Suppose 1000 people enter a chess tournament. The champion is determined in such a way that a player is eliminated after one loss and games are played until only one entrant has not lost. (Assume there are no ties.)
Required information:
The given tournament can be modeled as a full binary tree with the winner of the entire tournament as the root. Which of the following is true for the binary tree?
A. Each internal vertex represents the winner of the game played by its two siblings, and there are 1000 leaves, one for each contestant.
B. Each internal vertex represents the winner of the game played by its parents, and there are 2000 leaves, two for each contestant.
C. Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.
D. Each internal vertex represents the winner of the game played by its two children, and there are 1000 leaves, one for each contestant.
E. Each internal vertex represents the winner of the game played by its two children, and there are 2000 leaves, two for each contestant.

Answers

Answer 1

Answer:

Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.

Step-by-step explanation:

There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.

We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.

The sum of the figures in the third column is 999.

We could also use the formula for rooted trees to calculate the number of games that would be played.

[tex]i=\frac{l - 1}{m - 1}[/tex]

where i is the number of "internal nodes," which represents the number of games played for an "m-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.

The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by

[tex]i=\frac{l - 1}{m - 1} \\\\ i=\frac{1000 - 1}{2 - 1} \\\\= \frac{999}{1} \\\\=999[/tex]

Answer 2

Answer: C. Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.

Step-by-step explanation: A tree is a connected undirected graph with no simple circuits. When its elements has at most 2 children, it is a Binary Tree.

The tree is formed by nodes. The topmost node is called Root and except for it, every node is connected by a direct line from exactly one other node. This type of node is called Parent.

Parent can be direct connect to a number of other nodes, which are Children and can also be internal nodes.

NOdes with no children are Leaves or external nodes.

In the Binary Tree described by the question, the number of participants is 1000, so there will be 1000 leaves. Each internal vertex repsents the winner of a game played by its parents, i.e., each is a Child, a internal node.

The right answer is alternative C.


Related Questions

Evaluate the expression shown for x = 12.
Negative StartFraction 5 over 6 EndFraction x + 7

Answers

Answer:

-3 !!!!!

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

just did the test on edg

Is the relationship shown by the data linear? If so, model the data with an equation x: -7,-5,-3,-1 y: 5,9,13,17

Answers

Answer:

Y = 2X + 19

Step-by-step explanation:

the relationship is linear

gradient equals 2

Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0 elsewhere.
(a) Is the random variable Y discrete or continuous? Why?
This is a discrete random variable because the set of possible values is an interval.
This is a continuous random variable because the set of possible values is an interval.
This is a discrete random variable because it has a finite sample space.
This is a continuous random variable because it has a finite sample space.
(b) What is the height of the density curve between 0 and 2? Draw a graph of the density curve.
(c) Use your graph from (b) and the fact that probability is area under the curve to find P(Y ≤ 1).

Answers

Answer:

a) This is a continuous random variable because the set of possible values is an interval.

b) Height = 0.5

Graph attached.

c) P(Y≤1) = 0.5

Step-by-step explanation:

a) If the density curve of the outcomes has a constant height, we have a uniform distribution for values between 0 and 2 (outside this range, the density function has a value of 0).

This function is continous and has a value for each real number. The set of possible values has a is an interval between 0 and 2, all with equal probability (the ones that are otuside this interval have 0 probability, so they are not possible values).

b) The height is calculated so that the total area under the density curve has to be equal to 1.

Then, we have to calculate the integral between 0 and 2 of the density function:

[tex]\int\limits^2_0 {U(x)} \, dx =\int\limits^2_0 {H} \, dx =H\int\limits^2_0 dx=H(x_2-x_1)=H(2-0)=1\\\\2H=1\\\\H=0.5[/tex]

The height is H=0.5

(Graph attached)

c) The probability can be calculated by integrating the density function (which is equal to the area under the curve) between 0 and 1, or using the graph.

