Victor has 100 trading cards, each with a distinct power level between 101 and 200 inclusive. Whenever he heads out, he always randomly selects 21 cards to bring with him just in case he meets a fellow collector. Prove that no matter which 21 cards he brings, Victor will always be able to select 4 of those cards that exhibit the following property:
Let the average power level of all 4 cards bep. The cards can be split into two pairs, each of which also has an average power level of p.

Answers

Answer 1

Answer:

Victor will always be able to select 4 of those cards with the following property

Explanation:

Number of trading cards = 100

victor selects 21 cards

let the 4 cards be labelled : A,B,C and D

The average power level of : A,B,C,D = ( A + B + C + D )/ 4 = P

let the two pairs be : ( A + B ) and ( C + D )

note: average power of each pair = P  and this shows that

( A + B ) = ( C + D ) for Victor to select 4 cards out of the 21 cards that exhibit the same property

we have to check out the possible choices of two cards out of 21 cards yield distinct sums.

= C(21,2)=(21x20)/2 = 210.

from the question the number of distinct sums that can be created using 101  through 200 is < 210 .

hence it is impossible to get 210 distinct sums therefore Victor will always be able to select 4 of those cards


Related Questions

Determine the electrical force of attraction between two balloons
that are charged with the opposite type of charge but the same
quantity of charge. The charge on the balloons is 6.0 x 10-7 C and they
are separated by a distance of 0.50 m.

Answers

Answer:

F=1.3x10^-2N

Explanation:

Fe= k(6x10^-7C)^2/(0.5)^2

Electrical force of attraction between the balloons is F=1.3x10^-2N

The electric force of attraction between two balloons should be F=1.3x10^-2N.

Calculation of the electric force;

Since The charge on the balloons is 6.0 x 10-7 C and they are separated by a distance of 0.50 m.

So, here the electric force is

Fe= k(6x10^-7C)^2/(0.5)^2

F=1.3x10^-2N

hence, The electric force of attraction between two balloons should be F=1.3x10^-2N.

Learn more about force here: https://brainly.com/question/19848845

A pair of glasses are dropped from the top of a 32.0 m high stadium. A pen is dropped 2.00 s later. How high above the ground is the pen when the glasses hit the ground? (Disregard air resistance. a = -g = -9.81 m/s2.)

Answers

Answer:

Explanation:

the distance have the following relation:

d = (1/2)gt2

D=32.0 m

t =√ (2D/g) = √(2*32.0m/9.8m/s2) = 2.56s

it take 2.56s from the glasses to hit the ground

when the glasses hit the ground, the pen only travel Δt =2.56s - 2.00s = 0.56s

x = (1/2)g(Δt)2 = 0.5*9.8m/s2*(0.56s)2 = 1.54 m

the pen only travel 1.54m

so the pen is above the ground 32.0m - 1.54m = 30.46m

The pen is 30.46m above the ground. when the glasses hit the ground. It is represented by x.

What is the height?

Height is a numerical representation of the distance between two objects or locations on the vertical axis.

The height can refer to a physical length or an estimate based on other factors in physics or common use. |

The given data in the problem is;

h is the height from the top of a stadium = 32.0 m

t is the time period when the pen is dropped later =  2.00 s

x is the height above the ground

a is the air resistance. a = -g = -9.81 m/s²

From the second equation of motion;

[tex]\rm H =ut+\frac{1}{2} gt^2 \\\\ \rm H =\frac{1}{2} gt^2 \\\\ \rm t = \sqrt{\frac{2H}{g} } \\\\ \rm t = \sqrt{\frac{2 \times32.0 }{9.81} } \\\\ \rm t =2.56\ sec[/tex]

When the glasses fall to the ground, the pen only travels a short distance;

[tex]\rm \triangle t = 2.56 -2.00 \\\\ \rm \triangle t = 0.56 \ sec[/tex]

So the pen travel the distance;

[tex]\rm h= \frac{1}{2} g \triangle t^2 \\\\ \rm h= \frac{1}{2} \times 9.81 (0.56)^2 \\\\ h=1.54 \ m[/tex]

The pen above the ground is found as;

[tex]\rm x = H-h \\\\ \rm x = 32.0-1.54 \\\\ \rm x =30.46 \ m[/tex]

Hence the pen is 30.46m above the ground. when the glasses hit the ground.

