What is acceleration?​

Answers

Answer 1

Answer:

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Explanation:

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Related Questions

PLZ HELP, DUE TODAYYY!!!!!!​

Answers

Answer:

Explanation:

a. the sound energy is converted into electrical signals using diaphragm present in the microphone and these signals then reach to the speakers and then convert- ed back to sound. The electrical current generated by a micro- phone is very small and referred to as MIC-level; this signal is typically measured in millivolts.

b. Thermodynamics

A 1510 kg car is experiencing a 2650 N friction force from the road. What force must be applied to the car in order for the car to move forward with a constant velocity of 50.0 km/hr?

Answers

Answer:

The force that must be applied to maintain a constant velocity is equal o the friction force which is 2,650 N

The total force required from rest is (2,650·t + 20,972.[tex]\overline 2[/tex])/t N

Explanation:

The given data of the car in motion are;

The mass of the car, m = 1,510 kg

The force of friction from the road, [tex]F_f[/tex] = 2,650 N

When the car is moving at 50.0 km/hr, we have;

v = 50.0 km/hr = 250/9 m/s ≈ 13.88889 m/s

According to Newton's first Law of motion, a body will continue in a state of rest or in uniform motion along a straight line unless acted on by a force

The force acting on the car in motion = 2,650 N

When the car is moving at a constant velocity, the forces acting on the  car are in equilibrium and the net force is zero

Therefore;

The magnitude of the force that will keep the car moving at a constant velocity = The friction force of the road = 2,650 N

The direction of the force = In the direction of motion of the car

Where the time it takes the car to accelerate from rest to 50.0 km/hr = t seconds, we have;

The force required to move at a constant speed = 1,510 kg × (250/9 m/s - 0)/t s = 20,972.[tex]\overline 2[/tex]/t N

The total force required to move forward with a constant velocity of 50.0 km/hr becomes 20,972.[tex]\overline 2[/tex]/t N + 2,650 N = (2,650·t + 20,972.[tex]\overline 2[/tex])/t N

Where;

t = The time it takes the car to reach 50.0 km/hr from rest.

Why unit of pascal is called derived unit?​

Answers

Answer:

This is because it is derived from newtons and metres as shown in the expression;

Explanation:

[tex]pressure = \frac{force}{area} \\ P= \frac{F}{A} \\ P= \frac{newtons}{ {m}^{2} } \\ = pascals[/tex]

Answer:

Unit of pascal is called derived unit because it involves three fundamental units i.e.meter,kg,and second.

Explanation:

formula of pascal=kg/m/s^2

state and explain any effect on sensitivity of liquid in a glass thermometer (i) reducing the diameter of capillary tube​

Answers

Answer:

please give me brainlist and follow

Explanation:

The measuring sensitivity of liquid-in-glass thermometers increases with the amount of liquid in the thermometer. The more liquid there is, the more liquid will expand and rise in the glass tube. For this reason, liquid thermometers have a reservoir to increase the amount of liquid in the thermometer.

Force=k((q1q1)/r^2)

The force that one electrically charged object exerts on other charged objects can be calculated using Coulomb's law.
You can see this law here written in equation form. The q's represent the two charges, and the r the distance between
the charges. The constant kis 9109
Using this information, calculate the electric force exerted by a +2 coulomb charge on another +2 coulomb charge,
when the charges are 25 meters apart

A)1.44*10^11
B)5.76*10^11
C)8 Newton’s
D)64 Newton’s

Answers

Answer:

transferred from one object to another. Charged objects can exert forces on other charged ... Electric charge can be measured using the law for the forces between charges

The electric force exerted by the +2 C on another +2 C when at a distance of 25 m is 5.76×10⁷ N

Coulomb's law equation

F = Kq₁q₂ / r²

Where

F is the force of attraction K is the electrical constant q₁ and q₂ are two point charges r is the distance apart

How to determine the force Charge 1 (q₁) = 2 CCharge 2 (q₂) = 2 CElectric constant (K) = 9×10⁹ Nm²/C²Distance apart (r) = 25 mForce (F) =?

F = Kq₁q₂ / r²

F = (9×10⁹ × 2 × 2) / (25)²

F = 36×10⁹ / 625

F = 5.76×10⁷ N

Learn more about Coulomb's law:

https://brainly.com/question/506926

pls somebody help me quick

Answers

Answer:

greater than

Explanation:

A bowling ball is bigger than a golf ball and greater than means bigger.

