Sally travels by car from one city to another. She drives for 30 min at 80 km/hr, 12.0 min at 105 km/hr, and 45 min at 40.0 km/hr. What was the total distance traveled?

Answers

Answer 1

Given :

Sally travels by car from one city to another. She drives for 30 min at 80 km/hr, 12.0 min at 105 km/hr, and 45 min at 40.0 km/hr.

To Find :

The total distance traveled.

Solution :

Total distance traveled is given as sum :

Distance = sum of  product of speed and time

D = (v₁ × t₁) + (v₂ × t₂) + (v₃ × t₃)

Putting all given value in this we get :

[tex]D = 80\times \dfrac{30}{60} + 105 \times \dfrac{12}{60} + 40\times \dfrac{45}{60}\\\\D = 91\ km[/tex]

Hence, this is the required solution.


Related Questions

Once a disk forms around a star, the process of planetary formation can begin. Rank the evolutionary stages for the formation of planets from earliest to latest.

a. Small clumps of matter stick together via the process of accrection to form plantesimals a few hundred kilometers in diameter
b. Dust keeps matter inside the disk cool long enough for planet formation to start
c. Planetisimals begin to accrete, forming protoplanets
d. Dust grains form condensation nuclei on which surrounding atoms condense to form small clumps of matter
e. A collection of a few planet-sized protoplanets remain in a fairly cleared out disk around the star

Answers

Answer: See explanation

Explanation:

The evolutionary stages for the formation of planets from earliest to latest will be:

1. Dust keeps matter inside the disk cool enough for planet formation to start

2. Dust grains form condensation nuclei on which surrounding atoms condense to form small clumps of matter.

3. Small clumps of matter stick together via the process of accretion to form planetesimals a few hundred kilometers in diameter.

4. Planetesimals begin to accrete, forming protoplanets.

5. A collection of a few planet-sized protoplanets remain in a fairly cleared out disk around the star

DUE IN 1 MINUTE PLS ANSWER QUICK ...A sound wave moving with a speed of 1500 m/s is sent from a submarine to the ocean floor. It reflects off the
ocean floor and is received 15s later. What is the distance between the submarine and the ocean floor?

Answers

Answer:

s = 11250 m = 11.25 km

Explanation:

The distance covered by the sound wave while traveling from submarine to ocean floor and then back to submarine can be given as follows:

[tex]s = vt[/tex]

but, the distance between the floor and the submarine will be half of this value:

[tex]s = \frac{1}{2}vt[/tex]

where,

s = distance between submarine and ocean floor = ?

v = velocity of sound = 1500 m/s

t = time taken for the round trip = 15 s

Therefore,

[tex]s = \frac{1}{2}(1500\ m/s)(15\ s)[/tex]

s = 11250 m = 11.25 km

1./ The upward net force on the space shuttle at launch is 10,000,000 N. What is the least amount of charge you could move from its nose to the launch pad, 60 m below, and thereby prevent it from lifting off

Answers

Answer:

 [tex]Q=2C[/tex]

Explanation:

From the question we are told that:

Force [tex]F=10000000N[/tex]

Distance [tex]d=60m[/tex]

Where

 [tex]Q_1=Q_2[/tex]

Generally the equation for Force is mathematically given by

 [tex]F=\frac{KQ^2}{r^2}[/tex]

Where

 [tex]K=9*10^9[/tex]

Therefore

 [tex]Q^2=\frac{Fr^2}{K}[/tex]

 [tex]Q^2=\frac{10000000*60^2}{98*10^9}[/tex]

 [tex]Q=\sqrt{\frac{10000000*60^2}{9*10^9}}[/tex]

 [tex]Q=2C[/tex]

A seagull flying horizontally over the ocean at a constant speed of 2.60 m/s carries a small fish in its mouth. It accidentally lets go of the fish, and 2.50 s after the bird lets go, the fish lands in the ocean. (a) Just before reaching the ocean, what is the horizontal component of the fish's velocity in m/s

Answers

Answer:

Horizontal Component of Fish's Velocity = 2.6 m/s

Explanation:

In this scenario, we will neglect the effects of the air resistance on the small fish. Since there is no resisting force available in the horizontal direction. Therefore, the horizontal component of the velocity of the fish will remain equal to the horizontal component of the velocity of the seagull and it will remain the same throughout the whole motion.