To learn more about the height refer to the link;

https://brainly.com/question/10726356

What is the force of a 12 kg object that is accelerating 6 m/s

Answers

We are given:

Mass of object (m) = 12 kg

acceleration (a) = 6 m/s²

Solving for the Force:

From newton's second law of motion:

F = ma

replacing the variables

F = 12*6

F = 72N

What does the principle of superposition help scientists determine?
A) The super powers of a rock layer
B) The exact and absolute age of a rock layer
C) The relative age of a rock layer
D) The position of a fossil

Answers

Answer:

B

Explanation:

the exact and absolute age of a rock layer

Answer:

The relative age of a rock layer.

Explanation:

The answer is C.

A car with a mass of 2,000 kg travels a distance of 400m as it moves from one stoplight to the next. At its fastest , the car travels 18m/s. What is the kinetic energy at this point ?

Answers

Answer: KE= 324,000

Explanation: I hope that this helps! -_-

Answer:

324,000

Explanation:

A car with a mass of 1500kg is traveling at a speed of 30m/s. What force must be applied to stop the car in 3 seconds?

Answers

Answer:

The answer is 15,000 N

Explanation:

To find the force given the mass , velocity and time can be found by using the formula

[tex]f = \frac{m \times v}{t} \\ [/tex]

where

m is the mass

v is the velocity

t is the time

From the question

m = 1500 kg

v = 30 m/s

t = 3 s

We have

[tex]f = \frac{1500 \times 30}{3} = \frac{45000}{3} \\ [/tex]

We have the final answer as

15,000 N

Hope this helps you

What must be true if a wave's wavelength is short?
A
Its frequency is low.
B
It does not carry energy.
с
Its frequency is high.
D
The waves are visible.

Answers

C because it’s frequently is high

Answer:

im sure its A

Explanation:

the radius of the earth social

Answers

6,371km is the radius of the earth

how much power is used if it takes frank (a 450 N boy ) 3 seconds to run 2 meters ?

Answers

Answer:

300

Explanation:

450Newton × 2Meter ÷ 3sec

A diffusion couple, made by welding a thin onecentimeter square slab of pure metal A to a similar slab of pure metal B, was given a diffusion anneal at an elevated temperature and then cooled to room temperature. On chemically analyzing successive layers of the specimen, cut parallel to the weld interface, it was observed that, at one position, over a distance of 5000 nm, the atom fraction of metal A, NA, changed from 0.30 to 0.35. Assume that the number of atoms per m3 of both pure metals is 9 x 10^28. First determine the concentration gradient dnA/dx. Then if the diffusion coefficient, at the point in question and annealing temperature, was 2 10^-14 m^2/s.

Required:
Determine the number of A atoms per second that would pass through this cross-section at the annealing temperature.

Answers

Answer:

The value  is    [tex]H  =  18*10^{2} \  Atom / sec  [/tex]

Explanation:

From the question we are told that

  The atom fraction of metal A at point G is [tex] A  =  0.30 \ m[/tex]

   The atom fraction of metal  A at a distance 5000nm from G is  [tex]A_2 = 0.35[/tex]

   The number of atoms per [tex]m^3[/tex] is    [tex]N_h =  9 * 10^{28}[/tex]

    The diffusion coefficient is  [tex]D =   2* 10^{-14 } m^2/s[/tex]

Generally of the concentration of atoms of metal A at G is  

       [tex] N_A = A * N_h [/tex]

=>    [tex] N_A =  0.3  * 9 * 10^{28}[/tex]

=>     [tex] N_A =   2.7 * 10^{28} 2.7 atoms/m^3[/tex]

Generally of the concentration of atoms of metal A at a distance 5000nm from G is  