A uniform 1.5 T magnetic field points north. If an electron moves perpendicular (90 degrees) with a speed of 2.5x10 ^7 m/s, through this field, what force (magnitude and direction) will act on it?

Answers

Answer:

i think its 470

Explanation:

Ganymede, the largest of Jupiter’s moons,
is also the largest satellite in the solar system. Find the acceleration of
gravity on Ganymede if a simple pendulum with a length of 1.00 m has a period
of 10.5 s

Answers

Answer:hereeee for pointssss only

Explanation:

The acceleration of gravity on Ganymede will be [tex]g=0.35\ \frac{m}{s^2}[/tex]

What will be the acceleration of gravity on Ganymede?

It is given that for a simple pendulum on Ganymede

Lenth= 1.00 m

the time period  T= 10.5 sec

The formula for a time period of simple pendulum will be

[tex]T=2\pi\sqrt{\dfrac{l}{g} }[/tex]

By rearranging the formula

[tex]g=l\times (\dfrac{2\pi}{T} )^2[/tex]

[tex]g=1\times (\dfrac{2\pi}{10.5} )^2=0.3577\frac{m}{s^2}[/tex]

[tex]g=0.3577\ \frac{m}{s^2}[/tex]

Thus the acceleration of gravity on Ganymede will be [tex]g=0.35\ \frac{m}{s^2}[/tex]

To know more about simple pendulums follow

https://brainly.com/question/26449711

A cart moving at 4.0 m/s has 44 J of kinetic energy. What is the cart's mass?

Answers

[tex]ke = \frac{1}{2} m {v}^{2} [/tex]

[tex]44 = \frac{m {4}^{2} }{2} \\ \frac{88}{16} = m \\ 5.5 = m[/tex]

Atmospheric pressure is measured by a device called

Answers

Answer:

barometer

Explanation:

Answer:

barometer

Explanation:

A student performed an experiment in the lab and discovered that the material used has a PH of 8.54. What is true about this material

a
it is a base
b
it is an acid
c
more information needed to know if the material is acid or base

Answers

Answer: b it’s an acid
I hope this helps
it’s B !!!! good job stay in school ❤️❤️

Which of these statements describes protons and electrons?

Answers

The correct option is: "none of these statements is true".

To find out the correct option among all the options, we need to know more about the electron and proton.

What is electron?Electron is the fundamental particle of an atom.It is negatively charged.It is also a quantum particle. So, it can't stay at a place according to uncertainty principle i.e. it can move.  What is proton?Proton is a fundamental particle of an atom present inside the nucleus.It's positively charged.It can move.

Thus, we can conclude that the option (e) is correct.

Learn more about electron and proton here:

https://brainly.com/question/894705

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When do the heavier elements finally form? Give a few example.

Answers

Answer:

Some of the universe's heavier elements are created by neutron star collisions. ... Light elements like hydrogen and helium formed during the big bang, and those up to iron are made by fusion in the cores of stars. Some heavier elements like gallium and bromine need something more, such as a supernova.

Explanation:

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A projectile is launched from the ground with an initial velocity of 12m/s at an angle of 30° above the horizontal. The projectile lands on a hill 7.5m away. The height at which the projectile lands is most nearly

Answers

Answer:

[tex]1.78\:\mathrm{m}[/tex]

Explanation:

Kinematics equations used:

[tex]v_f=v_i+at,\\\\\Delta y = v_it+\frac{1}{2}at^2,\\\\v_f^2=v_i^2+2a\Delta x[/tex]

Other equations used:

[tex]\Delta x =v_i\cdot t,\\\text{-basic trigonometry for right triangles},\\\text{-application of physics concepts}[/tex]

By finding the horizontal component of the projectile's initial launch, we can find how long it will take for the projectile to reach the hill.

Since the projectile is launched at 12 m/s 30 degrees above the horizontal, we can use basic trig for a right triangle to find the horizontal component of the launch:

[tex]\cos 30^{\circ}=\frac{x}{12},\\x=12\cos 30^{\circ}\approx 10.3923048454\:\text{m/s}[/tex]

Now we can use [tex]\Delta x =v_x\cdot t[/tex] to find the time it will take to reach the hill:

[tex]7.5=10.3923048454\cdot t,\\t=\frac{7.5}{10.3923048454}\approx 0.72168783648\:\text{s}[/tex]

To find the total flight time the projectile would take if it were to land back to the same height it started out with, we can use the following kinematics equation:

[tex]v_f=v_i+at[/tex]

