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:
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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!!!
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 inchesThe 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
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SOLVE FOR X
2x+15=2x-15
[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
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
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
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.
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
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
Need help ASAP please!! See attached photo
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
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
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
Which is equivalent to 64^1/4?
2^4√4
4
16
16^4√4
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
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
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. 1/5Step-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
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.
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
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
collection of even numbers is well defined set or not
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?
9514 1404 393
Answer:
y = 4slope: 0slope of perpendicular: undefinedStep-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
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 ---------------
PLEASE HELP ASAP I NEED AN ANSWER WITHIN 10 MIN PLEASE
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
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
If 2x - 4= 16 for some value of x, then
what is the value of x + 2 for the same
value of x?
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
[tex]5^{6}[/tex]
Please show work:
On the test, when Tom simplified the expression he got 5.8. What mistake did Tom likely make when he simplified the expression?
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
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)?
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
Answer:
I have no idea either
Step-by-step explanation: