Invasive species often display a wave of advance as they colonize new areas. Mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the expression 2 Dr , where r is the reproductive rate of individuals and D is a parameter quantifying dispersal. Calculate v'(r), the derivative of the wave speed with respect to the reproductive rate r.

Answers

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The derivative is  [tex]v(r)' =  \sqrt{\frac{D}{r} }[/tex]

The correct option is option 1

Explanation:

From  the question we are told that

   The equation of the speed of the wave of invasion is  [tex]v(r)  = 2 \sqrt{Dr}[/tex]

=>  [tex]v(r)  = 2 (Dr)^{\frac{1}{2} }[/tex]

=>  [tex]v(r)  = 2 * D^{\frac{1}{2} } r^{\frac{1}{2} }[/tex]

    Here r is the reproductive rate and the D is the parameter qualifying dispersal

Generally the derivative of this speed is mathematically represented as

         [tex]v(r)' = \frac{2}{2}  *  D^{\frac{1}{2} } *  r^{-\frac{1}{2} }[/tex]

=>     [tex]v(r)' =  \sqrt{\frac{D}{r} }[/tex]  

This derivative of the speed represents the rate of change of the invasive speed with respect to the the reproductive rate of an individual

Invasive Species Often Display A Wave Of Advance As They Colonize New Areas. Mathematical Models Based

Related Questions

A high school bus travels 240 km in 6.0 h. What is its average speed for the trip? (in km/h).

Answers

Answer:

40 km/h

Explanation:

First...

Look at the formula speed is equal to the distance over time or s = d/t.

Next...

Use the formula: 240/6.0

Finally...

Solve: 40

So the answer: 40 km/h

1. If a ball is rolling horizontally on the floor with a velocity of 2.5 m/s, what are the x and y
components of the velocity?
Vx =
Vy =

Answers

Answer: Vx = 2.5m/s and Vy = 0m/s

             

Explanation: The ball is rolling horizontally on the floor, meaning there isn't a change in the vertical position, only horizontal. The ball is rolling with pure horizontal motion and isn't moving in the vertical direction.

MathPhys Pls PLS PLS PLS HELP ME!!!!
Which of these statements describes the relationship between mass and weight?

(1 Point)

Mass is always greater than weight.

Mass of an object changes based on location, weight stays constant.

Mass of an object is constant, weight changes based on location.

Mass and weight are the same measurement.

Answers

Answer:

Usually, the relationship between mass and weight on Earth is highly proportional; objects that are a hundred times more massive than a one-liter bottle of soda almost always weigh a hundred times more—approximately 1,000 newtons, which is the weight one would expect on Earth from an object with a mass slightly greater ...

If the Mass Number is the sum of the protons and neutrons in an atom, what is
the mass number of

Answers

Answer:

It's 31

Explanation:

add 15 and 16

The data table shows how the amplitude of a mechanical wave varies with
the energy it carries. Analyze the data to identify the mathematical
relationship between amplitude and energy. Use your equation to find the
energy if the amplitude is 6 units.
Amplitude
Energy
1 unit
2 units
2 units
8 units
3 units
18 units
4 units
32 units

Answers

Answer:

162

Explanation:

When the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units. Therefore, option C is correct.

What do you mean by an amplitude ?

The term amplitude is defined as the maximum distance moved by a point on a vibrating body or wave calculated from its equilibrium position.

We have given,

first amplitude, A = 1, corresponding energy = 2

second amplitude, A = 2, corresponding energy = 8

The energy of a string at  a given amplitude is calculated as follows;

E ∝ A²

Energy varies as the square of the change in amplitude.

If amplitude of one has energy of two

Amplitude of 2 (double of 1)

= ( 2 x 2 ) = 4 x 2

= 8  4 times the energy at amplitude of 1.

Then for 8 units of amplitude change

8 x 8 = 64 x 2

= 128  

Thus, When the amplitude of the wave is 8 units, the corresponding energy of the wave is 128 units, option C is correct.

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Your question is incomplete, most probably your question was

The data table shows how the amplitude of a mechanical wave varies with the energy it carries. Analyze the data to identify the mathematical relationship between amplitude and energy. Use your equation to find the energy if the amplitude is 8 units.