       [tex]D =  0.35 *9 * 10^{28}[/tex]

=>     [tex]D =  3.15 * 10^{28} \  atoms / m^3[/tex]

The concentration gradient is mathematically represented as

   [tex]\frac{dN_A}{dx}  =  \frac{(3.15 - 2.7) * 10^{28} }{5000nm - 0 }[/tex]

=> [tex]\frac{dN_A}{dx}  =  \frac{(3.15 - 2.7) * 10^{28} }{[5000 *10^{-9}] - 0 }[/tex]  

=>   [tex]\frac{dN_A}{dx}  = 9 * 10^{20} / m^4[/tex]  

Generally the flux of the atoms per unit  area according to Fick's Law  is mathematically represented as

       [tex]J =  -D* \frac{d N_A}{dx}[/tex]

=>    [tex]J =  -2* 10^{-14 * 9 * 10^{20} [/tex]

=>    [tex] J =  18*10^{6}\   atoms\ crossing\ /m^2 s  [/tex]

Generally if the cross-section area is [tex] a  =  1 cm^2 =  10^{-4} \  m^2[/tex]

Generally the number of atom crossing the above area  per second is mathematically is  

      [tex]H  =  18*10^{6}    *  10^{-4} [/tex]

=>    [tex]H  =  18*10^{2} \  Atom / sec  [/tex]

The volume of water in a water bottle, is about 398
g
cm
km/hr
Kg
g/mL
ml
km
m/s

Answers

Answer:

milliliters (ml)

Explanation:

millileters is the correct measurement for liquids

A car traveling at 32.4 m/s skids to a stop in 4.55 s. Determine the skidding distance of the car (assume uniform acceleration).

Answers

Answer:

x = 73.71 [m]

Explanation:

In order to solve this problem we must use two formulas of kinematics. It is important to make it clear that these formulate are for uniformly accelerated motion, i.e. with constant acceleration.

[tex]v_{f }= v_{i}-(a*t)[/tex]

where:

Vf = fnal velocity = 0

Vi = initial velocity = 32.4 [m/s]

t = time = 4,55 [s]

a = acceleration or desacceleration [m/s^2]

0 = 32.4 - (a*4.55)

a = 7.12 [m/s^2]

Note: it is important to clarify that the negative sign in the above equation is because the car stops and decreases its speed to zero, thus its final velocity is equal to zero.

Now using the following equation:

[tex]x = x_{o} + (v_{i}*t)-(\frac{1}{2} )*a*t^{2}[/tex]

where:

xo = initial distance = 0

x = final distance [m]

Therefore we have:

x = 0 + (32.4*4.55) - (0.5*7.12*4.55^2)

x = 73.71 [m]

1. According to its computer, a rocket launched
traveled 1200 m, had an average speed of 100.0
m/s. How-long did the trip take?

Answers

Answer:

I think it's = 12 seconds

Explanation:

the formula for speed is:

speed=[tex]\frac{distance}{time}[/tex] SO, time is equal to:

time=[tex]\frac{distance}{speed}[/tex]

(sub the numbers in the formula)

distance=1200m, speed=100m/s

time=[tex]\frac{1200}{100}[/tex]

=12 seconds

One student runs with a velocity of +10 m/s while a second student runs with a velocity of –10 m/s. Which student has the faster velocity? Why?

Answers

Answer:

The one with the faster velocity is the one with a velocity of -10m/s

How far will a 600 kg boat travel in 12 s if there is a constant 900 N force on it and it starts from rest?

Answers

Answer:

108 metres

Explanation:

Given

[tex]Force = 900N[/tex]

[tex]Mass = 600kg[/tex]

[tex]Time = 12s[/tex]

Required

Determine the distance moved

First, we need to determine the acceleration.