Horizontal Component of Fish's Velocity = Constant Horizontal Speed of Seagull

Horizontal Component of Fish's Velocity = 2.6 m/s

Instead of changing the the frequency you can change the tension to produce the next higher harmonic. What percentage of the tension would produce the next higher harmonic?

Answers

Answer:

  [tex]\frac{T}{T_o} = ( 1 + \frac{1}{n} )^2[/tex]

Explanation:

This is a string resonance exercise, the wavelengths in a string held at the ends is

          λ = 2L₀ / n

where n is an integer

the speed of the wave is

           v = λ f

            f = v /λ

the speed of the wave is given by the characteristics of the medium (string)

           v = [tex]\sqrt{\frac{T}{\mu } }[/tex]

we substitute  

            f = [tex]\frac{n}{2L_o} \ \sqrt{\frac{T}{\mu } }[/tex]

to obtain the following harmonic we change n → n + 1

            f’ =  [tex]\frac{n+1}{2L_o} \ \sqrt{\frac{T_o}{\mu } }[/tex]

In this case, it tells us to change the tension to obtain the same frequency.

            f ’= \frac{n}{2L_o} \  \sqrt{\frac{T}{\mu } }

how the two frequencies are equal

         [tex]\frac{n+1}{2L_o} \sqrt{\frac{T_o}{ \mu } } = \frac{n}{2L_o} \sqrt{\frac{T}{\mu } }[/tex]

           (n + 1) [tex]\sqrt{T_o}[/tex] = n [tex]\sqrt{T}[/tex]

             [tex]\frac{T}{T_o} = ( \frac{n+1}{n} )^2[/tex]

             [tex]\frac{T}{T_o} = ( 1 + \frac{1}{n} )^2[/tex]

this is the relationship of the voltages to obtain the following harmonic,

A ballistic pendulum is a device for measuring the speed of a projectile. The projectile is launched horizontally and embeds in a stationary block on the end of a string. The block-projectile system swings upward after the collision, reaching a maximum height. Which of the following statements is correct about the collision between the projectile-block system?

a. Kinetic energy of the system is conserved.
b. Linear momentum of the system is conserved.
c. Linear momentum of the system is not conserved.
d. The total mechanical energy of the system is conserved

Answers

(B) linear momentum of the system is conserved

4) The SI unit of time is second. why​?

Answers

Answer:

Second, fundamental unit of time, now defined in terms of the radiation frequency at which atoms of the element cesium change from one state to another. The second was formerly defined as 1/86,400 of the mean solar day—i.e., the average period of rotation of the Earth on its axis relative to the Sun.

source britannica

Explanation:

What the person up top said.. I was gunna explain but they person up top said everything correctly

Who is a socio-economically disadvantaged child? Explain any four ways forhelping such a child

Answers

Explanation:

A socio-economically disadvantaged child is the one who is disadvantaged in terms of social position and economic position. Such children have limited resources in terms of education, money and future options. Four ways of helping such children are as follows:

1) Help them in education - You can help such children by giving them free tuition. If you belong to a well off family, you can get them admitted in schools as well. Provide them with books and uniform.

2) Encourage them to do well in school and pursue their passions.

3) Provide them with meals, if they do not have access to regular meals.

4) encourage them to go school regularly.

