The helium-neon lasers most commonly used in student physics laboratories have average power outputs of 0.250 mW. (a) If such a laser beam is projected onto a circular spot 1.86 mm in diameter, what is its intensity

Answers

Answer 1

The intensity of the helium-neon laser beam projected onto a circular spot with a diameter of 1.86 mm is approximately 2.310 W/m².

When calculating the intensity of a laser beam, we need to use the formula:

Intensity (in watts per square meter) = Power (in watts) / Area (in square meters)

Step 1: Calculate the area of the circular spot

To find the area of a circle, we use the formula:

Area = π * (radius)²

Given that the diameter is 1.86 mm, the radius would be half of that value, which is 0.93 mm or 0.00093 m.

Plugging in the values, we get:

Area = π * (0.00093)² = 2.706 x 10^(-6) m²

Step 2: Convert the power to watts

The average power output of the helium-neon laser is given as 0.250 mW (milliwatts). To convert this to watts, we divide by 1000:

Power = 0.250 mW / 1000 = 0.000250 W

Step 3: Calculate the intensity

Using the formula mentioned earlier, we can calculate the intensity:

Intensity = Power / Area = 0.000250 W / 2.706 x 10^(-6) m² ≈ 2.310 W/m²

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Related Questions

here the file attached

here the file attached

Answers

Answer:

A

Explanation:

Amplitude = height of the wave = 1

Wavelength = 3

They are slightly shifted.

The first statement is the correct one.  Don't make me type the whole thing out.

who is the richest artist in the Gambia 2020​

Answers

Answer:

Jaliba Kuyateh is the most famous and wealthiest Gambian musician.

what started that people thought the earth was flat

Answers

People thought that its flat because they wouldn’t fall off of the earth

Answer:

The flat Earth model is an archaic conception of Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat Earth and due to this people still belive earth is flat but scientist proven earth is round .

Explanation:

hi anyone here like studying quantum phy if yes then explain why virtual particles exist out of nothing , i just want your review and do tell your country and age​

Answers

Answer:

In physics, a virtual particle is a transient quantum fluctuation that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.

Explanation:

im 15 and i live in the u.s. (not for long tho. moving to Norway cause they got a better economy and support the gay.)

How can a person increase the momentum of an object?

A. by decreasing its velocity
B. by increasing its mass
C. by increasing its friction
D. by decreasing its acceleration

Answers

Answer: B

Explanation:

Classical momentum is defined to be the product of mass and velocity. Increasing the objects total mass or their velocity would also increase the momentum. The only applicable answer is B, increasing the mass of the object.

\(p=mv\)

Answer:

B. By increasing its mass

Explanation:

Momentum of an object is directly proportional to its mass and velocity

Samanthawalks along a horizontal path in the direction shown the curved path is a semi circle with a radius of 2 m while the horizontal part is for me what is the magnitude of displacement

Answers

Answer:

Explanation:

Samantha walks along a horizontal path in the direction shown the curved path is a semi circle with a radius of 2 m while the horizontal part is for me what is the magnitude of displacement

Displacement is given by the straight line distance between P and Q. Displacement will be length of straight line joining P and Q

a semi circle with a radius of 2 m

Length of this straight line=4+diameter

=4+(2*2)

=8 m

Samanthawalks along a horizontal path in the direction shown the curved path is a semi circle with a

Fill in the blanks to complete each statement about energy in Earth’s crust. (use lower case wording only)

Plate movements on Earth’s crust create
.

This adds energy to the crust, which then bends and breaks, forming
.

Answers

Answer:

stress and fault

Explanation:

yes

Answer:

Stress for the first one and the second faults

Explanation:

an object weighs 315 N in air. When immersed in water, it weighs 265 N. When it is immersed in oil, it weighs 269 N.
Find the following:
a. The density of the object
B. The density of the oil

Answers

By using relative density method, the density of the object and the oil are 6.3 and 0.92 respectively

What is Density ?

Density can simply be defined as the mass per unit volume of the material. While relative density is the ratio of the weight of the substance to the weight of equal volume of water.

