Answers
Related Questions
Problem 3) A, B, and C are evenly matched tennis players. Initially A and B play a set and the winner then plays C. This continues, with the winner always playing the waiting player, until one of the players has won two sets in a row. That player is then declared the overall winner. Find the probability that A is the overall winner.
Answers
Answer:
the probability that A is the overall winner is 5/14 or 0.35714
Step-by-step explanation:
Given the data in the question;
probability that A is the overall winner P[A is the overall winner]
⇒ [tex]P_{A}[/tex][tex]P_{A}[/tex] + [tex]P_{A}[/tex][tex]P_{C}[/tex][tex]P_{B}[/tex][tex]P_{A}[/tex][tex]P_{A}[/tex] + [tex]P_{A}[/tex][tex]P_{C}[/tex][tex]P_{B}[/tex][tex]P_{A}[/tex][tex]P_{C}[/tex][tex]P_{B}[/tex][tex]P_{A}[/tex] [tex]P_{A}[/tex] + ................
= [tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{A}[/tex][tex]P_{A}[/tex] + [tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{A}[/tex][tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{A}[/tex][tex]P_{A}[/tex] + [tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{A}[/tex][tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{B}[/tex][tex]P_{C}[/tex][tex]P_{A}[/tex] + ........
P(A) = [tex]\frac{1}{2}[/tex] = [tex]P_{B}[/tex] = [tex]P_{C}[/tex] ∴{ they are evenly matched player}
so P(A is overall winner) will be;
= ([tex]\frac{1}{2}[/tex])² + ([tex]\frac{1}{2}[/tex])⁵ + ([tex]\frac{1}{2}[/tex])⁸ + ..........+ ([tex]\frac{1}{2}[/tex])⁴ + ([tex]\frac{1}{2}[/tex])⁷ + ([tex]\frac{1}{2}[/tex])¹⁰ + .............
= ([tex]\frac{1}{2}[/tex])² [1 + ([tex]\frac{1}{2}[/tex])³ + ([tex]\frac{1}{2}[/tex])⁶ + .........] + ([tex]\frac{1}{2}[/tex])⁴[1 + ([tex]\frac{1}{2}[/tex])³ + ([tex]\frac{1}{2}[/tex])⁶ + .........]
= [ ([tex]\frac{1}{2}[/tex])² + ([tex]\frac{1}{2}[/tex])⁴ ] [ 1 / 1 - ([tex]\frac{1}{2}[/tex])³ ]
= [ ([tex]\frac{1}{4}[/tex]) + ([tex]\frac{1}{16}[/tex]) ] [ [tex]\frac{8}{7}[/tex] ]
= [tex]\frac{5}{16}[/tex] × [tex]\frac{8}{7}[/tex]
= 5/14 or 0.35714
Therefore, the probability that A is the overall winner is 5/14 or 0.35714
The probability that A is the overall winner is; 5/14
Let P be the chance that a player will win the tournament when he gets a new opportunity to play against the victor of the previous game.Now, if the player loses, then it means that two games in a row are won by the same player, and then the tournament will be over. Thus; [tex]P_{L}[/tex] = 0
However, If the player wins first, and then loses his next game, it means that such a player will have to hope for a new opportunity. What this implies is that the player to whom he lost to will not win the next game. The probability of this happening is; [tex]P_{WLX}[/tex] = ¹/₂ × ¹/₂ × ¹/₂;[tex]P_{WLX}[/tex] = ¹/₈
Furthermore from that above, he will have another chance to win twice in a row which gives a probability in form of a geometric series as;
¹/₄ + (¹/₄ × ¹/₈ ) + (¹/₄ × ¹/₈² ) + (¹/₄ × ¹/₈³ ) + ........
Now, for that series, as n approaches infinity, the sum of the series would give us;
∑ = ¹/₄(1/(1 - ¹/₈ ))
⇒ ¹/₄(⁸/₇)
⇒ ²/₇
Since player C's first game would already be against another game's winner, then it means that P is also the chance player C will win the tournament but the probability that player A will win is same as probability that player B will win which is;
[1 - (²/₇)]/2
⇒ ⁵/₇ × ¹/₂
P(A) = P(B) = ⁵/₁₄
Read more on probability at; https://brainly.com/question/24855677
two families that live 270 mi apart plan to meet at a park located between their two homes.both leave at 9:00 am but one family averages 12 mph faster than the other family.
if the families meet at the designated spot 2 and half hours later, determine the average rate of speed for each family
Answers
Answer:
Family 1 average rate of speed was 66 miles per hour, while Family 2 average rate of speed was 54 miles per hour.
