Nine children are to be divided into an A team, a B team and a C team of 3 each. The A team will play in one league, the B team in another, the C team in a third league. How many different divisions are possible

Answers

Answer 1

Answer:

The answer is "840".

Step-by-step explanation:

Following are the number of ways in which selecting a team A  by 9 children:

[tex]= ^{9_{C_{3}}\\\\\\[/tex]

[tex]=\frac{9!}{3! \times 6!} \\\\=\frac{9\times 8\times 7\times 6!}{3 \times 2\times 1\times 6!}\\\\=\frac{9\times 8\times 7}{3 \times 2\times 1}\\\\=\frac{3\times 4\times 7}{1}\\\\=\frac{84}{1}\\\\=84[/tex]

Following are the number of ways in which selecting a team B  by remaining 6 children:

 [tex]= ^{6}_{C_{3}}[/tex]

[tex]= \frac{6!}{(3! \times 3!)}\\\\= \frac{6!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{6\times 5 \times 4 \times 3!}{(3\times 2\times 1 \times 3!)}\\\\= \frac{ 5 \times 4 \times 3!}{3!}\\\\= 5 \times 4 \\\\=20[/tex]

Following are the number of ways in which selecting a team C  by remaining 3 children:

[tex]= ^{3}_{C_{3}}\\\\=\frac{3!}{3!}\\\\= 1[/tex]

Following are the number of ways in which making 3 teams by 9 children:

[tex]= \frac{(84 \times 20 \times 1)}{3!}\\\\= \frac{(84 \times 20 )}{6}\\\\= 14 \times 20\\\\= 280\\\\[/tex]

(Note: we've split by 3! Because it also is necessary to implement three teams between themselves)

Now 3 leagues have to be played. One is going to be run by each team.

That is the way it is

Different possible divisions

[tex]= 280 \times 3!\\\\= 280 \times (3 \times 2 \times 1)\\\\= 840[/tex]  


Related Questions

Discussion Topic
29
The most important component of a physical structure is a solid foundation on which the
rest of the structure sits. A strong foundation allows buildings to last longer and withstand
many outside forces.
Just like the foundation of a building, a strong foundation for algebra is critical for success
and allows you to extend your understanding to more complex mathematical and real-
world situations. What are some of the foundational, or key, concepts of algebra that you
have learned so far?

Answers

We have that with a brief introduction to Algebra you are required to You are to refer to your curriculum and teachings and discover the foundational, or key, concepts of Algebra that you  have learned so far and  structure its respectively as you have learned

For This Question you are a asked to highlight what the are the foundational and  key concepts of algebra

So you are tasked to refer to your Notes and pick out the  foundational, or key, concepts of algebra that you  have learned so far according to your curriculum.

Algebra

This is a branch of mathematics that strictly focuses on mathematical Operator or Arithmetic operators and how the are used in there variant ways or combined to solve problems.

Mathematical  Operators(-,+,/,*)

To Identify some fundamental and  key concepts of Algebra like there use in

ExpressionsEquationsUsed in Graph plotsUsed to resolve Inequalities on the Number line.These are Few key concepts where  Algebras feature.

In conclusion

You are to refer to your curriculum and teachings and discover the foundational, or key, concepts of Algebra that you  have learned so far and  structure its respectively as you have learned.

For more information on this visit

https://brainly.com/question/14413003

Answer:

Some of the foundational key concepts I have learned from algebra so far are: we have learned Expressions, Equations, we have Used Graphs, we have learned how to resolve Inequalities on the Number line, I have learned how to do variables, constants, linear equations, and quadratic equations. those are just very few examples of things me and so many have learned so far in Algebra.

Step-by-step explanation:

Line K is parallel to line I.
k
m
n
Which angle is congruent to 24?
21
0 22
025

Answers

Answer:

<4 = <1

Step-by-step explanation:

Judging from the picture, <1 and <4 are opposite angles. Opposite angles are always congruent. Hope this helps!

please help this is due soon

Answers

For the A parts just make all the second numbers negative example: if it were 5,1 make it (5,-1) and for the B part make all the first numbers a negative example: if it were 5,1 make it (-5,1)

write as a polynomial (-2x^2+x+1)-(x^2-x+7)-(4x^2+2x+8)

Answers

Answer:

The answer would be -7x^2 - 14!

Step-by-step explanation:

We can remove the parentheses by distributing the subtraction sign! -2x^2 + x + 1 - x^2 + x - 7 - 4x^2 - 2x - 8. Simplifying this gives us -7x^2 - 14. Hope this helped! :)

find the missing length indicated​

Answers

Answer:

192

Step-by-step explanation:

geometric mean theorem :

with p and q being the segments of the Hypotenuse, then

h = x = sqrt(p×q)

p = 144

q = 400-144 = 256

h = x = sqrt(144×256) = 12×16 = 192

Find the area of the figure to the nearest tenth?