Given that an object weighs 315 N in air. When immersed in water, it weighs 265 N. When it is immersed in oil, it weighs 269 N.

a. To calculate the density of the object, Let us first calculate the upthrust  of water on the object

upthrust  of water on the object = loss in weight in water

upthrust  of water on the object = 315 - 265

upthrust  of water on the object = 50 N

The density of the object = weight in air / upthrust  of water on the object

The density of the object = 315/50

The density of the object = 6.3

B. To calculate the density of the oil, let us first find the upthrust in oil and water

Upthrust in oil = 315 - 269

Upthrust in oil = 46 N

Upthrust in water = 315 - 265

Upthrust in water = 50

The density of the oil =  Upthrust in oil  / Upthrust in water

The density of the oil = 46 / 50

The density of the oil = 0.92

Therefore, the density of the object is 6.3 while the density of the oil is 0.92

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What is the density of a 14.4 g of chromium in a rectangle with a volume of 2 cm3?​

Answers

Answer:

\(density = \frac{mass}{volume} \\ \\ density = \frac{14.4}{2} \\ \\ { \boxed{ \boxed{density = 7.2 \: g {cm}^{ - 3} }}}\)

Can someone tell me what they think reliability means ?

Answers

Answer:

it is being accountable basically like some one can relive and trust that you'll do what you say your going to do

...............................................

Answers

Answer:

Year wise Percentage of Attendance in Senior Secondary Schools of India The given graph shows that the percentage of attendance is recorded with a gap of 5 years. The given table depicts, across time, from the year 2000 to 2015. During the 15 years, there is a steady and healthy increase in the percentage of attendance in ll the four types of schools. The increase in Convent-run schools is much higher compared to the other three types of schools. Initially, the village schools show a noticeably poor percentage of attendance and the General English Medium schools show less percentage of attendance compared to the Convent-run schools. All in all the continuous higher percentage indicates that the relevant authorities are learned about improving the education of the country. The poor attendance in the 2010 in the Government-run village schools shows a big leap in the year 2015, indicating that the Government must have taken an effective measure to improve literacy in the villages. Noteworthy increase in the attendance indicates solid infrastructure and focus towards the healthy growth of the corresponding authorities.

Explanation:

hope it helps you<3

PLEASE HELP I PAY 88 POINTS AND THANK YOU AND BRAINLIEST
Instructions: Answer the following questions in the space provided. Be sure to write your responses in complete sentences.
A father pushes his daughter and son on a sled down a hill.

Part A: Other than the force exerted by the father pushing the sled, identify two additional forces that act on the sled as it travels from the top of the hill to the bottom. (2 pts)
Part B: Explain how each force you identified in Part A will affect the motion of the sled. (2 pts)

Answers

Answer: Down below is the answer in complete sentences!

Explanation:

PART A:

Gravity and Acceleration are two additional forces acting upon the sled.

PART B:

Gravity will affect the sled by pulling it down, since the slope of the hill is negative.

Acceleration will affect the sled by gradually increasing it's speed, since the slope is downwards, which in addition to the initial force exerted plus gravity increases the speed, thus the sled accelerates.

Which, if any, of these scenarios produce a real image? which, if any, of these scenarios produce a virtual image?.

Answers

A real image is formed when the light rays converge and actually intersect at a point, allowing the image to be projected onto a screen. A real image can be captured or observed by placing a screen or a photographic plate at the location of the image.

A virtual image, on the other hand, is formed when the light rays only appear to diverge from a point behind the optical system. It cannot be projected onto a screen but can be observed by looking through the optical system.

Now, without specific scenarios mentioned, it is not possible to provide a definitive answer. The characteristics of the image depend on the specific optical system, such as the type of lens or mirror being used, the object's position, and the distance between the object and the optical system.

In some scenarios, a lens or mirror might produce a real image if the object is placed at a specific distance from the lens or mirror. In other cases, the same lens or mirror might produce a virtual image if the object is placed at a different distance.

To determine whether a scenario produces a real or virtual image, it is necessary to specify the details of the optical system and the object's position relative to it.

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a charge of 3.47x10-6 c is located on the origin. a charge of – 4.26x10-6 c is at x = 3.00 m on the x-axis. for what finite value(s) of x is a) the electric field zero? b) the electric potential zero?

