Problem 11
Six friends who enjoy tennis decide to play a game of singles and a game
of doubles every day of the 7-week school holidays.
(a) Show that at least four of the games of singles will be between friends
playing each other for the fourth time.
(b) Show that at least four of the games of doubles will be between pairs
playing the same opposing pair for the second time.

Answers

Answer 1

Number combination can be used to find the number of selecting n  items from m items

The known parameters are;

Number of days the six friends play a game of tennis = Every day = 7 days

Number of weeks the six friends the friends play for = 7 weeks

Therefore the total number of days = 7 × 7 days = 49 days

Required:

(a) The number of ways the friends can play with each other once is given as follows;

[tex]The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15[/tex]

The number of ways the six friends can play with each other once is 15 ways

Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;

[tex]\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6[/tex]

Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time

(b) The number of ways the friends can play game of doubles is given as follows;

[tex]C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]

The number of pairs = ₆C₂ = 15

The number of games of doubles = 49

In 49 games, we have;

The number of times the same opposing  will play a game of doubles where a member of the pair can be on either side of the court will given as follows;

[tex]\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6[/tex]

Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time

Learn more about combination here:

https://brainly.com/question/22692807


Related Questions

Barry is measuring the length of his pencils. The red pencil is 4.32 inches long, the blue pencil is 6.1 inches long, and the green pencil is 2.27 inches long. What is the sum of the lengths of the pencils? 7.20 inches 12.61 inches 12.69 inches


I NEED ANWSER FAST! AND QUICK! PLEASE HELP! I give 38 points who ever answer!! PLEASE!!!

Answers

Answer: [tex]\boxed {12.69 inches}[/tex]

Step-by-step explanation:

Given information

Red pencil = 4.32 inches

Blue pencil = 6.1 inches

Green pencil = 2.27 inches

Expression deducted from the question

Total length = Red pencil + Blue pencil + Green pencil

Substitute values into the expression

Total length = (4.32) + (6.1) + (2.27)

Simplify by addition

Total length = 10.42 + 2.27

Total length = 12.69 inches

Hope this helps!! :)

Please let me know if you have any questions

The sum of the length of the pencils is 12.69 inches

To Obtain the sum of the length of the pencils, we use the addition operator on the given lengths :

Red pencil = 4.32 inches Blue pencil = 6.1 inches Green pencil = 2.27 inches

The sum of the lengths of the pencils :

(4.32 + 6.1 + 2.27) inches = 12.69 inches

Therefore. The total sum of the lengths of the pencils is 12.69 inches

Learn more : https://brainly.com/question/2610134

SOLVE FOR X
2x+15=2x-15

Answers

[tex]\\ \rm\Rrightarrow 2x+15=2x-15[/tex]

[tex]\\ \rm\Rrightarrow 2x-2x=-15-15[/tex]

[tex]\\ \rm\Rrightarrow 0=-30[/tex]

Hence

[tex]\\ \rm\Rrightarrow x=\infty[/tex]

a) make h the subject of the formula
T=26- h/500
b) the outside air temperature T°C,of an aircraft at a height, h feet , given by
T=26- h/500

the outside air temperature of an aircraft is -53°C
1 metre=3³/8 feet

calculate the height in metres of the aircraft

Answers

Answer:

11703.7 metres

Step-by-step explanation:

* means multiply

/ means divide

plug in the values

T=26- h/500

-53 =  26- h/500

-53 -26 = h/500

-79 = h/500

-79 * 500 = h

-39500 = h

-39500 is in feet

3³/8 =

39500 / 3.375 =

11703.7037037 metres

Find three consecutive integers that have the sum of -402

Answers

Answer:

-135, -134, -133

Step-by-step explanation:

Hi there!

Let x be equal to the first integer in the set of three consecutive integers.

Let x+1 and x+2 be the consecutive integers.

We're given that they have a sum of -402.

We can construct an equation:

[tex](x)+(x+1)+(x+2)=-402[/tex]

Combine like terms:

[tex]x+x+1+x+2=-402\\x+x+x+1+2=-402\\3x+3=-402\\3x=-405\\x=-135[/tex]

Therefore the first integer is -135.

The next two consecutive integers after -135 is -134 and -133.

Therefore, the three consecutive integers are -135, -134 and -133.

I hope this helps!

The perimeter of a rectangle can be found using the formula P = 4 s .


True or False

Answers

Answer:

[tex]{ \underline{ \sf{true}}}[/tex]

Answer:

The perimeter of a rectangle can be calculated by adding both lengths, and both widths

Step-by-step explanation:

Help anyone can help me do this question,I will mark brainlest.​

Answers

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

you are totally correct

Rewrite as a simplified fraction
0.67
7 is repeating

Answers

Answer:

[tex]\frac{17}{25}[/tex]

Step-by-step explanation:

So because it is a repeating decimal we have to round it off first. We can round it to the nearest hundredth making it 0.68. This then becomes [tex]\frac{68}{100}[/tex] as a fraction which can be reduced to its lowest terms by dividing both the numerator and denominator by 4 and then it becomes [tex]\frac{17}{25}[/tex].

