The mass of the planet Mars is 6.39 x 10^23 kg. Using Newton's Law of Gravitation, calculate the force of gravity between the planet Mars and the 74 kg Mars Rover drone on the surface if the distance between the center of Mars and surface is 2129.9 km. Show all work.
Need it ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answers

Answer 1

Answer:

F = 695.25 N

Explanation:

The force between Mars and Rover can be given by Newton's Law of Gravitation can be written as follows:

F = Gm₁m₂/r²

where,

F = Force of Gravity = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of rover = 74 kg

m₂ = mass of mars = 6.39 x 10²³ kg

r = distance between the centers of mars and rover = 2.1299 x 10⁶ m

Therefore,

F = (6.67 x 10⁻¹¹ N.m²/kg²)(74 kg)(6.39 x 10²³ kg)/(2.1299 x 10⁶ m)²

F = 695.25 N


Related Questions

definition of density

Answers

Answer:

the degree of compactness of a substance

Explanation:

So how much pressure that is inside something

what is the final speed of an object that starts from rest and accelerates uniformly at 4.0 meters per second over a distance of 8.0 meters

Answers

The final speed would be 8.0 m/s

Question: How is a triple beam balance used to find mass?1. Observe: The riders have masses of 10 grams (top), 100 grams (middle), and 1 gram (bottom). Drag the 100-gram rider to 300. At this position it balances a 300-gram mass.What happens to the pointer? ________________________________________________2. Compare: Place each object on the measurement tray, one at a time. Which objects have a mass greater than 300 grams? ________________________________________________ How do you know? _________________________________________________________

Answers

Answer:

1) For the weight to be correct, the pointer must be below the reference (zero) or in it

2)  mass greater than 300 g leave the pointer below the reference,

3) put weight on the other arms the pointer gets closer to the reference

Explanation:

1) A three-arm scale is used to determine the weight of a body by successive approximations, starting with the arm with the greatest mass (middle), when the pointer is close to zero without going over, weights are placed on the second arm (above ) weight is placed to bring the pointer closer to the reference without going over and when it is used the arm with the lowest mass is used (below) with this one, masses are placed until reaching the reference,

Taking all the jinetillos placed the total weight, the product of the position of the jinetillo by the precision of the arm and then the three values ​​are added.

In the example given, the jinetillo is placed in position 3 of the 100 arm, so the weight is 300 gr.

For the weight to be correct, the pointer must be below the reference (zero) or in it

2) objects with a mass greater than 300 g leave the pointer below the reference, it must be completed with the other two arms to reach the correct weight

3) when you put weight on the other arms the pointer gets closer to the reference

These littler girls are trying to shoot a question to research for the school science fair. Which question may not be answered through scientific investigation

Answers

Answer:

i had this question as well

Explanation:

The magnitude of the force associated with the gravitational field is constant and has a value FF . A particle is launched from point BB with an initial velocity and reaches point AA having gained U0U0 joules of kinetic energy. A resistive force field is now set up such that it is directed opposite the gravitational field with a force of constant magnitude 12F12F . A particle is again launched from point BB . How much kinetic energy will the particle gain as it moves from point BB to point AA ?

Answers

Answer:

The kinetic energy of the particle will be 12U₀

Explanation:

Given that,

A particle is launched from point B with an initial velocity and reaches point A having gained U₀ joules of kinetic energy.

Constant force = 12F

According to question,

The kinetic energy is

[tex]U_{0}=Fx[/tex]....(I)

Constant force = 12F

A resistive force field is now set up ,

Resistive force is given by,

[tex]F_{r}=12F[/tex]

When the particle moves from point B to point A then,

We need to calculate the kinetic energy

Using formula for kinetic energy

[tex]U=F_{r}x[/tex]

Put the value of [tex]F_{r}[/tex]

[tex]U=12Fx[/tex]

Now, from equation (I)

[tex]U=12U_{0}[/tex]

Hence, The kinetic energy of the particle will be 12U₀.

please help. ill make you BRAINLIEST

Answers

Answer:

because well I dont even know sorryy but you got this

A man walks 30 m to the west than 5 m to the east in 45 seconds.

A). what is his total distance walked?
B). What is his average velocity?

