lus
A cup has a mass of 0.0650 kg and a
volume of 0.000250 m3, and is floating
in fresh water. Pennies are put into the
cup until the top of the cup is level with
the water line. What is the mass of the
pennies in the cup?
[?] kg
Pwater = 1,000 kg/m3

Answers

Answer 1

Answer:

hey but the person at the top is right

Answer 2

Answer:

0.185

Explanation:

Volume of water displaced = 0.000250 ( volume of cup )

Mass of water displaced by cup = density of water X volume of water displaced

= 1000 X 0.000250 = 0.250 kg

Mass of water displaced = mass of cup + mass of pennies ( law of flotation)

0.25 = 0.0650 + mass of pennies

Mass of pennies = 0.2500 - 0.0650

= 0.185 kg

Don’t hesitate to like and rate this answer. It would mean a lot for me.


Related Questions

Which of the following correctly explains the difference between sound and light?


A.Sound is a longitudinal wave that does not require a medium through which to travel, and light is a transverse wave that does require a medium.

B.Sound is a longitudinal wave that requires a medium through which to travel, and light is a transverse wave that does not require a medium.

C.Sound is a transverse wave that requires a medium through which to travel, and light is a longitudinal wave that does not require a medium.

D.Sound is a transverse wave that does not require a medium through which to travel, and light is a longitudinal wave that does require a medium.

Answers

Answer: i think the answer is C

Explanation:

Please solve for 15 points. Please don’t input a link.

Answers

Answer:

a). Single replacement.

Explanation:

Because one element replaces another element in a compound

The following statements address the science behind the pulley system illustrated:
A. The pulleys increase the entropy of the system.
B. The force applied to the rope is less than the force needed to lift the object.
C. The pulleys help generate as much energy as possible.
D. The pulleys multiply energy input, resulting in more energy output.
E. The pulleys generate no thermal energy.
Which of these statements is/are true?
i. Statements A and B
ii. Statements D and E
iii. Only statement C
iv. All of the statements

Answers

Answer:

i. Statements A and B

Explanation:

Sana nakatulong

An airplane flies 1000 miles in 2 hours. What is its average speed in miles per hour?

Answers

Answer:

500km per hour

Explanation:

if in 2 hours the airplane flies 1000 km then 1000 divided by 2 is 500km per hour.

If each Coulomb of charge is given 20 Joules of energy, what is the voltage of the battery?
A. 20 V
B. 5 V
C. 10 V
D. Not enough info

Answers

Answer:

Explanation:

V = J/C

V = 20/1

= 20 v

Option A is the correct answer

Which nucleus completes the following equation?

Answers

Answer:

Option D. ²³⁹₉₃Np

Explanation:

From the question given above, the following data were:

²³⁹₉₂U —> ⁰₋₁e + __

Let ⁿₘX represent the unknown. Thus, the equation above becomes

²³⁹₉₂U —> ⁰₋₁e + ⁿₘX

Next, we shall determine n, m and X. This can be obtained as follow:

239 = 0 + n

239 = n

n = 239

92 = –1 + m

Collect like terms

92 + 1 = m

93 = m

m = 93

ⁿₘX => ²³⁹₉₃X => ²³⁹₉₃Np

Thus, the balanced equation becomes:

²³⁹₉₂U —> ⁰₋₁e + ⁿₘX

²³⁹₉₂U —> ⁰₋₁e + ²³⁹₉₃Np

Option D gives the correct answer to the question.

Answer:

D

Explanation:

239 93 Np

A mom pushes her 19.3 kg daughter on the swing. If she gives her an initial velocity of 7.5 m/s at the bottom of the swing and the swing sits 0.6 m above the ground at it's lowest point, what height does she reach above the ground?

Answers

Answer:

3.17333333333? I hope I get it right

Explanation:

..................hello

Predicted height and total energy

Answers

Answer:

The predicted height is 2.809 meters, writing this in centimeters we get (1m = 100cm):

h = 2.809 m = (2.809)*(100cm) = 280.9 cm

And the total energy is:

E = 6.696 J

Explanation:

First let's see the problem.

We have an object of mass m = 274g which is thrown upwards with an initial velocity v0 = 6.991 m/s, in a place with a gravitational acceleration of g = 8.7 m/s^2

When the object is on the air, the only force acting on it will be the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration, then we can write:

a(t) = -8.7 m/s^2

Where the negative sign is because this acceleration points down.

