2 . The footing base is at 1.5 m below the ground surface. Determine the maximum vertical central column load so that the elastic settlement of the footing will not exceed 50.0 mm. If the square footing is replaced by a 1.2 m wide wall footing with all other conditions remaining the same.

Required:
What will be the elastic settlement under the same footing pressure?

Answers

Answer:

somewhere around 34.2223 meters thick but that's what I am estimating.

an embankment that is 50 m high x 20 m wide is to be constructed to hold water. assuming the embankment is to be constructed using concrete density 2400kg/m3, what is the minimum t

Answers

1000 m2 x 2400 kg/m3 = 2400000 kg or 2400 m3 of concrete is required to construct the embankment.

What is quantity?

Quantity is a fundamental concept in mathematics and science. It is a property of a set or quantity of objects that can be measured or counted. Examples of quantity include mass, volume, length, time, and energy. Quantity is an important concept in economics, where it is used to measure the size of the market, the level of demand, and the amount of resources available. Quantity is also used in statistics to measure the size of a sample and to analyze data. In general, quantity refers to the magnitude or amount of something.

The minimum total quantity of concrete required to construct the embankment is 200 m3. This is calculated by multiplying the width and height of the embankment (20 m x 50 m = 1000 m2) and the concrete density (2400 kg/m3). Therefore, 1000 m2 x 2400 kg/m3 = 2400000 kg or 2400 m3 of concrete is required to construct the embankment..

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Complete questions as follows-
an embankment that is 50 m high x 20 m wide is to be constructed to hold water. assuming the embankment is to be constructed using concrete density 2400kg/m3, what is the minimum toral quantity of concrete required to construct the embankment?

11. If the fume generation rate of a FCAW wire is assumed to be 1 g/min ( grams per minute), calculate the weight of fumes produced by one welder working for one year operation. Assume working duty cycle based on the data given in the class to calculate your answer for semiautomatic processes

Answers

The weight of fumes produced by one welder working with an FCAW wire in a semi-automatic process for one year of operation is 28,800 grams.

The fume generation rate of a Flux-Cored Arc Welding (FCAW) wire is 1 g/min, we'll need to consider the working duty cycle of a welder in a semi-automatic process for one year to calculate the weight of fumes produced.

Assuming a typical working duty cycle for semi-automatic welding processes is 25%, and considering an 8-hour workday with 240 working days in a year, we can calculate the total fume generation as follows:

- Daily welding time = 8 hours/day × 60 minutes/hour × 25% duty cycle = 120 minutes/day
- Annual welding time = 120 minutes/day × 240 days/year = 28,800 minutes/year
- Annual fume generation = 28,800 minutes/year × 1 g/min = 28,800 grams/year

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The code beow shows the withdraw method of a bank account class.public boolean withdraw(long amount) {if (amount <= balance) {long newbalance = balance - amount;balance = newbalance;return true;} elsereturn false;}This code can cause a problem running in a multithreading environment. The problem can be by ____

Answers

The java code can cause a compilation error running in a multithreading environment. One of the reason could be the variable "balance" is not declared as volatile, so there is no guarantee that the code will correctly set the balance and return the correct boolean value after a withdrawal.

Also, the java compiler could alerts an error when the return instruction is inside a cyclic structure and also when it is inside a conditional structure as it is in this case.

So, to fix errors, the return statement must be placed outside the conditional structure and use a variable instead of the boolean values. Below is a java code with the correct form.

Java code:

import java. io.*;

public class Main {

public static void main(String args[]) throws IOException {

 BufferedReader in = new BufferedReader(new InputStreamReader(System. in));

 double amount;

 boolean enoughmoney = true;

 System.out.println("Program to know if you have enough money for withdrawing from bank");

// Data entry

 System.out.print("Enter the amount to withdraw: ");

 amount = Double.parseDouble(in.readLine());

// Call function

 enoughmoney = withdraw(amount);

// Output

 if (enoughmoney) {

  System.out.println("Withdraw completed");

 } else {

  System.out.println("Do not have enough money");

 }

}

public static boolean withdraw(double amount) {

 boolean enoughmoney = true;

 double newbalance = 0;

 double balance = 4000;

 if (amount<=balance) {

  balance = balance-amount;

  newbalance = balance;