With the graph, we see that the area is equal to the height (0.5) by the width of the interval (1), so the total area is 0.5 x 1 = 0.5.

The probability P(Y≤1) is equal to 0.5.

Using the uniform distribution, it is found that:

a)

This is a continuous random variable because the set of possible values is an interval.

b)

The height is [tex]\frac{1}{2}[/tex], and the sketch is given at the end of this answer.

c)

P(Y ≤ 1) = 0.5

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

In this problem, uniformly distributed between 0 and 2, thus [tex]a = 0, b = 2[/tex].

Item a:

Values in an interval, thus continuous. Discrete are for sample spaces, which is not the case here.

Item b:

The height is:

[tex]h = \frac{1}{b - a} = \frac{1}{2}[/tex]

The graph is sketched at the end of this answer.

Item c:

[tex]P(Y \leq 1) = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]

Thus, P(Y ≤ 1) = 0.5.

A similar problem is given at https://brainly.com/question/13547683

Write the equation of the line, given the y- and x-intercepts:

y-intercept (0, 19), x-intercept (–9.5, 0)

Answers

Answer:

y=2x+19

Step-by-step explanation:

Slope: 0-19/-9.5-0=-19/-9.5=2

y-intercept: 19

Answer:

y=2x+19

Step-by-step explanation:

What is the diameter of a sphere with a volume of 6329\text{ ft}^3,6329 ft

3

, to the nearest tenth of a foot?

Answers

Answer:

Diameter = 22.9 ft

Step-by-step explanation:

We are told that volume of the sphere is 6329 ft³

Now formula for volume of sphere is given as;

V = (4/3)πr³

Thus,

(4/3)πr³ = 6329

Multiply both sides by 3/4 to get;

πr³ = (6329) * 3/4

πr³ = 4746.75

Divide both sides by π to obtain;

r³ = 4746.75/π

r = ∛(4746.75/π)

r = 11.4749 ft

Now, diameter = 2 x radius

Diameter = 2 × 11.4749

Diameter = 22.9498 ft

Approximating to a tenth of a feet gives;

Diameter = 22.9 ft

Mr. Vectadore is buying two new cowboy hats. All
together the hats cost $75.12. The second hat costs
twice as much as the first hat. What is the price of the
more expensive hat?
Round to the nearest hundredth.

Answers

Answer:

$50.08

Step-by-step explanation:

Let's use x to represent the lesser expensive hat and 2x to represent the more expensive hat since the more expensive hat is twice the price.

So, our equation would be 2x + x = 75.12

We can combine them together to make 3x.

Then, we make the 3x equal to 75.12

3x = 75.12

Now, we solve it.

Divide both sides by 3 to solve for x.

75.12/3 = 25.04

x = 25.04

Lastly, plug it in for 2x to get the price of the more expensive hat.

2(25.04) = ?

2(25.04) = 50.08

Therefore, the price of the more expensive hat is $50.08

a bakery receives 100 loaves of bread each day of the week. The table below displays how much is spent each day last week. The bakery uses FIFO. It had 125 loaves of bread left on Friday afternoon, what is the current value of its stock

Answers

Answer:

$275

Step-by-step explanation:

Day                                   Price                     Unit price

Monday                            $245                        $2.45

Tuesday                           $315                          $3.15

Wednesday                     $275                         $2.75

Thursday                         $200                         $2.00

Friday                              $225                         $2.25

the first in, first out (FIFO) method uses the price of the oldest units to determine the cost of goods sold:

the ending inventory should = 100 units purchased Friday + 25 units purchased Thursday = (100 x $2.25) + ($25 x $2) = $225 + $50 = $275

Answer: $375

Step-by-step explanation:

Please choose the correct answer.

Answers

Answer:

976

Step-by-step explanation:

would you stop it already

Answer: 976m^2

Step-by-step explanation:

An easy way to find the surface area of a prism is to find the area of each side and add them all together.