Answer:

sorry i dont know the answer bit mark me as BRAINLIST

A single-story retail store wishes to supply all its lighting requirement with batteries charged by photovoltaic cells. The PV cells will be mounted on the horizontal rooftop. The time-averaged lighting requirement is 10 W/m2 , the annual average solar irradiance is 150 W/m2 , the PV efficiency is 10%, and the battery charging/discharging efficiency is 80%. What percentage of the roof area will the PV cells occupy

Answers

Answer:

83.33% of the roof area will be occupied by the PV cells

Explanation:

Given the data in the question;

time-averaged lighting requirement [tex]P_{lighting[/tex] = 10 W/m²

the annual average solar irradiance [tex]q_{solar[/tex] = 150 W/m²

the PV efficiency η[tex]_{pv[/tex] = 10% = 0.1

battery charging/discharging efficiency η[tex]_{battery[/tex] = 80% = 0.8

we know that; Annual average power to the light = [tex]P_{lighting[/tex] × A[tex]_{roof[/tex]

Now, the electrical power delivered by the solar cell battery system will be;

⇒  [tex]q_{solar[/tex] × A[tex]_{pv[/tex] × η[tex]_{pv[/tex] × η[tex]_{battery[/tex]

[tex]P_{lighting[/tex]A[tex]_{roof[/tex] = [tex]q_{solar[/tex] × A[tex]_{pv[/tex] × η[tex]_{pv[/tex] × η[tex]_{battery[/tex]

Such that;

A[tex]_{pv[/tex] = [tex]P_{lighting[/tex]A[tex]_{roof[/tex] / [tex]q_{solar[/tex] × A[tex]_{pv[/tex] × η[tex]_{pv[/tex] × η[tex]_{battery[/tex]

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = [tex]P_{lighting[/tex] /  [tex]q_{solar[/tex] × η[tex]_{pv[/tex] × η[tex]_{battery[/tex]

so we substitute

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = 10 W/m² / [ 150 W/m² × 0.1 × 0.8 ]

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = 10 W/m² / 12 W/m²

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = 0.8333

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = (0.8333 × 100)%

A[tex]_{pv[/tex] / A[tex]_{roof[/tex] = 83.33%

Therefore, 83.33% of the roof area will be occupied by the PV cells.

A 9.2 resistor and a 5.2 resistor are connected in series with a battery. The potential difference across the 5.2 resistor is measured as 12 V. Find the potential difference across the battery.

Answers

Answer:

V = 33.12 V

Explanation:

Given that,

A 9.2 resistor and a 5.2 resistor are connected in series with a battery.

The potential difference across the 5.2 resistors is measured as 12 V.

In series combination of resistors, the current is same throughout the circuit. Let I is the current. Using Ohm's law,

[tex]I=\dfrac{V}{R}[/tex]

Put all the values,

[tex]I=\dfrac{12}{5.2}\\\\I=2.30\ A[/tex]

The equivalent resistance is :

R = 9.2 + 5.2

= 14.4 ohms

Let V os the potential difference across the battery. So,

[tex]V=2.3\times 14.4\\\\V=33.12\ V[/tex]

So, the potential difference across the battery is equal to 33.12 V.

A bullet of m=30g reaches 900m/s in a 550mm long gun barrel. What total energy does the bullet have upon exiting the gun? *
A)12150000J
B)810000J
C)12150J
D)14850000J

show your work please

Answers

Answer:

C)12150J

Explanation:

KE = (1/2)(m)(v²)

KE = .5*30g(1kg/1000g)*(900m/s)²

KE = 12,150J

Engineers are working on a design for a cylindrical space habitation with a diameter of 7.50 km and length of 29.0 km. The habitation will simulate gravity by rotating along its axis. With what speed (in rad/s) should the habitation rotate so that the acceleration on its inner curved walls equals 8 times Earth's gravity

Answers

Answer:

The speed will be "0.144 rad/s".

Explanation:

Given that,

Diameter,

d = 7.50 km

Radius,

R = [tex]\frac{7.5}{2} \ Km[/tex]

Acceleration on inner curve,

= 8 times

Now,

As we know,

⇒ [tex]\omega^2R=8g[/tex]

or,

⇒ [tex]\omega=\sqrt{\frac{8g}{R} }[/tex]

On substituting the values, we get

⇒     [tex]=\sqrt{\frac{8\times 9.8}{\frac{7.5}{2}\times 10^3 } }[/tex]

⇒     [tex]=\sqrt{\frac{78.4}{3750} }[/tex]

⇒     [tex]=\sqrt{0.0209}[/tex]

⇒     [tex]=0.144 \ rad/s[/tex]

Explain what resonance is and give one example of a destructive outcome of resonance. Also give one example of a non-destructive outcome of resonance. Use details to support your answer.