[tex]Force = Mass * Acceleration[/tex]

[tex]900N = 600kg * a[/tex]

Solve for a

[tex]a = 900/600[/tex]

[tex]a = 1.5m/s^2[/tex]

Next, we determine the distance using:

[tex]S = ut + \frac{1}{2}at^2[/tex]

Since it starts from rest,

[tex]u = 0[/tex]

[tex]t = 12[/tex]

[tex]a = 1.5[/tex]

So:

[tex]S = 0 * 12 + \frac{1}{2} * 1.5 * 12^2[/tex]

[tex]S = \frac{1}{2} * 1.5 * 144[/tex]

[tex]S = \frac{1}{2} * 216[/tex]

[tex]S = 108m[/tex]

If Mary runs 5 miles in 50 minutes, what is her speed with the correct
label?

Answers

1 mile = 10 mins or 1 mile takes 10 mins to run

1
2
3
4
5
6
8
9
10
Dressing appropriately for exercise includes
A. wearing the same clothes for all exercises
B. choosing dark colored clothing when exercising at night
C. wearing sunscreen when exercising outside
D. making sure you wear the best brand-name clothes
Please select the best answer from the choices provided.
A
B.
C.
D.

The answer is C.

Answers

Answer:

the answer is C

Explanation:

you said its c

A person has a mass of 1000g and an acceleration of 20 m/s/s. What is the force on the person

Answers

Answer:

20000

Explanation:

Newtons Second law states that the force acting on an object is equal to its mass times its acceleration, f=ma. To solve for force, plug in your values for m and a, and then solve. f = (1000)*(20) = 20000

Matching type. Send help please. ASAP!

Answers

Answer:

46-D

47-C

48-F

49-A

50-B

I am not very sure I am right about those answers though.

Grass and plants get energy from
А
the sun.
B
eating food.
с
windmills.
D
electrons.

Answers

A is the answer for that question

Answer:

From the Sun

Explanation:

Plants can't eat any food. They don't ue or need windmills to get energy. They are plants so they don't have any electrons. The only way that they can recive energy from is the sun. Sometimes plants die when they don't get enough sun because they don't have any energy to live.

What is the approximate weight of a 400 kg object?

Answers

Answer:

881.84905 LBS

Explanation:

ThErE :p

3922.66 newtons.

This is an exact amount, to get newtons form kg, multiply by 9.8, or in this case, 10.

This gives you 4000 newtons

3. A wye-connected load has a voltage of 480 V applied to it. What is the voltage dropped across each phase?

Answers

Answer:

[tex]E_s = 277.13V[/tex]

Explanation:

Given

[tex]Load\ Voltage = 480V[/tex]

Required

Determine the voltage dropped in each stage.

The relation between the load voltage and the voltage dropped in each stage is

[tex]E_l = E_s * \sqrt3[/tex]

Where

[tex]E_l = 480[/tex]

So, we have:

[tex]480 = E_s * \sqrt3[/tex]

Solve for [tex]E_s[/tex]

[tex]E_s = \frac{480}{\sqrt3}[/tex]

[tex]E_s = \frac{480}{1.73205080757}[/tex]

[tex]E_s = 277.128129211[/tex]

[tex]E_s = 277.13V[/tex]

Hence;

The voltage dropped at each phase is approximately 277.13V

An object is dropped from rest and falls freely 20 m to Earth. When is the speed of the object 9.8 m/s?

At the end of the first second of its fall
At the end of the first second of its fall

During the entire time of its fall
During the entire time of its fall

At no time is the speed 9.8 m/s
At no time is the speed 9.8 m/s

During the entire first second of its fall
During the entire first second of its fall

After it has fallen 9.8 meters

Answers

During the entire time of its fall because as soon as it falls that’s what the speed it will be until acted on by a outside force

why do some athletes get injuries before and after the game?

Answers

Answer:

they don't strech so they tear a muscle when they perform

Explanation:

What is the change in internal energy (in J) of a system that absorbs 0.523 kJ of heat from its surroundings and has 0.366 kcal of work done on it

Answers

Answer:

The change in internal energy of the system is 2,054 J

Explanation:

The first law of thermodynamics relates the work and the transferred heat exchanged in a system through internal energy. This energy is neither created nor destroyed, it is only transformed.