Am I right?

Answers

No, it’s a. Figure the area of the circle, which is 153.86. But that’s for the whole circle which is 360 degrees. Since you just need 120 degrees, 360/120=3 so divide 153.86 by 3 and you get 51.3

Describe and correct the error in determining the formula for the sequence below

Answers

Answer:An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Step-by-step explanation:

y=0.0111x+2.7617 what is the x axis

Answers

Step-by-step explanation:

here's the answer to your question

Complete the statement below. A Type II Error is made... Choose the correct answer below. A. A Type II Error is made when​ there's not enough evidence to reject the null hypothesis and the null hypothesis is true. B. A Type II Error is made when​ there's evidence to reject the null​ hypothesis, but the null hypothesis is true. C. A Type II Error is made when​ there's not enough evidence to reject the null​ hypothesis, but the null hypothesis is not true. D. A Type II Error is made anytime we do not reject the null hypothesis.

Answers

I think it’s d I believe

Find the missing side. Round your answer to the nearest tenth please help me

Answers

9514 1404 393

Answer:

  16.9

Step-by-step explanation:

The marked sides are the hypotenuse and the one opposite the angle. The relevant trig function is ...

  Sin = Opposite/Hypotenuse

Multiplying by the hypotenuse gives an equation for the opposite side.

  x = 22·sin(50°)

  x ≈ 16.9

A trader sold 90 oranges at 3 for GHC 0.75.
How much did she get from selling all the
oranges?

Answers

Answer:

GHC22.5

Step-by-step explanation:

90/3=30

30=0.75

30×0.75

=22.5

Current
How many years will it take for an initial investment of $60,000 to grow to $90,000? Assume a rate of interest of
4% compounded continuously.

>It will take about _years for the investment to grow to $90,000.
(Round to two decimal places as needed.)

Answers

Answer:

I think i don't know the answer i am so sorry!!!

maybe someone else can Answer

Apply Simpson's rule to approximate the value of integration 1 to 4 e^x In x dx with n = 3.​

Answers

[tex]Here, h=41,0.25,y=1+x21

[/tex]

[tex]x     y101.020.25     0.9413 0.250.94140.750.64510.5

[/tex]

[tex]By Simpson's Rule:

[/tex]

[tex]∫011+x2dx=4×31

[/tex]

[tex][(1+0.5)+4(0.941+0.941+0.64)+2(0.8)]

[/tex]

[tex]=121[9.424]=0.785

[/tex]

the cost of 1 kg tomato is RS . 75.Find the cost of 14 kg​

Answers

Answer:

Cost of 1kg tomato=rs.75

Cost of 14kg tomato=(75×14)

rs.1050

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Consider the equation below.

[tex]3x^{3x-2}=81[/tex]

To solve the given exponential equation, solve the linear equation [tex]3x-2=[/tex]

Answers

Answer:

[tex]ıf \: {3x}^{3x - 2} = 81[/tex]

Step-by-step explanation:

use logarithmic function

[tex] log_{3x}(81) = 3x - 2[/tex]

Answer:

4 and x=2

Step-by-step explanation:

:}

Pippa had 35 stickers.
She gave an equal number of stickers to 8 friends.
She gave each friend as many stickers as possible and kept the rest for herself.
How many stickers did Pippa keep for herself?
What is the misconception if a student selects D) 27?

A)3
B)4
C)11
D) 27

Answers

Answer:

A) 3

Pippa kept 3 stickers for herself

Answer to question 2:

The misconception of if a student selects D) 27 is that instead of dividing to find out how many stickers Pippa kept for herself, the student subtracted. They subtracted instead of dividing.

Step-by-step explanation:

It said that Pippa gave each of her friends an EQUAL number of stickers and AS MANY STICKERS AS POSSIBLE. This tells us that to find our answer we need to divide and what ever the remainder is, is how many stickers Pippa kept for herself.

(You will kind of need to do long division for this)

35 ÷ 8 = 4

8 x 4 = 32

35 - 32 = 3

Pippa will give each of her friends 4 stickers and will keep 3 for herself.

