The phasor technique is not valid if the frequencies of the sinusoids in the time domain are different. Part F - Use phasors to combine sinusoids The phasor technique makes it pretty easy to combine several sinusoidal functions into a single sinusoidal expression without using trigonometric identities. However, you cannot use the phasor technique in all cases. Select the expressions below for which the phasor technique cannot be used to combine the sinusoids into a single expression.
a. 45 sin(2500t – 50°) + 20 cos(1500t +20°)
b. 25 cos(50t + 160°) + 15 cos(50t +70°)
c. 100 cos(500t +40°) + 50 sin(500t – 120°) – 120 cos(500t + 60°) -100 sin(10,000t +90°) + 40 sin(10, 100t – 80°) + 80 cos(10,000t)
d. 75 cos(8t+40°) + 75 sin(8t+10°) – 75 cos(8t + 160°)

Answers

Answer 1

Answer:

  a, c

Explanation:

As the problem statement tells you, the phasor technique cannot be used when the frequencies are different. The frequencies are different when the coefficients of t are different. The different ones are highlighted.

a. 45 sin(2500t – 50°) + 20 cos(1500t +20°)

b. 25 cos(50t + 160°) + 15 cos(50t +70°)

c. 100 cos(500t +40°) + 50 sin(500t – 120°) – 120 cos(500t + 60°) -100 sin(10,000t +90°) + 40 sin(10, 100t – 80°) + 80 cos(10,000t)

d. 75 cos(8t+40°) + 75 sin(8t+10°) – 75 cos(8t + 160°)

Answer 2

Answer:

A and C

By which the phaser technique cannot be used to combine the sinusoidal into a single expression.

Related Questions

Iman wanted to find out at what temperature butter melts. She placed a cube of solid butter in a beaker. She put the beaker on a hot plate. She turned up the temperature dial one degree every two minutes. Then she recorded the temperature at which the butter started to melt.

Iman wanted to determine if her results were reliable. She decided to repeat the experiment. Which statement describes the main purpose of repeating the experiment?


to test a different substance

to see if the results are similar

to practice completing experiments

to determine if butter will melt twice

Answers

Answer:

Ans: To see if the results are similar

name the process by which mild steel can be converted into high carbon steel and explain it briefly ?​

Answers

Answer:

please give me brainlist and follow

Explanation:

Mild steel can be converted into high carbons steel by which of the following heat treatment process? Explanation: Case hardening, also referred as carburizing increases carbon content of steel, thus, imparting hardness to steel.

(HVAC) PLEASE HELP neeed helpp

Answers

Answer

Sump heater

Explanation

A stainless steel ball (=8055 kg/m3, Cp= 480 J/kgK) of diameter D =15 cm is removed from theoven at a uniform temperature of 350oC. The ball is then subjectedto the flow of air at 1 atm pressure and 30oC with a velocityof 6 m/s. The surface temperature of the ball eventuallydrops to 250oC. Determine the average convection heat transfercoefficient during this cooling process and estimate howlong this process has taken.

Answers

Answer:

i) 25.04 W/m^2 .k

ii) 23.82 minutes = 1429.2 secs

Explanation:

Given data:

Diameter of steel ball = 15 cm

uniform temperature = 350°C

p = 8055 kg/m^3

Cp = 480 J/kg.k

surface temp of ball drops to  250°C

average surface temperature = ( 350 + 250 ) / 2 = 300°C

i) Determine the average convection heat transfer coefficient during the cooling process

Note : Obtain the properties of air at 1 atm at average film temp of 30°C from the table  " properties of air "  contained in your textbook

average convection heat transfer coefficient = 25.04 W/m^2 .k

ii) Determine how long this process has taken

Time taken by the process = 23.82 minutes = 1429.2 seconds

Δt = Qtotal / Qavg = 683232 / 477.92 = 1429.59 secs

attached below is the detailed solution of the given question

In order to be a Mechanical Engineer, you need to:
1. Have a Bachelor's Degree
2. Have a Master's Degree
3. Have a Ph.D.

Answers

Answer:

3

Explanation:

it is compulsory to have a bachelor's degree

Have a bachelor degree

What is the function and role of product tear down charts, and how do engineers utilize them in the reverse engineering process?

Answers

Answer:

Product Teardown 28 pieces (1) Plastic packaging: protect and display product for purchase. (4) Exterior screws: hold case halves together. (1) Right case half: acts as part of a handle and contains the rest of the parts. (1) Left case half: acts as part of a handle and contains the rest of the parts.