We'll use basic trig for a right triangle again to find the vertical component of the velocity at launch:

[tex]\sin 30^{\circ}=\frac{y}{12},\\y=12\sin 30^{\circ}=6\:\text{m/s}[/tex]. (recall [tex]\sin 30^{\circ}=\frac{1}{2}[/tex])

Now plugging this value in:

*Note: the projectile will hit the ground with a vertical velocity equal in magnitude but opposite in direction than the projectile's initial vertical velocity at launch

[tex]-6=6+(-9.8\cdot t),\\t=\frac{-12}{-9.8},\\t=1.22448979592\:\text{s}[/tex]

^This is the total flight time the projectile would take if it were to land back to the same height it started with. Since acceleration is constant, we can divide this time by two to find the time it would take to reach maximum height.

[tex]1.22448979592\div 2=0.61224489795\:\text{s}[/tex]

Thus, it will take [tex]0.61224489795\:\text{s}[/tex] to reach maximum height, meaning that it will take [tex]0.72168783648 - 0.61224489795=0.10944293853\:\text{s}[/tex] to land on the hill after reaching maximum height. Now that we've found this, we can use the following kinematics equation to find the vertical displacement from the projectile's max height to the hill:

[tex]\Delta y =v_it+\frac{1}{2}at^2[/tex]

At maximum height, the projectile's vertical velocity will be zero. Therefore, [tex]v_i=0[/tex] and we have:

[tex]\Delta y =\frac{1}{2}at^2[/tex]

Plugging in values , we have:

[tex]\Delta y =\frac{1}{2}\cdot 9.8\cdot 0.10944293853^2=0.05869100829\:\text{m}[/tex]

This means that the hill is [tex]0.05869100829\:\text{m}[/tex] lower than the max. height the object will reach.

To find the height of the hill from the ground, we will use the following kinematics equation:

[tex]v_f^2=v_i^2+2a\Delta x,\\-6^2=0+2\cdot-9.8\cdot\Delta x,\\36=-19.6\Delta x,\\\Delta x =\frac{36}{-19.6},\\\Delta x =-1.83673469388\:\text{m}[/tex]

Therefore, the max. height that the object will reach is [tex]1.83673469388\:\text{meters}[/tex].

Thus, the hill's height is [tex]1.83673469388-0.05869100829=1.77804368559\:\text{m}\approx\boxed{1.78\:\mathrm{m}}[/tex].

An object is 15.0 cm from a convex lens. Its image is 12.0 cm from the lens on the other side. What is the focal length of the lens?

Question 22 options:

1.25 cm


8.6 cm


6.67 cm


27.0 cm

Answers

Answer:

6.67

Explanation:

A ray of light passes from air into cubic zirconia at an angle of 56.0° to the normal. The angle of
refraction is 22.00°.
What is the index of refraction of cubic zirconia?

Answers

Answer:

η = 2.2

Explanation:

The index of refraction is given by the following formula:

[tex]\eta = \frac{Sin\ \theta_i}{Sin\ \theta r}[/tex]

where,

η = index of refraction of cubic zirconia = ?

[tex]\theta_i[/tex] = angle of incidence = 56°

[tex]\theta_r[/tex] = angle of refraction = 22°

Therefore,

[tex]\eta = \frac{Sin\ 56^o}{Sin\ 22^o}\\\\\eta = \frac{0.829}{0.375}[/tex]

η = 2.2

A child on a sled has a combined mass of 97 kg. At the top of a 3.1 meter hill, the sled has a velocity of 8 m/s. Assuming there is no friction, what would the velocity of the child and sled be when they reach the top of a different 1.2 meter hill?

Answers

Answer:

Explanation:

This is an energy conservation problem in that the total energy available to a system s constant trhoughout the whole problem. That is, in equation form:

TE = PE + KE. This is a bit of a problem due to sig figs here, but I will keep with the rules for them all the way up til the end of the problem (I'll tell you when I veer away from the rule and why I did when I get there).

We first need to find the total energy available to the system and then use that value throughout the rest of the problem.