HOPE THIS HELPED

67/99 if you divide 67 by 99 it equals to 67/99 which is also a repeated 67

Need help ASAP please!! See attached photo

Answers

Answer:

Angle ABC = 110 degrees

Step-by-step explanation:

Set angle ABC equal to the two parts and solve for x

17x + 8 = 42 + 12x - 4

17x + 8 = 12x + 38

5x = 30

x = 6

Plug in x to angle ABC and solve

17(6) + 8 = 110

2sin60° sin90°+ cos60°cos0​

Answers

Answer:

[tex]\sqrt{3 }[/tex] + [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using exact values

2sin60°sin90° + cos60°cos0°

= 2 × [tex]\frac{\sqrt{3} }{2}[/tex] × 1 + [tex]\frac{1}{2}[/tex] × 1

= [tex]\sqrt{3}[/tex] + [tex]\frac{1}{2}[/tex] ← exact value

Solve each for X. Show your work


2x - 3(x + 5) = -10


Answers

2x - 3(x + 5) = -10

2x - 3x - 15 = -10

2x - 3x = -10 + 15

-x = 5 / : (-1)

x = -5 ← the end

find the ratio in lowest terms a 1.5m and 75 cm​

Answers

Hope it helps !!!!!!

Which is equivalent to 64^1/4?
2^4√4
4
16
16^4√4

Answers

Answer:

Step-by-step explanation:

[tex]64^1/4\\\\=\dfrac{64^{1}}{4} \\\\=\dfrac{64}{4} \\\\=16\\\\Answer\ C[/tex]

Name:
Date:
Bell: Homework 5: Multi-Step & Compound
Inequalities
** This is a 2-page documenti **
Directions: Solve, graph, and write the solution to each inequality in interval notation,
1.-7a - 11 <1-10
2. 5-9(8 - 2x) = 2x - 115
Interval Notation:
3.-2(7 + y)2 -8(y + 1)
Interval Notation:
4.-5(k+ 4) 2-(3k + 6)
Interval Notation:
Interval Notation:
3(2x + 7)
> x+1
-3
6. r + 10 S-3(2r - 3) + 6(r + 3)
5.
Interval Notation:
Interval Notation:
7.-8m - 12 > -5(m - 8) - 3(m - 7)
8. 18(9-3)=-2{q+7)
Interval Notation:
Interval Notation:
O Gina Wilson (All Things Algebra

Answers

Step-by-step explanation:

what you have written I can't send one thing on

5(x + 1) - 8 = 5x(2-4)

what is the value of x?

a. -5
b. -1/5
c. 5
d. 1/5

Answers

Answer:

d) 1/5

Step-by-step explanation:

5(x + 1) - 8 = 5x(2-4)

5x+5-8 = 5x(-2)

5x-3=-10x

15x = 3

x = 1/5

Answer:

d. 1/5

Step-by-step explanation:

5(x + 1) - 8 = 5x(2-4)

=> 5x + 5 - 8 = 10x - 20x

=> 5x + 20x - 10x = 8 - 5

=> 15x = 3

[tex] = > x = \frac{3}{15} [/tex]

=> x = 1/5 (option d) (Ans)

five times the sum of two times a number and 3

Answers

Answer:

5×(2x+3)

Step-by-step explanation:

hope this helps:)

help pls ASAP im doing this for my sister.

10 points if you check that the work is correct or wrong!1
Also i need answers for the bottom.

Answers

Your answer for the greater than problem was wrong. You can only use each of the numbers once. You can use my example. It’s the right way



52,341 is bigger than 43,521. That is why 52,341 is greater than 43,521.

Answer:

1. Amy, Rick, Jeff, Bonnie (Bonnie wins)

2a. You're answer is correct since there is multiple ways to do it

2b. 52212 is greater than 43541 because it is a bigger number

Step-by-step explanation:

20 = 7x + 2 - 4x
What does x equal

Answers

Answer:

x = 6

Step-by-step explanation:

20 = 7x + 2 - 4x

7x + 2 - 4x  = 20    (switch the sides)

7x - 4x + 2 = 20     (group the like terms together)

3x + 2 = 20            (add similar numbers, in this case it's the both x's)

    -2     -2              (subtract 2 on both sides)

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

3x = 18

/3     /3                   (divide both sides by 3)

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

x = 6

The answer is 6 put it in to double check tho

collection of even numbers is well defined set or not​

Answers

Answer:

set of even counting number is well-defined

A line is parallel to the x-axis and passes through the point (-5,4)
What is the equation of that line, the slope of that line, and what would be the slope of a line perpendicular to that given line?

Answers

9514 1404 393

Answer:

y = 4slope: 0slope of perpendicular: undefined

Step-by-step explanation:

The x-axis is a horizontal line. As such, it has a slope of zero. The equation of a horizontal line is ...

  y = constant

__

For the line through (-5, 4), the constant must match the y-coordinate: 4. The equation is ...

  y = 4

As we said above, the slope of that horizontal line is zero.

