at soccer practice, each player must kick the ball to every other player present at least once. If there are 17 players at practice, what is the minimum number of kicks required?

Answers

Answer 1
Answer:   136

====================================================

Explanation:

Player 1 has 16 people to kick the ball toPlayer 2 has 15 people to kick the ball to (since player 1 already is accounted for)Player 3 has 14 people to kick the ball to

And so on.

We'll have this countdown: 16, 15, 14, ..., 3, 2, 1, 0. By the time we get to the 17th player, they won't have anyone to kick the ball to. This is because they've already been counted in the previous scenarios. This is to avoid double-counting.

So the problem simply boils down to us adding up the numbers 0,1,2,...14,15,16.

This is an arithmetic sequence with first term a = 0 and common difference d = 1. The sum of the first n = 17 terms is...

Sn = (n/2)*(a + d(n-1))

S17 = (17/2)*(0 + 1(17-1))

S17 = (17/2)*(16)

S17 = 17*8

S17 = 136 is the final answer

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

An alternative method:

Consider we have two slots A and B

For slot A, we have 17 choices because we have 17 players.

Then for slot B, we have 17-1 = 16 choices since we don't want to reselect whoever goes in slot A.

If order mattered, then we'd have 17*16 = 272 different permutations.

However, order doesn't matter. A sequence like {player1,player4} is identical to {player4,player1}. All that matters is the overall group rather than the order of it. Both of those examples say the same thing: they connect player 1 to player 4.

In short, the value 272 is too large and it double-counts the true answer. We need to divide by 2 to correct for this.

272/2 = 136

We arrive at the same answer as before. There are 136 kicks required so that each player kicks the ball to every other player.

Answer 2

The minimum Number of kicks required in other to ensure that each player kicks the ball to every other atleast once is 136 kicks.

The Number of kicks could be related to the sum of the nth term of an arithmetic series

[tex]S_n = \frac{n}{2} (2a_1 + (n-1)d)[/tex]

n = number of terms = 17 players

First term,

[tex]a_1 = 0[/tex]

Common difference, d = 1

Inputting the Values into the equation :

[tex]S_n = \frac{17}{2} (2(0) + 16 \times 1)[/tex]

[tex]S_n = 8.5(0 + 16)[/tex]

[tex]S_n = 0 + 136[/tex]

[tex]S_n = 136[/tex]

Hence, the minimum number of kicks which would be taken by the players in other to ensure that each player kicks to ball to every other atleast once is 136 kicks.

Learn more : https://brainly.com/question/24191787?referrer=searchResults


Related Questions

hey please help where it has the < thing it says “ones” “tens” “nines”

Answers

Answer:

[tex]9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ thank \: you [/tex]

What is the quotient of 8,595 ÷ 24?

Answers

its 3 hope this helpssss

358.125
That will be the answer

Product of (×-3)(2ײ-5×+1)

Answers

Answer:

The answer is 2x³+15x-6x²-2.

Step-by-step explanation:

(x-3)(2x²-5x+1)

2x³+1-6x²+15x-3

= 2x³-2+15x-6x²

solve the system of linear equations by eliminations x+5y=-2; 5x+y=14

Answers

I’ve attached my work….
Hope it helps!

4. Complete the following explanation to show that the sum of two rational numbers a
rational number.
Let a,b,c and d be integers. Let x and y be rational numbers. Consider the following
expression:
* = and y =
The above expressions represent the
If x + y = y + x
represents the
then, we can use the
to show that x +y = 3+. Using the rule for addition of
fractions to write an equivalent expression for x + y = 4+we obtain
The product of two integers results in an integer, so bd, ad and cb are all integers. Also.
since the sum of two integers results in an integer, ad + cb is an integer. Therefore,
xty is

Answers

Y +x=45 using integrated experience x +x = y

For the equation, x - 7 = 24, can a value be substituted for x to make the equation a true number sentence?