  System.out.println("New balance: "+newbalance);

  enoughmoney = true;

 } else {

  enoughmoney = false;

 }

 return enoughmoney;}}

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The code beow shows the withdraw method of a bank account class.public boolean withdraw(long amount)

One method that is used to grow nanowires (nanotubes with solid cores) is to initially deposit a small droplet of a liquid catalyst onto a flat surface. The surface and catalyst are heated and simultaneously exposed to a higher-temperature, low-pressure gas that contains a mixture of chemical species from which the nanowire is to be formed. The catalytic liquid slowly absorbs the species from the gas through its top surface and converts these to a solid material that is deposited onto the underlying liquid-solid interface, resulting in construction of the nanowire. The liquid catalyst remains suspended at the tip of the nanowire. Consider the growth of a 15-nm-diameter silicon carbide nanowire onto a silicon carbide sururface. The surface is maintained at a temperature of Ts = 2400 K and the particular liquid catalyst that is used must be maintained in the range 2400 K ≤ Tc ≤ 3000 K to perform its function. Determine the maximum length of a nanowire that may be grown for conditions characterized by h = 105 W/m2.K and T[infinity] = 8000 KT. Assume properties of the nanowire are the same as for bulk silicon carbide.

Answers

Answer: maximum length of the nanowire is 510 nm

Explanation:

 

From the table of 'Thermo physical properties of selected nonmetallic solids at At T = 1500 K

Thermal conductivity of silicon carbide k = 30 W/m.K

Diameter of silicon carbide nanowire, D = 15 x 10⁻⁹ m  

lets consider the equation for the value of m

m = ( (hP/kAc)^1/2 )  = ( (4h/kD)^1/2 )  

m =  ( ((4 × 10⁵)/(30×15×10⁻⁹ ))^1/2 ) = 942809.04    

now lets find the value of h/mk    

h/mk = 10⁵ / ( 942809.04 × 30) =  0.00353

lets consider the value θ/θb by using the equation

θ/θb = (T - T∞) / (T - T∞)

θ/θb =  (3000 - 8000) / (2400 - 8000)

= 0.893

the temperature distribution at steady-state is expressed as;

θ/θb = [ cosh m(L - x) + ( h/mk) sinh m (L - x)]   / [cosh mL+  (h/mk) sinh mL]

θ/θb = [ cosh m(L - L) + ( h/mk) sinh m (L - L)]   / [cosh mL+  (h/mk) sinh mL]

θ/θb = [ 1 ]  / [cosh mL+  (h/mk) sinh mL]

so we substitute

0.893 =  [ 1 ]  / [cosh (942809.04 × L) +  (0.00353) sinh (942809.04 × L)]

L = 510 × 10⁻⁹m

L = 510 nm

therefore maximum length of the nanowire is 510 nm

One method that is used to grow nanowires (nanotubes with solid cores) is to initially deposit a small

Fire properties of low E glass

Answers

Answer:

The radiant heat from low-e glass can melt vinyl, has burnt people, and there is a real fire risk in high ambient temperatures. ... The total solar reflectance of clear glass is typically around 13% of the incident solar radiation. Some low-e glass can reach reflectance greater than 50%

While completing your homework, imagine the study space you are using employs a space heater with a rating of 50 kW, a refrigerator (for snacks) that is rated for 6 kW, and a light fixture with two 120 W bulbs, all operating at a constant rate for the 2.0 hours it takes you to finish


Required:

a. What is the total power consumed at any given moment?

b. How much energy do you consume to complete the task?

c. Assume the utility company charges 6.5 cents per unit of energy in part b, how much did it cost you to complete the assignment?

d. If you were willing to pay the utility company $5, what would be the power rating of an additional appliance you could add to your study space?

