The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³
The reason for arriving at the above probability is as follows:
The given parameters are;
The number of teams in the tournament, n = 60
The chance of a team winning a game = 50% = 0.5
The number of ties = No ties
The required parameter:
The probability that no two teams win the same number of games
Method:
Calculate the number of ways no two teams win the same number of games, and divide the result by the total number of possible outcomes
Solution:
The number of matches played, n = [tex]\dbinom {60} {2}[/tex] = 1,770
The possible outcomes = 2; Winning or losing
The total number of possible outcomes, [tex]n_p[/tex] = 2¹⁷⁷⁰
The number of games won by each team is between 0 and 59
The ways in which no two teams won the same number of games is given by the games won by the teams to be 0, 1, 2,..., 57, 58, 59
Therefore, the number of ways no two teams won the same number of games, the required outcomes, [tex]n_k[/tex] = 59!
[tex]Probability = \dfrac{Number \ of \ possible \ outcomes}{Number \ of \ required\ outcomes}[/tex]
The probability that no two teams win the same number of games is given as follows;
[tex]\mathbf{P(No \ two \ teams \ won \ the \ same \ number \ of \ games)} = \dfrac{n_k}{n_p}[/tex]
Therefore;
[tex]P(No \ two \ teams \ won \ the \ same \ number \ of \ games) = \dfrac{59!}{2^{1,770}} \approx \mathbf{2.084 \times 10^{-453}}[/tex]
The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³
Learn more about probability theory here:
https://brainly.com/question/1539712
can Someone Answer This Please! The Question Is on the Attached Photograph Below: Thanks!
Answer:
a^5÷a^3=a^5×a^-3=a^5+-3=a^2
Answer:
[tex]a) \: \: {a}^{2} [/tex]
[tex]b) \: \: c[/tex]
Step-by-step explanation:
[tex]a) \: \: {a}^{5} \div {a}^{3} \\ = (a \times a \times a \times a \times a)(a \times a \times a) \\ = a \times a \\ = {a}^{2} [/tex]
[tex]b) \: \: \frac{ {c}^{4} }{ {c}^{3} } \\ \frac{(c \times c \times c \times c)}{(c \times c \times c)} \\ = c[/tex]
Hope it is helpful.....IN NEED OF HELP LIKE ASAP!
Answer:
Below
Step-by-step explanation:
2^-3 / 2^2 is equal to 1 / 2^5
Write the expression in exponential form
2^-5 = 2^-5
Set the exponents as equal
-5 = -5
So this is true
Hope this helps! Best of luck <3
-3(2d + 5) please help me solve this using distributive property
Answer:
-6d -15
Step-by-step explanation:
-3(2d + 5)
Distribute
-3 *2d -3*5
-6d -15
1. x/5 + 10 = 40
2. 4x - 36 = -2
i would really appreciate it if you'd help me
Answer:
1.) x = 150
2.) x = 8.5
Step-by-step explanation:
1.)
[tex]\frac{x}{5}+10=40\\\\\frac{x}{5}=30\\\\x=150[/tex]
2.)
[tex]4x-36=-2\\\\4x=34\\\\x=8.5[/tex]
Answer:
1. x = 150
2. x = 8.5
Step-by-step explanation:
1. x/5 + 10 = 40
Get x by itself and then solve for x.
First, subtract 10 from both sides
x/5 + 10 - 10 = 40 - 10
x/5 = 30
Then, multiply by 5 to get x by itself.
x/5 = 30
x/5 * 5 = 30 * 5
x = 150
2. 4x - 36 = -2
Get x by itself and then solve for x.
First, add 36 to both sides
4x - 36 + 36 = -2 + 36
4x = 34
Then, Divide each side by 4
4x/4 = 34/4
x = 8.5
Carrie likes to buy t-shirts at the local clothing store.
They cost $9.95 each. One day, she bought 25t-shirts.
How many money did she spend?
what is the square root of 465
Answer:
The square root of 465 with one digit decimal accuracy is 21.5.
Step-by-step explanation:
√465 = 21.5
Your bank account balance is -$20.85. You deposit the $15.50. What is your new balance?
Answer:
-5.35
Step-by-step explanation:
-20.85
+15.50
this helps with the problem
Need Help, with steps
Answer:
It is C
Step-by-step explanation:
PM = QM
[tex]6x - 8 = 2x + 4 \\ 6x - 2x = 4 + 8 \\ 4x = 12 \\ x = 3[/tex]
Answer:
C.) x = 3
Step-by-step explanation:
The diagonals of a rectangle are equal, and QM and PM are both half of the two diagonals. You can now say that 2 * (6x - 8) = 2 * (2x + 4), meaning that 12x - 16 = 4x + 8, where you can add 16 on both sides, then subtract by 4x on both sides to get that 8x = 24. Now divide by 8 on both sides to get that x = 3.
Determine if the following statement is true or false. If false provide a counterexample.
An equation with an integer coefficient will always have an integer solution.
Answer: An equation with an integer coefficient will NOT always have an integer solution.
Explanation: 3x=25⟹x=253 , therefore it is false.
Algebra! Question 18!!!!
-9(1 - 10n) - 2(3n + 9)
Step-by-step explanation:
-9(1-10n)-2(3n+9)
-9+90n-6n-18
-9-18+90n-6n
-27+84n
3(-9+28n)
please help with me #15 and #16
Answer:
just solve equation and you will get to know that
15 is d becoz both 8 gets cancelled
and
16 is b becoz then equation is simplified to x = smthng
The period of a compound pendulum is given by T=2π√(h²+k²/gh) express k in terms of T,h and g
Answer:
qss-qvcj-kwr join guys iam bored
Ari lives 4/5 of a mile from the park she has already walked 3/4 of the way to the park. How far has ari walked
fraction into the statement 1:50000
Answer:
am I supposed to change this to a statement like a sentence then one is to fifty thousand
is 16 a natural, whole, integer, rational or irrational number?