Now to get the velocity of the object we can integrate over time to get:

v(t) = (-8.7 m/s^2)*t + v0

Where v0 is a constant of integration, which is the initial velocity, then we can write this as:

v(t) = (-8.7 m/s^2)*t + 6.991 m/s

Now we can integrate again over the time to get the position equation.

p(t) = (1/2)*(-8.7 m/s^2)*t^2 + (6.991 m/s)*t + p0

Where p0 is the initial position, because the ball is being thrown from the ground, the initial position is 0.

Then the position equation is:

p(t) = (1/2)*(-8.7 m/s^2)*t^2 + (6.991 m/s)*t

Ok, now we know all the movement equations for the object.

The first thing we want to know is the maximum height of the object.

We know that the object reaches its maximum height when the velocity is zero (this is, the velocity stops being positive, meaning that the object stops going up, then in that time we have the maximum height)

We need to solve:

v(t) = 0m/s = (-8.7 m/s^2)*t + 6.991 m/s

(8.7 m/s^2)*t =  6.991 m/s

t =  6.991 m/s/( (8.7 m/s^2)  = 0.804 seconds

The maximum height of the object is given by:

p(0.804s) = (1/2)*(-8.7 m/s^2)*(0.804)^2 + (6.991 m/s)*(0.804) = 2.809 m

The maximum height of the object is 2.809 meters.

Now let's find the maximum energy.

Remember that the energy of an object can be written as the sum of the potential energy U and the kinetic energy K.

E = K + U

Such that for an object of mass m and velocity v, the kinetic energy is:

K = (1/2)*m*v^2

And for an object of mass m, at a height h from the ground and with gravitational acceleration g, the potential energy is:

U = m*g*h

Now, when the object is at its maximum height, the velocity is zero.

Then K = 0

And for conservation of energy, the total energy of the object becomes potential energy.

E = 0 + U

E = U

So if we find the potential energy at the maximum height of the object's path, we can find the total energy of the object.

We know that:

mass = m = 274g = 0.274 kg  (here i used that 1kg = 1000g)

height = h = 2.809 meters.

gravitational acceleration = g = 8.7 m/s^2

Then the potential energy at this point is:

U =  0.274 kg*(2.809 meters)*(8.7 m/s^2) = 6.696 J

This means that the total energy of the object is:

E = 6.696 J

The photograph shows part of the Great Plains of North America. How do
plains form?
A. Magma rises at a divergent plate boundary.
B. Tectonic movements make folds and faults in the crust.
C. Continental plates slip past each other at a transform boundary.
D. Water, wind, or glaciers either remove or deposit crust.
SUBMIT
2 PREVIOUS

Answers

Answer:

Some plains form as ice and water erodes, or wears away, the dirt and rock on higher land. Water and ice carry the bits of dirt, rock, and other material, called sediment, down hillsides to be deposited elsewhere. As layer upon layer of this sediment is laid down, plains form. Volcanic activity can also form plains.

hhhep faaast plssssss​

Answers

Answer:

false

Explanation:

I am in need of points sorry

Two identical copper blocks are connected by a weightless, unstretchable cord through a frictionless pulley at the top of a thin wedge. One edge of the wedge is vertical, and the tip makes an angle of 33. The block that hangs vertically weighs 2.85 kg, and the block on the incline weighs 2.94 kg. If the two blocks do not move, what is magnitude of the force of friction on the second second block

Answers

Answer:

13.6 N

Explanation:

Since one side of the wedge is vertical and the wedge makes and angle of 33 with the horizontal, the angle between the weight of the copper block on the incline and the incline is thus 90 - 33 = 57.

Let M be the mass of the block that hangs, m be the mass of the block on the incline and T be the tension in the weightless unstretchable cord.

We assume the motion is downwards in the direction of the hanging block, M.

We now write equations of motion for each block.

So

Mg - T = Ma    (1) and T - mgcos57 - F = ma where F is the frictional force on the block on the incline and a is their acceleration.

Now, since both blocks do not move, a = 0.

So, Mg - T = M(0) = 0     and T - mgcos57 - F = m(0) = 0

Mg - T = 0    (3) and T - mgcos57 - F = 0 (4)

From (3), T = Mg

Substituting T into (4), we have

T - mgcos57 - F = 0

Mg - mgcos57 - F = 0

So, Mg - mgcos57 = F  

F = Mg - mgcos57

F = (M - mcos57)g

Since g = acceleration due to gravity = 9.8 m/s², and M = 2.94 kg and m = 2.85 kg.