Answers

Answer:

35 m

0.56 m/s west

Explanation:

A) Total distance is the length of the path taken.

30 m + 5 m = 35 m

B) Velocity is displacement over time.  Displacement is the difference between the final position and the initial position.

If west is -x, and east is +x, then:

Δx = -30 m + 5 m

Δx = -25 m

v = Δx / t

v = -25 m / 45 s

v = -0.56 m/s

v = 0.56 m/s west

The total distance travelled = 35 m and average velocity = 0.55 [tex]m/s^{2}[/tex]

We have a man who walked 30 m to the west than 5 m to the east in 45 seconds.

We have to find out his total distance walked and his average velocity?

Define Average velocity of a body?

The average velocity is defined as the rate of change of displacement per unit time.

[tex]v_{avg} = \frac{x_{2} -x_{1} }{t_{2} -t_{1} }[/tex]

According to the question -

A). The total distance travelled will be equal to = [tex]X_{W} +X_{E}[/tex] = 30 + 5 = 35m

Since, the distance travelled is a scalar quantity, we have used simple addition method.

B). In order to calculate the average velocity, first we will calculate the displacement -

Consider the direction to the west as the + x axis, then -

displacement = [tex]30\overrightarrow{a_{x} } - 5\overrightarrow{a_{x} } = 25\overrightarrow{a_{x} }[/tex]

Magnitude of displacement = 25 x | [tex]\overrightarrow{a_{x} }[/tex]| = 25 x 1 = 25 m

[tex]v_{avg} = \frac{25}{45 } = 0.55[/tex] [tex]m/s^{2}[/tex]

Hence, the total distance travelled = 35 m and average velocity = 0.55[tex]m/s^{2}[/tex]

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are pool ball collisions elastic

Answers

Yes pool ball collisions elastic

Explanation:

I Think yes

Conjecture: The population of White is 80% of the total population.

Is this conjecture true?

A. No, the percentage of White is found by dividing 301,461,533 by 224,469,780 and gives 1.34%

B. No, the percentage of white is found by diving 301,461,533 by (301,461,533 - 224,469,780) and gives 3.92%

C. Yes.

D. No, the percentage of white is found by dividing (301,461,533 - 224,469,780) by 301,461,533 and gives 25.54%

E. No, the percentage of White is found by diving 224,469,780 by 301,461,533 and gives 74.46%

Answers

Answer:

E. No, the percentage of White is found by dividing 224,469,780 by 301,461,533 and gives 74.46%

Explanation:

Remember, the term percentage or finding a percentage means finding the proportion or share out a whole.

From the attached image we could notice that the total population is 301,461,533. According to the rules of mathematics,  to find the percentage of White citizens by dividing 224,469,780 by 301,461,533

[tex]\frac{224,469,780}{301,461,533}[/tex] x 100 = 74.46%.

Why do people calculate net force and make force diagrams?
O It allows us to calculate speed of an object
It allows us to predict the mass of objects
It allows us to predict motion and changes in motion
It allows us to calculate mass and weight

Answers

It allows us to predict motion and changes in motion
I think.

The questions at the bottom are 1. Both moving at a constant a velocity.2.Both accelerating.3.Both stopped.4.Bith have a force on them so what is the answer

Answers

They’re both moving at a constant velocity. The slope of a position vs time graph is velocity, and we can see the slope is constant at any point among both lines

What is the amount of heat, in calories, given off from a 5 g piece of aluminum when it cools from 80°C to 20°C? The specific heat capacity of aluminum is 0.215 cal/g∙°C. Show your work.

Answers

Answer:

Q (heat) = S * m * (T2 - T1)  where Q is heat gained (loss), S the specific heat capacity of the substance and T2, T1 are the final and initial temps

Q = .215 cal  / (g deg C) * 5 g * (20 - 80) deg C = -64.5 cal

Since the question specifies the heat emitted, then  64.5 cal is the

heat emitted (loss).

Which word contains a prefix that means against?
A
microwave
B
antidepressant
с
macrobiotic
D
overdramatic

Answers

B - antidepressant (anti meaning against)
A - microwave ...............

a ship sends a sound wave straight to the seabed and receives the echo 1.5s later. the speed of sound in sea water is 1500 m/s how deep is the sea at that place​

Answers

Answer:

Approximately [tex]1125\; \rm m[/tex].