Answers

Answer:

yes, 31

Step-by-step explanation:

just switch the equation around:

24+ 7 = 31

and then back again:

31- 7= 24

Yes , the answer is 31
x - 7 = 24
x = 24 + 7
= 31

A rectangle has perimeter 66 cm and length 27 cm. What is its width?
(help pls it’s my hw)

Answers

Answer:

Step-by-step explanation:

A rectangle has the perimeter of 66cm, and since a rectangle has 2 lengths and 2 widths, we can tell that 2 widths = 66-27*2 = 12

so 1 width is half of 12 which is 6

Find x. Simplify completely.
х
9
10

Answers

Answer:

10

Step-by-step explanation:

geometric mean theorem :

h = sqrt(pq)

p, q being the segments on the Hypotenuse of the right-angled triangle.

so, x = sqrt(9×10) = 3×sqrt(10)

formula to calculate area of quadrilateral when Co ordinates are given please answer it anyone please...​

Answers

[tex]\sf \orange {Please \: attach \: the \: picture \: of \:}[/tex]

[tex]\sf \green {the \: Quadrilateral \: please.} \: [/tex]

You have to find the side lengths of the quadrilateral by using the coordinates. There isn’t really a formula for that. Once you have the side lengths, the formula for area will depend on the type of quadrilateral.

Estimate the value of the following to the tenths decimal place.

Answers

Answer:

-12.2

Step-by-step explanation:

-12.247448....

-12.2

plss mark me brainliesttt

Where is the blue dot on the number line?
-4.5
-5
-5.5

Answers

I think the blue dot is on -4.9

Answer:

the answers is -4.9

Step-by-step explanation:

if you count from -4.5 to the blue dot it will be -4.9

Factor this polynomial completely.
x2 - 81

Answers

The first answer is right
(x - 9) (x + 9)
It’s me again lol

HELP PLS: If f(x) = 2x – 3 and g(x) = 2x2 + 5x + 1, find:
a. f(4) + g(1)

Answers

Answer:

13

Step-by-step explanation:

f(x) = 2x - 3,

f(4) = 2(4) - 3,

f(4) = 5

g(x) = 2x^2 + 5x + 1,

g(1) = 2(1)^2 + 5(1) + 1,

g(1) = 2 + 5 + 1,

g(1) = 8

f(4) + g(1) =

5 + 8 =

13

Hope this helps :)

Answer:

Step-by-step explanation:

find the cube of a+3​

Answers

Answer:

(a+3)^3

a^3 + b^3 + 3ab [identity : (a+b)^3 )]

a^3+ 3^3 + 3×a×3

a^3 +27+9a

answer : a^3+27+9a

hope it helps you

mrk me braniliest plz

Answer:

[tex] {a}^{3} +9 {a}^{2} +27a+27[/tex]

Step-by-step explanation:

[tex](a + 3 {)}^{3} [/tex]

[tex] {a}^{3} +3 {a}^{2} \times 3+3a \times {3}^{2} + {3}^{3} [/tex]

[tex] {a}^{3} +9 {a}^{2} +3a× {3}^{2} + {3}^{3} [/tex]

[tex] {a}^{3} +9 {a}^{2} +27a+ {3}^{2} [/tex]

[tex] {a}^{3} +9 {a}^{2} +27a+27[/tex]

Hope it is helpful...

What are the missing numbers on the two number lines?

Answers

Answer:

C is -14, 7, 14, 28

not sure what D is

Step-by-step explanation:

Helpppppppppppppppppppp

Answers

Answer:

Step 1

Step-by-step explanation:

[tex]7 \times (8 - 3\times 2)[/tex]

Step 1:

[tex] = 7 \times (8 - 6)[/tex]

Step 2:

[tex]7 \times 2[/tex]

Step 3:

[tex]14[/tex]

more algebra............

Answers

Answer:

C

Step-by-step explanation:

this is the answer since it involves a minus sign

Cindy multiple her age by 5, subtracted 12, and then divide by 3. The result was 16. How old is Cindy?

Answers

Let's give Cindy's age a variable.

Cindy's age = x

Cindy multiplies her age by 5

x(5)

Subtracted by 12

x(5) - 12

Divide by 3

(5x - 12)/3

The result was 16

(5x - 12)/3 = 16

Let's solve

Multiply both sides by 3

(5x - 12) = 48

Open brackets

5x - 12 = 48

Add 12 to both sides

5x = 60

Divide by 5 on both sides to isolate x

x = 12

Cindy is 12 years old.

Wayne plans to replace the ventilating fand in the oldest greenhouse and needs to know its volume. The greenhouse is shaped of a half of a cylinder, Its diameter is 40 feet, Its length is 120 feet, using 3.14 for pi, how many cubic feet does the greenhouse enclose?​

Answers

Answer:

628.

