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

A scientist views different objects using a light microscope. which features would the scientist most likely see for samples from multicellular organisms?

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Through the use of a light microscope it is possible to observe in multicellular organisms different types of cells and organelle features, and in general, they are all very small.

What are multicellular organisms?

They are all those forms of life whose bodies are composed of a diversity of cells organized, hierarchical, at the cellular level through organelles that are specialized cell differentiations.

The cells that make up these organisms have different shapes and sizes and, in general, they are all very small, so to see them it's needed a light microscope, an instrument that increases many times the size of samples.

Therefore, we can conclude that through the use of a light microscope it is possible to observe in multicellular organisms different types of cells and organelle features, and in general, they are all very small.

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The decomposition of n2o5 can be described by the equation 2n2o5(soln)⟶4no2(soln)+o2(g) consider the data in the table for the reaction at 45 ∘c in carbon tetrachloride solution.

Answers

The reaction rate between 0 -195 seconds for the decomposition of N2O5 is 0.0006 M/s.

What is the rate of a reaction?

The rate of reaction can be estimated in terms of the consumption of the reactants in the reaction.

From the given information, the equation N2O5 has been the reactant that has been used in 2 moles.

The rate of the reaction is expressed as:

[tex]\mathbf{Reaction \ rate = -\dfrac{1}{2} \times \dfrac{dN_2O_5}{dt}}[/tex]

The reaction rate for a time interval between (0 - 195) sec is expressed as follows:

[tex]\mathbf{Reaction rate = -\dfrac{1}{2} \times \dfrac{1.86556-2.10195}{195s - 0s}}[/tex]

[tex]\mathbf{Reaction \ rate = -\dfrac{1}{2} \times \dfrac{-0.23639}{195s}}[/tex]

= 0.0006 M/s.

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Gerry bought two apples and five oranges for 4.75 Molly bought four apples and one orange from the same store for 2.75 what is the combined cost of one apple and one orange

Answers

Answer:

Try adding the amounts as a start?

Explanation:

I forget how to complete these equations. We went over this back in Algebra 1.

You are high up in the mountains and boil water to make some tea. however, when you drink your tea, it is not as hot as it should be. you try again and again, but the water is just not hot enough to make a hot cup of tea. which is the best explanation for this result?

Answers

Answer:

temperatures are all low on topbof the mountains

Answer:the cold

Explanation:mountains have this thing called an ice cap at the top

You work every saturday from 9:00 a.m. to 5:00 p.m. find the measure of the angle generated by the hour hand of a clock during this time in both degrees and radians. compare this angle with the angle generated by the minute hand from 9:00 a.m. to 5:00 p.m.

Answers

The angle generated by the hour hand measures -270° or -4.71 radians, and we will see that the angle generated by the minute hand is 12 times the one generated by the hour hand.

How to get the angle generated?

Remember that in a complete rotation we have an angle of 360°, and in a complete rotation we have 12 hours, then there is a relation:

12 hours = 360°

1 hour = 360°/12 = 30°

From 9:00 a.m to 5:00 p.m. there are 9 hours, so the angle that the hour hand does is:

A = 9*(30°) = -270°

(the negative sign is because this angle is measured clockwise)

Now we can write this in radians, remember that:

3.14 radians = 180°

Then:

1 = (3.14 rad/180°)

Then:

270° = -270°*(3.14 rad/180°) = -4.71 rad

What is the angle generated by the minute hand?

Each hour that passes, the minute hand does a complete revolution. Then in 9 hours, the minute hand does an angle of:

A = 9*(-360°) = -3,240°

To compare this angle to the one generated by the minute hand we take the quotient:

-3,240°/-270° = 12

So this angle generated by the minute hand is 12 times the one generated by the hour hand.

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Based on the model of cellular transport, the conversion of atp to adp provides a mechanism for

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Based on the model of cellular transport, the transport of a substance against its electrochemical gradient is accomplished with energy input from ATP.

What is active transport?