Area of rectangle:

14mx10m=140m^2

Area of rectangle:

25mx10=250m^2

Since there are 2 of the long rectangles, you multiply by 2:

250m^2x2=500m^2

Area of triangle:

(24mx14m)/2=168m^2

Since there are 2 triangles, you multiply by 2:

168m^2x2=336m^2

Surface Area:

140+500+336=976m^2

guys, I don't understand this question is this correct??

Answers

Answer:

I think you are correct. bc you have 4 different caps, and four different sections of a spinner that are equal same with the cap. So I believe so.

Step-by-step explanation:

I hope this helps! Im in algebra 2 so its been awhile since i have done this. Good Luck!!:)

Answer:

A

Step-by-step explanation:

I agree with your answer. The question is basically just saying the beverage company randomly chooses one of those letters to put under the bottle caps. For example, one bottle cap might have a T on it, and another might have an A on it. If you try to get all 4 letters, then you will have to keep buying those drinks until you manage to collect all 4 letters. Therefore, there are only 4 possible options for which letter you can get.

If you spin a spinner that has 4 equal sections, then this is similar. You have 4 possible options you can get.

Hope this helps! :)

If you could help me, please answer the attachment below.

Answers

You need to add all of those
...

A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 230 feet by 180 feet

Answers

Answer:

14 bags

Step-by-step explanation:

Dimension of lawn : 230 feet by 180 feet

area of rectangle is given by length * width

Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet

Given that one bag of fertilizer covers 3000 square feet of lawn.

Thus , to find no. of bags required to cover whole lawn will be

total area of lawn/area which one bag of  fertilizer covers

no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet

    = 13.8 bags.

As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.

Milly measured a cereal box it was 2inches wide six inches long and three inches what is the volume

Answers

Answer:

2*6*3

Step-by-step explanation:

Volume = 6×2×3 = 36 feet cubed

Consider random samples of size 40 from a population with proportion 0.15.
(a) Find the standard error of the distribution of sample proportions.
Round your answer for the standard error to three decimal places.
mean=______
standard error=_______
(b) Is the sample size large enough for the Central Limit Theorem to apply?
1. Yes
2. No

Answers

Answer:

a) The mean is 0.15 and the standard error is 0.056.

b)  1. Yes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportions p, in samples of size n, the mean is [tex]\mu = p[/tex] and the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]. The Central Limit Theorem applies is np > 5 and np(1-p)>5.

In this question:

[tex]n = 40, p = 0.15[/tex]

So

(a) Find the mean and the standard error of the distribution of sample proportions.

[tex]\mu = 0.15, s = \sqrt{\frac{0.15*0.85}{40}} = 0.056[/tex]

So the mean is 0.15 and the standard error is 0.056.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

np = 40*0.15 = 6 > 5

np(1-p) = 40*0.15*0.85 = 5.1>5

So yes

The standard error of the distribution of sample proportions is 0.056 and mean is 0.15.

Yes, the sample size is enough for the Central Limit Theorem to apply.

(a). Given that, size of sample, [tex]n=40[/tex]

        Proportion, [tex]p=0.15[/tex]

In the distribution of sample proportions, mean [tex]\mu=p[/tex]  

and, standard error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

So, mean [tex]\mu=0.15[/tex]

Standard error =[tex]\sqrt{\frac{0.15(1-0.15)}{40} }=0.056[/tex]

(b). The Central Limit Theorem applies if np > 5 .

 [tex]np=40*0.15=6>5[/tex]

Thus, the Central Limit Theorem is applied.

Learn more:

https://brainly.com/question/22233199

I need help with this??

Answers

A = 1/2h(b1 + b2)
A = 1/2*9.28(10.5 + 21.1)
Using calculator
A = 146.624 square cm

Which is the closet to the volume of the concrete needed to fill the pillar?