Explanation:

A product teardown process is an orderly way to know about a particular product and identify its parts, system functionality to recognize modeling improvement and identify cost reduction opportunities. Unlike the traditional costing method, tear down analysis collects information to determine product quality and price desired by the consumers.

Answer:

?

Explanation:

Some wire of radius is 1.262mm has a resistance of 20Ω. Determine the resistance of a wire of the same length and material if the diameter is 1.6mm

Answers

Answer:

  12.44Ω

Explanation:

For a question such as this, the assumption must be that the resistance is inversely proportional to the square of the diameter. The resistance will be ...

  20Ω × (1.262/1.6)² ≈ 12.44Ω

Answer:

12.44

[tex]ohms[/tex]

the resistance of a wire of the same length and material if the diameter is 1.6 mm of the given measures

Explanation:

hope it helps

A driver younger than 18 years of age may not operate a motor vehicle with any passenger who is not an immediate family member until 6 months from the date that the person's driver's license was issued.
O True
O False

Answers

i think that’s true
the answer is true .











ahahahahaggaaggagagag

(TCO 3) Below is the frequency response of the IIR realization of an analog band-pass filter. What type of filter is this?

Answers

Answer:

Hello the frequency response is missing attached below is the missing image

answer : Elliptic Filter

Explanation:

The filter with such frequency response that is an analog band-pass filter as well is called an Elliptic filter.

And this is because an Elliptic filter posses a constant ripple in the stop band and a unity gain is seen in the pass band

How do Geothermal plowerplants relate to engineering?

Answers

Geothermal energy is an increasingly popular and rapidly expanding technology. Geothermal engineers explore new ways to harness and use this technology by creating processes and equipment that convert thermal energy stored in the earth into electrical power.

By using the heat that naturally radiates below the earth's surface and taking advantage of the fact that the temperature underground is always constant, geothermal technology can be used for both cooling in the summer and heating in the winter. Hope this helps! Mark Brainly please!

Trent is designing the grounds for a massive outdoor skate park. He has no experience with skateboarding at all, and although he is excited about this new project, he’s not sure where to begin. In planning this project, where should Trent concentrate his research? (Select all that apply.)

library research

skate-themed video games

interviews with skaters

documentaries on skater culture

Answers

Answer:

I’m sorry I don’t understand this is there more steps?‍♀️

Explanation:

Answer:

skate-themed video games

library research

interviews with skaters

documentaries on skater culture

(I got a 90% on the test so I dont  know if this was the one that gave me the 90% but it said it was right)

How many FastEthernet interfaces does a 2960 switch have?

Answers

Answer:

24 i believe

Explanation:

It should be around 24.

Sasha goes back through her architectural design books for inspiration and designs the new country club to have a Romanesque feel, using rounded arches for the doorways and windows and constructing the walls with extra thickness to give a feeling of imposing massiveness to the building. The client is mystified by Sasha’s approach. He says he can’t visualize it working at all and demands she rethink the entire design. What would be best for Sasha to do in response to this criticism?


She should create a computer animated view of the design to walk the client through it.

She should get a better idea for what the client wants and expects.

She should try a different architectural style for her design.

She should build a model of her design to show the client how it will look when finished.

Answers

She should create a computer animated view of the design to walk the client through it so that client will understand and get the picture of the design.

The most common type of pressure gauge is the 1. Piston 2. Linkage 3. Bourdon Tube 4. 5. Temperature​

Answers

Answer:

Bourdon Tube gauge

Explanation:

The most popular type of pressure gauge in several countries is the Bourdon pressure tube gauge, that is used to determine medium and high loads. Bourdon tube  will measure pressures ranging between 600 mbar - 4,000 bar. While the inner pressure is greater than the exterior pressure, the tube pushes forward, and vise versa.

A magician claims that he/she has invented a novel, super-fantastic heat engine. This engine operates between two reservoirs of temperatures 250 K and 750 K, respectively. Please verify and explain if this is possible for any of the following QH (heat received from the hot reservoir), QL (heat rejected to the cool reservoir), and W (mechanical work produced):
a. (3a). (3p) QH= 900 kJ, Wmech = 400 kJ, QL = 600 kJ.
b. (3b). (3p) Qu= 900 kJ, W mech = 400 kJ, QL = 500 kJ.
c. (3c). (3p) Qh= 900 kJ, Wmech = 600 kJ, QL = 300 kJ.
d. (3b). (3p) Qh= 900 kJ, Wmech = 800 kJ, QL = 100 kJ.