Taking into account that the internal energy is the sum of all the energies of the particles that the system has, you have:

ΔU= Q + W

where U is the internal energy of the system (isolated), Q is the amount of heat contributed to the system and W is the work done by the system.

By convention, Q is positive if it goes from the environment to the system, or negative otherwise, and W is positive if it is carried out on the system and negative if it is carried out by the system.

In this case:

Q= 0.523 kJ (because the energy is absorbed, this is,it goes from the environment to the system)W= 0.366 kcal= 1.531 kJ  (because the work is done on the system, and being 1 kcal= 4.184 kJ)

Replacing:

ΔU= 0.523 kJ + 1.531 kJ

Solving:

ΔU= 2.054 kJ = 2,054 J (being 1 kJ=1,000 J)

The change in internal energy of the system is 2,054 J

An object is dropped from a 45 m high building. At the same time, another object is thrown
upward with a velocity of 8.5 ms 1. How high above the ground will the two objects meet?

(With work please)

Answers

Answer:

-92.33 (meaning the objects will not meet above the ground).

Explanation:

We can use the kinematic equation displacement = initial velocity*time + 1/2*acceleration*time^2.

We can plug in the known values of the 2 objects into the equation, where t is the time and x is the displacement:

x = 0*t + 1/2*(-9.8)*t^2+45

x = 8.5*t + 1/2*(-9.8)*t^2

We need to first solve for t to solve for x. Since both equations are equal to x, we can set them equal to each other and solve for t:

0*t + 1/2*(-9.8)*t^2+45 = 8.5*t + 1/2*(-9.8)*t^2

-4.9*t^2 +45 = 8.5*t + -4.9*t^2

45 = 8.5*t

t = 45/8.5 ≈5.294

Now, we can plug t as 5.294 into any of the equations above to solve for x:

x = 0*5.294 + 1/2*-9.8*(5.294)^2+45 ≈ -92.33

That means, the objects will not meet above the ground.

if a ramp is 12 meters long has a mechanical advantage of 6 whats its height brainly HELPP!

Answers

Answer:

h = 2 m

Explanation:

Mechanical advantage of a ramp is given by :

MA = length of incline/height of incline

Length of the ramp, l = 12 m

MA = 6

We need to find the height of the ramp.

So,

height of ramp = length of incline/MA

h = 12/6

h = 2 m

So, the height of the ramp is 2 m.

a motor boat is traveling at 25 knots towards 340 degree on a river flowing at 20 knots towards 175 degrees. What is the actual speed of the boat as seen by a helicopter piolet hovering above?

Answers

Answer:

Vbx = 25 * cos 340 = 23.5 knot        x-component of boats speed

Vrx = 20 cos 175 = -19.9 knot        x-component of rivers speed

Vx = 3.58 knot      x-component of boat and river speed

Vby = 25 sin 340 = -8.55 knot    y-component of boat speed

Vry = 20 sin 175 = 1.74 knot    y-component of river speed

Vy = -6.81 knot     y-component of boat and river speed

V = (Vx^2 + Vb^2)^1/2 = (3.58^2 + 6.81^2)^1/2 = 7.69 knots

calculating light in physics

Answers

Formula: c = f where:
c = the speed of light = 300,000 km/s or 3.0 x 108 m/s.
= the wavelength of light, usually measured in meters or Ångströms (1 Å = 10-10 m)
f = the frequency at which light waves pass by, measured in units of per seconds (1/s).

An object moving 20 m/s
experiences an acceleration of 4 m/s' for 8
seconds. How far did it move in that time?
Variables:
Equation and Solve:

Answers

Answer:

We are given:

initial velocity (u) = 20m/s

acceleration (a) = 4 m/s²

time (t) = 8 seconds

displacement (s) = s m

Solving for Displacement:

From the seconds equation of motion:

s = ut + 1/2 * at²

replacing the variables

s = 20(8) + 1/2 * (4)*(8)*(8)

s = 160 + 128

s = 288 m

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Robin, who is a head of household and age 42, provides you with the following information from his financial records for 2019. Robin itemizes deductions. Regular income tax liability $142,125 PositiveAMT adjustments 30,000 AMT preferences 100,000 Taxable income 481,000 Calculate Robin's AMT for 2019. a.$12,636. b.$3,757. c.$12,032. d.$15,126. please I need help!!! Using information from the diagram, state one reason why the movement in the third image represents active transport which of the following is NOT a physical change to adolescence?A. Have erratic emotions and behaviors.B. Rapid increase in heigth and weigth.C. Sweat and oil glands become more active.D. Sudden increase in hormorone production. please someone help quick PLEASE HELP Line A is represented by the equation, y = 1/4x + 5 . (a) Write in slope-intercept form, the equation of a line that is steeper than line A. (b) Write in slope-intercept form the equation of a line that is a vertical shift down 4 units from line A. What are the Hudson's Bay Company, The Virginia Company, The PlymouthCompany, and The Massachusetts Bay Company examples of? (2 points)Economic partiesMercantilism groupChartered companiesO Trading corporation What were conditions like in Europe during the 800s? Can someone help me with this please!! Which of the following molecules may show a pure rotational microwave absorption spectrum: (i) H2, (ii) HCl, (iii) CH4, (iv) CH3Cl, (v) CH2Cl2? A _____ is a smaller image of a slide.templatetoolbarthumbnailpane ASAP I need help on this what is the chimestry Radiation transfers thermal energy through _________. Which accurately completes the statement? waves direct contact particles liquid movement True or False: Squires were servants to medieval peasants. HURRY!Cellular respiration and photosynthesis have similar equations. Which additional resource is part of photosynthesis, but not cellular respiration? sunlight nitrogen carbon water What is the definition of author's purpose?(1 point)the author's topic of the writingthe author's reason for writingthe author's attitude about the topicthe author's main ideaWhat is the definition of point of view?(1 point)the author's topicthe author's attitude toward the topicthe author's main ideathe author's reason for writingAn author's purpose for writing is to inform. How do writers accomplish this purpose?(1 point)by persuading readers to agree with their ideas and think or act differently as a resultby describing people, places, or events in an enjoyable wayby presenting facts to teach their readers about a topicby making readers understand their point of viewRead the following passage. Many people take in their daily dose of caffeine with the first cup of coffee or sips of soda. While a moderate amount of caffeine consumption is safe, experts warn that too much caffeine can pull too much water from a person's body and lead to dehydration. An elevated amount of caffeine can also affect sleep patterns and blood pressure. Make sure to enjoy the right amount of caffeine by following the recommended guidelines and staying below 400 milligrams of caffeine per day.What is the author's point of view?(1 point)Follow the recommended guidelines of daily caffeine consumption to maintain a healthy lifestyle.Dehydration can be avoided by increasing daily water consumption.People should not drink coffee or soda because both beverages contain too much caffeine.The right amount of water regulates functions of the body better than the right amount of caffeine. The following events pertain to James Cleaning Company: 1. Acquired $15,000 cash from the issue of common stock.2. Provided services for $6,000 cash.3. Provided $18,000 of services on account.4. Collected $11,000 cash from the account receivable created in Event 3.5. Paid $1,400 cash to purchase supplies.6. Had $100 of supplies on hand at the end of the accounting period.7. Received $3,600 cash in advance for services to be performed in the future.8. Performed one-half of the services agreed to in Event 7.9. Paid $6,500 for salaries expense.10. Incurred $2,800 of other operating expenses on account.11. Paid $2,100 cash on the account payable created in Event 10.12. Paid a $1,000 cash dividend to the stockholders.Required:Show the effects of the events on the financial statements using a horizontal statements model like the following one. In the Cash Flows column, use the letters OA to designate operating activity, IA for investing activity, FA for financing activity, NC for net change in cash and NA to indicate accounts not affected by the event. The first event is recorded as an example. (Enter any decreases to account balances and cash outflows with a minus sign 36% of what number is 64.8? The diagram of a living room is shown below. What fraction of the living room is covered by the rug? need done ASAP