I run a book club with $n$ people, not including myself. every day, for $365$ days, i invite three members in the club to review a book. what is the smallest positive integer $n$ so that i can avoid ever having the exact same group of three members over all $365$ days?

Answers

Answer 1

The smallest positive integer n so that you can avoid ever having the exact same group of three members over all 365 days is; 11

How to solve probability combination?

if we have n people and we want to do groups of 5, the total number of different combinations is:

ⁿC₅ = n!/((n - 5)!5!)

By using the Brute force method, we have;

If n = 5,

c = 5,

Thus;

C₅ = 5

If n = 6,

c = 6,

Thus;

C₅ = 6

If n = 7,

c = 7,

Thus

C₅ = 21

If n = 8,

c = 8,

Then;

C₅ = 56

Now, If n = 9,

C = 9!/((9 - 5)!5!)

C = 126

We want to find the smallest n such that c > 365. Thus, C = 126 is too small.

Let's try n = 11;

C = 11!/(6! * 5!) =  462

This is greater than 365 and so we need at least 11 members in the club.

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Related Questions

Which best describes the cold war? question 1 options: a battle over who would control the korean peninsula during the 1950s a struggle between the eastern bloc and the west that lasted 40 years a race between the soviet union and the united states to rebuild europe after wwii a fight to prevent the communist takeover of cuba

Answers

Answer:

A struggle between the Eastern Bloc and the West that lasted 40 years.

Why can’t the moon be eclipsed when it is halfway between nodes of its orbit?

Answers

Answer: Because the moon's orbit is at it's maximum deviation, meaning that it is leaving it's course from the sun's path, which would make the shadow fall way below or above the moon. So, because of that, the moon can't eclipsed.

Hope this helps!

A constant net force of 20 n is applied to a 32 kg car, causing it to speed up from 4. 0 to 9. 0 m/s. how long is the force applied?

Answers

Given :- Constant force, F = 20 NMass of Car = 32 kgInitial speed, u = 4 m/sFinal Speed = 9 m/s

To Find:-Duration for which force is appiled

Solution:-

[tex]\green{ \underline { \boxed{ \sf{Force,F= Mass \times Acceleration }}}}[/tex]

So,

[tex] \sf Acceleration,a = \frac{Force}{Mass}[/tex]

[tex] \sf \implies \frac{20}{32} [/tex]

[tex]\implies \frac{5}{8} m/s^2[/tex]

Now,

By first equation of motion -

[tex]\green{ \underline { \boxed{ \sf{v-u=at}}}}[/tex]

So,

[tex]\sf t = \dfrac{v-u}{a} [/tex]

where

v = final velocityu = initial velocitya = accelerationt = time duration

Putting Values -

[tex]\sf t = \dfrac{9-4}{ \dfrac{5}{8}} [/tex]

[tex]\sf t = \dfrac{5}{ \dfrac{5}{8}} [/tex]

[tex]\sf t = \cancel5 \times \dfrac{8}{\cancel{5}} [/tex]

[tex]\sf t = 8 \:seconds[/tex]

>>>Therefore, Force is applied for 8 seconds.

Lesson 16 solve problems with equations answer key

Answers

Based on the calculations, the value of x and y in this equation are both equal to 5.

What is a system of linear equations?

A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

Given the following data:

x + y = 10  .....equation 1.

x = 5.       .....equation 2.

How to evaluate an equation.

In order to evaluate the given mathematical equation, we would substitute equation 2 into equation 1 as follows:

[tex]5+y=10\\\\y=10-5[/tex]

y = 5.

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The dipole moment of the water molecule (h2o) is 6.17×10−30c⋅m. consider a water molecule located at the origin whose dipole moment p⃗ points in the +x-direction. a chlorine ion (cl−), of charge −1.60×10−19c, is located at x=3.00×10−9m. assume that x is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used.

Answers

Answer:

6.58 X 10⁻¹³ N

Explanation:

According to lamarck’s theory of evolution, organisms change during their lifetime to survive then pass these changes to their offspring. what supports the hypothesis of lamarck?

Answers

Answer:

Lamarckism, a theory of evolution based on the principle that physical changes in organisms during their lifetime—such as greater development of an organ or a part through increased use—could be transmitted to their offspring.