Answers

Answer:

A) Not possible, B) Posible, C) Possible, D) Not possible.

Explanation:

The maximum theoretical efficiency for any thermal engine is defined by Carnot's cycle, whose energy efficiency ([tex]\eta[/tex]), no unit, is expressed below:

[tex]\eta = 1-\frac{T_{L}}{T_{H}}[/tex] (1)

Where:

[tex]T_{L}[/tex] - Cold reservoir temperature, in Kelvin.

[tex]T_{H}[/tex] - Hot reservoir temperature, in Kelvin.

If we know that [tex]T_{L} = 250\,K[/tex] and [tex]T_{H} = 750\,K[/tex], then the maximum theoretical efficiency for the thermal engine is:

[tex]\eta = 1-\frac{T_{L}}{T_{H}}[/tex]

[tex]\eta = 0.667[/tex]

For real thermal engines, the following inequation is observed:

[tex]0 \le \eta_{r} \le \eta[/tex] (2)

Where [tex]\eta_{r}[/tex] is the efficiency of the real heat engine, no unit.

There are two possible criteria to determine if a given heat engine is real:

Efficiency

[tex]\eta_{r} = 1 - \frac{Q_{L}}{Q_{H}}[/tex] (3)

Where:

[tex]Q_{L}[/tex] - Heat rejected to the cold reservoir, in kilojoules.

[tex]Q_{H}[/tex] - Heat received from the hot reservoir, in kilojoules.

Power output

[tex]W = Q_{H}-Q_{L}[/tex] (4)

Where [tex]W[/tex] is the power output, in kilojoules.

Now we proceed to verify each case:

A) [tex]Q_{H} = 900\,kJ[/tex], [tex]Q_{L} = 600\,kJ[/tex], [tex]W_{m} = 400\,kJ[/tex]

[tex]\eta_{r} = 0.333[/tex]

[tex]0 \le \eta_{r} \le \eta[/tex]

[tex]W = 300\,kJ[/tex]

[tex]W \ne W_{m}[/tex]

This engine is not possible.

B) [tex]Q_{H} = 900\,kJ[/tex], [tex]Q_{L} = 500\,kJ[/tex], [tex]W_{m} = 400\,kJ[/tex]

[tex]\eta_{r} = 0.444[/tex]

[tex]0 \le \eta_{r} \le \eta[/tex]

[tex]W = 400\,kJ[/tex]

[tex]W = W_{m}[/tex]

The engine is possible.

C) [tex]Q_{H} = 900\,kJ[/tex], [tex]Q_{L} = 300\,kJ[/tex], [tex]W_{m} = 600\,kJ[/tex]

[tex]\eta_{r} = 0.667[/tex]

[tex]0 \le \eta_{r} \le \eta[/tex]

[tex]W = 600\,kJ[/tex]

[tex]W = W_{m}[/tex]

The engine is possible.

D) [tex]Q_{H} = 900\,kJ[/tex], [tex]Q_{L} = 100\,kJ[/tex], [tex]W_{m} = 800\,kJ[/tex]

[tex]\eta_{r} = 0.889[/tex]

[tex]\eta_{r} > \eta[/tex]

[tex]W = 800\,kJ[/tex]

[tex]W = W_{m}[/tex]

The engine is possible.

(TCO 3) Linear-phase filters are desirable in many applications because Group of answer choices they have a sharper frequency response. they do not cause phase-distortion of an input signal. they have better stop-band performance by eliminating side-lobes. they have the smallest number of filter coefficients compared to nonlinear filters.

Answers

Answer:

They do not cause phase-distortion of an input signal. ( option 2 )

Explanation:

Linear-phase filters are desirable in many applications simply because  they do not cause phase-distortion of an input signal.  

The signals inputted into a Linear-phase filter ( FIR type ) are delayed equally as frequency is delayed in the pass band but they are are distorted.

The main special function of the Linear-phase filter is to reduce signal distortion.

Two HVAC/R technicians are discussing the soldering of copper pipes. Technician A says that when soldering, it's important to apply flux all the way to the end of the pipe. Technician B says that when soldering, you should twist the pipe inside the fitting to help spread the flux around the joint area. Which one of the following statements is correct?

Answers

Answer:

B is correct

Explanation:

flhsmv lesson 6 circle the road way user who must yield the right of way

Answers

Answer:

  entering drivers

Explanation:

Drivers entering a traffic circle must yield the right-of-way to those already in the traffic circle. (Among other things, this rule helps avoid gridlock.)