Amplitude

1

2

3

4

energy

2

8

18

32

A.66 units

B. 108 units

C. 128 units

D. 88 units ​

Your mother has called you on your cell phone and asked you to pick up a few items at the grocery store on your way home. As you heard your mother state each item, which process transferred this information from your sensory memory to your short-term memory so you could jot each grocery item down?

Answers

Answer:

Encoding

Explanation:

Encoding is the initial learning of information. Encoding is the process of passing new information coming from sensory input  into our brain so that it can be easily retrievable. In a nutshell, it is the sum total of the processes by which external information such as the list of items your mother asked you to pick up at the grocery store to be converted into a manner that can be stored within the brain and recalled later from long-term memory.

Encoding has to do with transferring external stimuli into short term and subsequently long-term memory.

a train starting from a distance of velocity of 90 km.h
-1 in 10 minutes assuming that the acceleration is uniform find the acceleration and the distance travelled by the train for attending the velocity​

Answers

To make this problem solvable and you can get the help you need, I'll complete and arrange some data.

Answer:

Acceleration: [tex]0.0417\ m/s^2[/tex], Distance=7,500 m

Explanation:

Uniform Acceleration Motion

It's a type of motion in which the velocity of an object changes uniformly over time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:

[tex]v_f=v_o+at\qquad\qquad [1][/tex]

The distance traveled by the object is given by:

[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2][/tex]

Using the equation [1] we can solve for a:

[tex]\displaystyle a=\frac{v_f-v_o}{t}\qquad\qquad [3][/tex]

The problem will be rewritten as follows:

A train starting from rest reaches a velocity of 90 km/h in 10 minutes. Assuming that the acceleration is uniform, find the acceleration and the distance traveled by the train for attending the velocity​.

Let's take the relevant data:

vo=0

vf=90 Km/h*1000/3600 = 25 m/s

t = 10 minutes = 10*60 = 600  seconds

Now compute the acceleration by using [3]:

[tex]\displaystyle a=\frac{25-0}{600}=0.0417[/tex]

[tex]a=0.0417\ m/s^2[/tex]

Finally, compute the distance:

[tex]\displaystyle x=0*600+\frac{0.0417\cdot 600^2}{2}[/tex]

[tex]x=7,500\ m[/tex]

Note: We used the value of the acceleration with more precision than shown.

Acceleration: [tex]\mathbf{0.0417\ m/s^2}[/tex], Distance=7,500 m

You use a knife to cut a piece of bread. What kind of simple machine are you
using?
A. Wedge
B. Inclined plane
C. Screw
O D. Lever

Answers

Answer:

the answer is A.) Wedge

A knife to cut a piece of bread is a A. Wedge

What is a simple machine?

A simple machine, any of several devices with few or no moving parts that are used to modify motion and the magnitude of a force in order to perform work.

since , a wedge is a simple machine  with two inclined planes which when put together forms a sharped edge, which forms a triangular shaped tool which can be used to separate portion of  two objects .

hence , a knife to cut a piece of bread is a A. Wedge

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To decorate for a party, Simon needs 1,850 centimeters of colorful streamers. If the ratio of meters to centimeters is 1 : 100, how many meters of streamers does he require?

A.
18,500 meters
B.
185 meters
C.
18.5 meters
D.
1.85 meters

Answers

C because 1,850 divided by 100 is 18.50 but since zeros do not matter in decimals ( unless it is money ) we can removes the zero making it 18.5 meters

convert 9.2 km to m​

Answers

Answer:

9,200 m

Explanation:

1 kilometer = 1000 meters so if there is 9 kilometers then it is 9000 meters, then .2 kilometer is equal to 200 meters. Add the numbers together to get 9,200 meters


If you apply a net force of 3 N on 100g -box, what is the acceleration of
the box? *
30 m/s/s
20 m/s/s
10 m/s/s
5 m/s/s

Answers

Answer:

I believe the correct answer is 30m/s/s

13. A baseball pitcher throws a fastball at a speed of 46m/s. The
acceleration occurs as the pitcher holds the ball in his hand and moves it
through an almost straight line distance of 3.5 m. Calculate the
acceleration, assume it is constant and uniform. (Answer in 3 sig figs and
do not include units) *

Answers

Answer: Approximately 302 m/s^2

================================================

Work Shown:

s = starting velocity = 0

f = final velocity  = 46

d = distance = 3.5

a = acceleration = unknown (we're solving for this)

[tex]f^2 = s^2 + 2a*d \ \ \text{ ..... one of the kinematics equations}\\\\46^2 = 0^2 + 2a*3.5\\\\2116 = 7a\\\\7a = 2116\\\\a = \frac{2116}{7}\\\\a \approx 302.28571\\\\a \approx 302[/tex]

The acceleration to three sig figs is roughly 302 m/s^2

The acceleration is so large because the ball's final velocity is incredibly fast in such a short amount of time.