Answers

a) The total power consumed by the appliances can be calculated as follows:

P = P₁ + P₂ + P₃ Where, P₁ = Power of space heater = 50 kW. P₂ = Power of refrigerator = 6 kW. P₃ = Power of light fixture = 2 x 120 W = 240 W = 0.24 kW. Substituting the values in the above formula: P = 50 kW + 6 kW + 0.24 kW = 56.24 kW.

b) Energy consumed, E = P × t Where, t = 2 hours (time taken to finish) and P = 56.24 kW (as calculated above)Substituting the given values, E = 56.24 kW × 2 h = 112.48 kWh

c) Cost of energy used = Energy consumed × Cost per unit of energy Where, cost per unit of energy = 6.5 cents = 0.065 dollars. Substituting the values, Cost of energy used = 112.48 kWh × 0.065 $/kWh= $7.30

d) Power rating of an additional appliance can be calculated as follows: Power rating, P = Amount willing to pay/Cost per unit of energy Where, Amount willing to pay = $5 and Cost per unit of energy = 0.065 dollars Substituting the values, P = 5/0.065 = 76.92 W.

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Using a definition of the limit of function, prove that the following functions are continuous
at = 0:
) () = 1 − 2 + 52, 0 = 1

Answers

Answer:

... you gotta do divson?

Explanation:

1 A power transmission includes a belt drive, a chain drive and a gear drive. Which of the following is the best arrangement between a motor and a working machine? (a) belt drive gear drive chain drive (b) chain drive gear drive belt drive (c) belt drive chain drive gear drive (d) chain drive belt drive gear drive

Answers

Answer:d

Explanation:

(d) chain drive belt drive gear drive

The chain drive belt drive gear drive. Thus option D is correct.

Waht is power trasmisson ?

The power transmission includes the bulk of the electrical energy form the generating sites such as the power station or the power plant and send to the anelectric substation where the voltage gets transformed and distributed to the insurers on other substations.

They can be mechanical, electrical and hydrologic, etc. The power transmission can move the electricity over larger distances.

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The figure below appeared three heat treatments processes of steel (A, B and C),

select only One and answer the following:

1- Named the heat treatment process.

2- The temperature range of heating process.

3- The cooling process method.

4- The aims of process.​

Answers

Answer:

b

Explanation:

The flow between two infinitely flat parallel plates displays a parabolic profile, and is called plane Poiseulle flow.

a. True
b. False

Answers

Answer:

a. True

Explanation:

The study of fluids in a state of rest or in motion and the forces involved in it is called fluid mechanics. Fluid mechanics has a wide range of applications in the field of mechanical engineering as well as civil engineering.

When we study the flow of fluid between any two flat plates that is indefinitely flat and is parallel, the flow of the fluid is known as plane Poiseulle flow. The profile of a plane Poiseulle flow is parabolic.

The velocity profile of a plane Poiseulle flow is :

\($\frac{u(y)}{U_{max}}=1-\left(\frac{2y}{h}\right)^2$\)

Thus the answer is TRUE.

The quarter-wave monopole antenna of Problem 7.2.2 is replaced by a 1 5 l0 lossless monopole that has an input impedance of (20 j50) V. Determine the total average power radiated.

Answers

A 1 5 l0 lossless monopole with an input impedance of (20 j50) V is used in place of the quarter-wave monopole antenna from Problem 7.2.2. The total average power emitted is 13.86 /λ watts.

To determine the total average power radiated by the 1.5 λ lossless monopoles with an input impedance of (20 j50) V, we can use the formula:
P = (|V|^2 / 4R)
Where P is the power radiated, |V| is the magnitude of the voltage at the input impedance, and R is the radiation resistance of the antenna.
The radiation resistance of a monopole antenna is given by:
R = (2π)^2 * (h / λ)^2
Where h is the height of the antenna and λ is the wavelength of the operating frequency.
Assuming that the monopole is operating at its resonant frequency, we can find the height of the antenna using the formula:
h = λ / 4
Therefore, h = (1.5 * λ) / 4 = 0.375 λ
Substituting the values of h and λ in the formula for radiation resistance, we get:
R = (2π)^2 * (0.375)^2 * λ = 0.878 λ
Now, we can calculate the total average power radiated as follows:
P = (|V|^2 / 4R) = (|20 + j50|^2 / 4 * 0.878 λ) = 13.86 / λ watts
Therefore, the total average power radiated by the 1.5 λ lossless monopole with an input impedance of (20 j50) V is 13.86 / λ watts.