Answer:

entering drivers

the road way user who must yield the right of way

Calculate the power required for heating a 1.5 kg sample of water for 10 minutes in a thermal system. What is the amount of energy required to raise the temperature of the water from 25°C to 60°C ? How much minimum amount of power does the heater have to supply per unit time? Why does the actual power rating of the heater need to be higher than this minimum amount? (The specific heat of water is 4.18 J/g°C .)

*60 points to anyone who can help*

Answers

Answer:

Power= Heat energy\ time

heat energy= mc∆T

specific heat of water = 4180

1.5*4180*(60-25)

=219450

time = 10× 60= 600 secs

power = 219450/600

Power= 365.75 Watt

=0.37 KW

Explanation:

the actual has to be bigger because the heater might be required to handle more ...also to accommodate extra energy.

180 kg/h of a liquid feed enters an extraction column with 98% paraffin oil and 2% ethyl alcohol at room temperature and pressure. Liquid absorbent is 100% water. Required recovery (extraction) of ethyl alcohol from paraffin oil is 97%. Given that paraffin oil and water are immiscible with each other and the extraction column operates in a counter current fashion. Assume isothermal and isobaric conditions and that only ethyl alcohol is absorbed. Equilibrium relation between mass fractions of ethyl alcohol in water and paraffin oil is given by Xwater = 1.7544 * Xparaffin oil (a) Find minimum amount of water required (Answer – 97.5 kg/hr) (b) If you have 1.5 times minimum water amount, how many equilibrium stages are required? (Answer ~ 6)

Answers

I’m not sure..............

Based on the concept that it is better to prevent falls happening in the first place, which of the following safety methods meets that criteria?

Answers

Answer:fall arrest harness

Explanation:cuz it’s just right

. A fire hose with an inside diameter of 6.40 cm is connected to a water hydrant very close to the ground. The other end is attached to a nozzle with an inside diameter of 3.5 cm and is brought 8.0 m above the ground. The flow rate on the hose is 30.0 L/s. What is the pressure in the nozzle assuming the pressure inside the hose on the ground is 1.50 x 106 N/m2

Answers

Answer:

Solving

Explanation:

The rate of heat transfer between a certain electric motor and its surroundings varies with time as , Q with dot on top equals negative 0.2 open square brackets 1 minus e to the power of negative (0.05 t )end exponent close square brackets , where t is in seconds and Q with dot on top is in kW. The shaft of the motor rotates at a constant speed of omega equals 100 space r a d divided by s (about 955 revolutions per minute, or RPM) and applies a constant torque of tau equals 18 space N m to an external load. The motor draws a constant electric power input equal to 2.0 kW. For the motor, provide an expression to show the change in total energy, increment E, as a function of time.

Answers

Answer:

the required expression is [tex]E_2 - E_1[/tex] = 4[ 1 - [tex]e^{(-0.05t)}[/tex] ]

Explanation:

Given the data in the question;

Q = -0.2[ 1 - [tex]e^(-0.05t)[/tex] ]

ω = 100 rad/s

Torque T = 18 N-m

Electric power input = 2.0 kW

now, form the first law of thermodynamics;

dE/dt = dQ/dt + dw/dt = Q' + w'

dE/dt = Q' + w'  ------ let this be equation 1

w' is the net power on the system

w' = [tex]w_{elect[/tex] - [tex]w_{shaft[/tex]

[tex]w_{shaft[/tex] = T × ω

we substitute

[tex]w_{shaft[/tex]= 18 × 100

[tex]w_{shaft[/tex] = 1800 W

[tex]w_{shaft[/tex] = 1.8 kW  

so

w' = [tex]w_{elect[/tex] - [tex]w_{shaft[/tex]

w' = 2.0 kW - 1.8 kW

w' = 0.2 kW

hence, from equation 1, dE/dt = Q' + w'

we substitute

dE/dt = -0.2[ 1 - [tex]e^{(-0.05t)[/tex] ] + 0.2

dE/dt = -0.2 + 0.2[tex]e^{(-0.05t)[/tex] ] + 0.2

dE/dt = 0.2[tex]e^{(-0.05t)[/tex]

Now, the change in total energy, increment E, as a function of time;

ΔE = [tex]\int\limits^t_0}\frac{dE}{dt} . dt[/tex]

ΔE = [tex]\int\limits^t_0} 0.2e^{(-0.05t)} dt[/tex]