TE = PE + KE where

PE = mgh (mass times gravity times height of the object) and

KE = [tex]\frac{1}{2}mv^2[/tex] (one-half times the mass of the object times the square of the velocity of the object). We solve for PE first, rounding to the correct number of sig figs:

PE = 97(9.8)(3.1) and

PE = 2900 J (2 sig figs here since all the numbers given have 2 sig figs in them). Now for KE

[tex]KE=\frac{1}{2}(97)(8.0)^2[/tex] which, to 2 sig figs (notice I added a .0 to the 8), is

KE = 2200. This means that the total energy available to the sled throughout the whole trip is

TE = 2900 + 2200 so

TE = 5100 J

Now for the second part of the problem, the sled is at a different height so the PE is different, and we are asked to find the velocity at the top of this second hill. The total energy equation then is

5100 = PE + KE. Solving for PE first:

PE = (97)(9.8)(1.2) and, to 2 sig figs:

PE = 82. Now for the KE:

[tex]KE=\frac{1}{2}(97)v^2[/tex]. Plugging all of that into the total energy equation gives us:

[tex]5100=82+\frac{1}{2}(97)v^2[/tex] and isolating the v:

[tex]v=\sqrt{\frac{2(5100-82)}{97} }[/tex] and this is where I veer away from the sig figs. Doing the subtracting first, as we should, means that we would round to the hundreds place. Since the least significant place in the number 82 is the tens place and the least significant place in the 5100 is in the hundreds place, we round to the hundreds place. But I didn't keep to this rule because I'm not sure how adamant your physics teacher is about sig figs. I'll give you the answer that I would expect from my students (the right one) after I give you this one. I just simply subtracted 5100 - 82 and used the answer the calculator gave me which was 5018:

[tex]v=\sqrt{\frac{2(5018)}{97} }[/tex] gives us that the velocity at the top of the 1.2 meter hill is

10.2 m/s.

Doing this the right way, using the rules for sig figs properly:

[tex]v=\sqrt{\frac{2(1500)}{97} }[/tex] gives us, to 2 sig figs,

v = 1.0 × 10¹ m/s

Question 3.Two forces are acting on a 30-kg object, 200 N up and 300 N

down. What is the magnitude and direction of its acceleration?

A. It is 100 m/s2 upward,

B. It is 100 m/s2 downward.

C. It is 3 m/s2 upward.

D. It is 3 m/s2 downward.

Answers

Answer:

It is 3 m/s² downward.

Explanation:

The mass of an object, m = 30 kg

Upward force, F = 200 N

Downward force, F' = -300 N

We need to find the magnitude and direction of its acceleration.

Net force = F+F'

= 200+(-300)

= -100 N

We know that,

Force, F = ma, a is acceleration of the object

[tex]a=\dfrac{F}{m}\\\\a=\dfrac{-100}{30}\\\\a=-3.33\ m/s^2\approx -3\ m/s^2[/tex]

Hence, the acceleration is -3 m/s² and it is acting in the downward direction.

A submarine is at an ocean depth of 3.00 km.
(a) Calculate the absolute pressure at this depth. Assume that the density of water is 1.025 ✕ 103 kg/m3 and that atmospheric pressure is 1.01 ✕ 105 Pa.
Pa
(b) Calculate the total force exerted at this depth on a circular submarine window with a diameter of 35.0 cm.
N

Answers

Answer:

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Explanation:

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sjksjsosjsnshf ruor uw eigen website aanmaken r y fav u can u to uf the owner u will tu tutururu ba sa inyo ay walang naging y rin h results ry from y yifuirfjofjkrjirhieifr Fu t I

Ms Jo Jo rubbed two balloons with a piece of wool. What will happen when the balloons are brought near each other?

Answers

It will creat a static charge because rubbing the balloons together creates static electricity

A traveler at Newark airport pulls his 294N suitcase with constant velocity to the check-in counter applying a force of 159N at an angle of 37 degrees with the horizontal. Calculate the Normal force, frictional force and the coefficient of friction between the suitcase and the airport floor.

Answers

Answer:

N = 198.3 N,  fr = 126.98 N and    μ = 0.64

Explanation:

For this exercise we must use the translational equilibrium condition.

Let's set a reference system with the x-axis horizontally and the y-axis vertical. Let's use trigonometry to decompose the applied force

      cos θ = Fₓ / F

      sin θ = F_y / F

      Fₓ = F cos θ

      F_y = F sin θ

      Fₓ = 159 cos 37 = 126.98 N

      F_y = 159 sin 37 = 95.69 N

Y axis  

    N + F_y - W = 0

    N = W - F_y

    N = 294 - 95.69

    N = 198.3 N

X axis

    Fₓ -fr = 0

     Fₓ = fr

     fr = 126.98 N

the expression for the friction force is

       fr = μ N

       μ = fr / N

       μ = 126.98 / 198.3

       μ = 0.64

[tex] \underline{ \text{QUESTIONS}} : [/tex]
1. Write any three applications of electromagnetic waves. Complete the given ray diagram [ See the attached picture ]

2. The power of a bulb of car is 100 W. If 5A current flows through the filament of the bulb , calculate the voltage of the battery used in the car [ Ans : 20 V ] Please show your workings!