We find F, thus

F = (2.94 kg - 2.85 kgcos57)9.8 m/s²

F = (2.94 kg - 2.85 kg × 0.5446)9.8 m/s²

F = (2.94 kg - 1.552 kg)9.8 m/s²

F = (1.388 kg)9.8 m/s²

F = 13.6024 kgm/s²

F ≅ 13.6 N

a disk of radius 10 cm speeds up from rest. it turns 60 radians reaching an angular velocity of 15 rad/s. what was the angular acceleration?
b. how long did it take the disk to reach this velocity?​

Answers

Answer:

a) The angular acceleration is 1.875 radians per square second.

b) The time taken by the disk to reach the final angular speed is 8 seconds.

Explanation:

a) Let suppose that the disk accelerates uniformly, given that initial and final angular speed ([tex]\omega_{o}[/tex], [tex]\omega_{f}[/tex]), in radians per second, and change in angular position ([tex]\Delta \theta[/tex]), in radians, are known. The angular acceleration ([tex]\alpha[/tex]), in radians per square second, are found by using this expression:

[tex]\alpha = \frac{\omega_{f}^{2}-\omega_{o}^{2}}{2\cdot \Delta \theta}[/tex] (1)

If we know that [tex]\omega_{o} = 0\,\frac{rad}{s}[/tex], [tex]\omega_{f} = 15\,\frac{rad}{s}[/tex] and [tex]\Delta \theta = 60\,rad[/tex], then the angular acceleration of the disk is:

[tex]\alpha = \frac{\omega_{f}^{2}-\omega_{o}^{2}}{2\cdot \Delta \theta}[/tex]

[tex]\alpha = 1.875\,\frac{rad}{s^{2}}[/tex]

The angular acceleration is 1.875 radians per square second.

b) The time taken by the disk to reach the final angular velocity is determined by the following kinematic formula:

[tex]t = \frac{\omega_{f}-\omega_{o}}{\alpha}[/tex] (2)

Where [tex]t[/tex] is the time, in seconds.

If we know that [tex]\omega_{o} = 0\,\frac{rad}{s}[/tex], [tex]\omega_{f} = 15\,\frac{rad}{s}[/tex] and [tex]\alpha = 1.875\,\frac{rad}{s^{2}}[/tex], then the time taken by the disk is:

[tex]t = \frac{\omega_{f}-\omega_{o}}{\alpha}[/tex]

[tex]t = 8\,s[/tex]

The time taken by the disk to reach the final angular speed is 8 seconds.

As the time period of an object’s momentum change becomes longer, the force
needed to cause this change becomes _______________________.

Answers

Answer:

Speesd

Explanation:

A cars engine can deliver 300,000 watts of power to its wheels.
A. If the engine acts for 6 seconds, what is the work done on the car?
B. If the car travels 0.25 miles, what force acted on the car?
C.If the cars mass is 1200 kg, what is the acceleration of the car?

Answers

Answer:

A. 1,800,000 J

B. 4473.87 N

C. 3.728 m/s²

Melvina has a mass of 70 kg and is about to jump from the window ledge of a burning building.
The ledge is 80 m above the ground. What is Melvina's potential energy?

Answers

Melvina's potential energy is 54,880 Joules.

To calculate Melvina's potential energy, we need to use the formula for gravitational potential energy:

Potential energy = mass × gravitational acceleration × height

Potential energy is a measure of the energy an object possesses due to its position relative to other objects. In this case, Melvina's potential energy is a result of her height above the ground. As she stands on the ledge of the burning building, her potential energy is stored and can be converted into other forms of energy if she were to jump or fall. The potential energy will decrease as she descends, and it will be converted into kinetic energy (energy of motion).

Given that Melvina has a mass of 70 kg and the ledge is 80 m above the ground, we can substitute the values into the formula:

Potential energy = 70 kg × 9.8 m/s² × 80 m

Calculating this, we find:

Potential energy = 54,880 Joules

For such more questions on energy

https://brainly.com/question/30369234

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What causes the Coriolis effect?
A
The sun's position relative to Earth
B.
Earth's orbit around the sun
с
Moon phases
D
Earth's rotation

Answers

Correct answer is D. Earths rotation
The answer is D. Earths Rotation

Which of the following best describes wind?
A А
Sinking warm air moving a few feet above the ground
B
An air current formed by changes in ocean tides
с
Cool air rushing in to fill an area of low pressure
D
Rising warm air pushing cool air down toward Earth

Answers

The correct statement about the wind is:

Cool air rushing in to fill an area of low pressure

What is the wind?

