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.

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Answer:

1.6

Step-by-step explanation:

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Answers

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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.

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find the cube of a+3​

Answers

Answer:

(a+3)^3

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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]

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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

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Answer:

Step-by-step explanation:

What are the missing numbers on the two number lines?

Answers

Answer:

C is -14, 7, 14, 28

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Step-by-step explanation:

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
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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

10

Step-by-step explanation:

geometric mean theorem :

h = sqrt(pq)

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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

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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]

What is the quotient of 8,595 ÷ 24?

Answers

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Answers

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Answers

Answer:

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Answers

Answer:

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

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

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(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

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Divide by 5 on both sides to isolate x

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Cindy is 12 years old.

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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

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

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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

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a+ 1 = -6

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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,

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

Hence, It satisfy the equation of line.

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⇒ (- 3 - 1) = (2/3) (a + 1)

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⇒ a = - 7

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-4.5
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Answers

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Answer:

the answers is -4.9

Step-by-step explanation:

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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!

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….
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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.

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

-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:

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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.

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

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

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