Step-by-step explanation:
Since two families that live 270 mi apart plan to meet at a park located between their two homes, and both leave at 9:00 am but one family averages 12 mph faster than the other family, if the families meet at the designated spot 2 and half hours later, to determine the average rate of speed for each family, the following calculation must be performed:
Family 1: ((270/2) + (12 x 2.5)) / 2.5
Family 1: (135 + 30) / 2.5
Family 1: 165 / 2.5
Family 1: 66 miles per hour
Family 2: (270/2) / 2.5
Family 2: 135 / 2.5
Family 2: 54 miles per hour
In this exercise we have to use the knowledge of speed to calculate the speed each family achieves, thus we find that:
Family 1 the average rate of speed for each family is 66 miles per hour.Family 2 the average rate of speed for each family is 54 miles per hour
Since two families that live 270 mi apart plan to meet at a park located between their two homes, and both leave at 9:00 am but one family averages 12 mph faster than the other family, if the families meet at the designated spot 2 and half hours later, to determine the average rate of speed for each family, the following calculation must be performed:
So looking at family 1 we found that:
[tex]F_1:\frac{ ((\frac{270}{2.5})+(12*2.5))}{2.5} \\F_1: \frac{(135 + 30)}{2.5}\\F_1: \frac{165}{2.5}\\F_1: 66 \ miles \ per \ hour[/tex]
So looking at family 2 we found that:
[tex]F_2: \frac{(\frac{270}{2})}{2.5}\\F_2: \frac{135}{2.5}\\F_2: 54 \ miles \ per \ hour[/tex]
See more about speed at brainly.com/question/7359669
I really really need help with this! I will give brainliest! It is a 3 part question, but i really need help with it.
The graphs of y=p(x) and y=q(x) are shown. The graph of y=q(x) is a transformation of the graph of y=p(x).
a. Write a formula for the function p.
b. Describe how the graph of y=q(x) can be obtained from the graph of y=p(x).
c. Write a formula for the function q.
Answers
Answer:
Step-by-step explanation:
The function p is an absolute value equation p(x)=|x| or it could be described as the sqare root of x squared.
q(x) could be the negative of p(x) raised by two units
q(x)=-|x|+2
Which of the following is not a desired characteristic of a ‘model?’
a. Correspondence (with real-world phenomenon being modeled).
b. Abstraction (inclusion of fewer features than the real-world phenomenon being modeled).
c. Simplification (i.e., simpler than real-world phenomenon being modeled).
d. Complexity (i.e., more complex than real-world phenomenon being modeled)
Answers
Answer:
Step-by-step explanation:
D.. Complexity (i.e., more complex than real-world phenomenon being modeled
find the percent change from $20 to $25
Answers
Answer:
20%decrease
Step-by-step explanation:
sorry I'm bad at explaining things
7. -3.5, 5, 0.6,-0.2
Witch one is least to greatest
Answers
Answer:
-3.5,-0.2,0.6,5 ... is the answer
Find the unknown coordinate so the line through the points has a given slope.
(2, Y), (4, 20); slope = 5
Answers
Answer:
8888888888888888888888 my dude
!!!!!!!!!PLEASE HELP ME!!!!!
Ernesto received a raise in his hourly pay, from $20.65 to $23.55. find the percent change round to the nearest tenth of a percent
Answers
2.9 / 20.65 = 0.140436
0.140436 x 100 = 14.0436
Therefore that to the nearest tenth of a percent would be:
14% increase
A new sports equipment company, Sports EQUIP, sold 2,835 helmets in their second year
of operation. This is 225% of the number of helmets they sold in their first year. Another
sports equipment company, Sports Inc., sold 446 helmets in their second year of
operation. This is 35% of the number of helmets they sold in their first year. Which
company sold more helmets in their first year?