Exercise will help you prepare for the material covered in the next section. solve: −2x − 4 = x 5

Answers

Answer:

-4/7

Explanation:

5x+2x=-4

x=-4/7

i think its the answer

For approximately what values of x can you replace sin x by x-(x^3/6)

Answers

Answer:

15

Explanation: cause 1/2

Christopher runs a farm stand that sells apples and bananas. Yesterday christopher sold 35 pounds of apples and 34 pounds of bananas for a total revenue of $163. 50. Today he sold 15 pounds of apples and 17 pounds of bananas for a total revenue of $76. 75. Determine the price of each pound of apples and the price of each pound of bananas

Answers

The equation computed shows that the price of apple is $2 and the price of banana will be $2.75.

How to compute the equation?

Christopher sold 35 pounds of apples and 34 pounds of bananas for a total revenue of $163.50. This will be:.

35a + 34b = 163.50

He also sold 15 pounds of apples and 17 pounds of bananas for a total revenue of $76.75. This will be:

15a + 17b = 76.75

Equate both equations

35a + 34b = 163.50 ..... i

15a + 17b = 76.75 ...... ii

Multiply equation i by 15.

Multiply equation ii by 35

525a + 510b = 2452.50 .... iii

525a + 595b = 2686.25 .... iv

Subtract equation iii from iv

85b = 233.75

b = 233.75/85

b = 2.75.

The price of banana is $2.75.

The price of apple will be:

35a + 34b = 163.50

35a + 34(2.75) = 163.50

35a + 93.50 = 163.60

35a = 163.50 - 93.50

35a = 70

a = 70/35

a = 2

The price of apple is $2.

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Glencoe math course 2 volume 2 answer key 7th grade pdf

Answers

The volume of the figure is the amount of space in it.

Using the assumed values, the volume of the cone is 37.68

How to calculate volumes?

The question is incomplete; so I will give a general explanation on how volumes can be calculated..

Assume the figure is a cone of the following dimension:

Radius (r) = 3 meters

Height (h) = 4 meters

The volume of a cone is calculated as:

[tex]V = \frac13 \pi r^2h[/tex]

So, we have:

[tex]V = \frac13 * 3.14 * 3^2 * 4[/tex]

[tex]V = 37.68[/tex]

Using the assumed values, the volume of the cone is 37.68

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What is the force between two 1.0 x 10-5 c charges separated by 2.0 m?

Answers

The force between the two identical electrical charges with the given distance of seperation is 0.2247N.

Given the data in the question;

Two Charge; [tex]q_1\ and \ q_2 = 1.0* 10^{-5}C[/tex]Distance between [tex]q_1\ and \ q_2[/tex]; [tex]r = 2.0m[/tex]Force between [tex]q_1\ and\ q_2[/tex]; [tex]F = ?[/tex]

Coulomb's law

Coulomb's law states that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between the two charges.

This is expressed as;

[tex]F = k\frac{q_1q_2}{r^2}[/tex]

Where [tex]q_1\ and \ q_2[/tex] are the two electrical charges, r is the distance between the charges and k is the Coulomb constant ( [tex]k = 8.98755*10^9 kgm^3/s^2C^2[/tex] )

To determine the force between the two charges, we substitute our values into the expression above.

[tex]F = k\frac{q_1q_2}{r^2}\\\\F = (8.98755*10^9 kgm^3/s^2C^2)\frac{(1.0*10^{-5}C)(1.0*10^{-5}C)}{(2.0m)^2}\\\\F = (8.98755*10^9 kgm^3/s^2C^2)\frac{1.0*10^{-10}C^2}{4.0m^2}\\\\F = \frac{0.898755kgm^3/s^2}{4.0m^2}\\ \\F = 0.2247kgm/s^2\\\\F = 0.2247N[/tex]

Therefore, the force between the two identical electrical charges with the given distance of seperation is 0.2247N.

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the elastic rebound theory for the origin of earthquakes was first proposed by ________ following the ________ earthquake.

Answers

Answer:

1. 1906 2. San Francisco

The writer is considering deleting the underlined independent clause in sentence 7 (reproduced below), adjusting the punctuation as necessary. In a classic experiment, students who watched their schools compete in a football game subsequently remembered the adversary’s team performing worse than their own: confirmation bias caused the students, who already believed in their own school’s superiority, to interpret what they had seen as support for their preexisting beliefs. Should the writer keep or delete the underlined text?