Answers

Answer:

resonance is when a body is made to vibrate with the frequency of another body without touching it.

Explanation:

example of destructive: soldiers matching on a bridge unanimously can make the bridge collapse.

Answer:hi

i like ears

and lemon

and poetry

Explanation:

Your tutor says atomic nuclei are converted to nuclear energy in a nuclear reaction. why should you seek a new tutor?

Answers

Answer:

The answer is "Momentum and net Energy(that contains mass)".

Explanation:

No matter which type of nuclear reaction, the momentum always is maintained. According to the formula, E = mc^2 of Einstein, energy conservation on the atomic level requires the change in mass of its core which may have been shared throughout the reaction as mass and energy, that's why we can say that the nuclei aren't fully converted into electrical energy rather rearranged and the mass could be changed and dispensed to the nucleon as energy.

A closed container initially holds 50 monatomic Aparticles that have a combined energy of 480 units. After 100 monatomic B particles with a combined energy of 720 units are added to the container, the system is allowed to come to thermal equilibrium.Part A) At equilibrium, how many energy units does each A particle have?Part B) At equilibrium, how many energy units does each B particle have?

Answers

Answer:

"8 units" is the appropriate answer.

Explanation:

According to the question,

Throughout equilibrium all particles are of equivalent intensity, and as such the integrated platform's total energy has been uniformly divided across all individuals.

Now,

The total energy will be:

= [tex]480+720[/tex]

= [tex]1200 \ units[/tex]

The total number of particles will be:

= [tex]50+100[/tex]

= [tex]150[/tex]

hence,

Energy of each A particle or each B particle will be:

= [tex]\frac{1200}{150}[/tex]

= [tex]8 \ units[/tex]

a) Find the current in the 1 Ω resistor.
b ) Find the current in the 8 Ω resistor.
c ) Find the current in the 5 Ω resistor.

PLEASE HELP I NEED THIS TODAY

Answers

Answer:

a)I=V/R

39.5 amp

Explanation:

because the voltage in serious with 1ohm resistor

A pair of glasses uses a nonreflective coating of index of refraction 1.4 to minimize reflection of light with wavelength 500nm. If the index of refraction of the glass is 1.5, what is the minimum non-zero thickness of the coating

Answers

Answer:

 d = 178.57 10⁻⁹ m

Explanation:

For this exercise we must find the thickness to minimize the reflection, so the interference for the reflection must be destructive.

To find the expression we must take into account, two things:

* When the light goes from an index mordant medium to one with a higher refractive incoe, it undergoes a phase change of 180 (pi radians)

* within the film the wavelength of light is modulated by the index of refraction

           λₙ = λ₀/ n

In this case the light passes from the air to the reflective layer and undergoes a phase change of ∫π rad,  then it is reflected in the film-glass layer where it undergoes another phase change of π rad, therefore the total change of phase is 2π radians, this change is the or changes its value

period of the trigonometric functions, therefore its value does not change

  the expression for destructive interference is

           d sin θ = (me + ½) λₙ

           d sin θ = (m + ½) λ₀ / n

 

the minimum thickness occurs for m = 0 and if we take perpendicular incidence the sine = 1

          d = λ₀ /2 n

l

et's calculate

          d = 500 10⁻⁹ /( 2  1.4)

         d = 178.57 10⁻⁹ m

John is going to use a rope to pull his sister Laura across the ground in a sled through the snow. The rope makes an angle of 25 with the ground He is pulling horizontally with a constant force of 400 N. John and manages to get the sled going from 0 to 4 m/s in 5 s. The force due to friction on the sled is 310 N. What is the mass of Laura and the sled combined

Answers

the mass of Laura and the sled combined is 887.5 kg

Ferdinand the frog is hopping from lily pad to lily pad in search of a good fly
for lunch. If the lily pads are spaced 2.4 m apart, and Ferdinand jumps with a
speed of 5.4m/s, taking 0.60 s to go from lily pad to lily pad, at what angle
must Ferdinand make each of his jumps?