Explanation:

Calculate the distance that sound would travel in [tex]1.5\; \rm s[/tex] at [tex]1500\; \rm m \cdot s^{-1}[/tex]:

[tex]s = v\cdot t = 1500\; \rm m\cdot s^{-1}\times 1.5\; \rm s = 2250\; \rm m[/tex].

Sound waves in this question here needs to:

travel from the ship to the bottom of the sea,get reflected at the ocean floor, andtravel back to the ship from the bottom of the ship.

Hence, the total distance that sound travelled in that [tex]1.5\; \rm s[/tex] would be the sum of:

the length of the path from the ship to the ocean floor, and the length of the path from the ocean floor back to the ship.

Therefore, the distance [tex]2250\; \rm m[/tex] here is supposed to be approximately twice the depth of the sea at that place. The depth of the sea would thus be approximately:

[tex]\displaystyle \frac{1}{2}\times 2250\; \rm m = 1125\; \rm m[/tex].

7.In North America, a magnetic compass will point to
a - magnetic north
b- Santa's workshop
C - the South Pole
d - Italy

Answers

Answer:

I think then answer for this question is number c. the South pole

Jason walks 20 m East, turns around and 20 m West, Finally, he walks 10 rn North. This takes 20 s. what is Jason's velocity​

Answers

Answer:

0.5 m/s north

Explanation:

Take east to be +x, west to be -x, north to be +y, and south to be -y.

His displacement in the x direction is:

x = 20 m − 20 m = 0 m

His displacement in the y direction is:

y = 10 m

His total displacement is therefore 10 m north.

His velocity is equal to displacement divided by time.

v = 10 m north / 20 s

v = 0.5 m/s north

9 write the Greek etymological meaning of Tracheophyta.​

Answers

Answer:

Etymology. From Ancient Greek τραχεῖα (trakheîa, “windpipe”) +‎ -ophyta; compare English trachea

Explanation:

Measure Your Reaction Time Here's something you can try at home-an experiment to measure your reaction time. Have a friend hold a ruler by one end, letting the other end hang down vertically. At the lower end, hold your thumb and index finger on either side of the ruler, ready to grip it. Have your friend release the ruler without warning. Catch it as quickly as you can. If you catch the ruler 6.4 cm (~2.5 inches) from the lower end, what is your reaction time?

Answers

Answer:

Explanation:

The reaction time will be equal to the time the ruler takes to fall by 6.4 cm .

the ruler is falling with acceleration due to gravity which is equal to

9.8 m /s²

S = ut + 1/2gt²

s is distance of fall , u is initial velocity , t is time and g is acceleration due to gravity .

6.4 = 0 + 1/2 x 9.8 t²

t = 1.14 s .

So reaction time is 1.14 s .

Answer:

0.114s

Explanation:

--------------------------------------------------------------------------------------------------------------

The reaction time is simply how long it takes the ruler to fall 6.4 cm.

For this problem, all you gotta do is convert your units and then plug them into a kinematic equation for t (time).

{*0.01 the conversion from cm to m}

--------------------------------------------------------------------------------------------------------------

Units:

Δx (change in x) or d = 6.4 cm = 0.064m

Vi = 0 m/s

a = 9.81 m/s^2

t = ?

--------------------------------------------------------------------------------------------------------------

[tex]d = Vi * t + \frac{1}{2} *a*t^{2}[/tex]

(0.064) = 0 * t + 1/2 * (9.81) * t^2

0.064 = 1/2 * (9.81) * t^2

0.064 = 4.905 * t^2

0.01304791 = t^2

t = 0.114s

--------------------------------------------------------------------------------------------------------------

Your reaction time is 0.114s

why would a sound wave travel faster through a solid than a gas? Why can they not travel in outer space (which is a vacuum) at all? explain

Answers

Answer:

They travel fastest when the particles are able to collide more. Because there is no medium in a vacuum, it will travel the fastest. ... Solids, because of how close the particles are.

Explanation:

They travel fastest when the particles are able to collide more. Because there is no medium in a vacuum, it will travel the fastest. ... Solids, because of how close the particles are.