Answers

The answer to whether the writer should keep or delete the underlined text is; Keep it, because it provides an example that explains how confirmation bias affects memory

What are clauses and punctuations?

In language, a clause is a constituent that connects a semantic predicand and a semantic predicate. A common clause is made up of a subject and a syntactic predicate, the last ordinarily an action word with any items and different modifiers.

A modifier clause depicts or gives more data about the action word lets us know when, where, how, how much, or under what condition something is going on. Model she cried in light of the fact that her shell was broken. A thing clause replaces a thing in the sentence.

Punctuation fills our composition with quiet inflection. We stop, stop, underline, or question utilizing a comma, a period, an interjection point or a question mark.

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Find the mass of alcl3 that is produced when 10.0 grams of al2o3 react with 10.0 g of hcl according to the following equation.

Answers

12.2g answer

Try the stoichiometry method. You should get 12.2g as the answer

8-5 skills practice using the distributive property page 33

Answers

This exercise refers to the explanation of what distributive property is especially in relationship to addends.

What is distributive property?

The process of obtaining the product of the addition of two or more addends by a figure that gives the same result as multiplying each addend individually by that figure and then adding their products together is referred to as distributive property.

How is Distributive Property Applied?

A great example of distributive property is given below:

When asked for the answer of 5 (6 +1), applying distributive property, we have:

5(6+1) = 5 x 6 + 5 X 1 = 35.

Note that the 5 outside the bracket is used to multiply everything inside the bracket, hence the effect of Distributive Properties.

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Go math grade 7 practice and skills fluency workbook answer key

Answers

There are a lot of  math for  grade 7. An example of practice and skills fluency work is Adding and Subtracting Integers.

An example of Adding and Subtracting Integers is: Solve for  -5+(-3)

−5+(−3).

What is the rule for adding integers?

Note that to  add integers having the same sign, one has to keep the same sign and then they can add the absolute value of each number.

We are given the expression −5+(−3)

The next step is to use counters to stand in place of the numbers -5 and -3:

Note that there  are 5+3 - -8 counters and all the counters stands as negative integer.

To evaluate the expression, on can see that there are:

8 countersnegative counters -8−8

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To the heated water 0.5 kg of water at t3 = 20° c is added. what is the final temperature of the water, in kelvin?

Answers

The final temperature of the water after addition to the heated water at 20° C in degree kelvins' is calculated as; 295.23 K

What is the Final Temperature?

We are given;

mass of the initial water; m₁ = 2.5 kg

specific heat capacity of water; c = 4189 J/kg.K

initial temperature of water; T₁ = 13.5 ⁰C

final temperature of the water; T₂ = 22.5 ⁰C

mass of the final water; m₂ = 0.5 kg

initial temperature of the final water; T₁,i = 20 ⁰C

If the system is isolated, then we have;

m₁*c*(T_f - T₂) + m₂*c*(T_f - T₁,i) = 0

c will cancel out to give;

[2.5T_f - (2.5*22.5)] + [0.5T_f - (0.5*20)] = 0

2.5T_f - 56.25 + 0.5T_f - 10 = 0

3T_f = 66.25

T_f = 66.25/3

T_f = 22.08°C = 295.23 K

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In order to be allowed to engage in activities to promote and enhance

Answers

In order to be allowed to engage in activities to promote and enhance the sale of an alcoholic beverage on behalf of a brewery or winery, a person must obtain

block x of mass m slides across a horizontal surface where friction is negligible. block x collides with block y of mass 2m that is initially at rest, as shown in figure 1. after the collision, both blocks slide together with a speed vs , as shown in figure 2.

Answers

The kinetic energy of the two-block system with the given masses before the collision is determined as ³/₂Mvs².

Kinetic energy of the blocks before collision

The kinetic energy of the blocks before the collision is calculated as follows;

For a negligible friction effect, the kinetic energy of the two - block system after the collision is equal to the kinetic energy before the collision.

K.E(initial) = K.E(after)

K(after) = ¹/₂(m₁ + m₂)vs²

K(after) = ¹/₂(m + 2m)vs²

K(after) = ¹/₂(3m)vs²

[tex]K.E(after) = \frac{3}{2} Mv_s^2[/tex]

Thus, the kinetic energy of the two-block system with the given masses before the collision is determined as ³/₂Mvs².

The complete question is below:

block x of mass m slides across a horizontal surface where friction is negligible. block x collides with block y of mass 2m that is initially at rest, as shown in figure 1. after the collision, both blocks slide together with a speed vs , as shown in figure 2.