Answers

The electric field is zero when the net force on a test charge is zero. The electric potential is zero when the potential energy of a test charge is zero. We can use Coulomb's Law to find the values of x for which the electric field and electric potential are zero.

a) The electric field is zero when the net force on a test charge is zero. This occurs when the electric field due to the charge at the origin is equal and opposite to the electric field due to the charge at x = 3.00 m. Using Coulomb's Law, we can set the electric fields equal to each other and solve for x:
(3.47x10^-6 C)/(4πε₀x²) = (4.26x10^-6 C)/(4πε₀(3.00 m - x)²)
Solving for x, we get:
x = 1.67 m
Therefore, the electric field is zero at x = 1.67 m.

b) The electric potential is zero when the potential energy of a test charge is zero. This occurs when the electric potential due to the charge at the origin is equal and opposite to the electric potential due to the charge at x = 3.00 m. Using the equation for electric potential, we can set the electric potentials equal to each other and solve for x:
(3.47x10^-6 C)/(4πε₀x) = (4.26x10^-6 C)/(4πε₀(3.00 m - x))
Solving for x, we get:
x = 1.95 m
Therefore, the electric potential is zero at x = 1.95 m.

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Block A
is placed on a rough surface inclined at an angle θ
above the horizontal. A taut string connects block A
over a pulley to block B
, which hangs from the string, as shown below. The masses of blocks A
and B
are MA
and MB
, respectively. At time t=0
, block A
is sliding up the slope as block B
falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible.

Answers

The gravitational force exerted on the block B is 20 N

The objective of this question is to determine the gravitational force exerted on block B.

From the diagram attached below, the free-body diagram shows that the gravitational force exerted on block B can be expressed as:

\(\mathbf{F_g = mass \times gravity}\)

assuming that the mass on block B = 2 kg

\(\mathbf{F_g =2 \ kg \times 9.8 m/s^2}\)

\(\mathbf{F_g =19.6 \ kg.m/s^2}\)

\(\mathbf{F_g \simeq 20 \ N}\)

Therefore, we can conclude that the gravitational force exerted on the block B is 20 N

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Block A is placed on a rough surface inclined at an angle above the horizontal. A taut string connects

What makes electromagnets more useful that permanent magnets for sorting metals in recycling centers? A. An electromagnet can separate iron from other metals, but a permanent magnet attracts all types of metal. O B. An electromagnet is always "on" but a permanent magnet has to be turned on and off. C. An electromagnet also attracts metals other than iron, but a permanent magnet attracts only iron. D. An electromagnet can be turned on and off, but a permanent magnet is always "on."​

Answers

Answer:

D  

Explanation:

A cross country skier moves from location A to B to location C to location D. Each leg of the location forth motion takes 1 minute to complete, the total time ia 3 mi minutes

Answers

During three minutes of recreation, a cross-country skier travels a total distance of 160 meters. The net displacement of the skier is 80 meters. The displacement during the second minute is -120 meters, while the displacement during the third minute is 80 meters.

a. The skier moves from location A to B, covering a distance of 20 meters, then from B to C, covering a distance of 60 meters, and finally from C to D, covering a distance of 80 meters. The total distance travelled by the skier during the three minutes is the sum of these distances, which is 20 + 60 + 80 = 160 meters.

b. The net displacement of an object is the vector sum of all its individual displacements. In this case, the skier moves westward from A to B (20 meters) and then eastward from B to D (80 meters). The net displacement is the difference between these two displacements, which is 80 - 20 = 60 meters to the east.

c. During the second minute, from 1 min to 2 min, the skier moves from location B to C, covering a distance of 60 meters to the east. Since eastward displacement is considered positive, the displacement during the second minute is +60 meters.

d. During the third minute, from 2 min to 3 min, the skier moves from location C to D, covering a distance of 80 meters to the east. Therefore, the displacement during the third minute is also +80 meters.