~Random/Irrelevant answers will be reported! ​

Answers

Answer:

Solution given:

any three applications of electromagnetic waves are:

Used for cooking purpose in microwave.Used in RADAR system for aircraft navigation.Used in communication.

2.

Solution given;

power [P]=100W

Current [I]=5A.

Voltage [V]=?

we have

P=IV

100=5*V

V=[tex] \frac{100}{5} [/tex]=20V

the voltage of the battery used in the car is 20V.

Answer:

Explanation:

1. Electromagnetic waves are used to broadcast radio and TV signals. It is also used for wireless charging cell phones. Cell phone itself uses electromagnetic waves for its cell signal.

See attached drawing for ray diagram.

2. Given: the power of a bulb of car is 100 W and 5A current flows through the filament of the bulb.

Power of a bulb is given by voltage * current.

So 100W = voltage * 5A

Voltage = 100/5 = 20V

Which conclusions about alcohol and teen driving are supported by the data provided? Check all that apply. Rates of drinking and driving increased significantly between 2004 and 2014. Approximately 22 percent of teens admitted to driving after drinking in 2004. Fewer teens admitted to drinking and driving in 2013 than in 2004. In 2013, about one in five teens admitted to riding with a driver who had been drinking.

Answers

Answer: • Fewer teens admitted to drinking and driving in 2013 than in 2004.

• In 2013, about one in five teens admitted to riding with a driver who had been drinking.

Explanation:

The conclusions about alcohol and teen driving that are supported by the data provided will be:

• Fewer teens admitted to drinking and driving in 2013 than in 2004.

• In 2013, about one in five teens admitted to riding with a driver who had been drinking.

Other options are incorrect as the conclusion wasn't gotten from the data that was orovufed

Answer:

Fewer teens admitted to drinking and driving in 2013 than in 2004.

In 2013, about one in five teens admitted to riding with a driver who had been drinking.

Explanation:

A baseball is thrown at a 22.5° angle and an initial velocity of 65 m/s. What will be its horizontal
and vertical velocity?

Guys pls someone answer my question I have an exam and this question has 5 marks

Answers

Answer:

Horizontal component = 60.05 m/s

vertical component = 22.96 m/s

Explanation:

cosine(angle) = adjacent / hypotenuse or  horizontal / angled velocity

angled velocity * cosine (angle) = horizontal velocity

65 m/s * cosine(22.5) = 60.05 m/s

sine(angle) = adjacent/ hypotenuse or vertical/ angled velocity

angled velocity * sine (angle) = vertical velocity

65m/s sine(22.5) = 22.96 m/s

can anyone help me please​

Answers

Answer:

Gravity.

Rocket ships.

Ball.

Basketball.

Explanation:

Gravity has to do a lot with air. It puts the planets in there area.

Rocket Ship has to do a lot with air. If i'm right, they calculate the area, weather, about the air.

A ball gets throwed in the air, which gravity comes into place.

Basketball is also a similar example to a ball.

When light is incident on a boundary between two mediums, it often slows
down or speeds up. When it does this, the path the light travels can change.
This is called:
A. diffraction
B. reflection.
c. translocation.
D. refraction

Answers

Answer:

the answer is

D.refraction

How do we calculate efficiency?

Answers

Explanation:

Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output ("product") produced per the amount C ("cost") of resources consumed.

i dont know what the answer really is but this is what i think


Calculate the critical angle for Zircon which has a refractive index of n = 2*

Answers

Answer:

Given that refractive index of the material is √2. i.e. n = √2. Hence, critical angle for the material is 45°

Mercury -197 is used for kidney scans and has a half-life of 3 days. If the amount of mercury-197 needed for a
study is 1.0 gram and the time allowed for shipment is 15 days, how much mercury-197 will need to be ordered?

Answers

Answer:

32 g

Explanation:

Applying,

R = (R')2ᵃ/ⁿ............... Equation 1

Where R = Amount of mercury-197 needed to be ordered, R' = amount of mercury-197 needed for the study, a = time allowed for shipment, n = half life.