Step-by-step explanation for question 2:

35 stickers - 8 friends = 27

D) 27 is the wrong answer to question 1/part 1

I hope this helped! c:

10. Write (2x + 1)(x - 3)(x - 2) in standard form.

Answers

Answer:

[tex]2x^3-9x^2+7x+6[/tex]

Step-by-step explanation:

The standard form of a polynomial is a method of writing a polynomial such that the terms are organized by degrees. In essence, the first term, or the left-most term has the highest degree or largest exponent. The right-most term or last term has the lowest degree or smallest exponent. One is given an expression in factored form. Distribute, multiply every term by another in the parenthesis, then simplify. Repeat this process until there are no more factored terms. Finally, rewrite the expression in standard form.

[tex](2x+1)(x-3)(x-2)[/tex]

Distribute,

[tex](2x+1)(x-3)(x-2)[/tex]

[tex]((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)[/tex]

Simplify,

[tex]((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)[/tex]

[tex](2x^2-6x+x-3)(x-2)[/tex]

[tex](2x^2-5x-3)(x-2)[/tex]

Distribute,

[tex](2x^2-5x-3)(x-2)[/tex]

[tex](2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)[/tex]

Simplify,

[tex](2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)[/tex]

[tex]2x^3-5x^2-3x-4x^2+10x+6[/tex]

[tex]2x^3-9x^2+7x+6[/tex]

This polynomial is already in standard form, thus there is no need to reorganize it. The leading term or the left-most term has the highest degree, three, the succeeding terms are in respective order of decreasing exponents.

round to the nearest Ten-thousand: 849,708​

Answers

Answer:

850,000

Step-by-step explanation:

Answer: 850,000

Concept:

Here, we need to know the order and name of each place value.

Please refer to the attachment below for the specified names.

Solve:

8 = Hundred thousands

4 = Ten thousands

9 = One thousands

7 = Hundreds

0 = Tens

9 = Ones

Since the values before the ten thousands place, which would be the one thousands place, is greater than 5, then we should round up.

Therefore, the rounded value would be [tex]\boxed{850,000}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Remy drinks 2/1/4 cups of water every 1/4/5 hours.

How many cups of water does he drink in 1 hour?

Answers

Answer:

1¼ cups

Step-by-step explanation:

2¼ ÷ 1/4/5 =

9/4 ÷ 9/5 =

9/4 x 5/9 =

5/4 = 1¼

A construction crane lifts a bucket of sand originally weighing 145 lbs at a constant rate. Sand is lost from the bucket at a constant rate of .5lbs/ft. How much work is done in lifting the sand 80ft?

Answers

Answer: [tex]10,000\ lb.ft[/tex]

Step-by-step explanation:

Given

Initial weight of the bucket is [tex]145\ lb[/tex]

It is lifted at constant rate and rate of sand escaping is [tex]0.5\ lb/ft[/tex]

At any height weight of the sand is [tex]w(h)=145-0.5h[/tex]

Work done is given by the product of applied force and displacement or the area under weight-displacement graph

from the figure area is given by

[tex]\Rightarrow W=\int_{0}^{80}\left ( 145-0.5h \right )dh\\\\\Rightarrow W=\left | 145h-\dfrac{0.5h^2}{2} \right |_0^{80}\\\\\Rightarrow W=\left [ 145\times 80-\dfrac{0.5(80))^2}{2} \right ]-0\\\\\Rightarrow W=11,600-1600\\\\\Rightarrow W=10,000\ lb.ft[/tex]

look the image below

Answers

Answer:

Does the answer help you?

Does the answer help you?Please choose my answer as a brainliest answer and please rate.

Does the answer help you?Please choose my answer as a brainliest answer and please rate.It take a few mins to solve your question.

Answer:

V≈696.91

Step-by-step explanation:

V=4

3πr3=4

3·π·5.53≈696.90997

(4x^5)^3 what is the equivalent?

[A] 4x^5+3
[B] 4x^5*3
[C] 4^3x^5+3
[D] 4^3x^5*3

Answers

Answer:

A

Step-by-step explanation:

They are different exponents but they have the same bas so you add them up.

4x^5+3 = 4x^8

[tex] \pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: as \: we \: know \: that \\ \\ \bf\: \: \rightarrow \: {(xy)}^{n} = {x}^{n} . {y}^{n} \\ \\ \bf \rightarrow \: {( {a}^{m} })^{n} = {a}^{m \times n} \\ \\ \bf \: now \\ \: \\ \blue{ {\boxed{\begin{array}{cc} \maltese \bf\: \: \: {(4 {x}^{5} })^{3} \\ \bf = {4}^{3} \times ({x}^{5} )^{3} \\ \bf = {4}^{3} \times {x}^{5 \times 3} \end{array}}}}\end{array}}}}[/tex]