Answers
Answer:
sports Inc sold more helmets
mUTS=172, mATS=x+116 and mUTA=x+64 Find mUTA
Answers
Answer:
m<UTA=56⁰
Step-by-step explanation:
172-116=56
if you know that UTS is equal to 172. take 172 subtracting 116(which is angle ATS). 56 would be the degree for angle UTA
Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? ) What is the greatest number of packages of soap and toothbrushes that Marcus can make? Marcus can make at most 12 packages. ) How many bars of soap and toothbrushes are in each package? 2 toothbrushes in each pockage 6) There are ? bars of soap and ? toothbrushes in each package?
Answers
Answer:
Marcus can make 12 packages, with 2 toothbrushes and 3 bars of soap in each package.
Step-by-step explanation:
For all the packages to be identical, they must all contain the same numbers of soaps and the same nuber of toothbrushes.
The ratior of soaps to brushes is 36/24 = 3/2
He could make 24 packages, each with 1 tootbrush and (3/2) bars of soap.
Assuming he is not going to cut soap bars in half, that is no good.
To make the numbers of individual items come out as integers, the smallest number he can multiply them by is the denominator on the (3/2) bar of soap. That would be a 2.
So he can makes packages with toothbrushes = 2 x 1 =2
and soap bars = 3/2 x 2 = 3
He can put 5 items in each package - 3 soap bars and 2 toothbrushes.
That means he makes 12 packages.
The greatest number of packages is 12 with 2 toothbrushes and 3 soap bars in each package.
It is given that the Marcus has 36 bars and 24 toothbrushes and wants to arrange the items so the packages are identical.
It is required to find the greatest number of packages that Marcus can make using all the soap and toothbrushes.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.
Marcus has number of bars of soap = 36 and
Number of tooothbrush = 24
The ratio of soap bars to toothbrushes = 36:24 or
= 3:2
It meanse Marcus can make 24 packets with [tex]\frac{3}{2}[/tex] soap bars and toothbrush
Because there are 24 toothbrushes but the number of bars can not be in fraction so multiply by 2 on denominator, we get:
Number of toothbrushes = 2×1 = 2
Number of soap bars = [tex]\frac{3}{2}[/tex] ×2 = 3
Now he can make total 12 packets with 2 toothbrushes and 3 soap bars.
Sum of toothbrushes and soap bars = 24+36 = 40
Number of soap bars and toothbrush in each packet = 2+3 = 5
Number of packages= [tex]\frac{60}{5}[/tex] = 12
Thus, the greatest number of packages is 12 with 2 toothbrushes and 3 soap bars.
Learn more about the fraction here:
brainly.com/question/1301963
what is 5/9 + 1/5= ??
Answers
Answer:
34/45
Step-by-step explanation THERE IS NO NEED 5/9 +1/5=34/45
~!!!!! LEASE HELP ME IN IN 7TH GRADE LEARNING 9TH AND 8TH !!!!!!~
Answers
Answer:
15 dollers per hour
Step-by-step explanation:
HOPE THIS HELPS!
BRAINLIST?????
Answer:
The fixed cost is 15 dollars an hour.
Step-by-step explanation:
At zero hours it is 15 dollars so y=5x+15
After each hour the price goes up by 5 dollars so it is 5 dollars an hour.
A compound inequality is graphed, and its graph consists of all real numbers.
Which open sentence could have resulted in this solution set?
A. r < 3 or r > –2
B. r > 3 or r > –2
C. r < 3 or r < –2
D. r > 3 or r < –2
Answers
Answer:
A
Step-by-step explanation:
Domain of r<3: (-∞,3)
Domain of r>-2: (-2,+∞)
(-∞,3)U(-2,+∞)=(-∞,+∞) = ℝ
what is the value of x if 2x-41=13
Answers
Answer:
x = 27
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
2x - 41 = 13
Step 2: Solve for x
[Addition Property of Equality] Add 41 on both sides: 2x = 54[Division Property of Equality] Divide 2 on both sides: x = 27Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 2(27) - 41 = 13Multiply: 54 - 41 = 13Subtract: 13 = 13Here we see that 13 does indeed equal 13.
∴ x = 27 is the solution to the equation.
please help view the attached screenshot below.