A virtual image of a marble is located 13 cm in front of a diverging lens with a focal length of 29 cm.
Where is the marble located?
PLS ANSWER AM IN DESPERATE NEED OF HELP

Answers

Answer:

Image distance = 23.6cm

Explanation:

Given

[tex]Focal\ Length\ (f) = 29cm[/tex]

[tex]Object\ Distance (u) = 13\ cm[/tex]

Required

Determine the image distance (v)

This can be calculated using:

[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]

[tex]\frac{1}{29} = \frac{1}{13} + \frac{1}{v}[/tex]

Collect Like Terms

[tex]\frac{1}{v} = \frac{1}{29} - \frac{1}{13}[/tex]

[tex]\frac{1}{v} = \frac{13 - 29}{29 * 13}[/tex]

[tex]\frac{1}{v} = \frac{-16}{377}[/tex]

[tex]v = \frac{-377}{16}[/tex]

[tex]v = -23.5625[/tex]

[tex]v = -23.6\ cm[/tex]

This implies that the image distance is 23.6cm and it is a virtual image.

The kinetic energy of an object increases as its ____ increases.
Question 12 options:

gravitational energy

potential energy

specific heat

velocity

Answers

Answer:

velocity

Explanation:

velocity is the answer

The kinetic energy of an object increases as its velocity increases. The correct option is D.

An object's kinetic energy is linearly related to the square of its velocity. In other words, an object's kinetic energy grows more quickly the faster it moves. The equation below describes this relationship:

Kinetic Energy = (1÷2) × mass × velocity²

Therefore, the increase in kinetic energy of an item depends on its velocity. Potential energy, not kinetic energy, includes gravitational and potential energy.

Specific heat is a quality associated with a substance's ability to retain heat; it is unrelated to the kinetic energy of an object.

Thus, the correct option is D.

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Your question seems incomplete, the probable complete question is:

The kinetic energy of an object increases as its ____ increases

A. gravitational energy

B. potential energy

C. specific heat

D. velocity

To ancient peoples, why were planets special?

Answers

Answer:

Planets were like gods.

Explanation:

To the people of many ancient civilizations, the planets were thought to be deities. Our names for the planets are the Roman names for these deities. For example, Mars was the god of war and Venus the goddess of love.

pls help with these two last questions

Answers

Answer:

F = 50[N], to the left.

v = 10.52 [m/s]

Explanation:

First problem

In order to solve this problem we must apply Newton's laws, in such a way that we must perform a summation of forces on the horizontal axis. In this way we will analyze each force and the direction of action.

The offensive player is applying a force of 100N to the right, while the defensive player applies a force of 150N to the left. In this way performing the summation of forces we have.

100 - 150 = F

F = - 50 [N]

Note: The negative sign indicates that the resulting force is to the left.

Second problem

We must remember that the definition of speed is equal to the relationship between distance over time.

x = distance = 100 [m]

t = time = 9.5 [s]

v = x/t

v = 100/9.5

v = 10.52 [m/s]

A car traveling at a speed of 30 m/s comes to a stoplight. How much time will it take for the car to stop if its acceleration is -4.0 m/s2?

A) 0.75 sec

B) 1.3 sec

C) 7.5 sec

D) -7.5 sec

Answers

Answer:

i belive its a or c

Explanation:

A crane lifts 4 bricks per minute through a height of 1.5m. Find the power that is expected if each brick weighs 100N
A. 2.5w
B. 10.0w
C. 150.0w
D. 600.0w​

Answers

Answer is c I hope it helps

At the end of the school day, at exactly 2:30 pm, a group of students run out of the school building and reach the edge of the school property at 2:30:45 s. Which of the following correctly describes the motion in terms of time?
Question 2 options:

A)

t1= 0, t2 = 2:30:45 s, ∆t = 45 s

B)

t1= 2:30, t2 = 45 s

C)

∆t = 2:30

D)

t2= 2:30:45 s, ∆t = 45 s

Answers

Explanation:

Initial time, t₁ = 2:30 pm

Final time, t₂ = 2:30:45

We need to find the motion of students in terms of time. Final time is 45 seconds more than the initial time.

Change in time,

[tex]\Delta t=t_2-t_1\\\\\Delta t=2:30:45-2.30\\\\\Delta t=45\ s[/tex]

Hence, this is the required solution.