ΔE = [tex]\int\limits^t_0} \frac{0.2}{-0.05} [e^{(-0.05t)}]^t_0[/tex]

[tex]E_2 - E_1[/tex] = 4[ 1 - [tex]e^{(-0.05t)}[/tex] ]

Therefore, the required expression is [tex]E_2 - E_1[/tex] = 4[ 1 - [tex]e^{(-0.05t)}[/tex] ]

Air at 1.00 atm is passed through a horizontal 1.5-in. Schedule 40 (steam-jacketed) steel pipe at a velocity of 2.10 ft/s and an inlet and outlet temperature of 25.0 °C and 95.5 °C, respectively. The pipe wall temperature is maintained at 121.1 °C. (HINT: You may neglect the viscosity correction in your calculations.) a) Assuming only heat transfer by forced convection, how long must

Answers

Answer:

missing question; How long must the heated section be

answer : 5.898 meters

Explanation:

Given parameters:

Diameter of steel pipe = 1.5 inches = 0.0381 m

velocity of air = 2.10 ft/s = 0.64 m/s

Inlet temperature = 25°C

Outlet temperature = 95.5°C

pipe wall temperature = 121.1°C

Average temperature = ( 25 + 95.5 ) / 2 = 60.25°

determine Reynolds number of air at 60.25°

= VD / v = ( 0.64 * 0.0381 ) / ( 1.83 * 10^-5 )

              = 1332.46  this means the flow is laminar

hence mass flow rate ( m ) = eAv = 1.08 * πd^2 * velocity

= 1.08 * 0.0046 * 0.64 = 0.0032 g/s

attached below is the remaining part of the solution

A gas mixture containing 3 moles CO2, 5 moles H2 and 1 mole water is undergoing the following reactions CO2+3H2 →cH3OH + H2O Develop the expressions for the mole fraction of the species in terms of the extent of the reaction?

Answers

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If it takes 35 s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest, determine the force of the rope on the tugboat. The propeller provides the propulsion force F which gives the tugboat forward motion, whereas the barge moves freely. Also, determine F acting on the tugboat. The barge has a mass of 75 Mg.

Answers

Answer:

- the force of the rope on the tugboat is 14.87 kN

- Force acting on the tugboat is 24.79 kN

Explanation:

 Given the data in the question;

tugboat increases its speed uniformly to 25 km/h

v₁ = 25 km/h = (25 × 1000) / ( 1 × 60min × 60sec )

= 25000m / 3600s

=  6.94 m/s

Now, lets determine the force on the rope using the following relation;

T = [tex]m_b[/tex]v₁ / t₁

[tex]m_b[/tex] is mass of barge( 75 Megagram = 75 × 10³ Kilogram  ), time t₁ is 35 s and v₁ is 6.94 m/s

so we substitute

T = [(75 × 10³) × 6.94 ]  / 35

T = 520500 / 35

T = 14871.43 N

T = 14871.43 / 1000

T = 14.87 kN

Therefore, the force of the rope on the tugboat is 14.87 kN

Now, to determine F acting on the tugboat;

[tex]Ft_1[/tex] = ( [tex]m_t[/tex] + [tex]m_b[/tex] )[tex]v_1[/tex]

we solve for F

F = ( [tex]m_t[/tex] + [tex]m_b[/tex] )[tex]v_1[/tex] / [tex]t_1[/tex]

where [tex]m_t[/tex] is mass of tugboat (50 Megagram = 50 × 10³ Kilogram  )

so we substitute

F = [( (50 × 10³) + (75 × 10³) )6.94] / 35

F = [ 125000 × 6.94 ) / 35

F = 867500 / 35

F = 24785.7 N

F = 24785.7 / 1000

F = 24.79 kN

Therefore, Force acting on the tugboat is 24.79 kN

Air enters the combustor of a jet engine at Pressure=10 atm, T=1000R and M=0.2. Fuel is injected and burned with fuel-air ratio (by mass) of 0.06. The heat released during the combustion is 4.50000000 ft-lb per slug of fuel. Assuming one-dimensional frictionless flow with r=1.4 for the fuel-air mixture, calculate M2, p2 and T2 at the exit of combustor?

Answers

Air enters the combustor of a jet engine at p1 = 10 atm, T1 = 1000 °R and M1 = 0.2. The
heat released during combustion is 4.5x108 ft-lb per slug of fuel. Assuming onedimensional
frictionless flow with γ = 1.4 for the fuel air mixture, calculate M2, p2, T2 at
the exit of the combustor. Hope this helps! Can I get brainly please? Plus safety first if you see any links don’t klick them please don’t.