Wind is the movement of air currents in relation to the Earth's surface, which is caused by pressure differences and air movement.

Characteristics of the wind

It is a meteorological phenomenon originated in the movements of rotation and translation of the Earth.

When the rising air cools and loses the moisture it was carrying, due to condensation and rain, the result is dry and cool air.

Therefore, we can conclude that the wind is the current of air that occurs in the atmosphere due to natural causes, from high pressure areas to low pressure areas.

Learn more about Characteristics of the wind here: https://brainly.com/question/11463167

Please help me please with both questions

Answers

Answer:

6 - iron

7 - by stringing many magnets together

Explanation:

6 - substances such as iron, cobalt, and nickel, most of the electrons spin in the same direction. This makes the atoms in these substances strongly magnetic—but they are not yet magnets. ... The piece of iron has become a magnet. Some substances can be magnetized by an electric current.

7 - it is that only

I beg you plz help me asap!!!
Q. How does new planet change our understanding about the universe?​

Answers

Answer:

a.

Explanation:

there would be a new planet is our solar system which could cause different gravitation pull on all the planets also there could be possible be new life form or other valuable metals that haven't been discovered on this planet. hope this helps somewhat

Well, considering there's countless planets out there that haven't been discovered on top of the ones that have been, it definitely changes our understanding of the universe by showing that there's more out there to explore and the fact that conditions in space support a lot more planets than previously thought I'm sure.

A substance whose shape can easily change is a

Answers

There are many. But if this is a chemistry question it’s liquid

What happens to warm air when it cools?
A
It sinks back down to Earth.
B
It is absorbed into clouds.
с
It remains in Earth's upper atmosphere.
D
It breaks apart and disappears.

Answers

Answer:

b I'm pretty sure sorry if I'm wrong

Answer:

I think the answer is B

Explanation:

The warm air turns cold and then it goes back to clouds

Please help me with this review question.

Answers

Answer:

28.7%

Explanation:

efficiency = work output /work input × 100

What causes an electric field?

Answers

Answer: The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. ... The force created by the electric field is much stronger than the force created by the magnetic field.

Explanation: An electric field is an invisible force field created by the attraction and repulsion of electrical charges (the cause of electric flow), and is measured in Volts per meter (V/m).

Answer:

The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field.  The force created by the electric field is much stronger than the force created by the magnetic field.

Explanation:

Ggl

An object carries a +15.5 uC charge.
It is 0.525 m from a -7.25 uC charge.
What is the magnitude of the electric
force on the object?

Answers

Answer:

3.67 N

Explanation:

From the question given above, the following data were obtained:

Charge of 1st object (q₁) = +15.5 μC

Charge of 2nd object (q₂) = –7.25 μC

Distance apart (r) = 0.525 m

Force (F) =?

Next, we shall convert micro coulomb (μC) to coulomb (C). This can be obtained as follow:

For the 1st object

1 μC = 1×10¯⁶ C

Therefore,

15.5 μC = 15.5 × 1×10¯⁶

15.5 μC = 15.5×10¯⁶ C

For the 2nd object:

1 μC = 1×10¯⁶ C

Therefore,

–7.25 μC = –7.25 × 1×10¯⁶

–7.25 μC = –7.25×10¯⁶ C

Finally, we shall determine the force. This can be obtained as follow:

Charge of 1st object (q₁) = +15.5×10¯⁶ C

Charge of 2nd object (q₂) = –7.25×10¯⁶ C

Distance apart (r) = 0.525 m

Electrical constant (K) = 9×10⁹ Nm²/C²

Force (F) =?