Step-by-step explanation:

We need to calculate the radius of the cylinder :

   40/2 = 20 feet

We then will calculate the volume of the whole cylinder:

  [tex]V = \pi * r^{2} * h = 3.14 * 20^{2} * 120 = 1256[/tex] cubic feet.

However, Wayne greenhouse is just a half of a cylinder, so it's volume are:

  [tex]1256 / 2 = 628[/tex] cubic feet.

I'm vietanh and have a good day!

Help Me with this Math question Please

Answers

9514 1404 393

Answer:

  21 square units

Step-by-step explanation:

The formula for the area of a parallelogram is ...

  A = bh

where h is the height measured perpendicular to the base.

Here, it is convenient to use the horizontal dimension as the height, and the vertical dimension as the base. The vertical bases are 3 units long and 7 units apart horizontally.

  A = (3)(7) = 21 . . . . square units

Hiii! can someone please help me with my maths question

Form a quadratic equation and find the length of AB ​

Answers

Step-by-step explanation:

a^2 + b^2 = c^2

(x+2)^2 + 4x^2 = (3x+4)^2

(x+2)(x+2)+ 4x^2= (3x+4)(3x+4)

x^2 + 2x + 2x + 4 + 4x^2 = 9x^2 + 12x + 12 x + 16

5x^2 + 4x + 4 = 9x^2 + 24x + 16

-4x^2 - 20x - 12 = 0

now we can use the quadratic formula

(-b±√(b²-4ac))/(2a)

I can't type all this so

.....

x = -0.697224362 or -4.302775638

AB can't be negative so it's the first one

so it's equals to 1.302775638

Anyone know how to do this ( pls show work) pls help me

Answers

Answer:

Step-by-step explanation:

Temperature at 5 am = -7° F

Temperature at 9 am = 4° F

Temperature at 11 am =4 + 3.5 * 4 = 4 +  14 = 18° F

Total increase = 18 - (-4) = 18 + 4 = 22° F

ɪ ɴᴇᴇᴅ ʜᴇʟᴘ ᴡɪᴛʜ ᴛʜɪꜱ !
ᴍᴀᴛʜ ᴇxᴘᴇʀᴛꜱ ᴏɴʟʏ

Answers

Answer:

1.6

Step-by-step explanation:

an integer is defined as any positive or negative whole number.

1.6=16/10=8/5 . This is a fraction

0 is a whole number

8 is a whole number

-15 is a whole number

pls mark as brainliest. Thanks

-13 = [tex]\frac{r}{9}[/tex] +8

what is r?

Answers

Answer:

[tex] - 13= \frac{r}{9} + 8 \\ \frac{r}{9} = - 13 - 8 \\ \frac{r}{9} = - 21 \\ r = 9 \times - 21 \\ r = - 189[/tex]

I hope I helped you^_^

A and B are partners sharing profit and loss in the ratio of 3:2. A new partner C is admitted and 1/4 share off profit is given.what is the new profit sharing ratio ?

Answers

Answer:

Correct option is: 9:6:5

Step-by-step explanation:

I'm not sure but hope it helps.

p- (9-(m + q)); use m=4, p=5, and q=3

Answers

Answer:

3

Step-by-step explanation:

p-(9-(m+q))

5-(9-(4+3))

=5-(9-7)

=5-2

=3

1.
Input
Output
-5
0
1
2
(2,0)
% (-5,314)
1 27
3,87
2
3
8
a. Is the relation a function? Explain

Answers

Yes it’s function because each element of input is related to exactly one element in output

Click the picture and please help I need it fast because it’s timed

Answers

Answer:

y=3

Step-by-step explanation:

6=2(y+2)-4

6=2y+4-4

6-4+4=2y

6=2y

3=y

The answer you are looking for is y=3.

Solution/Explanation:

First, writing out the problem,

6=2(y+2)-4.

Next, using the Distributive Property for 2(y+2), which is 2y+4,

6=2y+4-4.

Now, canceling out the 4, since 4-4=0,

6=2y+0, or 6=2y.

Finally, dividing both sides by 2,

6/2=2y/2.

6/2=3.

2y/2=y.

3=y, or y=3.

So, therefore, the final answer is y=3.

I hope that this has helped answer your question. Good day to you.

Evaluate (2-5i)(p+q) when p=2 and q=5i​

Answers

Answer:

(2-5i)(p+q)

p=2

q=5i

(2-5i)(2+5i)

a²-b²=(a+b)(a-b)

2²-(5i)²

4-(5i)²

i²=-1

4+25=29

answer 29

HELP ASAP!!!