The perpendicular line will be a vertical line of the form x=constant. The slope of a vertical line is undefined.

Find f(3x-2) for f(x)=x-5

Answers

Answer:

f(x)=x–5

f (3x–2) = (3x–2) –5

f (3x–2) = 3x–7

I hope I helped you^_^

pls help with the last question ---------------

Answers

The answer is ‘describe’

PLEASE HELP ASAP I NEED AN ANSWER WITHIN 10 MIN PLEASE

Answers

Answer:

hope this helps you

have a great day

Terri's project for the Math Fair is a magnificent black box that she called a function machine. If you put 3 into her machine, the output is 8. If you put in 10, the output is 29; and if you put in 20, the output is 59. Homework help

a. What would her machine do to an input of 5? What about -1? What about x?

b. Write an equation for Terri's machine​

Answers

Answer:

a) An input of 5 gives an output of 14. An input of -1 gives an output of -4.

An input of x gives an output of 3x - 1

b) y = 3x - 1

Step-by-step explanation:

The pattern is that you multiply the number by 3 then subtract 1.

3*3 - 1 = 9 - 1 = 8

10 * 3 - 1 = 30 - 1 = 29

20 * 3 - 1 = 60 - 1 = 59

So:

a)

For an input of 5,

5 * 3 - 1 = 15 - 1 = 14

For an input of -1:

-1 * 3 - 1 = -3 - 1 = -4

For an input of x:

x * 3 - 1 = 3x - 1

So the equation is

b) y = 3x - 1

where x is the input value.

Ill give brainlyest I just need help asap!
solve for x in the problem below and show all work
7x - 5x/3 (20/x - 8) -48=0

Answers

Hello!

Let’s work this out step by step.

The first thing you want to do is move that 48 to the other side. To do that, add 48 to both sides:

7x-5x/3(20x-8)=48

Now, the equation isn’t equal to zero… so it is solvable! Remember in order of operations: PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction. So, let’s start by multiplying the (-5x/3) by the components inside the parentheses to get rid of the parentheses altogether!

7x-100x/3x+40x/3=48

Since both the numerator and denominator have an “x” in them in “100x/3x”, you can cancel out the “x”s to just get 100/3, which is 33.333333

7x-100/3+40x/3=48

Let’s get rid of that 100/3 by adding it to both sides.

7x+40x/3=81.33333333333

Transform 7x to a fraction that can be added to 40x/3 (common denominators)

7x=7x/1

7x/1* (3/3)= 21x/3

Now, add the two fractions together

21x/3+40x/3= 61x/3

61x/3=81.333333333

Get rid of the 3 by multiplying on both sides:


61x= 244

Divide by 61 to get x

X=4

Hope this helped! Comment if you have any questions!

If 2x - 4= 16 for some value of x, then
what is the value of x + 2 for the same
value of x?

Answers

Answer:

12

Step-by-step explanation:

2x - 4= 16

Divide by 2

2x/2 -4/2 = 16/2

x -2 = 8

Add 4 to each side

x-2+4 = 8+4

x+2 = 12

Final Answer: 12
Step 1:
2x - 4 = 16
+4 = +4
2x = 20
2x/2 = 20/2
x = 10

Step 2:
x + 2
10 + 2 = 12

So your answer is 12.

[tex]5^{6}[/tex]

Please show work:

Answers

Hope this helps

5x5x5x5x5x5= 15625
5^6 plugged into a calculator is 15625

If you’re looking for a way to do the math with a calculator, however, just multiply 5*5, then that answer with 5, and repeat until you’ve done with six “5”s. For that method, your original 5*5 counts as two of your six “5”s.

On the​ test, when Tom simplified the expression he got 5.8. What mistake did Tom likely make when he simplified the​ expression?

Answers

Answer:

It is likely that Tom did not expand brackets fully or forgot to subtract and add from both sides.

Step-by-step explanation:

Find XZ if Y is the midpoint of XZ, XY = 2a + 11, and YZ = 4a - 5

Answers

Answer:

XZ=54

Step-by-step explanation:

X___Y___Z

XY= YZ

2a+11=4a-5

4a-2a= 11+5

2a=16

a=16/2

a=8

XY=2a+11=2(8)+11=16+11=27

YZ=4a-5 = 4(8)-5=32-5=27

XZ=XY+YZ =27+27=54

I hope I helped you^_^

-6x –(-9 – 4x) = -2(3x – 5)?

Answers

Answer:

x = 1/4

Step-by-step explanation:

-6x –(-9 – 4x) = -2(3x – 5)

-6x + 9 + 4x = -6x + 10

-2x + 9 = -6x + 10

-2x + 6x = 10 - 9

4x = 1

x = 1/4

I have no idea what I am doing

Answers

Answer:

I have no idea either

Step-by-step explanation:

Answer: -14
Start by plugging in the given.
-6 -8/4 -6 =
Then continue on by simplifying.
Add the like terms.
-12 -8/4 =
Simplify the fraction so it’s easier to add.
-2-12 =
-14 =
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