F = Kq₁q₂ / r²

F = 9×10⁹ × 15.5×10¯⁶ × 7.25×10¯⁶ / 0.525²

F = 3.67 N

Therefore, the force on the object is 3.67 N

Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and
the other has a mass of 52.0 kg. What is the gravitational force between them?
A. 8.01 x 10-9
B. 1.08 x 10-2
C. 2.28 x 10-8

Answers

Answer:

B

Explanation:

A mass MM uniform solid cylinder of radius RR and a mass MM thin uniform spherical shell of radius RR roll without slipping. If both objects have the same kinetic energy, what is the ratio of the speed of the cylinder to the speed of the spherical shell

Answers

Answer:

vcyl / vsph = 1.05

Explanation:

The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.The traslational part can be written as follows:

       [tex]K_{trans} = \frac{1}{2}* M* v_{cm} ^{2} (1)[/tex]

The rotational part can be expressed as follows:

       [tex]K_{rot} = \frac{1}{2}* I* \omega ^{2} (2)[/tex]

where I = moment of Inertia regarding the axis of rotation.ω = angular speed of the rotating object.If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:

       [tex]v = \omega * R (3)[/tex]

For a solid cylinder, I = M*R²/2 (4)Replacing (3) and (4)  in (2), we get:

       [tex]K_{rot} = \frac{1}{2}* \frac{1}{2} M*R^{2} * \frac{v_{cmc} ^{2}}{R^{2}} = \frac{1}{4}* M* v_{cmc}^{2} (5)[/tex]

Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:

       [tex]K_{cyl} = \frac{1}{2}* M* v_{cmc} ^{2} +\frac{1}{4}* M* v_{cmc}^{2} = \frac{3}{4}* M* v_{cmc} ^{2} (6)[/tex]

Repeating the same steps for the spherical shell:

        [tex]I_{sph} = \frac{2}{3} * M* R^{2} (7)[/tex]  

       [tex]K_{rot} = \frac{1}{2}* \frac{2}{3} M*R^{2} * \frac{v_{cms} ^{2}}{R^{2}} = \frac{1}{3}* M* v_{cms}^{2} (8)[/tex]

      [tex]K_{sph} = \frac{1}{2}* M* v_{cms} ^{2} +\frac{1}{3}* M* v_{cms}^{2} = \frac{5}{6}* M* v_{cms} ^{2} (9)[/tex]

Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.Rearranging, and taking square roots on both sides, we get:

       [tex]\frac{v_{cmc}}{v_{cms}} =\sqrt{\frac{10}{9} } = 1.05 (10)[/tex]

This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.

A 85-W lamp is connected to 100 V. What is the resistance of the lamp?

Answers

P=V2/R
R=V2/P =100x100/85 =117.64 Ohum

A wheel rotates about a fixed axis with an initial angular velocity of 24 rad/s. During a 4 s interval the angular velocity decreases to 14 rad/s. Assume that the angular acceleration is constant during the 4 s interval. How many radians does the wheel turn through during the 4 s interval

Answers

Answer:

[tex]\theta=76\ rad[/tex]

Explanation:

Hoven that,

Initial angular velocity of the wheel = 24 rad/s

Final angular velocity = 14 m/s

Time, t = 4 s

We need to find how many radians does the wheel turn through during the 4 s interval. Let the displacement is [tex]\theta[/tex]. Using second equation of rotational kinematics to find it such that,

[tex]\theta=\omega_i t+\dfrac{1}{2}\alpha t^2[/tex]

Where

[tex]\alpha[/tex] is angular acceleration

[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{14-24}{4}\\\\\alpha =-2.5\ rad/s^2[/tex]

So,

[tex]\theta=24\times 4+\dfrac{1}{2}\times (-2.5)\times 4^2\\\\\theta=76\ rad[/tex]

So, it will turn 76 radian during the 4 s interval.

Which of the following could be an example of chemical weathering?

a. rocks tumbling against each other

​b. water seeping into the ground, dissolving the limestone to form a cave​

c. a waterfall boring out a whole in a rock under it

Answers

Answer: B

Explanation:

Answers A and C are examples of physical weathering while B is chemical weathering when water and lime mix it creates a reaction

Two protons (each with q = 1.60 x 10-19)
in a nucleus are located 1.00 x 10-15 m
apart. How much electric force do they
exert on each other?
[?] N.

Answers

Answer:

230.4 N

Explanation:

From the question given above, the following data were obtained:

Charge (q) of each protons = 1.6×10¯¹⁹ C

Distance apart (r) = 1×10¯¹⁵ m

Force (F) =?