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Gold and silver rings can receive an arc and turn molten. True or False

Answers

Micropulse arc welding is a well-known tool for speeding up simple bench operations during the welding process like ring size, making connections near thermally sensitive gemstones, and mending porosity castings.

The practice performs effectively on gold, silver, copper, and stainless steel whether joining tiny jewelry materials or bigger pieces for miniature metal sculptures.

The welding arc temperatures typically range from 6000°C to 8000°C, which translates to about 10000F to 15000F.

This increased range of thermal heat is high enough to turn Gold and silver rings into a molten state. A molten state is a phase at which a solid element is being melted and turns into a liquid state under the influence of a high temperature.

Therefore, from the above explanation, we can conclude that it is possible and true for gold and silver rings to receive an arc and turn molten.

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For a bronze alloy, the stress at which plastic deformation begins is 275 MPa, and the modulus of elasticity is 115 GPa. (a) What is the maximum load that may be applied to a specimen with a cross-sectional area of 325 mm2 without plastic deformation

Answers

Answer:

89375 N

Explanation:

Rearrange the formula for normal stress for F:

\(\sigma=\frac{F}{A}\)

\(F=\sigma*A\)

Convert given values to base units:

275 MPa = \(275*10^{6}\) Pa

325 \(mm^{2}\) = 0.000325 \(m^{2}\)

Substituting in given values:

F = \((275*10^{6})*(0.000325)=89375\) N

Which of the following is an example of biomimicry? (Select all that apply.)
a ceramic material that can be given a rough, natural-seeming texture
a support material designed like cartilage in the human body
a synthetic polymer whose internal composition is similar to tree sap
a wood material that when sanded smooth looks remarkably like stone

Answers

Answer:

a synthetic polymer whose internal composition is similar to tree sap

a support material designed like cartilage in the human body

a ceramic material that can be given a rough, natural-seeming texture

Explanation:

all of these mimic naturally occurring structures/phenomenon

For an engineering audience, credible arguments require a sound _____ with credible evidence.

Answers

For an engineering audience, credible arguments require a sound logical argument with credible evidence.

An engineering audience refers to individuals who are professionally trained to apply mathematical and scientific principles to design and develop practical applications for the advancement of society. An engineering audience is quite knowledgeable in technical and scientific fields.

Credible evidence refers to evidence that is considered trustworthy. Credible evidence is evidence that is based on facts and is supported by reputable sources. Credible evidence is critical when making a persuasive argument.For an engineering audience, credible arguments require a sound logical argument with credible evidence. This means that a credible argument should be based on sound reasoning and supported by credible evidence that is supported by reputable sources. Credible evidence is essential when presenting an argument to an engineering audience because they are knowledgeable in technical and scientific fields.

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For an engineering audience, credible arguments require a sound rationale with credible evidence.

In engineering, credibility is paramount, and arguments must be based on a solid rationale that is logical, well-reasoned, and supported by reliable evidence. This means that the argument should be built upon a foundation of sound engineering principles, theories, and established practices.

Credible evidence plays a crucial role in supporting the rationale of an argument. This evidence can take various forms, including experimental data, empirical research, scientific studies, simulations, case studies, expert opinions, and published literature. The evidence should come from reputable sources and be subjected to rigorous analysis and verification.

By presenting a well-structured rationale supported by credible evidence, an engineering audience can evaluate and assess the validity and reliability of the arguments being presented. This approach ensures that decisions, designs, and solutions are based on solid foundations and have a higher likelihood of being effective, safe, and reliable in engineering practice.

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Does a bridge anchored resting on two pillars have any torque?.

Answers

Answer: Yes, but it is at equilibrium

Explanation:

The pyramids in Egypt are cited as an ancient world wonder. What is the main
reason that the pyramids are important to the study of engineering?

Answers

The pyramids are important to the study of engineering because they were some of the first structures built using engineering principles. The pyramids are an example of how engineering can be used to create amazing structures.

What is pyramid?

A pyramid is a structure with triangular exterior surfaces that converge to a single step at the summit, giving the shape the shape of a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any polygon shape. A pyramid, as a result, has at least three exterior triangle surfaces. A typical variant is the square pyramid, which has a square base and four triangular exterior surfaces. The design of a pyramid, with the majority of the weight closer to the bottom and the pyramidion at the apex, means that less material will be pushed down from above. This weight distribution enabled early civilizations to build stable massive constructions.