Answers
Answer:
x = 1
Step-by-step explanation:
Vertical Angles equal each other
Angle A = Angle B
5x - 4 = 2x - 1
3x - 4 = -1
3x = 3
x = 1
Determine which of the following is an equivalent ratio for 2:7 
Answers
Answer:
4:14
multiply or divide both quantities by the same number
PLEASE HELPS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: If I had to guess it would be the fourth one down
A school fundraiser needs to raise a total of $1000. The students are selling artwork for $25 a piece. They have already raised $300 toward their goal. Write and solve an equation to represent this situation
Answers
EXPLANATION: $25 is how much each artwork is worth so you multiply that by how many artworks needed to make 1000, but since you don’t know how many you need you put an x. You’ve already made $300, so you add that to 25x so you get 25x+300 and then finally because you need your outcome to be 1000 you put that as what the equation should equal to and you should get 25x+300=1000.
20 POINTS
look at the rectangle below. the sum of the measures of the 3 interior angles of any triangle is always 180° . What is the measure of
A- 30°
B- 45°
C- 60°
D- 120°
Answers
In the figure below, tan B = 4/3. If BC = 15 and DA = 3, what is the length of DE ?
A. 8
B. 12
C. 6
D. 9
Answers
Answer:12
Step-by-step explanation:
The length of the segment in the right triangle is 6 unit.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
A right angle triangle,
In which, tan B = 4/3, BC = 15 and DA = 3,
the length of DE = ?
suppose, the length of BD is x
and the length of DE is h.
we can use trigonometric formula her;
sin B = AC/BC
sin B = AC/15
if the value of tan B is 4/3 then the value of sin B will be 4/5.
AC/15 = 4/5
AC = 12
Now, tan B = 4/3 = 12/AB
AB = 16
Now we can use similarity of triangles;
DE/BD = AC/AB
DE = BD x (AC/AB)
BD = AB/2
DE = 8 x 12/16
= 6
Therefore, the length of DE is 6 unit.
To know more about angle check:
https://brainly.com/question/28451077
#SPJ2
A store has two different brands of laundry detergent. Brand A can
do 80 loads of laundry and costs $12.75. Brand B does 36 loads of
laundry and costs $6.75
Answers
Answer:
20=3.19
1=0.16
Step-by-step explanation:
Rounded to the nearest cent
12.75/80 to get unit price
Then unit price multiplied by 20
When all the kids who tried out for the Little league were divided into teams of 16 players, there were exactly 8 teams. How many kids tried out?
Answers
Answer:
128
Step-by-step explanation:
16 x 8 = 128
Answer:
128
Step-by-step explanation:
you multiply 16 and 8 because each team has 16 and there are 8 teams so, 16×8=128
Find m2. The diagram is not to scale.
770
270
a
76
b
104
С C
103
86
Answers
Answer:
The answer is A
Step-by-step explanation:
find the perimeter (help pls)
Answers
Answer:
14
Step-by-step explanation:
63²
Note:I'm hoping the bottom of the other side is 10 as well or this is wrong
Find the slope given: (-2,-1) & (-8, 11)
m =
Answers
Answer:
[tex]\displaystyle m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, -1)
Point (-8, 11)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{11+1}{-8+2}[/tex][Fraction] Add: [tex]\displaystyle m=\frac{12}{-6}[/tex][Fraction] Divide: [tex]\displaystyle m=-2[/tex]Last month, Carla’s neighbors paid her to take care of their cat when they went on vacation.she spent $3 of her earnings on an afternoon snack and $14 on a new book. Afterwards, she had at most &8 left. How can u best describe how much Cala’s neighbors paid her?
Answers
Answer:
She had at least 21
Step-by-step explanation:
She had at least 4+ 12 +5
She had at least 21
She spent 4 and 12 so she had 16 dollars
She had at least 5 left
so at the very least she had 16+5 which is 21, she may have had more
Given that f (x) = 5x – 8, what is f (1)?
Answers
Answer:
-3
Step-by-step explanation:
f (1) = 5(1) - 8
5 - 8 =
-3
5-8
-3
Substitute the 1 for the x and then multiply and subtract.
How many 3/8 are in 8?
Answers
Answer: 8 times
Step-by-step explanation: 3 divided by 3/8.
3 is equivalent to 3/1. And when you divide fractions, you have to multiply by the reciprocal. the reciprocal of 3/8 is 8/3
have a good day
Can someone help plz
Answers
Answer:
(-2) + (3-7)
(-1) * (-2)
EVALUATE THE EXPRESSION
Step-by-step explanation:
HELP ME