Answers

Answer:

θ = 33°

Explanation:

Here, we can use the formula for the total time of flight of a projectile to calculate the launch angle of frog:

[tex]T = \frac{2\ u\ Sin\theta}{g} \\\\Sin\theta = \frac{Tg}{2u}[/tex]

where,

θ = launch angle = ?

T = Total time of flight = 0.6 s

g = acceleration due to gravity = 9.81 m/s²

u = launch speed = 5.4 m/s

Therefore,

[tex]Sin\theta = \frac{(0.6\ s)(9.81\ m/s^2)}{(2)(5.4\ m/s)}\\\\\theta = Sin^{-1}(0.545)[/tex]

θ = 33°

while hunting in a cave a bat emits sounds wave of frequency 39 kilo hartz were moving towards a wall with a constant velocity of 8,32 meters per second take the speed of sound as 340 meters per second calculate frequency​

Answers

Complete question:

while hunting in a cave a bat emits sounds wave of frequency 39 kilo hartz were moving towards a wall with a constant velocity of 8.32 meters per second take the speed of sound as 340 meters per second. calculate the frequency​ reflected off the wall to the bat?

Answer:

The frequency reflected by the stationary wall to the bat is 41 kHz

Explanation:

Given;

frequency emitted by the bat, = 39 kHz

velocity of the bat, [tex]v_b[/tex] = 8.32 m/s

speed of sound in air, v = 340 m/s

The apparent frequency of sound striking the wall is calculated as;

[tex]f' = f(\frac{v}{v- v_b} )\\\\f' = 39,000(\frac{340}{340 -8.32} )\\\\f' = 39978.29 \ Hz[/tex]

The frequency reflected by the stationary wall to the bat is calculated as;

[tex]f_s = f'(\frac{v + v_b}{v} )\\\\f_s = 39978.29(\frac{340 + 8.32}{340} )\\\\f_s = 40,956.56 \ Hz[/tex]

[tex]f_s\approx 41 \ kHz[/tex]

Please helppppppp!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

I think the Bulb No. 2 will stop emitting light if the bulb No. 1 burns out.

Air in a thundercloud expands as it rises. If its initial temperature is 292 K and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has tripled

Answers

Answer:

Explanation:

It is a case of adiabatic expansion .

[tex]T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}[/tex]

T₁ , T₂ are initial and final temperature , V₁ and V₂ are initial and final volume.

Given ,

V₂ = 3 V₁ and T₁ = 292 . γ for air is 1.4 .

[tex]( 3 )^{\gamma-1}= \frac{292}{ T_2}[/tex]

[tex]( 3 )^{1.4-1}= \frac{292}{ T_2}[/tex]

1.552 = 292 / T₂

T₂ = 188 K .

The maximum amount of pulling force a truck can apply when driving on
concrete is 8760 N. If the coefficient of static friction between a trailer and
concrete is 0.8, what is the heaviest that the trailer can be and still be pulled
by the truck?
O A. 8760 N
O B. 12,680 N
O C. 10,950 N
O D. 7240 N

Answers

Answer:

8760 N

Explanation:

think this is the right answer :)

A 1.2 kg mass is suspended from the ceiling by a string. A second horizontal string holds the mass at rest next to the wall. The angle between the string and the ceiling is 65o. What is the tension force in the horizontal rope

Answers

Answer:

The tension in the horizontal string is 25.2 N.

Explanation:

mass, m = 1.2 kg

Angle, A = 65 degree

The tension in the string is T.

So, T cos A = m g

T x cos 65 =  1.2 x 9.8

T x 0.4226 = 11.76

T = 27.83 N

Tension in the horizontal string, T' = T sin A = 27.83 x sin 65 = 25.22 N

Answer:

Explanation:

See the figure attached . T₁ and T₂ are tension in the inclined and horizontal string .