What is the kinetic energy of the two-block system before the collision?

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Glencoe algebra 1 7-3 practice rational exponents answers

Answers

The expressions are illustrations of rational exponent expressions

The equivalent expressions are [tex](8x)^\frac 12 = 2\sqrt{2x[/tex], [tex]6z^\frac 12 = 6\sqrt z[/tex] and [tex]\sqrt{19} = 19^\frac 12[/tex]

How to simplify the rational exponent expressions?

From the complete question (see attachment), we are to simplify or rewrite the following expressions

[tex](8x)^\frac 12[/tex]

[tex]6z^\frac 12[/tex]

[tex]\sqrt{19[/tex]

For [tex](8x)^\frac 12[/tex], we simply apply the exponent rule of indices

[tex](8x)^\frac 12 = \sqrt{8x[/tex]

Express 8 as 4 * 2

[tex](8x)^\frac 12 = \sqrt{4 * 2x[/tex]

Take the square root of 4

[tex](8x)^\frac 12 = 2\sqrt{2x[/tex]

For [tex]6z^\frac 12[/tex], we apply the exponent rule of indices

[tex]6z^\frac 12 = 6\sqrt z[/tex]

For [tex]\sqrt{19[/tex], we apply the the same rule

[tex]\sqrt{19} = 19^\frac 12[/tex]

Hence, the equivalent expressions are [tex](8x)^\frac 12 = 2\sqrt{2x[/tex], [tex]6z^\frac 12 = 6\sqrt z[/tex] and [tex]\sqrt{19} = 19^\frac 12[/tex]

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According to the law of supply, sellers are likely to reduce their supply of a good when

Answers

Answer:

sellers all suppliers are likely to reduce the supply of goods when there is a a decrease in the prices of the complementary goods. similarly the prices can be lowered when there is an exhaust supplies in the market. this means that when the supply is higher the prices tends to be lower and the demand decreases.

Answer: the goods selling price has gone down

Explanation: just took test

Which design element is used to organize the text in orderly fashion? a. Proximity b. Alignment c. White space d. Balance

Answers

Answer:

Explanation:

The correct answer is the option B: alignment.

Explanation:

On one hand, design elements comprehends the term that describes fundamental ideas about the practice of visual design, such as the color, the points the lines, etc.

On the other hand, alignment is the name given, in the field of design, to the term that describes how a text is placed in order on the screen. Moreover, it enables the composition of a text document using different text positioning on the whole or selected part of a page.

Answer:B.

Explanation:

What is the temperature of 12.20 mol of gas in a 18.35 l tank at 16.40 atm? round your answer to the tenths place.

Answers

Based on the calculations, the temperature of this ideal gas is equal to 300.5 K.

How to calculate the temperature.

Mathematically, the temperature of an ideal gas is given by this formula:

[tex]PV=nRT\\\\T=\frac{PV}{nR}[/tex]

Where:

P is the pressure.R is the ideal gas constant.T is the temperature.n is the number of moles.V is the volume.

Given the following data:

Number of moles = 12.20 moles.

Volume = 18.35 L.

Pressure = 16.40 atm.

Substituting the given parameters into the formula, we have;

[tex]T=\frac{16.40 \times 18.35}{12.20 \times 0.0821}\\\\T=\frac{300.94}{1.00162}[/tex]

T = 300.5 K.

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At which event must special care be taken when preparing food

Answers

Answer:

occasions

Explanation:

During occasions such as Easter, Christmas etc when preparing a food take risk and measures make it delicious

This map illustrates the countries occupied by germany. the countries occupied by france. that norway was not under german occupation. that belgium was not under german occupation.

Answers

Answer:

Late answer, but the answer is: A the countries occupied by Germany.

Explanation:

For future people I guess

The United States, Great Britain, the Soviet Union, and France participated in a joint occupation of the German state following Germany's defeat in the Second World War. Thus, option A is correct.

What are factor that led to Germany occupy countries?

In Germany's defeat in World War II, the country was jointly occupied by the continent's four major allies: the United States, Great Britain, the Soviet Union, and France.

The military overthrow of the Soviet Union; the abolition of the alleged Communist menace to Germany; and the seizing of valuable Soviet-controlled land as Lebensraum (German for “Living space”) for long-term German settlement.

