Answer:
142
Step-by-step explanation:
6 day av 144 / day so total =144*6
first 3 day av 132 so total =132*3
next 2 days av 163 so total =163*2
144*6= 132*3+163*2+final day
so final day = 142
table 6 gives the regression statistics from estimating the model Δln (Salest) = b0 + b1Δln (Salest −1) + εt. table 6 Change in the natural log of Sales for Cisco Systems Quarterly Observations, 3Q:1991–4Q:2000 regression Statistics R-squared Standard error Observations Durbin–watson intercept Δln (Salest −1) Coefficient 0.0661 0.4698 0.2899 0.0408 38 1.5707 Standard error 0.0175 0.1225 t-Statistic 3.7840 3.8339 a. Describe the salient features of the quarterly sales series. b. Describe the procedures we should use to determine whether the ar(1) specification is correct. C. assuming the model is correctly specified, what is the long-run change in the log of sales toward which the series will tend to converge
As per the regression equation, the value of intercept coefficient is 1.5707
Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.
In this case, the regression statistics provided in table 6 show the results of estimating the model
=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,
where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.
The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.
The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.
If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.
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Solve the system using the substitution method.
10x - 16y = 17
3x + 3y = 9
Please help ASAP the question is in the picture
The data represent a quadratic function.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
To calculate the second difference,
select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then find the difference of these two resulting values . If all second differences are equal, the data represent a quadratic function.
1) -7,-5, -1
second y value - first y-value = 2
third y value - second y value = 4
difference of these two resulting values = 2
2) -5,-1,5
second y value - first y-value = 4
third y value - second y value = 6
difference of these two resulting values = 2
The data represent a quadratic function.
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Mr. Gabriel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months. Find the simple intresr rate for his loan.
The simple interest rate for his loan could be 6%
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Given that Mr. Gabel borrowed $1860 to buy a computer. He will pay $71Mr. Gabel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months.
To Find the simple interest rate for his loan.
P= 1860R= x
T= 30 months = 2.5 years
I = $279
Therefore, I= prt
279 = 1860 (r)(2.5)
279 = 4650r
0.06 = r
r = 6%
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Kiara measured a swimming pool and made a scale drawing. The scale she used was 13 centimeters : 6 meters. In the drawing, the pool is 26 centimeters wide. What is the width of the actual pool?
Quetion Number 27
You are comparing price at two local torage vendor. Rent-A-Space charge a monthly fee of 22 cent per cubic foot plu 5. 5% ale tax. Store-Ur-Stuff charge a monthly fee of 25 cent per cubic foot plu 5. 5% ale tax. If you pay the Store-Ur-Stuff bill prior to the firt of the month, you will get a 4% dicount, but you will till have to pay ale tax on the pre-dicount cot. Auming you pay the bill prior to the firt of the month, what i the difference in cot between the two vendor if you are toring a total of 400 cubic feet?
The distinction in cost between the two sellers is $1.44, with Store-Ur-Stuff being savvier.
Expect you to take care of the two bills preceding the first of the month, the distinction in cost between leasing from Lease A-Space and Store-Ur-Stuff is $10. Lease A-Space would cost $88 (400 cubic feet x 22 pennies/cubic foot + 5.5% deals charge) while Store-Ur-Stuff would cost $78 (400 cubic feet x quarter/cubic foot + 4% markdown + 5.5% deals charge).
The distinction in cost between Lease A-Space and Store-Ur-Stuff can be determined as follows:
Lease A-Space: 400 cubic feet x $0.22/cubic foot = $88 in addition to burden = $92.64
Store-Ur-Stuff: 400 cubic feet x $0.25/cubic foot = $100 in addition to 4% markdown = $96 less expense = $91.20
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1. What's the measure of AC?
2. What is the measure of AC'
3. What is the measure of C'B'?
1. The measure of AC = 8.4
2. The measure of AC' = 6
3. The measure of C'B' = 12.6
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
Segment B'C' is parallel to segment BC.
A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.
Then,
10/4 = 6/x
x = 2.4
The measure of AC = 2.4
And,
14/8.4 = 21/y
y = 12.6
The measure of C'B' = 12.6
Therefore, all the required values are given above.