So option D) is the correct answer

The temperature in Buffalo, New York, was -2 °F one day. This was 42 degrees warmer than the temperature in Nome, Alaska, on the same day. Find the temperature in Nome. Justify your answer by writing and solving an equation. pls I'll make the first to answer with equation get brainlyest​

Answers

The temperature in Buffalo, New York, was -2 °F one day. This was 42 degrees warmer than the temperature in Nome, Alaska, on the same day. Find the temperature in Nome. Justify your answer by writing and solving an equation

Answer:

40

Step-by-step explanation:

HURRY PLEASE!!!!!!
Line AB has a slop of 1/2
What would the slope of line CD have to be if we knew CD was perpendicular to AB?
2
-2
1/2
-1/2

Answers

Answer:

-2

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals

Take the slope of AB = 1/2

-1/(1/2)

-1 * 2/1

-2

The slope of a line perpendicular is -2

it says 'solve the following systems of equations. solve one using substitution and solve the other using elimination' the problems are x - 3y = 16 and 3x - 2y = 13 i don't know how to solve these please help

Answers

Step-by-step explanation:

you gave me only one system of 2 equations. not 2 systems or more.

maybe you missed something.

I can solve this one system in two ways, though.

substitution :

x - 3y = 16

3x - 2y = 13

the first equation gives us

x = 3y + 16

that we can use now in the second equation

3×(3y+16) - 2y = 13

9y + 48 - 2y = 13

7y + 48 = 13

7y = -35

y = -5

x = 3y + 16 = 3×-5 + 16 = -15 + 16 = 1

that's it. that is all the secret of substitution. you use one equation to express one variable by the other. and then you use that in the second equation to have suddenly only one equation with one variable that you can solve. and then from that result you calculate back the other "substituted" variable.

elimination :

x - 3y = 16

3x - 2y = 13

we multiply one equation completely by a factor and then add both equations. of course we should pick a factor that will eliminate one variable, when we add the equations.

e.g.

multiply the first equation by -3

-3x + 9y = -48

3x - 2y = 13

--------------------

0 7y = -35

y = -5

now we pick any one of the equations to use that result and calculate the other variable

e.g. the second equation

3x - 2×-5 = 13

3x + 10 = 13

3x = 3

x = 1

done.

as you can see : of course, both results are identical.

use the described principles to solve any other systems of equations you might have missed here.

this question confuses me so much helpppppp

Answers

Answer:

-11°C or 1°C

Step-by-step explanation:

The question said that, by the noon, the temperature changes by 6°C, but it doesn't tell you if it changes for a hotter or colder temperature, so its possible the temperature at the noon to be:

-5 -6 = -11°C

or

-5 +6 = 1°C

To graph the possible temperatures, you have to draw a dot at the numbers -11 and 1

this is the question of geometry can you solve this for me ☺️​

Answers

Answer:

x = 130 degrees

Step-by-step explanation:

let's imagine we move the point x further and further to the right (and move the connected lines with it) until we get a flat line that connects the two parallel lines.

in this case we have x = 180 degrees, and the top and bottom angles are both 90 degrees.

so, we have a total of all angles of 180 + 90 + 90 = 360 degrees.

this total had to stay the same no matter how we move x outward or inward.

so, even in the situation in the picture the sum of all 3 angles must be 360 degrees.

therefore we get

360 = 120 + 110 + x

360 = 230 + x

x = 130 degrees

The length of the red line segment is 8 and the length of the blue line segment is 4. How long is the major axis of the eclipse?

Answers

The major axis of the eclipse is 12 units long

The given parameters can be represented as:

[tex]Red = 8[/tex]

[tex]Blue = 4[/tex]

See attachment for illustration

To solve this question, we make use of the following theorem

The distance between a point and the foci sums up to the major axis

This translates to:

[tex]Major\ axis = Red + Blue[/tex]

[tex]Major\ axis = 8 + 4[/tex]

[tex]Major\ axis = 12[/tex]

Read more at:

https://brainly.com/question/11395328

a recent survey shows that 66% of college students have a cat and 37% have a HBO subscription. Assuming these two events are independent, what is the probability that a randomly selected student has neither a cat nor HBO

Answers

Answer:

[tex]P(C'\ and\ H') =0. 2178[/tex]

Step-by-step explanation:

Let

[tex]C \to[/tex] Student with cat

[tex]H \to[/tex] Student has HBO sub

[tex]P(C) = 66\% \\ P(H) = 37\%[/tex]

Required

[tex]P(C'\ and\ H')[/tex]

This is calculated as:

[tex]P(C'\ and\ H') = P(C') * P(H')[/tex]

Using complement rules, we have:

[tex]P(C'\ and\ H') = [1 - P(C)] * [1 - P(H)][/tex]

So, we have:

[tex]P(C'\ and\ H') = [1 - 66\%] * [1 - 37\%][/tex]

[tex]P(C'\ and\ H') = [33\%] * [66\%][/tex]

[tex]P(C'\ and\ H') =0. 2178[/tex]

The number 42 has the prime factorization 2.3.7. Thus 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors):

1.42, 2 · 21,3 · 14, and 6. 7.