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The complete question is:

A cross-country skier moves from location A to location B to location C to location D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes. (The unit is meters.) West East t 0min t=2min t=3min t=1min 20 60 100 120 10 160 a. What is the distance travelled by the skier during the three minutes of recreation? b. What is the net displacement of the skier during the three minutes of recreation? c. What is the displacement during the second minute (from 1 min. to 2 min.)? d. What is the displacement during the third minute (from 2 min to 3 min.) -120 +80

Give me right solution with clear calculations
. Tourists arrive at the Manila Zoo at a rate of 250 vehicles per hour. But before entering the zoo, the vehicles must get a brochure and pay the entrance fee at the single entrance booth. If the vehicles can be serviced at a rate of 400 vehicles per hour, determine the percentage of time that the operator of the single entrance booth will be free.
Note: Round off your answers to the nearest thousandths. Only include the numeric value of vour answer without the unit (i.e. 0.123).

Answers

The percentage of time the operator of the single entrance booth will be free is approximately 38.462%.

To determine the percentage of time that the operator of the single entrance booth will be free, we need to calculate the service rate and the arrival rate. The service rate is given as 400 vehicles per hour, and the arrival rate is 250 vehicles per hour. The percentage of time the operator will be free can be calculated using the formula:

Free time percentage = (Service rate - Arrival rate) / Service rate * 100

Substituting the given values into the formula:

Free time percentage = (400 - 250) / 400 * 100

= 150 / 400 * 100

= 0.375 * 100

= 37.5%

Rounding off the answer to the nearest thousandths, the percentage of time the operator of the single entrance booth will be free is approximately 38.462%.

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Which occurrence would lead you to conclude that lights are connected in a series circuit?


A. When one bulb burns out, all the other lights stay lit.

B. When one bulb burns out, a circuit breaker is tripped.

C. When one bulb burns out, all the lights go out.

D. When one bulb burns out, a small section of lights goes out.

Answers

Answer:

A. When one bulb burns out, all the other lights stay lit.

Answer: C.. all bulbs go out.

Explanation:

how many orbitals are in the 5th principal energy level

Answers

Answer:

25

Explanation:

(1 + 3 + 5 + 7 + 9) orbitals = 25 orbitals

soap bubbles can display impressive colors, which are the result of the enhanced reflection of light of particular wavelengths from the bubbles' walls. for a soap solution with an index of refraction of 1.29, find the minimum wall thickness that will enhance the reflection of light of wavelength 729 nm in air.

Answers

Soap bubbles reflect certain wavelengths of light, find minimum wall thickness for enhanced reflection of 729 nm light.

When light passes through a material with a higher refractive index than air, such as soap solution, it can be reflected back with greater intensity.

The thickness of the soap bubble's wall determines which wavelengths of light are reflected more efficiently.

To find the minimum wall thickness for enhanced reflection of 729 nm light, we can use the equation for constructive interference:

2nt = mλ, where n is the refractive index of the soap solution, t is the wall thickness, m is the order of the interference, and λ is the wavelength of the light in air.

Solving for t, we get t = (mλ)/(2n), or t = (729 nm)/(2*1.29) = 224 nm for m=1.

Therefore, the minimum wall thickness for enhancing the reflection of 729 nm light in air is 224 nm.

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what is technology?

Answers

Answer:

Technology is the application of scientific knowledge to the practical aims of human life or, as it is sometimes phrased, to the change and manipulation of the human environment.

Please Mark it as brainlist answer.

The simplest answer is: the application of scientific knowledge for practical purposes, especially in industry.

To set up a good experiment to test whether hypothesis H is true or not, try to get evidence E such that:
Select one:
a.
The value of P(E | H) is higher than the value of P(E | ~H)
b.
The value of P(H) is higher than the value of P(~H)
c.
There is as big a difference between P(H) and P(E | H) as possible.
d.
There is as big a difference between P(E | H) and P(E | ~H) as possible

Answers

To set up a good experiment to test whether hypothesis H is true or not, try to get evidence E such that there is as big a difference between P(E | H) and P(E | ~H) as possible. This means the correct option is d.

For a good experiment to test whether hypothesis H is true or not, it is necessary to gather the right evidence. This evidence should be such that there is as big a difference between P(E | H) and P(E | ~H) as possible.

P(E | H) and P(E | ~H) are the conditional probabilities of evidence E given hypothesis H and evidence E given not-H respectively. The difference between these two probabilities measures how well evidence E supports hypothesis H versus not H.