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
I am pretty sure the answer would be (2,3)
three strangers meet at a taxi stand and decide to share a cab to cut down the cost. each has a different destination but all are heading in more-or-less the same direction. bob is traveling 10 miles, sally is traveling 20 miles, and mike is traveling 30 miles. if the taxi costs $2 per mile, how much should each contribute to the total fare? what do you think is the most common answer to this question?
The most common answer to this question is that people would suggest splitting the fare equally i.e. each person contributes $40.
Each stranger should contribute to the total fare based on the distance traveled, so the fare would be divided as follows -
Bob: 10 miles * $2/mile = $20
Sally: 20 miles * $2/mile = $40
Mike: 30 miles * $2/mile = $60
Total fare: $20 + $40 + $60 = $120
Therefore, each stranger should contribute $120/3 = $40 to the total fare.
The most common answer to this question is that people would suggest splitting the fare equally, i.e. each person contributes $40, regardless of the distance traveled. This is because it is a simpler and fairer solution, as each person benefits from the shared ride and the cost savings, regardless of the distance traveled.
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can someone please help me(20 points will give brainliest!!!)
Answer: A: 50,000
Answer: B: 55
Step-by-step explanation:
You can use ratio proportions to answer this problem
10/10,000 = 50/x
Cross multiply: 10x/10 = 500,000/10
x = 50,000
You can use ratio proportions to answer this problem
10/10,000 = x/55,000
Cross mupltipy: 10,000x/10,000 = 550,000/10,000
x = 55
May or may not be correct
[WILL GIVE BRAINLIEST!]
Angle α is in quadrant III and angle β is in quadrant IV. If sin α = –5/6 and cos β = 1/2, find cos(α + β).
Answer:
Step-by-step explanation:
The expansion for cos(x+y) is cosx*cosy - sinx*siny. We have sin x and cos y, now we need cosx and siny.
Angle x is in QIII and has a sin ratio of -5/6. Since the hypotenuse will never be negative and sin is opposite over hypotenuse, the side across from the reference angle, aka the height of the triangle, is -5 and the hypotenuse is 6. Using Pythagorean's Theorem we can find the third side:
[tex]6^2=(-5)^2+x^2[/tex] and
[tex]36=25+x^2[/tex] and
[tex]36-25=x^2[/tex] so
x = √11.
We do the same for the other angle y. We have the cos of angle y is 1/2 and since the cos ratio is adjacent over hypotenuse, the side next to the reference angle is 1 and the hypotenuse is 2 and we will find the third side using Pythagorean's Theorem:
[tex]2^2=1^2+y^2[/tex] and
[tex]4=1+y^2[/tex] and
[tex]3=y^2[/tex] so
y = √3.
We already know sinx = -5/6, now we know that cosx = -√11/6.
We already know cosy = 1/2, now we know that siny = -√3/2.
Now we can fill in the expansion for cos(x+y):
[tex](-\frac{\sqrt{11} }{6})(\frac{1}{2})-(-\frac{5}{6})(-\frac{\sqrt{3} }{2})[/tex] Multiplying straight across the top and bottom we get
[tex]-\frac{\sqrt{11} }{12}-\frac{5\sqrt{3} }{12}[/tex] which simplifies to
[tex]\frac{-\sqrt{11}-5\sqrt{3} }{12}[/tex]
And you're done!
find a parametrization of the tangent line to ()=(ln()) −10 10 at the point =1.
The tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10
To find the tangent line to the curve y = ln(x) - 10 at the point (1, -9), we need to find a parametrization of the line. We can do this by finding the slope of the tangent line and the point at which the tangent line intersects the y-axis.
First, we find the slope of the tangent line by taking the derivative of the function y = ln(x) - 10 at x = 1:
dy/dx = d/dx ln(x) = 1/x
So, the slope of the tangent line at (1, -9) is m = 1/1 = 1.
Next, we find the y-intercept of the tangent line. This can be found by using the point-slope form of a line:
y - y1 = m(x - x1)
Substituting in the values for m, x1, and y1, we get:
y - (-9) = 1(x - 1)
Simplifying, we find:
y + 9 = x - 1
y = x - 10
So, the y-intercept of the tangent line is -10.
Putting everything together, we find that the parametrization of the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is given by:
x = t
y = x - 10 = t - 10
So, the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10.
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What conjectures can you make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle ?
The conjectures which you can make about a point on the perpendicular bisectors of a segment and a point of a bisector of an angle include the following below:
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.What is a Bisector?Th line that divides something into two equal parts and it is usually applied to the line segments and angles.
