====================================================
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 toAnd 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.
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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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
Anyone know how to do this ( pls show work) pls help me
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
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 ?
Answer:
Correct option is: 9:6:5
Step-by-step explanation:
I'm not sure but hope it helps.
HELP ASAP!!!
The line (y-1)=(2/3)(x+1) contains point (a,-3).
What is the value of a? Show
your work.
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:
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Estimate the value of the following to the tenths decimal place.
Answer:
-12.2
Step-by-step explanation:
-12.247448....
-12.2
plss mark me brainliesttt
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
Helpppppppppppppppppppp
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]
Help Me with this Math question Please
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
find the cube of a+3
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...Factor this polynomial completely.
x2 - 81
more algebra............
Answer:
C
Step-by-step explanation:
this is the answer since it involves a minus sign
Evaluate (2-5i)(p+q) when p=2 and q=5i
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
hey please help where it has the < thing it says “ones” “tens” “nines”
Answer:
[tex]9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ thank \: you [/tex]
-13 = [tex]\frac{r}{9}[/tex] +8
what is r?
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^_^
Click the picture and please help I need it fast because it’s timed
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.
ɪ ɴᴇᴇᴅ ʜᴇʟᴘ ᴡɪᴛʜ ᴛʜɪꜱ !
ᴍᴀᴛʜ ᴇxᴘᴇʀᴛꜱ ᴏɴʟʏ
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
Find x. Simplify completely.
х
9
10
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)
For the equation, x - 7 = 24, can a value be substituted for x to make the equation a true number sentence?
Answer:
yes, 31
Step-by-step explanation:
just switch the equation around:
24+ 7 = 31
and then back again:
31- 7= 24
p- (9-(m + q)); use m=4, p=5, and q=3
Answer:
3
Step-by-step explanation:
p-(9-(m+q))
5-(9-(4+3))
=5-(9-7)
=5-2
=3
Where is the blue dot on the number line?
-4.5
-5
-5.5
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
A rectangle has perimeter 66 cm and length 27 cm. What is its width?
(help pls it’s my hw)
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
Product of (×-3)(2ײ-5×+1)
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
HELP PLS: If f(x) = 2x – 3 and g(x) = 2x2 + 5x + 1, find:
a. f(4) + g(1)
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:
Hiii! can someone please help me with my maths question
Form a quadratic equation and find the length of AB
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
What are the missing numbers on the two number lines?
Answer:
C is -14, 7, 14, 28
not sure what D is
Step-by-step explanation:
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?
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!
formula to calculate area of quadrilateral when Co ordinates are given please answer it anyone please...
[tex]\sf \orange {Please \: attach \: the \: picture \: of \:}[/tex]
[tex]\sf \green {the \: Quadrilateral \: please.} \: [/tex]
solve the system of linear equations by eliminations x+5y=-2; 5x+y=14
What is the quotient of 8,595 ÷ 24?
its 3 hope this helpssss
Cindy multiple her age by 5, subtracted 12, and then divide by 3. The result was 16. How old is Cindy?
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.