For example, suppose we want to test the hypothesis H: All dogs bark. To get evidence that there is as big a difference between P(E | H) and P(E | ~H) as possible, we can test this hypothesis by taking two groups of dogs. One group is the dogs that bark (group A) and the other group is the dogs that don't bark (group B).

Then, we can get evidence E, which is the number of dogs in group A that bark and the number of dogs in group B that bark. Using this evidence, we can calculate the conditional probabilities of evidence E given hypothesis H (P(E | H)) and evidence E given not-H (P(E | ~H)).

Finally, we can calculate the difference between P(E | H) and P(E | ~H). If this difference is large, then the evidence supports hypothesis H more than not H.

To set up a good experiment to test whether hypothesis H is true or not, it is necessary to gather the right evidence. This evidence should be such that there is as big a difference between P(E | H) and P(E | ~H) as possible.

For example, suppose we want to test the hypothesis H: All dogs bark. To get evidence that there is as big a difference between P(E | H) and P(E | ~H) as possible, we can test this hypothesis by taking two groups of dogs. One group is the dogs that bark (group A) and the other group is the dogs that don't bark (group B).

Then, we can get evidence E, which is the number of dogs in group A that bark and the number of dogs in group B that bark. Using this evidence, we can calculate the conditional probabilities of evidence E given hypothesis H (P(E | H)) and evidence E given not-H (P(E | ~H)).

Finally, we can calculate the difference between P(E | H) and P(E | ~H). If this difference is large, then the evidence supports hypothesis H more than not H.

Hence, it is important to get evidence that has a significant difference between P(E | H) and P(E | ~H) to set up a good experiment to test whether hypothesis H is true or not.

It is necessary to gather the right evidence to set up a good experiment to test whether hypothesis H is true or not.

Evidence E should be such that there is as big a difference between P(E | H) and P(E | ~H) as possible. The difference between these two probabilities measures how well evidence E supports hypothesis H versus not H. Therefore, option d is the correct answer.

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Help quick please thank u

Help quick please thank u

Answers

Answer:

I. 56

II. c is the speed of light in vacuum.

III. 385.180×10¯²⁷ Kg.

Explanation:

I. Determination of the value of p.

²³⁸₉₂U + ¹₀n —> ¹³⁹ₚBa + ⁹⁷₃₆Kr + 3 ¹₀n

92 + 0 = p + 36 + 3(0)

92 = p + 36

Collect like terms

92 – 36 = p

56 = p

Therefore, the value of p is 56

II. Determination of the meaning of c

ΔE = Δmc²

In the Einstein's equation above,

E => is the energy

m => is the mass

c => is the speed of light in vacuum.

III. Determination of the total mass of the element formed after the reaction.

From the reaction above, the elements formed after the reaction are:

Barium–139 and Krypton–97. Thus, we can obtain the total mass of the elements formed as follow:

Mass of Ba–139 = 232.560×10¯²⁷ Kg

Mass of Kr–97 = 152.620×10¯²⁷ Kg

Total mass =?

Total mass = mass of Ba–139 + mass of Kr–97

Total mass = 232.560×10¯²⁷ + 152.620×10¯²⁷

Total mass = 385.180×10¯²⁷ Kg

I need help with this science question...
What does an ecosystem's biodiversity tell you about its health?
pls help I need this answer now pls help.thanks...

Answers

A wide variety of producers, consumers, & decomposers can coexist in the ecosystem.

What leads to a decline in biodiversity?

The variety of all living creatures on our world, known as biodiversity, has been disappearing at an alarming rate in recent years. This is largely due to human activities such changing land use, pollution, and climate change.

How would you define biodiversity in plain English?

All living creatures and their interactions are represented by the term "biodiversity," which is short for biological diversity. Because of extinctions and the emergence of new species, biodiversity is always changing. Three types of diversity—species, genetic, and ecosystem—are frequently mentioned by scientists.

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HEYY! Please help!
Turn this Algebraic expression into a Verbal expression!
2(3j+5+8j)
Thank you! <33

Answers

Answer:

22J+10

Explanation:

that is it in verbal expression

THE
Ammeter
А
1
592
o
12
Р
А
er
1002
w
Circuit 2​

Answers

Answer:

child i dont even know the answer for this question

Explanation:

What is the estimated volume of the table tennis ball?

cm3

What is the estimated volume of the golf ball?

cm3

Answers

Answer:

The estimated volume of a standard table tennis ball is approximately 2.7 cm³.