Please help A.S.A.P
If the bands in an igneous rock are dark. What kind of magma was present when it was formed?

Answers

Answer:

The magma, molten rock under the surface, and lava (molten rock on the surface) harden into igneous rock. The igneous rock then breaks apart over time through the process of weathering.

Explanation:

In the desert air, sound travels at 358 meters per second (m/s). In the polar air, sound travels at 330 meters per
second (m/s). What can you conclude from this information?
A - The speed of sound is constant.
B - Sound waves travel fastest in a vacuum.
C-The temperature of the air affects the speed of sound.
D-Sound waves travel at the same speed everywhere on Earth.
Please provide your answer below using CER
1. Claim: What is your choice for the correct answer?
2. Evidence: What evidence did you observe from the test-like question that made you decide on your answer?
3. Reasoning: Provide an elaboration on your evidence, possible prior knowledge about your claim.

Answers

Answer:

The correct option is;

C. The temperature of the air affects the speed of sound

Explanation:

The information given are;

The speed with which sound travels in the desert air = 358 m/s

The speed with which sound travels in the polar air = 330 m/s

The major difference between the desert air and the polar air is that the temperature of the desert air is hotter than the temperature of the air in the polar region. Therefore the speed of sound is affected by the air temperature.

The equation that gives the relationship of the speed of sound in air, [tex]v_{air}[/tex], to temperature is presented as follows;

[tex]v_{air} = 331\frac{m}{s} \times \sqrt{\dfrac{T_K}{273 K} } = 331\frac{m}{s} \times \sqrt{1 + \dfrac{T_{^{\circ}C}}{273 ^{\circ} C} }[/tex]

Which shows that the speed of sound in air, [tex]v_{air}[/tex], rises as the temperature of the air rises.

Where;

[tex]T_{^{\circ}C}[/tex] = The temperature of the air in degrees Celsius

[tex]T_K[/tex] = The temperature of the air in degrees Kelvin.

An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below. (a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second? (b) What is t the first time that the object is at its farthest right? (c) At the time found in part (b), what is the object's velocity? (d) At the time found in part (b), what is the object's acceleration?

Answers

Answer:

a.) 10Hz

b.) 0.1 s

c.) 187.4 m/s

d.) -412.6 m/s^2

Explanation:

Given that an object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?

from the equation given,  the angular speed w = 20π

but w = 2πf

where f = frequency.

substitute w for 20π

20π = 2πf

f = 20π/2π

f = 10 Hz

(b) What is t the first time that the object is at its farthest right?

since F = 1/T

T = 1 / f

T = 1/10

T = 0.1 s

Therefore, the t of  first time that the object is at its farthest right is 0.1 s

(c) At the time found in part (b), what is the object's velocity?

The velocity can be found by differentiating the equation;

x(t) = 3sin(20πt)

dx/dt = 60πcos(20πt)

where dx/dt  = velocity V

V = 60πcos(20π * 0.1)

V = 187.4 m/s

(d) At the time found in part (b), what is the object's acceleration?

to get the acceleration, differentiate equation  V = 60πcos(20πt)

dv/dt = -1200πSin(20πt)

dv/dt = acceleration a

a = -1200πSin(20πt)

substitute t into the equation

a = -1200πSin(20π * 0.1)

a = - 412.6 m/s^2

The type of motion the object undergoes that consist of a back-and-forth

movement that is repetitive is a simple harmonic motion.

The correct responses are;

(a) Number of complete back-and-forth motions per second is 10(b) The first time is after 0.025 seconds(c) Velocity is 0(d) Acceleration is approximately -11843.53 m/s²

Reasons:

The equation that represents the motion of the object is x(t) = 3·sin(20·π·t)

Where;

t ≥ 0

x(t) is in cm, and t is in seconds.