The vertical component of T₁ will balance weight and horizontal component will balance the tension T₂.

T₁ sin 65 = mg and T₁ cos 65 = T₂

Dividing ,

Tan 65 = mg / T₂

T₂ = mg / tan 65

= 1.2 x 9.8 / 2.1445

= 5.5 N

Two people that have identical weight are holding onto a massless pole while standing on horizontal frictionless ice. 1)If the guy on the left starts to pull on the pole, where do they meet

Answers

Answer:

Explanation:

From the missing image attached below, it is obvious that there no external force. This implies that they cannot change their position by merely just pulling the ropes. As a result, there will be no movement and no net force will exist.

So, if there is no external force;

The center of mass of the two people is:

[tex]X_{cm}= \dfrac{m_1x_1+m_2x_2}{m_1+m_2} \\ \\ X_{cm}= \dfrac{m(-3m)+m(+3m)} {m+m}\\ \\ X_{cm}= \dfrac{0}{2m} \\ \\ X_{cm} =0[/tex]

Thus, In the system, no movement occurs and all forces remain the same.

A FBD of a rocket launching into space should include:

Answers

Answer:

Explanation:

the force of the rocket engine pushing it up,  the force of gravity pulling it down,    maybe some force of air resistance as the rocket goes fast,   hmmm    Free Body Diagrams  (FBD)  should have any and all forces on the model,  unless they are negligible . or so slight they really make little difference in the total  outcome.  

which one of the following is not a simple machine
1 ladder
2 wheel Barrow
3 pulley
4 electric pole​

Answers

4.) an electric pole is not a simple machine

A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in place a distance d above the first plate. Assume that d is much smaller than r. The two plates are attached by wires to a battery that supplies voltage V.

Required:
a. What is the tension in the cable?
b. Compute the energy stored in the electric field after the top plate was raised.

Answers

Answer:

A) F = V²E_o•πr²/2d²

B) U = E_o•Aπr²V²/2d

Explanation:

A) Since we have two circular plates, the formula for the electric field is expressed as;

E = V/d

Where;

V is voltage

d is distance

However, the net electric field produced is given by;

E' = V/2d

The tension in the cable can then be expressed as;

F = qE'

Where q is charge

Thus;

F = qV/2d - - - (eq 1)

We also know that;

C = q/V = E_o•A/d

A is area = πr²

Thus;

q/V = E_o•πr²/d

q = VE_o•πr²/d

Let's put VE_o•πr²/d for q in eq 1 to get;

F = V²E_o•πr²/2d²

B) formula for the energy stored in the electric field is;

U = ½CV²

From earlier, we saw that; C = E_o•A/d

Thus;

U = ½E_o•AV²/d

A = πr²

Thus;

U = E_o•Aπr²V²/2d

POR FA ME PODRIAN AYUDAR. URGENTE!!!!

¿Cuál es la energía cinética de un 0,01kg bala viajando a una velocidad de 700Sra?

Answers

Answer:

K.E = 2450 Joules

Explanation:

Given the following data;

Mass = 0.01 kg

Velocity = 700 m/s

To find the kinetic energy;

La energía cinética (K.E) se puede definir como una energía que posee un objeto o cuerpo debido a su movimiento.

Matemáticamente, la energía cinética viene dada por la fórmula;

[tex] K.E = \frac{1}{2}mv^{2}[/tex]

Sustituyendo en la fórmula, tenemos;