Answer:
16 is a natural, whole and integer
Step-by-step explanation:
16 is a natural, whole and integer
it is not rational or irrational because
rational numbers are written in p/q as well as irrational
natural numbers start from 1 till infinite
whole numbers start from 0 to infinite
integers include all the positive and negative numbers
The GCF of two numbers is 3.
Their LCM of the two numbers is less than 20.
Which could not be the two numbers?
Answer:
Step-by-step explanation:
Let say a and b the 2 natural integers with 0 < a< b.
Since a*b=GCF(a,b)*LCM(a,b)
a*b < 3*20=60
[tex]\begin{array}{c|c|c|c|c|c}a&b&a*b&GCF&LCM&GCF*LCM\\---&---&---&---&---&---\\3&6&18&3&6&18\\3&9&27&3&9&27\\3&12&36&3&12&36\\3&15&45&3&15&45\\3&18&54&3&18&54\\6&9&54&3&18&54\\---&---&---&---&---&---\\\end {array}[/tex]
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
1.Write the linear equation that models the equation?
2.What is the cost per T-shirt?
3.What is the standard shipping and handling bag?
Step-by-step explanation:
Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.
Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.
The second word problem is:
It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)
Cost= m x+b
x is the cost per shirt, b is the handling charge
295=40m+b
565=80m+b
subtract the first equation from the second:
370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b
One the second question,
Cost= variable cost * n + Fixedcosts or
cost= n*v+F
1250=500v+f
1050=100v+f
subtract the second equation from the first
200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.
Determine the supplement of each angle measure.
63°
Answer:
117 is the answer of your questions
Step-by-step explanation:
supplement=180
given angle=63
180-63=117
Point W is on line segment V X. Given VX = 18 and VW = 14 determine the length W X
Answer: WX = 4
Concept:
Here, we need to know the idea of segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Given information
VX = 18
VW = 14
Given expression deducted from the segment addition postulate
WX = VX - VW
Substitute values into the expression
WX = 18 - 14
Simplify by subtraction
WX = 4
Hope this helps!! :)
Please let me know if you have any questions
What is (x)
9.4x+17.5
Answer: x=1.8617
Step-by-step explanation: 9.4x+17.5 9.4x/9.4=17.5/9.4 x=1.8617
step by step
6x+1<9-2x
2x-1 less than or equal to 5x+20
3-(2x-7) less than or equal to 34-6x
Answer:
6x+1<9-2x
6x+2x<9-1
8x<8
x<1
2x-1 ≤ 5x+20
2x-5x≤20+1
-3x≤21
x≥-7
3-(2x-7) ≤ 34-6x
3-2x+7 ≤ 34-6x
-2x+6x ≤ 34-3-7
4x ≤ 24
x ≤ 6
Write an equation in slope-intercept form of a line that passes through the point (-4,9) and has a slope of 1/2.
Answer:
y = 1/2x + 11
Step-by-step explanation:
y = 1/2x + b
9 = 1/2(-4) + b
9 = -2 + b
b = 11
What is 3(x-6)+12=6(x+1)-3x show your work.
Answer:
No solution.
Step-by-step explanation:
3(x - 6) + 12 = 6(x + 1) - 3x
3x - 18 + 12 = 6x + 6 - 3x
3x - 6 = 3x +6
-6 = 6
-6 ≠ 6
How many meters does a runner cross in a circular runway with radious of 100 meters [R=3, 14]
The length of each side of an equilateral triangle having an area of 9√3 cm² is
Answer:
6 cm
Step-by-step explanation:
Let each side of the equilateral triangle be a.
Given, area of an equilateral triangle = 9√3 cm2
Area of an equilateral triangle = (√3)/4 × (Side)²
=> (√3)/4 × a² = 9√3
[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]
=> a² = 36
[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]
∴ Side = 6 cm [taking positive square root because side is always positive]
another easy question pls answer
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
complementary angles add up to 90°
x + 3x = 90°
4x = 90
90/4 = x
x = 22.5
The first angle is 22.5
The second angle is 3 times as much
22.5 x 3 = 67.5
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
s= zh - 2zt^3 solve for z
Hi ;-)
[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]
Answer:
z = [tex]\frac{s}{h-2t^3}[/tex]
Step-by-step explanation:
Given
s = zh - 2zt³ ← factor out z from each term
s = z(h - 2t³ ) ← divide both sides by h - 2t³
[tex]\frac{s}{h-2t^3}[/tex] = z
Which is the graph of the equation y- 1= 5(x-3)?
Answer:
linked below
Step-by-step explanation:
If you use desmos, it show this which is the correct graph :)
suppose a 13 foot ladder is leaning against a building. Reaching to the bottom of a second floor window 12 ft above the ground. How far is the base of the ladder from the building? Round your answer to the nearest 10th
5 ft
4ft
3ft
6ft
Answer: First Choice. 5ft
Step-by-step explanation:
Here we need to know the idea of the Pythagorean theorem.
Since a building is straight, the base angle is a right angle, thus it would be a right triangle.
Pythagorean Theorem: a² + b² = c²
**NOTE** Please refer to the attachment below for the figure. (I drew it, so if it was not clear and understandable for you, please tell me.)
Solve:
Given information
a = 12 ft
c = 13 ft
b = unknow base length
Given formula for Pythagorean Theorem
a² + b² = c²
Substitute values into the formula
12² + b² = 13²
Simplify exponents
144 + b² = 169
Subtract 144 on both sides
144 + b² - 144= 169 - 144
b² = 25
Square root both sides
√b² = √25
[tex]\boxed{b=5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