It is a cellular mechanism by which some molecules cross the plasma membrane against a concentration gradient with the consequent expenditure of energy.

The carrier proteins that intervene in the transport of molecules require an energy supply, in the form of ATP, it is carried out at the expense of respiration and photosynthesis processes; by hydrolysis of ATP by membrane ATP hydrolases.

Therefore, we can conclude that based on the model of cellular transport, the transport of a substance against its electrochemical gradient is accomplished with energy input from ATP.

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Every real zero of a polynomial function appears as​ a/an

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to 0 are called the zeros of f. These values of x are the roots, or solutions, of the polynomial equation f(x) = 0. Each real root of the polynomial equation appears as an x-intercept of the graph of the polynomial function.

What is the main reason sundiata is remembered in legends?

Answers

Answer:

Sundiata killed the Soso King, Sumanguru, with a poisoned arrow.

Explanation:

Sundiata killed the Soso King, Sumanguru, with a poisoned arrow.

a student wants to determine whether a certain problem is undecidable. which of the following will demonstrate that the problem is undecidable?

Answers

A scenario which demonstrate that the problem is undecidable is when for an instance of the problem, no algorithm written provides a correct YES or NO answer.

What is an algorithm?

An algorithm can be defined as a standard formula and procedures with a set of finite steps and instructions that are executed on a computer system, in order to proffer solutions to a specific problem under appropriate conditions.

This ultimately implies that, a scenario which demonstrate that a certain problem is undecidable is when for an instance of the problem, no algorithm can be written by a programmer is capable of providing either a correct YES or NO answer.

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A) how can cells from a single plant have different characteristics?

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The plant cell wall is a specialized form of extracellular matrix that surrounds every Plant cells can be distinguished from most other cells by the presence of chloroplasts, which are also found in certain algae.

How has the earth's climate changed over the last 150 years

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Answer:

The University of California Riverside and NASA estimate human activity has increased the amount of carbon dioxide in the atmosphere by about 30 percent in the past 150 years. The amount of methane, a potent greenhouse gas produced by decomposing plant and animal matter, is also increasing

Explanation:

Which process is most likely driven by light energy?

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Answer:

answer is

hope it help u

mark as brainliest

Houghton mifflin harcourt geometry volume 2 answer key

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Houghton Mifflin Harcourt geometry volume 2 is one that covers the topics on the use of Similar Triangles, transformation and others. It is a textbook that helps students to sharpen their knowledge on geometry.

What is Hmh Geometry?

This is known to be the 21st Edition geometry textbook that was written by Houghton Mifflin Harcourt . Some of the topics covered in this geometry textbook are:

Transformations and SymmetryLines and AnglesAngles and Segments in Circles.Congruent Figures, etc.

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How does housman use the structure of the poem to create surprise?

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The poet offers an elegy for a young, athletic man who recently passed away in "To an Athlete Dying Young." Naturally, this is a tragic subject, and the poet begins his poem with a sorrowful and solemn tone of pity. The author, on the other hand, uses the poem's structure to surprise his audience. Despite the melancholy tone of the opening line, the tone of the poem shifts to one of satisfaction and praise as the poem goes on, surprising the reader. The author can express various opposing views in each stanza. While he feels that dying young is a pity, he considers how rapidly youth fades and how many men lose their reputation by the time they reach retirement age. He says that if an athlete dies young, he will never have to deal with old age, decline, or loss of glory. Despite the melancholy, the author can draw some constructive conclusions from the incident

15.1 central angles and inscribed angles homework answers

Answers

The central and inscribed angle theorem is used to solve angles and arc measure in a circle.

What is the Central and Inscribed Angles Theorem?

The theorem shows the relationship of the measures of an inscribed angle, central angle, and their intercepted arc.

It states that:

central angle measure = measure of inscribed angle.inscribed angle measure = 1/2(measure of inscribed angle)

Therefore, the central and inscribed angle theorem is used to solve angles and arc measure in a circle.