K.E = ½ * 0.01 * 700²

K.E = 0.005 * 490000

K.E = 2450 Joules

Fill in the blanks. Power station produce electricity at __________.​

Answers

Answer:

heat

Explanation:

heat is the answer hdhhdhdhdhdhdhdhdhdhd

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Your deodorant sprays with a force of 15 N. What mechanical advantage isachieved if your finger presses the deodorant nozzle with a force of 60 N?Explain your answer.(4)[TOTAL: 20 02. Why did Veronica make the kids leave the ice cream shop?03. Why did Jack change his mind about meeting August in the end?04. What are the four things Jack mentions in the section titled Four Things?05. What are some of the things Jack likes about August?06. Who does Jack blame for their friendship ending?07. What did Jack name his sled?08. Why do people assume Jacks family is rich?09. In the section titled In Science, how does Jack feel after realizing what he had done? please help (Determine the slope of the line. Show the work you did to find the slope.)10 POINTS! What is your opinion of the idea that accepting live difficulties make it easier to bear? Susan spent fifty dollars of the $250 she had in her savings account. Whatpercent of her money was still in the bank?* What is true about plate tectonics?A. The plates are always moving, just too slow for us to feel most times.B. The Earths core is cold.C. The plates havent moved for over a million years.D. Landforms like mountains, volcanoes, and valleys existed before the movement of the plates. 1. Factory in WichitaThe cost per unit for Wichitas factory is graphed as a piecewise function over the domain [0, 35000]. a. Write one or two sentences to describe the cost function for the Wichita factory. (5 points) b. Write the piecewise function for the cost per unit for production of units in the Wichita factory. That is, state the function (), where is the number of units produced. (10 points) c. What is the cost per unit for 35,000 units? (5 points) d. According to the graph, if only one unit was produced, the cost per unit would be $1.00. In reality, the company would not call in its worker and start up the equipment to produce one unit. What safeguard do you think that many manufacturers use to avoid this type of problem? (5 points) e. Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the Cost Function for Wichitas factory. (10 points) ___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.___ The plants production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.___Overtime wages were required to produce at levels above 25,000 units.2. Factory in Seattle Seattles factory is the companys newest. It was constructed with sustainable building techniques and materials, so its cost structure has been affected in several ways. The Seattle plant uses a mix of solar power (not very reliable with so many clouds), thermal power, and wind. It has an array of batteries, so at the beginning of each production day, there is free stored energy that can produce up to 8,000 units. Of course, energy is just one factor of the cost of production, but it is significant.The cost function for the Seattle factory is given by the following piecewise function. That is, ()is the cost function, where is the number of units produced. The plants maximum capacity is 42,000 unitsper day.() = { 0.35 8,0000.75 8,000 < 20,0000.83 ( 200,000) 20,000 < 42,000a. Sketch a graph to model Seattles cost structure over the domain [0, 42000]. Be sure to label the axes and any endpoints where the graph breaks. (5 points)b. Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part. (5 points)3. Factory in Omaha Omahas factory has yet another type of cost structure. Its cost function is provided graphically. Its maximum capacity is 38,000 units per day. a. At what rate is the cost per unit decreasing for production levels above 12,000?(5 points) b. State the function for the domain over [12000, 38000]. (10 points)c. What is the cost per unit at the production level of 19,000? (5 points)Omahas city council approved a special growth incentive that decreases the companys tax burden for production levels above last years average. Explain how this is reflected by the Cost Function for Omahas factory. 4. Analysis and Making Production Decisions You have now provided your companys management with powerful tools that model the cost of Given that y2 is directly proportional to the cube of x and y is always positive. Find thevalue of. when x = 3 if y = 18 when x =4A) 27 B) 11.67 C) 29 Every given minute an ameba is equally likely to do one of 3 things: (1) Die (2) Divide into two (3) Stay the same. If the ameba divides, each of the two cells will continue the above cycle independently. What is the probability that the ameba colony generated from a single cell will eventually die out. Required:What is the probability that the ameba colony generated from a single cell will eventually die out? The train will take one hour, then the bus will take two and a half hours. I need to allow half an hour to change between them. How long will the whole journey take? whats the correct equation to solve for x PLEASE HELP7) What are examples of a polyhedron? Check ALL that apply. *cylinderstriangular prismsspheresrectangular prismssquare prismscubescones 2. What is the area of this triangle?84 Please help me I have no idea how to solve!Polynomial puzzle Fill in the blank to complete the polynomial puzzle. Remember to ADD across to the right and ADD down to the bottom.