The line (y-1)=(2/3)(x+1) contains point (a,-3).

What is the value of a? Show
your work.

Answers

Answer:

-7

Step-by-step explanation:

The line (y-1)=(2/3)(x+1) contains point (a,-3)

=> (-3-1) = (⅔)(a+1)

-4 = (⅔)(a+1(

(a+1)= -4 ÷ ⅔

a + 1 = -4 × 3/2

a+ 1 = -6

a = -6-1

a = -7

The value of 'a' will be;

⇒ a = - 7.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of line is,

⇒ (y - 1) = (2/3) (x + 1)

And, The point on the line = (a, - 3)

Now,

Since, The point on the line = (a, - 3)

Hence, It satisfy the equation of line.

Substitute x = a and y = - 3, we get;

⇒ (y - 1) = (2/3) (x + 1)

⇒ (- 3 - 1) = (2/3) (a + 1)

⇒ - 4 × 3 = 2a + 2

⇒ - 12 - 2 = 2a

⇒ 2a = - 14

⇒ a = - 7

Thus, The value of a = - 7

Learn more about the substitution method visit:

https://brainly.com/question/26094713

#SPJ2

Other Questions
Is quadrilateral DEFG a parallelogram? Why or why not?Question 2 options:A) Yes, because adjacent angles aren't supplementary.B) No, because adjacent angles aren't congruent.C) There isn't enough information. D) Yes, because opposite angles are congruent. 4 2(x + 7) = 3(x + 5) Parte 1. Choose the subject pronoun that can substitute for theunderlined word(s).Escoge los pronombres que sustituyen las palabrassubrayadas.1. Las chicas son de Espaa.a. Ellas b. Ellos c. Nosotros2. La computadora es de Andrea.a. ellas b. ellac. el3. Pablo y Berta son profesores.a. lb. Ellosc. Ellas4. El conductores de los Estados Unidos.a. Yob. Tc. El5. Mnica, de dnde eres?b. Ella6. Quin es el seor Arango?a. nosotros b. ellosca7. Los mapas son de las chicas.a. nosotras b. ellasc. ellos8. La turista es estudiante.a. Yob. Elc. Ella9. Diego y yo somos hombres.a. Ellosb. Nosotros c. Nosotrasa. Tuc. Ela. Yo10. El autobs es de Daniel.a. ellasb. elc. ellos11. Las mujeres son jvenes.b. Ellosc. Ellas12. Laura Camila y yo somos unas chicas de Ecuador.a. Nosotras b. Tuc. Ellas13. Carolina, eres la chica de la fotografia?a. Nosotrasb. Tu14. De dnde son los pasajeros?b. ella15. Son las maletas de la estudiante.a. yob. ellac. ellasc. Yoa elc. ellos What's a good example using the word genocide? In your own words ? Which resident may a temporary feeding assistant?a. A resident with dementia b. A resident with swallowing problems c. A resident who has a tendency to aspirate or choke d. A resident who receives IV feedings A housepainter buys 40 gallon-size cans of paint for $920. Some of these are blue paint that cost $30 per gallon and the rest are white paint that cost $20 per gallon. How many gallons of white paint does the painter buy? Which system of inequalities is represented by the graph? y12x+2y2x1y4 y>2x+2y12x1y4 y 1. The plane .. (leave) Buenos Aires at midnight last night. I need help with this problem and please show step by step what would u change about yourself if u could Please help Q15!!!it will mean a lot +20 points what did Charles darwin discover on the galapagos islands? Multiply (FOIL)( x - 3)( 2x + 5)(3x + 7)(2x - 1) PLEASE HELP PLEASE PLEASE PLEASEAlvin's age is three times Elga's age. The sum of their ages is 112. What is Elga's age? What is DNA barcoding? Tech A says that open loop is when the PCM pretty much ignores the oxygen sensor signals. Tech B says that closed loop is when the PCM shuts off the fuel injectors during a collision. Who is correct The total number of elements in the power set of a set A containing n elements is Do you know this it is for social studies The student looks up the word count on his favorite book, if the book has pages that are 5.5 in. x 6.5 in. and 59,540 words how many pages is the book? (This sentence and picture combine.) If there are 3.28 feet in a meter , how many are in the 110 meter dash?