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the greatest demon lord is reborn as a typical nobody anime episode 1

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Answer:

ok

Explanation:

A chair has a mass of 10 kilograms on earth. What is the mass of the chair on mercury?

Answers

Answer:

The mass of the chair is 10kg.

Explanation:

The Mass of an object is unaffected by gravity. The Weight of an object is affected by gravity.

in the small intestine, which of the following enzymes breaks down oligosaccharides?

Answers

in the small intestine, the enzymes that breaks down oligosaccharides is glucoamylase.

What enzymes break down oligosaccharides ?

The  enzymes are known to be  dextrinase and glucoamylase. They help to break down oligosaccharides.

They are known to be brush border enzymes and they consist of:

MaltaseSucraseLactase

Note that Lactase is not found in most adult humans and when compared to most poly-saccharides, it cannot be digested in the small intestine.

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How many ways can you listen to 3 songs from a cd that has 12 selections?

Answers

Taking into account the definition of permutation, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.

What is permutation

Permutations refer to the action of arranging all the members of a set in some kind of order or sequence. This means that if a set is already ordered, the process of rearranging its elements is called permutation.

In other words, permutations of m elements in n positions are the different ways in which the m elements can be arranged occupying only the n positions.

In this case, the elements are not repeated, since if they are repeated or equal to each other, exchanging them does not generate a new permutation. And the order does matter, since the exchange between two different elements generates a new permutation

To obtain the total of ways in which m elements can be placed in n positions, the expression is used:

[tex]P=\frac{m!}{(m-n)!}[/tex]

The sign ! indicates the factorial function, which indicates that all positive integers between the number that appears in the formula and the number 1 must be multiplied.

Number of ways you can listen to 3 songs

The order in which songs are listening is important as there is no plan to listen to the same song twice. So, the permutation can be applied.

Being:

m=12n=3

and replacing in the expression for permutation, you get:

[tex]P=\frac{12!}{(12-3)!}[/tex]

[tex]P=\frac{12!}{9!}[/tex]

[tex]P=\frac{479001600}{362880}[/tex]

P= 1320

Finally, there are 1320 ways you can listen to 3 songs from a cd that has 12 selections.

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A hyperbola has vertices (±5, 0) and one focus (6, 0). what is the standard-form equation of the hyperbola?

Answers

Answer:

x²/25  -  y²/11 = 1

Explanation:

The standard form equation of the hyperbola:

x² / a² - y² / b² = 1

a = 5,

a² = 25

c = 6

c² = a² + b²

36 = 25 + b²

b² = 36 - 25

b² = 11

17.3 subtracting polynomial expressions answer key

Answers

An example of 17.3 subtracting polynomial expressions question is solve for 2q² - q - 8) - (2 q² + q - 4).

What is polynomial expressions?

A polynomial is known to be a type of  an expression that is made up of variables, constants and exponents. They are often combined using the mathematical terms such as addition, subtraction, etc.

2 q² - q - 8) - (2 q² + q - 4)

= (2 q² - q - 8) + (-2 q² - q + 4)

Then you have to rewrite subtraction as addition and then Group like terms together;

= (2 q² - 2 q²) + (-q - q) + (-8 + 4)

= -2q - 4

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the long-run aggregate supply curve is vertical because

Answers

Answer:

The long-run aggregate supply curve is vertical because, the economy that produces the potential output, is not related to the price level of the products. The long-run aggregate supply curve is vertical at the full-employment output level as this amount is produced as and when the prices are fully adjustable.

Explanation:

What is the slope of the line that passes through the points (6,2) and (4,10)?

Answers

10-2/4-6 = 8/-2 = -4 is the slope

Society is a joint-stock company, in which the members agree, for the better securing of his bread to each shareholder, to surrender the liberty and culture of the eater. The virtue in most request is conformity. Self-reliance is its aversion. Based on the excerpt, what is emerson’s view of the relationship between society and individuals? society helps people feel more free. Society protects people’s rights. Society pushes people to be more unique. Society encourages people to be alike

Answers

Emerson’s view of the relationship between society and individuals is; D; Society encourages people to be alike.