The students need 45 seconds to reach out at the edge of the school property with the final interval of 2:30:45 s. Hence, option (D) is correct.

What is a time interval?

The difference between the moment of starting an event and the completion of the same is known as the time interval.

Given data -

The exact time to start the day at school is, t1 = 2:30 pm.

The time given to reach the edge of the school property is, t2 = 2:30:45 s.

In order to describe the motion, we need to obtain the change in the time interval. Then the expression for the change in the time interval is,

Δt = t2 - t1

Solving as,

Δt = 2:30:45 - 2:30

Δt = 45 s

Thus, we can conclude that the students need 45 seconds to reach out at the edge of the school property with the final interval of 2:30:45 s.

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who was the creator of sports

Answers

The first Olympic Games were in Greece

Answer:

James Naismith (November 6, 1861 – November 28, 1939) was a Canadian-American physical educator, physician, Christian chaplain, sports coach, and innovator.

Explanation:

Select the appropriate shape for the given volume formula.
V = trh
va
V = jwh
V=

Answers

Answer: hope this helps

Explanation:

A wildebeest and chicken participate in a race over a 2.00km long course. the wildebeest travels at a speed of 16.0m/s and chicken can do 2.50m/s. the wildebeest runs for 1.600km and then stops to tease the slow-moving chicken, which eventually passes by. the wildebeest waits for a while after the chicken passes and then run toward the finish line. both animal cross the finish line at the exact same instant. assume boat animals, when moving, move steadily at their respective speed.
(a) how far (in m) is the chicken from the Finish Line when the wildebeest resume the race?
(b) for how long in time (in s) was the wildebeest stationary?

Answers

Answer:

(a)  The distance of the chicken from the finish line is 62.5 m

(b) The stationary time of the wildebeest is 675 s

Explanation:

Given;

total distance traveled by wildebeest and chicken, d = 2 km = 2000 m

speed of the wildebeest, [tex]v_w[/tex] = 16 m/s

speed of the chicken, [tex]v_c[/tex] = 2.5 m/s

Time for wildebeest to finish the race without stopping, 2000 / 16 = 125 s

Time for chicken to finish the race without stopping, 2000/2.5 = 800 s

(b) for how long in time (in s) was the wildebeest stationary?

t(stationary) = t(chicken) - t(wildebeest)

t = 800s - 125 s

t = 675 s

(a) how far (in m) is the chicken from the Finish Line when the wildebeest resume the race?

The time taken for the wildebeest to run 1.6 km (1600 m) is given by;

t = 1600 / 16 = 100 s

The total time spent by the wildebeest before it resumed the race = stationary time + 100s

t (total) = 675 s + 100 s = 775 s

Distnace traveled by the chicken when the wildebeest resumed the race = 2.5m/s x 775s = 1937.5 m

Thus, the distance of the chicken from the finish line = 2000 m -  1937.5 m

the distance of the chicken from the finish line = 62.5 m

(a) Chicken is "62.5 m" far.(b) For "675 s" the wildebeest stationary.

Speed and Distance:

According to the question,

Distance, [tex]S = 2 \ km \ or \ 2000 \ m[/tex]

                       [tex]S_1 = 1.6 \ km \ or \ 1600 \ m[/tex]

Speed, [tex]V_w = 16 \ m/s[/tex]

                    [tex]V_c = 2.5 \ m/s[/tex]

Time, [tex]t_1 = \frac{S_1}{V_w}[/tex]

                    [tex]= \frac{1600}{16}[/tex]

                    [tex]= 100 \ s[/tex]

                 [tex]t_2 = \frac{400}{16}[/tex]

                     [tex]= 25 \ s[/tex]

Now,

→ [tex]T= \frac{S}{V_c}[/tex]

      [tex]= \frac{2000}{2.5}[/tex]

      [tex]= 800 \ s[/tex]

(a)

Distance will be:

→ [tex]S_c' = V_c\times t_2[/tex]

By substituting the values,

      [tex]= 2.5\times 25[/tex]

      [tex]= 62.5 \ m[/tex]

(b)

Time will be:

→ [tex]T_{static} = T-(t_1+t_2)[/tex]

           [tex]= 800-125[/tex]

           [tex]= 675 \ s[/tex]

Thus the responses above are correct.