(a) The general sine function is y = A·sin(B·(t - C) + D

[tex]\mathrm{The \ period \ P} = \dfrac{2 \cdot \pi}{B}[/tex]

By comparison, we have;

B = 20·π

Therefore;

[tex]P = \dfrac{2 \cdot \pi}{20 \cdot \pi} = \dfrac{1}{10} = 0.1[/tex]

The period, which is the time to complete one cycle = 0.1 seconds

The number of cycle completed per second, is the frequency, f

[tex]f = \dfrac{1}{P} = \dfrac{1}{0.1} = 10[/tex]

f = 10 Hz = 10 cycles

The number of cycle completed per second is f = 10 cycles

(b) When the object is at the farthest right, we have;

sin(20·π·t) = Maximum = 1

[tex]\mathbf{sin\left(\dfrac{\pi}{2}\right)} = 1[/tex]

Therefore,

[tex]20 \cdot \pi \cdot t = \dfrac{\pi}{2}[/tex]

[tex]t = \dfrac{\pi}{20 \cdot \pi \cdot 2} = \dfrac{1}{40} = 0.025[/tex]

The first time it is at the farthest right is t = 0.025 seconds after start

(c) [tex]\mathrm{Velocity, \ v, \ is \ given \ by \ v = \dfrac{dx(t)}{dt}}[/tex]

Therefore;

[tex]v = \dfrac{dx(t)}{dt} = \dfrac{dx(t)}{dt} \left(3 \cdot sin \left(20 \cdot \pi \cdot t \right) = 60\cdot \pi \cdot cos \left(20 \cdot \pi \cdot t \right)[/tex]

At t = 0.25 seconds, we have;

[tex]v = \dfrac{dx(t)}{dt} = 60\cdot \pi \cdot cos \left(20 \times \pi \times 0.025 \right) = 0[/tex]

The velocity of the object at the t = 0.025 seconds is v(t) = 0

(d) Acceleration, a, is given by [tex]a = \dfrac{dv(t)}{dt}[/tex]

Therefore;

[tex]a = \dfrac{dv(t)}{dt} = \dfrac{d}{dt} \left( 60\cdot \pi \cdot cos \left(20 \times \pi \times t\right) \right) =-1200 \cdot \pi ^2 \cdot sin(20 \cdot t \cdot \pi)[/tex]

a = -1200·π²·sin(20·t·π)

∴ a = -1200×π²×sin(20×0.025×π)

sin(20×0.025×π) = 1

∴ a = -1200×π²×1 ≈ -11843.53

At the time found in part b the acceleration of the object, a ≈ -11843.53 m/s²

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Zach listed the process of how laser beams are produced with crystals.

A flashlamp pumps energy through the crystal.
Atoms in the crystal absorb and then release some of the energy as light.
Light bounces off mirrors and occasionally bounces off crystal atoms, increasing in energy.
Some light escapes the tube through the highly reflective mirror, forming a concentrated beam.

Which best describes Zach’s error?

The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal.
The atoms in the crystal do not release energy; they only absorb energy.
Light does not bounce off mirrors; it focuses through glass lenses.
Light escapes through the partially reflective mirror, not the highly reflective mirror.

Answers

The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal best describes Zach’s error.

What is a laser?

A device that uses stimulated emission of photons from excited atoms or molecules to produce a strong beam of coherent monochromatic light is a laser.

When electrons in optical materials like glass, crystal, or gas absorb energy from an electrical current or light, a laser is formed.

The increased energy excites the electrons, causing them to migrate from a lower-energy orbit around the nucleus to a higher-energy orbit.

The crystal pumps energy through the flashlamp; the flashlamp does not pump energy through the crystal. This statement is incorrect.

Hence Option A best describes Zach’s error.

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Answer:

D. Light escapes through the partially reflective mirror, not the highly reflective mirror.

Explanation:

edge 2022, I took the test.

State the forces acting on an object that is stationary/moving. Explain how acceleration changes when the same object is kicked with a great force and a small force. Describe the difference in the movement if the initial object now weighs 50 lbs and is acted on by a small force and a large force.​

Answers

Answer:

it all is force I the barly kick you then it won't do that much date but If the full force kick you then it might hurt.