Required:
List the distinct ways the number 770 can be written as a product of two positive integer factors.

Answers

Answer:

Step-by-step explanation:

770 = 2*5*7*11

So they are:

2*385

10*77

5*154

7*110

14*55

11*70

22*35

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You report to Sofia Cardenas-Bratton, the Marketing Manager for Klamath, but she confesses that her experience with social media consists of an online course that she took on how businesses effectively use social media, so she is relying on you to help shape Klamath's social media strategy. You suggest that you'd like to start with regularly publishing a blog to reinforce Klamath's value to its customers. You point out it's important to publish posts on a regular basis in order to keep visitors engaged, and one study found that publishing blogs at least 11 times per month generated the most traffic on company websites. You and Sofia brainstorm about topics for the first week's blogs and come up with a list of three topics that you both feel will be of value to Klamath's customers: improving your credit score, the advantages of community banks vs. large banks, and buying a house. In which order are you going to tackle these blogs Can anyone pls help me with this I'll mark as brainlist for correct answer please do explain in detail each answers Ty! (I'm preparing for my maths exam tmr) What does quantization refer to? I need help this question is worth 20 points and cant fail this class HELP ASAP!!!!Lydia is creating floral centerpieces for a friend's wedding. She is trying to decide the amount of tulips and peonies she should include in the centerpieces. The table below shows the number of flowers she plans to use in each centerpiece. The total number of flowers used for each centerpiece should be no more than 21 flowers.Flower Type NumberSweet Pea 8Hyacinth 2Tulip tGardenia 3Peony pFirst, select the inequality that can be used to represent the number of peonies, p, and tulips, t, Lydia can use in each centerpiece. Then, select possible combinations of peonies and tulips that could be in a centerpiece to satisfy the inequality.answers13 - (t + p) 2113 + p + t 213 tulips and 9 peonies2 tulips and 3 peonies13 + t + p 216 tulips and 4 peonies5 tulips and 3 peonies21 - p + t 13 the cost of plastering a wall of a room having length 8m and heights 4m at Rs 15 per m is Rs 1560 . find the cost of carpeting the room at rs 300 per m what is the additive inverse of -61 Which of the following equations is written in standard form?A. 2+3x6y=0B. 4x2y=0C. 8x+4y=1D. 3y+x4=0 Which of the following is NOT a power that the Constitution gives the Vice President?1. Presides over the Senate.2. Determine if a law passed by Congress is unconstitutional.3. Assumes the role of President if he/she is unable to hold office.4. Casts the deciding vote if the Senate is deadlocked with a tie. Can someone please help me I dont know how to do this (Due today) necesito las respuestas porfa II. Transformation1. We couldnt go out because it was so dark.- It was too __________________.2. Kevin said, What does she do Jack?- Kevin _____________________.3. Nam spoke English well, so they offered him the job.- Nam spoke English so well_________________________.4. I wont phone him if he doesnt phone him first. - Unless ________________________________.5. She has never moulded an animal out of clay before.- This is ________________________________________________. What are the elements of a tour?? A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds. a) Conduct the appropriate hypothesis test using a 0.1 level of significance.b) What is the test statistic? Give your answer to four decimal places.c) What is the P-value for the test? Give your answer to four decimal places.d) What is the appropriate conclusion?i. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.ii. Fail to reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1. iii. Reject the claim that the mean amount per bin is 50 pounds because the P-value is larger than 0.1.iv. Reject the claim that the mean amount per bin is 50 pounds because the P-value is smaller than 0.1. What is the solution set to this equation?log_4(x + 3) + log_4x = 1 Teddy wants to taste all of the flavors of ice cream at the mall, one by one. Tasting any one flavor will change the way the next flavor taste after it. The flavors are chocolate, vanilla, strawberry, birthday cake, Rocky Road, and butter pecan. In how many ways can he taste the ice cream.A. 30B.120C. 360D.720 Adam sleeps for nine hours each night, five nights a week, and 11 hours for two nights a week.Which is closest to the percentage of the whole week that Adam spends sleeping?A) 25%B) 30%C) 33%D) 40%E) 50% How do you Graph 3x+4y< -16 on the coordinate plane The protagonist and antagonist are in conflict with each other. pls pls pls help meeeeee