During World War II, Germany's air raids posed the toughest challenges to halting its incursions into Europe. For the neighboring European nations, Adolf Hitler's military prowess and fast-moving ground forces made life extremely tough.

Therefore, the countries occupied by Germany.

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What function is the inverse of the exponential function y = 4x?

Answers

Answer:

y

=

ln

x

ln

4

Explanation:

Switch the places of

x

,

y

and subsequently solve for

y

:

y

=

4

x

x

=

4

y

ln

(

4

y

)

=

ln

x

We need to get an explicit solution, IE, isolate

y

.

Recalling that

ln

(

a

b

)

=

b

ln

a

:

y

ln

(

4

)

=

ln

x

y

=

ln

x

ln

4

Explanation:

a persistent pattern of disregard for and violation of the rights of others; callousness, or lack of empathy; deceitful; aggressive, manipulative; little to no capacity for intimacy in personal relationships; failure to confirm to social norms and laws; disregard for work, school, and family obligations; commonly referred to as sociopath.

Answers

A persistent pattern of disregard for and violation of the rights of others which is commonly known as sociopath is an: antisocial personality disorder (ASPD).

What is ASPD?

ASPD is an acronym for antisocial personality disorder can be defined as a type of personality disorder that is primarily characterized by disregard for people, destruction, violation of people's rights, infliction of injuries on others and a lack of close friendships or relationships.

In Psychology, an antisocial personality disorder (ASPD) includes the following characteristics and signs:

Lack of empathy.CallousnessDisregard for school, work and family obligations.Non-conformance to social norms and laws.

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scalable flexible and adaptable operational capabilities are included in

Answers

Ans The NRF guiding principles

Explanation:

The NRF is built on scalable, flexible, and adaptable concepts.

Scalable, flexible, and adaptable operational capabilities are indeed included in the (NRF)National Response Framework's five key principles.

The National Response Framework (NRF) is a comprehensive guide developed by the United States Department of Homeland Security to facilitate effective response and recovery efforts during emergencies, disasters, and incidents. The NRF's five key principles, known as the "Five Mission Areas," outline the fundamental aspects of emergency management. These mission areas include:

1. Prevention: Activities aimed at preventing emergencies or disasters from occurring. This involves measures such as risk assessment, hazard mitigation, and public education to minimize the likelihood of incidents.

2. Protection: Actions focused on safeguarding individuals, critical infrastructure, and key assets from potential threats and hazards.

3. Mitigation: Efforts to reduce the impact and severity of disasters by implementing measures to minimize the potential damage and disruption caused by hazards.

4. Response: Immediate actions are taken to address and manage the consequences of an incident. This includes coordinating emergency response activities, mobilizing resources, conducting search and rescue operations, providing medical assistance, and ensuring public safety.

5. Recovery: Activities aimed at restoring affected communities and rebuilding the impacted areas after an incident. This includes facilitating the recovery process, providing assistance to individuals and businesses, restoring critical services, and rebuilding infrastructure.

In summary, scalable, flexible, and adaptable operational capabilities are integral to the National Response Framework's five key principles, as they enable effective emergency management and response during various incidents and disasters.

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A wave of infrared light has a speed of 6 m/s and a wavelength of 12 m. What is the frequency of this wave? 0. 5 hz 2. 0 hz 18 hz 72 hz

Answers

Answer:

0.5hz

Explanation:

The main acid in the stomach is hydrochloric acid (hcl). which chemical equations show a reaction that occurs when someone takes an antacid? check all that apply.

Answers

The chemical equations that show  a reaction that occurs when someone takes an antacid are;

HCl + NaHCO₃ -> NaCl + H₂O + CO₂2HCl + CaCO₃ -> CaCl₂ + CO₂ + H₂O2HCl + Mg(OH)₂ -> MgCl₂ + 2H₂O

What is the correct chemical equation?

Hydrochloic acid would normally react with the basic substances in the stomach. Now, these substances that react with hydrochloric acid in the stomach are magnesium hydroxide, sodium bicarbonate and calcium carbonate.

Thus, from the above dewscription, the chemical equations that show  a reaction that occurs when someone takes an antacid are;

HCl + NaHCO₃ -> NaCl + H₂O + CO₂2HCl + CaCO₃ -> CaCl₂ + CO₂ + H₂O2HCl + Mg(OH)₂ -> MgCl₂ + 2H₂O

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