From the question,

Given: R' = 1 g, a = 15 days, n = 3 days

Substitute these values into equation 1

R = 1(2¹⁵/³)

R = 1(2⁵)

R = 32 g

The different between capactance wnd capacitor

Answers

Answer:

The parallel plate capacitor is the simplest form of capacitor. ... The property of a capacitor to store charge on its plates in the form of an electrostatic field is called the Capacitance of the capacitor. Not only that, but capacitance is also the property of a capacitor which resists the change of voltage across it.

Explanation:

credits :- adultsscience

Explanation:

Capacitance exists wherever conductive material is separated by insulating material. 

Capacitive structures have the ability to store energy as an electric field;

when a capacitive structure has been designed as an electrical component that has a specified amount of capacitance, it is called a capacitor.

Capacitance symbol is C

you can get a meter for Capacitance

Capacitance formula is C = ε(A/d) where ε represents the absolute permittivity of the dielectric material being used.

simple piece of wire has very low capacitance

Other Questions
Which could be the area of the base of the triangular prism?[Not drawn to scale)6 ft10 ft12 ft20 ft Tricia's doctor is giving her information about her heart rate, blood pressure, and brainwaves. She is using this data to learn to control her physical processes with her mind.What is Tricia practicing?biofeedbackmeditationhypnosisO psychoactive drug useNext A national health organization warns that alcohol use among middle school students is on the rise. Concerned, a local health agency randomly and anonymously surveys 110 of the middle school students in its city. 21 of them report having been intoxicated. Create a 90% confidence interval. Find p-hat. (p -hat = x/n) Reading The Outsiders. What do all these words mean?Fake-outBumPack a punchBlowinWeedMade (as in have it made)Stick up forItchingHold-upTake onDoughAll overPretty bad ofCool itFuzzBeltedDigCoolBoozehoundCancer stickJumpedBopperTrapBuggin sustantivo abstracto de labor y de famoso 10pts PLS HELP!!! Who were the leaders of the United States and the USSR at the start of the Cold War?A.Franklin Roosevelt and Joseph StalinB.Harry Truman and Joseph StalinC.Franklin Roosevelt and Nikita Khrushchev D.Harry Truman and Nikita Khrushchev Who was the audience for White Man's Burden ? What is the means of salvation that Christ established on earth ? What is 100 percent of 39 Which is the best way to complete the text?The city's infrastructure favors motorists over _______ more prevalent than bicycle lanes.parking is fara. Cyclists; curbsideB. Cyclists, but curbsideC. Cyclists, consequently, curbside Antwon is building his technical writing portfolio.He created the following checklist: check whether any part of the portfolio violates a a nondisclosure agreement. check whether the content in the portfolio corresponds to the job requirements. make sure that I am clear about my role in creating each document in the portfolio. Which element of the portfolio does this checklist best apply to? A.Cover letter B.resume C.templatesD.writing samplesE.task summaries To calculate the percentage of people who have a particular allele population studies are conducted to collect data.true or false This apparent path of the Sun through the sky is caused byA) the Sun's rotation on its axisB) the Sun's revolution around EarthC) Earth's revolution around the SunD) Earth's rotation on its axis WILL GIVE BRAINLIEST+100 POINTS!!! HIGH SCHOOL GEOMETRY!!SOLVE NUMBER 12 (Simplify):6/2-24/12+248-38 HURRY PLS !!!Which statements about the graph of the function f(x) =2x^2 - x - 6 are true? Select two options.The domain of the function is {xlx > 1/4}The range of the function is all real numbers.The vertex of the function is (1/4, -6 1/8).The function has two x-intercepts.The function is increasing over the interval (-6 1/8, ). Find the value of x such that the data set has the given mean. A. Use this diagram of a right triangle to derive and prove the Pythagorean Identity based on sin 0 and cos 0. Start withwhat you know about the relationship among a (adjacent side), o (opposite side), and h (hypotenuse). Using the diagramand the labeled components, define sine and cosine. Incorporate these definitions in your equation. In your response,include all steps and calculations.hB. With respect to 0, the adjacent side of the triangle has a length of 12 cm and the opposite side has a length of 10 cm.Find the values of the hypotenuse, h, 0, and e. Then, use these values to confirm the Pythagorean Identity for thistriangle. How are unicellular organisms important? Provide one example.WRITE IN YOUR OWN WORDS PLZ AND NO LINKS TOO ! Thank you! Dayquan decided to run some laps around the track. If the diameter of the track is 75 feet, how far around the track did he run?