The estimated volume of a standard golf ball is approximately 41.6 cm³.

Explanation:

Which statement about force is true?
A. It transfers energy only when one object touches another.
OB. It always makes objects move.
C. It only affects large objects.
D. It can act between objects that touch, or it can act at a distance.
SUBMIT

Answers

Answer: D

Explanation: I saw it in a bill nye video.

A:it transfers energy only when one object touches another

How does a change in the solar constant impact the absorption of shortwave radiation and the emission of longwave radiation by the earth-atmosphere system?.

Answers

Solar constant never change, and hence there is no change in shortwave as well as longwave radiation by the earth's atmosphere

Solar constant is the rate at which the solar energy from the sun intercepts the earth's surface. It's value is 1,338watts per square meter.

Long wave radiation is a type of radiation emitted from earth whose wavelength ranges from 4 to 30 micrometers. While shortwave radiation is the radiant energy which is produced by the sun whose wavelength ranges from infrared to ultraviolet through visible.

We know that solar constant never change (constant), and the amount of shortwave that reaches the earth's atmosphere is called solar constant. As the solar constant does not change, there will be no change in shortwave as well as longwave radiation by the earth's atmosphere.

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el,la,los,or lasamigos de Adela son de Puerto Rico. Which of the following is not a common type of hazardous mechanical motion?a) In-running nip pointsb) Transversingc) Shearingd) Reciprocating how many pounds are in 8 kilograms? 1kg = 2.2Ibs 8kg = ? Ibs Jeff adds 5 Xbox games to his collection but then has to give half of his collection away. He now has 8 Xbox games. How many Xbox games did Jeff originally have? Paul had a job during his summer vacation. He earned $8.75 per hour. He worked 20 hours per week for 8 weeks. How much money did Paul earn? The annual per capita consumption of bottled water was \( 33.2 \) gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 33.2 and a stand Solve the following problem:5x - 3 = 4x + 3A. x = 5B. x = 6C. x = 7 PLS HELP!!! WILL GIVE BRAINLIST!!!!! what canyon separates the western halves of oregon and washington? Read the following paragraph. How does sentence 3 develop the main idea of the paragraph? (5 points)Gertrude Belle Elion was born on Jan. 23, 1918, in New York City.She graduated from Hunter College in New York City with a degree in biochemistry in 1937.Unable to obtain a graduate research position because she was a woman, she took a series of jobs, including lab assistant, chemistry and physics teacher in New York City high schools, and research chemist.During this time she also took classes at New York University, where she earned a master's degree in 1941.Because she could not devote herself to full-time studies, Elion never received a doctorate. can someone help me with it? Write each expression so that all exponents are positive.xyz Make full sentences from the cues using the Present Perfect + Future Perfect or Future Simple.1.When / I / eat / this, I / need to do lots of exercise to burn off the calories2.When the school year / finish / we / do / about 300 hours of homework3.When I / save / enough money / I / start / my own business4.By the time you / send / those invitations, / the party / finish5.When / you / tidy / your room / I / give / you your pocket money Which statement best describes the distances between planets in the solar system?1. It has varying distances with no specific pattern.2. It stays the same for all planets in the solar system.3. It increases the farther you move from the sun.4. It decreases the farther you move from the sun. Which of the following statements is FALSE?a.In 1820 there were 11 free states and 11 slave states.b.The South wanted more slave territories and the North wanted more free territories.c.The Kansas-Nebraska Act made both the North and South happy.d.The Missouri Compromise made both the North and South happy.Please select the best answer from the choices providedABCD sucrose is the monomer of what A/lipids B)starchesC)carbohydratesD)proteinsE)sugar Elizabeth works for the lawn care company and earns $15 per day plus $35 for every lawn mows. Let x be the amount of lawns she mows and y be the total money she made for the day. Write the linear equation that models her total pay for the day. Using the information provided, how many money would she make if she mows eight lawns today? which expression is an equavalent expression of 12x+10+4y Whats the answer? ANSWER THIS NOW PLEASE Subtract -7a^2+3a-9 5a^2-6a-4