Answers

Answer:

c) 21.4

Step-by-step explanation:

9.5 times 1.5 times 1.5 is 21.375 or 21.4 rounded

Please answer this correctly

Answers

Answer:

13

Step-by-step explanation:

Find the scale factor by 39 / 30

Take that times 10

1.3 x 10 = 13

Since the questions states these two shapes are "similar" the side will have identical scale factors.

Divide the longest side of the bigger shape to the smaller shape.

39 / 30 = 1.3

The scale factor is 1.3.

Now, multiply the shortest side if the smaller shape by the scale factor.

10 * 1.3 = 13

Therefore, the length of w is 13mm

Best of Luck!

How many decimal places are in the product of the expression below?
256
x142
one
two
three
four

Answers

Answer:

36352.0

Step-by-step explanation:

For 256x142 = 36352.0

There is none actually

What’s the correct answer for this?

Answers

Answer: Option A
Center: (3,-2)
Radius: 6

Rewrite in standard form to find the center (h,k) and radius r.
im pretty sure its option A. :)

What is the number of permutations for a 4 digit number using the digits 0 – 9, if numbers cannot be repeated.

Answers

Answer:

Number of permutations for a 4 digit number using the digits 0 – 9 (10 available digits in total), supposing numbers cannot be repeated, is calculated by:

10P4 = 10!/(10-4)! = 5040

Hope this helps!

:)

Help Please???? Question is above, it has to do with repeating decimal converting to a fraction

Answers

For number 3.it would be 87/200 and 4. Would be 713/500

Use the change of variables s=y, t=y−x^2 to evaluate ∫∫Rxdxdy over the region R in the first quadrant bounded by y=0, y=16, y=x^2, and y=x^2−5. ∫∫R x dxdy=

Answers

Answer:

Step-by-step explanation:

[tex]s=y, t = y- x^2[/tex]

[tex]x^2=y-t[/tex]

[tex]x=\sqrt{s-t}[/tex]

[tex]y=0, y=16, y=x^2, and\\ y=x^2-5.[/tex]

[tex]y-x^2=0,y-x^2=-5[/tex]

therefore,

[tex]s=[(s,t)10\leq s\leq 16,-3\leq t \leq 0][/tex]

Taking partial derivatives

[tex]\frac{dx}{ds} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dx}{dt} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dy}{ds} =1\\\\\frac{dy}{dt} =0[/tex]

[tex]\frac{\delta (x,y)}{\delta (s,t)} =\left|\begin{array}{ccc}\frac{1}{2\sqrt{s-t} } &-\frac{1}{2\sqrt{s-t} } \\1&0\end{array}\right|[/tex]

[tex]=\frac{1}{2\sqrt{s-t} }[/tex]

[tex]\int\limits \int\limits_R {x} \, dx \, dy=\int\limits\int\limits_s {x} \sqrt{s-t} |\frac{\delta(x,y)}{\delta (s,t)} |dsdt[/tex]

[tex]=\int\limits^{16}_0\int\limits^0_{-5} \sqrt{s-t} \frac{1}{2\sqrt{s-t} } dt ds[/tex]

[tex]=\frac{1}{2} \int\limits^{16}_0 ds\int\limits^0_{-5} \, dt \\\\=\frac{1}{2} [s]^{16}_0[t]^0_{-5}\\\\=\frac{1}{2} (16)(5)\\\\=40[/tex]

The line that passes through the point (2, −8) and has a slope of −1 is given by the equation y + = (x − ).

Answers

Answer:

8 = -1 (x - 2)

:)

Answer:

8 = -1 (x - 2)

Step-by-step explanation:

Find the surface area of the cylinder. Round your answer to the nearest hundredth.
A. 569.26 in2
B. 724.34 in2
C. 795.45 in2
D. 1,707.77 in2

Answers

Answer:

  C.  795.45 in^2

Step-by-step explanation:

The formula for the surface area of a cylinder is ...