True or false, Increasing the spring force of the pressure plate that clamps the clutch disc to the flywheel increases torque capacity
but takes more foot pressure to operate the clutch pedal.

Answers

Answer: True

Explanation:

# derive is a kind of which dependency

Answers

Types of dependency relationships
Type of dependency Keyword or Stereotype
Abstraction «abstraction», «derive», «refine», or «trace»
Binding «bind»
Realization «realize»
Substitution «substitute

If you are designing a space heater to warm a room and are required by safety codes to keep its surface temperature below 350 K (170 F or 77 C), the only variable you have to work with is the surface area, and you want to minimize that to make it convenient and inexpensive. Neglecting convection entirely, and assuming all the heat is transferred as infrared light, suppose it is to radiate 1200 W. How much area would it have

Answers

Answer:

A = 1.41 m²

Explanation:

The ara can be found out by using Stefan Boltzman Law:

[tex]P = \sigma AT^4[/tex]

where,

A = Area = ?

P = Radiation Power = 1200 W

σ = Stefan Boltzman Constant = 5.6703 x 10⁻⁸ W/m².k⁴

T = surface temperature = 350 k

Therefore:

[tex]1200\ W = (5.6703\ x\ 10^{-8}W/m^2.k^4)(A)(350\ k)^4\\\\A = \frac{1200\ W}{850.9\ W/m^2}[/tex]

A = 1.41 m²

Other Questions
Help on this please asap Use the quadratic formula to find both solutions to the quadratic equationgiven below.3x2 - X+5 = 0 Which of the following information would be found in the Georgia constitution but NOT in the United States Constitution? 43a * 5 points The Freedom of Conscience The Right to Bear Arms Info on the Responsibilities of the President Info on Federal Laws I NEED HELP PLS!!!!How did the use of metal tools most affect the development of civilizations during the Neolithic Age? aby allowing for the development of long-distance trade bby improving the transportation of goods between regions cby expanding the productivity of agricultural labor dby increasing dependence on hunting and gathering pls help i need to turn this in today If f(x) = 3x 2, what is f(5)? HELP PLS DUE NOW BRAINLIEST AND A THANKS what is ten more than 90 3. Describe three characteristics of cell membranes.What should I describe First?? Why is it not possible to make a right triangle using lengths of 4 feet, 8 feet, and 10 feet? What is coal used for Need some help :(What is the speed of a jet plane that flies 8100 km in 9 hours?A. 900 km/secB. 900 km/hrC. 900 meters/secD. 900 km/hr/hrI will give Brainliest !! Which of the following is true? In a one-shot game, a collusive strategy always represents a Nash equilibrium. A subgame perfect equilibrium occurs when each player is doing the best he can regardless of what the other player is doing. Each Nash equilibrium is a subgame perfect equilibrium. Correct! Every subgame perfect equilibrium is a Nash equilibrium. Describe at least two costs and two benefits of using a desalinization plant to obtain more freshwater? . Campbell's paycheck was $257.20. She put 1/4 of her paycheck in her savings account and used 1/3 of what was left to pay bills. How much money does she have remaining from her paycheck after her bills are paid? A private lake sells boating memberships and currently has 600 members. During the application process the potential members are asked which recreational activity they do the most. Their choices are fishing, skiing, boarding, swimming, or tubing. The lake manager chooses clients according to their interests to maximize the use of all areas of the lake. Every month, the lake rangers randomly sample the boats on the lake and categorize them according to the activity they are doing. The lake manager performs a chi-square goodness-of-fit test using the following null hypothesis to see whether their samples differ significantly from what the original applications claim.H0:pfish=0.26,pski=0.21,pboard=0.30,pswim=0.12,ptube=0.11In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples?a. n30b. 30n50c. 46n60d. n46e. n60 In the figure below, DF is a straight line. What is the degree measure of Margret is 23 years old and has been experiencing a painful burning sensation during urination. She noticed that despite the pain, she felt like urinating more frequently and with more urgency. Her urine is cloudy and has a foul odor. She is worried that it may contain blood as well due to the color. She has a slight fever that has been going on for the past few days. Evaluating ExpressionsUse the order of operations to help you solve.5 x (20 = 4)62-2 x 6????? Define a class Complex to represent complex numbers. All complex numbers are of the form x + yi, where x and y are real numbers, real numbers being all those numbers which are positive, negative, or zero.