NOTE: Electric constant (K) = 9×10⁹ Nm²/C²

The force exerted can be obtained as follow:

F = Kq₁q₂ / r²

F = 9×10⁹ × (1.6×10¯¹⁹)² / (1×10¯¹⁵)²

F = 9×10⁹ × 2.56×10¯³⁸ / 1×10¯³⁰

F = 2.304×10¯²⁸ / 1×10¯³⁰

F = 230.4 N

Therefore, the force exerted is 230.4 N

Answer:

230.4

Explanation:

acellus

Other Questions
In Year 1, Kim Company sold land for $80,000 cash. The land had originally cost $60,000. Also, Kim sold inventory that had cost $110,000 for $198,000 cash. Operating expenses amounted to $36,000. 1. Prepare a Year 1 multistep income statement for Kim Company. 2. Assume that normal operating activities grow evenly by 10 percent during Year 2. Prepare a Year 2 multistep income statement for Kim Company. 3. Determine the percentage change in net income between Year 1 and Year 2. 4. Should the stockholders have expected the results determined in Requirement c? What is the solution to the equation 32x 1 = 243? options: A) x = 2 B) x = 3 C) x = 4 D) x = 2 A cup filled with water has more _____ than an empty cup. A. Mass B. Space C. Volume D. Gravity 60 74 81 91 100 110 120 130 140 150 160 176 180 190 200 210 220 230 240 250 A stock just paid a dividend of DO = $1.45. The required rate of return is rs = 13%, and the constant growth rate is g = 6.5%. 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Give examples. 150-300 words what is the temperature of a star (in kelvin) if its peak wavelength is 425 nm? your answer: the moderating effect of the financial literacy on thedecision to use financial technologycan you elabotare the research paradigm/ theory basedon the title ?? An undamped mass-and-spring system undergoes simple harmonic motion. Is this process reversible or irreversible? Reversible Irreversible Can you tell me the reason why?Simple Harmonic MotionIn physics, simple harmonic motion (SHM) is a special case of oscillatory motion. In SHM, the restoring force is directly proportional to the displacement and acts into the opposite direction. If no damping is involved in SHM, the oscillation will go on forever. define water pollution, point source pollution, and non-point-source pollution. which of the two (point source or non-point-source) is easier to identify? which is easier to legislate? which currently poses the greatest threat to freshwater? Who has the comparative advantage when it comes to cleaning the house? Listen to the question and choose the correct response.Nos despertamos a las siete.Te despiertas a las siete.Me despierto a las siete.Se despierta a las siete. 2. Suppose that an incompressible fluid passes through a pipe that changes in cross-sectional area from 0.25 m2 to 0.125 m2. How will this affect the fluid velocity? (10 points) which of the following is the most likely explanation for the lack of a filter blocking the passage of alcohol between the maternal and fetal circulations in humans?such a barrier would probably also block important molecules that need to be passed to the fetus.alcohol has some positive effects on the fetus, so evolution has resulted in an intermediate level of filtering that blocks all but the worst abuses of alcohol.there has not been enough time to evolve such a barrier.the maternal and fetal blood mix directly together in an area with many villi, so a barrier is impossible. Suppose g is a function from A to B and f is a function from B to C. Prove the following statements: a) If fog is onto, then f must be onto. b) If fog is one-to-one, then g must be one-to-one. c) If fog is a bijection, then g is onto if and only if f is one-to-one. d) Find examples of functions f and g such that fog is a bijection, but g is not onto and f is not one-to-one. You have four different books and are going to put two on a bookshelf. How many different ways can the books be ordered on the bookshelf?Group of answer choicesA. 4B. 8C. 32D. 6E.12F. 24 a. Suppose that two firms emit a certain pollutant. The marginal cost of reducing pollution for each firm is as follows: MC1 = 300E1 and MC2 =100E2, where E1 and E2 are the amounts (in tons) of emissions reduced by the first and second firms, respectively. Assume that in the absence of government intervention, Firm1 generates 100 units of emissions and Firm 2 generates 80 units of emissions. i. Suppose regulators decide to reduce total pollution by 40 units. In order to be cost effective, how much should each firm cut its pollution? ii. What emissions fee should be imposed to achieve the cost-effective outcome? How much would each firm pay in taxes? iii. Suppose that instead of an emissions fee, the regulatory agency introduces a tradable permit system and issues 140 permits, each of which allows the emission of one ton of pollution. Firm 1 uses its political influence to convince the regulatory agency to issue 100 permits to itself and only 40 permits to Firm 2. How many, if any, permits are traded between the firms? What is the minimum amount of money that must be paid (total) for these permits? By how many tons does each firm end up reducing its pollution? Do you agree that continuous improvement is the implementationof a large number of small, incremental improvements in all areasof the organization on an ongoing basis? Justify your answer.