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Ability to make things move is called

Answers

Answer:

Force

Explanation:

You can't "make" things move but you can apply enough force on to an object for it to move, pls brainliest!

Other Questions
List and define the 4 steps in marketing research. (7 points) the area of the floor in a square room is $225$ square feet. the homeowners plan to cover the floor with rows of $6$-inch by $6$-inch tiles. how many tiles will be in each row? observation is a form of qualitative research that poses some challenges for researchers. which of the following are challenges in using observation as a research technique? (choose every correct answer.) multiple select question. researchers must try their best to attach to members of the group. researchers must be careful that the relationships they develop with the subjects do not influence the subjects' behavior. researchers do not need to gain acceptance from the group, just respect. researchers must remain detached to some degree from the subjects under study. Teslas mission to "accelerate the worlds transition to sustainable energy" is always front and center. They believe that shifting from fossil fuels toward a zero-emissions future is the #1 solution to climate change. They want to lead this charge by making the worlds most efficient electric vehicles.They make it easy for owners to get their cars serviced by sending them to convenient dealerships. This helps avoid customer-service issues when theyre servicing vehicles at dealerships.It has been common for new car companies only to offer limited support after the sale. But Tesla marketing strategy has made a different choice, and they believe they need to be there for their customers even after selling the car. They provide 24/7 customer service with a team of trained technicians ready to assist. Tesla also offers a wide range of resources to help its owners. For example, they provide free access to their website for their owners, where they have forums dedicated to answering questions, providing information about the vehicle, and even offering special deals.What are the extrinsic motivators through which Tesla is trying to connect with their target audience to buy? PLEASE PICK ALL THAT APPLY (can be multiple answers)A.Providing the worlds most efficient electric vehicles.B.24/7 customer service with a team of trained technicians ready to assistC.Free access to their website for their owners, where they have forums dedicated to answering questions, providing information about the vehicle, and even offering special deals.D.Their mission to accelerate the worlds transition to sustainable energy. Exercise 17-23 (Algorithmic) (LO. 3) Renata Corporation purchased equipment in 2019 for $324,600 and has taken $146,070 of regular MACRS depreciation. Renata Corporation sells the equipment in 2021 for $194,760. 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Cash, $2.000; Prepaid Rent. $5,500, Accounts Payable $2.400: Common Stock $21000: Service Revenue, $23,500, Salaries Expense. $6,300: Accounts Receivable. $4,200: Land, $41000; Deferred Revenue, $1.350, Retained Earnings, $18,250: Supplies Expense $7,500. Required: Prepare a trial balance with the list of accounts in the following order: assets, liabilities, stockholders' equity, revenues and expenses. One major problem facing governments in Central and South America is:O A. indigenous groups holding most of the political power.B. violence from rebels and criminal organizations.O C. limited access to international trade routes.O D. few valuable natural resources for industry.SUBMI Time is discrete. There is a continuum of agents. In each period, each agent is in one of three states: unemployed, employed, and independent. In each period, each unemployed agent is matched with an employer with probability . In a match between an unemployed agent and an employer, the unemployed agent receives a wage offer from the employer. The value of the offered wage is constant, denoted by w. If the unemployed agent accepts the offered wage, the agent becomes employed, and receives the wage from the next period. With probability 1, an unemployed agent is not matched with any employer, and remains unemployed in the period, with no chance to change the agent's state until the next period. The agent's income in the period is zero in this case. With probability , an employed agent loses employment, and becomes unemployed at the beginning of each period. In this case, the agent does not receive the wage in the period. Instead, the agent is matched with an employer with probability within the same period, like the other unemployed agents. With probability , an employed agent has chance to be independent. If the agent chooses to be independent, then the agent receives the wage w in the period, and a constant income, y, from the next period. Assume y>w. With probability 1, an employed agent remains employed, receiving the wage w in the period, with no chance to change the agent's state until the next period. With probability , an independent agent loses the agent's clients, and becomes unemployed at the beginning of each period. In this case, the agent does not receive the income for an independent agent, y, in the period. Instead, the agent is matched with an employer with probability within the same period, like the other unemployed agents. Assume >, so that an independent agent has more chance to become