Explanation:

i hope this helps

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2.

Answers

Explanation:

Acceleration is the rate of change in the speed of an object. If initial and final speed are v₁ and v₂. It changes speed in time t. Its formula is given by :

[tex]a=\dfrac{v_2-v_1}{t}[/tex]

The problem is "A skater increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration? "

In this problem,

v₁ = 2 , v₂ = 10 m/s and t = 3 s

Acceleration of the object,

[tex]a=\dfrac{10-2}{3}\\\\a=2.67\ m/s^2[/tex]

So, the acceleration of the skater is [tex]2.67\ m/s^2[/tex].

A student is given a 5.4 g mineral sample. She determines that the volume of her sample is 2 cm3. What is the density of her mineral

Answers

Answer:

6.7

Explanation:

If two cars are 5 m apart, and one car has a mass of 2,565 kg and the other
car has a mass of 4,264 kg, what is the gravitational force between the two
cars? Newton's law of gravitation is F gravity
Gm; m2 The gravitational
constant G is 6.67 x 10-11 Nm2/kg?.
A. 5.84 x 10-6N
B. 4.37 % 105 N.
C. 1.46 10-4N
D. 2.92 x 10-5 N

Answers

Gravitational force between two cars are 2.92 × 10 ⁻¹¹ Nm²/kg.

The universal force of attraction happened between two objects is called as gravitational force.

The mass of the two cars, m₁ = 2565 kg

                                            m₂ = 4264 kg

                                             r = 5m

                                            G = 6.67 ₓ 10 ⁻11 Nm²/kg

How gravitational force can be calculated?

Definition of gravitational force: The force of attraction between any two bodies is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

                            F ∝ m₁ m₂ ÷ r²

where the force exerted between the two masses m₁ and m₂,

                            F = G (m₁ m₂) ÷ r²

where as,  F - Gravitational force between two bodies,

                 G - Gravitational constant,

                 m₁ - mass of the first body,

                m₂ - mass of the second body,

                r² - square of the distance between two bodies.

                        F= 6.67 × 10⁻¹¹ Nm²/kg ( 2565 kg × 4264 kg) ÷ ( 5²)

         Hence,

                         F = 2.92 × 10⁻⁵ N

Option D is correct answer.

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Can someone please help me on this?

Answers

Answer:

80

Explanation:

How many significant figures? 53,598 m/sec

Answers

Answer:

This has 5 significant figures.

Describe effect of artificial selection on the process of evolution

Answers

Answer: The process is called artificial selection because people (instead of nature) select which organisms get to reproduce.

Explanation: This is evolution through artificial selection and the characteristics to reproduce, causing the evolution of farm stock.

The two objects have different masses, the more massive object pulls with a greater force. TRUE OR FALSE?

Answers

Answer:

on earth yes, but in space no because there is no gravity

Explanation:

plz can i have some points

The force exerted by an object depends on the mass of the object. Greater mass results in greater force. Hence, the statement is true.

What is force?

Force is an external agent acts on a body to change the substance from the state of rest or motion. There are various kinds of force such as nuclear force, magnetic force, frictional force etc.

According to Newton's law of motion force in a moving body is the product of its mass and acceleration. Hence, force is directly proportional to mass and acceleration and an increase in these quantities will increase the force exerted by the body.

Thus, greater force is needed to a move a body with greater mass. If two objects of different masses exerts force each other, the greater force will be exerted by the massive body.

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A car moved 40 km north and 90 km south. What is the displacement of the car?
A. 50 km south
B. 50 km north
C. 10 km east​

Answers

Answer:

A. 50 km south

Explanation:

hope this helps!

dimensional formula of energy​

Answers

Answer:

[M L2 T-2]

Explanation:

hope this is what you're looking for.

[M L2 T2] SI Symbol: J

How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating at 5 km/hr^2

Answers

Answer:

8.8 hours

Explanation:

plz give me a Brainliest

How many layers of data can a DVD store?
3
2
4
1
1

Answers

Answer:

Capacidad de almacenamiento ofrecida por los DVD

Hay que mencionar que es posible conseguir DVD de una o dos capas. Los DVD que cuentan con una capa son capaces de almacenar aproximadamente 4.7GB de datos, mientras que los de doble capa ofrecen la posibilidad de almacenar alrededor de 8.5GB

Explanation:

Answer:

4 layers

Explanation:

i took the quiz

which refers to the distance between two crests or two troughs on a transverse wave?
wavelength
amplitude
frequency
hertz

Answers

Answer:

wavelength

Explanation:

the definition of wavelength is the distance from one Crest to the next crest,or one trough to the next trough

The phenomenon that refers to the distance between two crests or two troughs on a transverse wave is wavelength.