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Arthur files a singe income tax return and his maximum tax-free interest under the education savings bond program is $6,000.00. How much of the interest is excludible if his modified adjusted gross income exceeds the applicable dollar limit by $5,000 (one-third of the phaseout range)?

Answers

The excludable interest is just $1,000 because Arthur's modified adjusted gross income exceeds the applicable dollar limit by $5,000.

What is tax?

Tax can be defined as the sum that is received by an individual or an organization on its profits or other income, and it is then received by the government.

Interest on education savings bonds is tax-free up to a maximum of $6,000 per bond.

$5,000 is the excess of the modified adjusted gross income.

Arthur should not exceed the phase-out limits in terms of adjusted gross income.

As a result, since Arthur's modified adjusted gross income is $5,000 more than the applicable dollar limit, the excludable interest is $1,000.

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Refrigerant 134a enters the evaporator of a refrigeration system operating at steady state at -8oC and a quality of 20% at a velocity of 5 m/s. At the exit, the refrigerant is a saturated vapor at -8oC. The evaporator flow channel has constant diameter of 1.7 cm. Determine the mass flow rate of the refrigerant, in kg/s, and the velocity at the exit, in m/s.

Answers

Refrigerant 134a enters the evaporator of a refrigeration system operating at a steady-state at -8oC and a quality of 20% at a velocity of 5 m/s. The mass flow rate of the refrigerant is 0.0594 kg/s  and the velocity at the exit is 24.191  m/s.

From the information given, we can use the properties table of refrigerant-134a to determine the values of the specific volume of saturated liquid and vapor at -8° C.

\(\mathbf{v_f= 0.0007570 \ m^3/kg}\)\(\mathbf{v_g= 0.092438 \ m^3/kg}\)

Now the specific volume of the refrigerant at the inlet of the evaporator can be computed by using the formula;

\(\mathbf{v_1=v_f +x(v_g-v_f)}\)

where;

x (quality of refrigerant) = 20% = 0.20

\(\mathbf{v_1=0.0007570 +0.2(0.092438-0.0007570)}\)

\(\mathbf{v_1=0.0007570 +0.2(0.091681)}\)

\(\mathbf{v_1=0.0007570 +0.0183362}\)

v₁ = 0.0191 m³/kg

The density of the refrigerant at the inlet of the evaporator is:

\(\mathbf{\rho_1 = \dfrac{1}{v_1}}\)

\(\mathbf{\rho_1 = \dfrac{1}{0.0191} }\)

\(\mathbf{\rho_1={52.356 \ kg/m^3}}\)

However, the density of the  refrigerant at the outlet of the evaporator is:

\(\mathbf{\rho_g = \dfrac{1}{v_g}}\)

\(\mathbf{\rho_g= \dfrac{1}{0.0092438} }\)

\(\mathbf{\rho_g={10.818 \ kg/m^3}}\)

Recall that:

the diameter of the evaporation flow channel = 1.7 cm = 0.017 mvelocity of refrigerant at the entrance of evaporation \(v_1\) = 5 m/s

Now, the mass flow rate of the refrigerant can be computed by using the formula:

\(\mathbf{m = \rho_1 \Big[ \dfrac{\pi}{4} \times d^2 \Big] v_1 }\)

\(\mathbf{m = 52.356 \Big[ \dfrac{\pi}{4} \times (0.017)^2 \Big] 5 }\)

mass flow rate (m) = 0.0594 kg/s

Also, the velocity of the refrigerant at the exit of the evaporator is determined by using the formula:

\(\mathbf{m=\rho_2 \Big[ \dfrac{\pi}{4} \times d^2 \Big] v_2}\)

\(\mathbf{ 0.0594 kg/s = 10.818 \Big[ \dfrac{\pi}{4} \times (0.017)^2 \Big] v_2 }\)

\(\mathbf{v_2 = 24.191 \ m/s}\)

Therefore, we can conclude that the mass flow rate of the refrigerant is 0.0594 kg/s  and the velocity at the exit is 24.191  m/s.

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