  SA = 2πr^2 +2πrh = 2πr(r +h)

For r=6 and h=15.1, the surface area is ...

  SA = 2π(6)(6 +15.1) = π(12)(21.1) = 253.2π

  SA ≈ 795.45 . . . . square inches

PLS PLS HELP FAST. Given an isosceles triangle with a leg length of 12. Determine the length of the hypotenuse.

Answers

Answer:

12*sqrt(3)

Step-by-step explanation:

since it is isosceles its angles are 45, 45, 90, therefore the hypotenuse is 12*sqrt(3).

ANYONE PLZZZ THSI IS DUE IN AN HOUR!!!!! Will mark the brainliest

Answers

Answer:

A is correct.

Step-by-step explanation:

Left figure's area = base x height = L x h x 6 = 6Lh

Right figure's area = L x h + L x h + L x h + L x h + L x h + L x h = 6Lh

Hope this helps!

:)

Triangle PQR is similar to triangle FGH.

Solve for n.

QP:10.5

QR:9

RP:6


GF:7

HF:4

GH:n

Answers

Answer:

n = 6

Step-by-step explanation:

See attachment for diagram

Triangle PQR is similar to triangle FGH.

Similar triangles are similar in shape but different in size.

The ratio of their corresponding sides are equal.

QP=10.5

QR=9

RP=6

GF=7

HF=4

GH=n

(Hypotenuse in ∆PQR)/ (hypothenuse in ∆FGH)

=(Adjacent in ∆PQR)/(adjacent in ∆FGH)

= 6/4 = 9/n

Cross multiply

6×n = 9×4

6n = 36

n = 36/6

n = 6

Therefore ratio of their corresponding sides = 3/2

What is the slope of the equation y-3=-4(x-5) ?

Answers

Answer:

m(slope)=-4

Step-by-step explanation:

the slope is the thing you see before x so in this case y-3=-4x+20 so the slope or m is -4.

The slope of the equation y - 3 = -4 ( x - 5 ) is -4.

Given,

y - 3 = -4 ( x - 5 )

We need to find the slope of this equation.

What is the equation of a line with a slope?

The equation is given by:

y - b = m ( x - a)

Where (a, b) is a point that the line passes through and m = slope.

We have,

y - 3 = -4 ( x - 5 )

Here we see that the equation is in the form of y - b = m ( x - a).

Where,

(a, b) = (5, 3)

m = -4

We have,

Slope = m

m = -4

Thus the slope of the equation y - 3 = -4 ( x - 5 ) is -4.

Learn more about how to find slope from a graph here:

https://brainly.com/question/23164168

#SPJ2

what is the solution for x^2 +14x +15​

Answers

...................................

Step-by-step explanation:

the solution are

x = 1 or x = -15

x^2 + 14x - 15 =0

x^2 + 14x = 15

to write the left hand side as a perfect square we add 49 to both sides :

x^2 + 14x + 49 = 15 + 49

x^2 + 2.x.7 + 7^2 = 64

using the identity (a^2 + b^2) = a^2 + 2ab + b^2

(x + 7)^2 = 64

x + 7 = √64 or x + 7 = -√64

x = 8 - 7 or x = - 8 - 7

= 1 = - 15

Write the number pairs that relate the number of half dollar to the number of dimes

Answers

Answer:

0.10 + 0.10 + 0.10 + 0.10 + 0.10 equal to 5 dimes or a half of dollar.

Step-by-step explanation:

0.10 + 0.10 + 0.10 + 0.10 + 0.10 = 0.50 (half of a dollar)

There are 140 coins in a piggy bank of which 20​% are dimes. What is the least possible amount of money that could be in the piggy​ bank?

Answers

Maybe it’s 28? If you multiply 140 coins by 0.20
A penny is worth 1 cent.
So, the smallest amount of money is $4 plus 64 cents. $4.64
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