unemployed than an employed agent. With probability 1, an independent agent remains independent, receiving the income y in the period, with no chance to change the agent's state until the next period. Each agent's lifetime utility is defined by the expected present discounted value of future income. The discount rate is denoted by r (i.e., the time discount factor is 1/(1+r) ). In the following questions, assume r=0.1,w=1,=0.5, =0.1,=0.1,=0.2 a. What is the minimum value of y that makes an employed agent choose to be independent when it is possible? (Assume that if an agent is indifferent between being employed and becoming independent, the agent always choose to be independent.) Derive the answer with 2 decimal places (i.e., if the minimum value of y is 1.6875, only answer 1.68). b. If the value of y takes the minimum value derived above, what is the expected lifetime utility for an employed agent? Derive the answer with 2 decimal places. it is 1937 and anna has been arrested for her part in publishing an anti-nazi underground newspaper. anna is arrested by the gestapo and, without a trial, sent for detainment in a concentration camp. to which camp will anna most likely be sent? Explain the Supreme Court Case McClesky versus Kemp and how does it relate to sentencing and prosecution according to Mauer?The approach to race has changed but has the law caught up? Are the policies in place just to everyone? The faculty at the Smith School have started sharing their business contacts with the administration and students to help in recruiting efforts. The hope is that these business contacts will provide job leads for students, potential students for the school and possibly donations to the school. The new dean of the Office of Career Management (OCM) surveyed MBA students, undergraduates, and administration officials to determine how much value they place on these faculty contacts. These three groups represents all the members of the Smith School who receive any value from these contacts. The survey revealed that full-time MBA students (as a whole) valued the senior faculty contacts at $100 each and the junior faculty contacts at $50 each. Senior faculty contacts are often higher up in an organization and thus potentially more valuable to students and administrators. The undergraduate students (as a whole) valued both junior and senior faculty contacts at $50 each. Finally, administrators (as a whole) valued senior faculty contacts at $50 each and junior faculty contacts at $30 each. The total number of senior faculty contacts available is 100 . The total number of junior faculty contacts available is 50 . The Smith School plans to make these contacts available to students and administrators at no charge. a. Draw a demand curve combining the demand curves of each of the three sets of consumers for all 150 contacts. b. Faculty claim that the cost of providing this contact information is $160 per contact. If faculty are paid $160 to provide these contacts, how many contacts should the Smith School purchase? N c. Suppose the administration asks for contributions from students who make use of the contacts in order to raise the money paid to faculty. Will enough money be collected to generate the optimal number of contacts? Explain. d. The companies that comprise the faculty contacts also value the distribution of their employee names to students. In the past this form of networking has been beneficial in finding the best new employees. These companies place a value of $50 on the distribution of each senior and junior faculty contact. Will the Smith School change the number of contacts it purchases given this new information? Explain. e. If the companies offered to contribute $25 per contact distributed by the Smith School, would this change your answer to part d? Explain. Anya and Bob cannot decide which movie to watch together. Anya proposes the following procedure: she will write on a piece of paper either the number 2 or the number 4 or the number 6, while Bob will write on his piece of paper either the number 1 or 3 or 5. They will write their numbers secretly and independently. They then will show each other what they wrote and choose a movie according to the following rule: if the sum of the two numbers is 5 or less, they will watch a thriller, if the sum is 7 they will watch a romcom and if the number is 9 or more they will watch a documentary. (a) Let Anya be Player 1 and Bob Player 2. Represent this situation as a game frame by using a table (label the rows with Anya's strategies and the columns with Bob's strategies, so that we can think of Anya as choosing the row and Bob as choosing the column). (b) Suppose that Anya and Bob have the following preferences (where T stands for 'thriller', R for 'romcom' and D for 'documentary'): for Anya: TAnya R>Anya D for Bob: R Bob T>Bob D Using a utility function with values 1, 2 and 3 represent the corresponding game as a table. (c) Does Anya have any strictly dominated strategies? If yes, write the dominated strategy(s) and which one it is dominated by. (d) Does Bob have any weakly dominated strategies? If yes, write the dom- inated strategy(s) and which one it is dominated by. Write the fraction representing the total number of natural numbers in the collection of numbers -3, -2, -1, 0, 1, 2, 3, 4, 5. What fraction will it be for the whole numbers? What will be the fraction for negative integers? Find the sum of all these fractions?