What is wavelength?

Wavelength is simply defined as the distance between successive crests of a wave, particularly in a sound.

In conclusion, wavelength refers to a traveling particle.

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Which object has the least average speed?

A. object A
B. object B
C. object C
D. object D

Answers

Answer:

D

Explanation:

I could be wrong, But I'm pretty sure it's D

Other Questions
Helppp I will give brainiest. I will have three more questions after. What are Technological Contribution of Inca Empire What is the domain of the given function? Find the average rate of change from x = 2to x =4 The density of sugar is 1.6 g/cm3. What is the mass of a sugar cubewith a volume of 5.0 cm3? Name a Robber baron and tell me why they were called that? A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?O $1.26O $5.40O $19.26O $30.60 Which is an implied power of the federal government?raising taxesregulating tradedrafting soldiersdeclaring warSave and ExitNark this and return Un programa famoso de Venezuela que ahora se reconoce en los Estados Unidos y que ayuda a estudiantes, es de _____.artemsicaestudios en la universidadHelpppp me guys!!!! Giselle pays $240 in advance on her account at the athletic club. Each time she uthe account. Model the situation with a linear function and a graph.1. b= 225-15x 2. B=240-15x3. B=225+15x4. B=240+15xHelp plz god bless you I really need help asappp what is computer system Which student, if either, is most correct in their claim regarding the ATP/ADP cycle?A. Brianna's claim is correct - the removal of a phosphate group (or the breaking ofa chemical bond) supplies a great deal of energy from the cell and the ATP/ADP process is not continuous.B. Neither student is completely correct. Oscar is correct in that this process is acycle and Brianna is correct in that the removal of the phosphate group supplies the most energyC. Oscar's claim is correct - the addition of a phosphate group (or the making of achemical bond) supplies a great deal of energy from the cell and the ATP/ADPcycle is continuous.D. Both students are correct - Oscar's claim is correct for the process ofphotosynthesis and Brianna's claim is correct for the process of cellularrespiration. pleaseeeWrite down some examples of abstract nouns. Find the percent of each number a. 50% of 46 b. 70% of 110 What are the three products of the light reaction of photosynthesis Which of the following is not one of the major physical regions of Australia?A. the Western PlateauB. the Eastern HighlandsC. the Canterbury PlainsD. the Central Lowlands Simplify the expression:4 + 7(-7 + -9k) PLZZ HELP ME ONLY GIVE ME THE CORRECT ANSWER PLZZZ this due today !!!!HELPP I BEGGING YOU PLZZZ!!!The water level in Ricky Lake changes at an average of -7/16 inch every 3 years.a. Based on the rate above, how much will the water level change after one year? Show your calculations and you can use the vertical number line to help you., using 0 as the original water level.Show all your work and explanation in order to receive full points.b. How much would the water level change over a 7-year period?Show all your work and explanation in order to receive full pointC. When written in decimal form, is your answer to part (b) a repeating decimal or a terminating decimal? Justify your answer using long division.Show all your work and explanation in order to receive full points.THIS IS FOR THE FIRST IMAGE----------------------------------------------------------------------------------------------------------------------------ravis received a letter from his bank saying that his checking account balance fell below zero. His account transaction log is shown below.A. On which line did Travis make a mathematical error? Explain Traviss mistake.Show all your work and explanation in order to receive full points.B. The bank charged Travis a $20 fee because his balance dropped below $0. He knows that he currently has an outstanding charge for $7.85 that he has not recorded yet. How much money will Travis have to deposit into his account so that the outstanding charge does not create another bank fee? Explain.Show all your work and explanation in order to receive full points.THIS IS FOR THE SECOND IMAGE---------------------------------------------------------------------------------------------------------------------------- Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, howmany pages will Emilia have written in total? Assume the relationship is directly proportional.