What is the relationship between views?

From the question, we see the society being referred to as a  "joint-stock company" where the members agree on what they want and what they do not want.

Subsequently, we see how the society must work hand in hand to make sure that they give everyone what belongs to them so that everyone is self reliant.

Finally, we can say that the relationship between society and individuals is one where society encourages people to be alike which is depicted where the passage calls for conformity.

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Answer:

your answer is d

Explanation:

In most production environments, _______ will be used as the source of data input.

Answers

They In most production environments, _______ will be used as the source of data input.

1.0 l of a buffer is prepared. it contains 0.125 m ha (pka = 4.74) and 0.115 m a−. what is the ph of this buffer after 0.0100 mol of strong acid is added?

Answers

Answer:

pH=4.63

Explanation:

pH = pKa + log(base/acid)

Glencoe math course 1 volume 1 answer key 6th grade pdf

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Since this cylinder has a radius of 2 inch, its volume is equal to 25.12 cubic inches.

Given the following data:

Radius of cylinder = 2 inch.Height of can = 2 inch.[tex]\pi =3.14[/tex]

What is volume?

In Mathematics, volume can be defined as a scalar quantity that is used to express the amount of three-dimensional (3D) space that is occupied by an object such as a cylindrical can, or enclosed by a boundary.

How to calculate the volume.

Mathematically, the volume of a cylinder is given by this formula:

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

Where:

h is the height.r is the radius.

Substituting the given parameters into the formula, we have;

[tex]V = 3.14 \times 2^2 \times 2\\\\V=3.14 \times 4\times 2\\\\V=6.28 \times 4[/tex]

V = 25.12 cubic inches.

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12.1 arithmetic sequences evaluate homework and practice answers

Answers

The table is an illustration of arithmetic sequence

The equation of the arithmetic sequence is B(s) = 7.5s

How to complete the table of the arithmetic sequence

From the table (see attachment), we have the following formula

B(s) = 7.5s

For s =0 to 4, we have:

B(0) = 7.5(0) = 0

B(1) = 7.5(1) = 7.5

B(2) = 7.5(2) = 15

B(3) = 7.5(3) = 22.5

B(4) = 7.5(4) = 30

So, the complete table is:

s       B(s)

0        0

1         7.5

2        15

3       22.5

4       30

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Scan the highlighted line by clicking on either an accent mark ( ) or breve ( ) and putting it in its correct position. symbols will be used more than once. use a dictionary for help.

Answers

The right position for the highlighted line are:

For U symbol over: the, has, r'd (in weathr'd) ry (in every) the, we, isFor ' symbol over: ship, weat (in weather'd) ev (in every) rack, prize, sought, won

Which is an accent mark?

Accent marks are known to be a kind of symbols that are often employed over letters, such as vowels.

These marks are known  to help a person to show or emphasize the right or correct pronunciation of a word. They are the marks that are often found in languages such as French, German, etc.

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how "reusing, reducing, or recycling" could decrease the amount of fossil fuels used

Answers

Answer:

it lowers global warming/litter

Explanation:

if those fossil fules get in the air it bad gib brainiest

"Reusing, reducing, or recycling" could decrease the amount of fossil fuels used as it lowers global warming/litter.

Why are 3R's used?

Reduce is referred to the lowering use of the substance, resources, or any other items. Reuse refers to the repeated benefit or a resource, item, or any substance.Recycling is the process of collecting and processing the materials again to avoid it throwing them in the trash.

The 3R's are the reduce, reuse, and recycle the waste or products. Reduce is referred to diminish the use of certain products or resources, reuse is to repeated use of items, and recycle is to mold and develop into a new item.

Throwing antifreeze can become ilegal because it gets heavy metals such as lead, cadmium and chromium that make it hazardous waste, which should not be thrown in public areas.

Therefore, "Reusing, reducing, or recycling" could decrease the amount of fossil fuels used as it lowers global warming/litter.

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