The following relationships between them is that if there is a point which lies on the perpendicular bisector of a segment, then it is most likely to be equidistant from the endpoints of the segment when scrutinized thereby making it the correct choice.
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Show that DF is parallel to AB in that DF equals 1/2 of AB
The segments DF and AB are parallel, as they have the same slope.
How to obtain the slope of a segment?A segment is composed by two endpoints, and then the slope is calculated as the change in y divided by the change in x of these points.
The endpoints of segment AB are given as follows:
A(-5,2) and B(1,-2).
Hence the slope is of:
m = (-2 - 2)/(1 - (-5)) = -4/6 = -2/3.
The endpoints of segment DF are given as follows:
D(-4,-2) and F(-1,-4).
Hence the slope is of:
m = (-4 - (-2))/(-1 - (-4)) = -2/3.
As the segments have the same slope, they are parallel.
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what is the unsigned decimal equivalent (with 5 digits after the decimal point, truncated, e.g., 12.34567) of the following unsigned base 9 value? 1101.101
The decimal equivalent of 1101.101 in base 9 is 729.1184.
The decimal equivalent of an unsigned base 9 value is simply the number represented in the decimal system.
To find the decimal equivalent of 1101.101 in base 9, we need to convert each digit to its decimal equivalent.
First, we'll convert the whole number portion of 1101.101.
1101 in base 9 is equivalent to
=> 9³ + 1 = 729
Now, we'll convert the fractional portion.
The first digit after the decimal point, 1, represents 1/9.
The next digit, 0, represents 0/9².
The last digit, 1, represents 1/9³.
Adding these values together, we get
=> 729 + 1/9 + 1/729 = 729.1184
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HELP HELP HELP!!!!! Mason and Jack are lifting weights. Mason uses a 19-kg bar, increasing the weight by 7 kg on each set. Jack starts with an 18-kg bar and increases by 8 kg on every set. Eventually, Mason and Jack will be lifting the same amount. A. How many sets will they have completed? B. How much weight will they be lifting then?
They will lift the same weight (which is 26 kilograms) after one set.
How many sets will they have completed when they lift the same weight?Mason starts at 19kg bar and adds 7kg after each set, so after x sets, he will be lifting:
M(x) = 19 + 7*x
And Jack starts at 18kg, and after each set adds 8kg, then in this case the linear equation is:
J(x) = 18 + 8*x
They will lift the same weight when:
M(x) = J(x)
19 + 7*x = 18 + 8*x
19 - 18 = 8x - 7x
1 = x
So they will be lifting the same weight after one set, and that is:
J(1) = 18 + 8*1 = 26
26 kilograms.
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Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.
Check picture for full question.
Answer:
The picture won't show. are there answer options?
Step-by-step explanation:
Small room (S) - hold 3 people
Large room (L)- hold 4 people
Hudson reserved twice as many large rooms = 2x Large room #
2L + S = 66
So,
Let S = Small room
Let L = Large room
I hope this can make things slightly easier for you. I tried to make it more visible for you. Please comment if you need more help.
the owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 270 feet long, as one of the sides of the enclosed area. there are 500 feet of fencing available for the other three sides of the enclosure. find the dimensions of the outdoor enclosure with the most area.
The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.
One side of the store is 270 feet long
There are 500 feet of fencing available for the other three sides of the enclosure.
The Perimeter of rectangular outdoor storage = 2x + y
2x + y = 500
To maximize the area
y = 500 - 2x...............(1)
Area of rectangle;
A = xy
Now putting the value of y
A = x(500 - 2x)
Solve
A = 500x - 2x^2...................(2)
To finding the value of x differentiating on both side with respect to x.
dA/dx = 500 - 4x...................(3)
Equating dA/dx = 0
500 - 4x = 0
Subtract 4x on both side, we get
4x = 500
Divide by 4 on both side, we get
x = 125
Now putting the value of x in equation 1
y = 500 - 2(125)
y = 500 - 250
y = 250
Differentiating equation 3 again with respect to x
d^2A/dx^2 = -4 < 0 (Maximum)
Hence, for the maximum storage area
Length parallel to the store wall = 250 feet
Length perpendicular to the store wall = 125 feet
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Hey can you please help me what is 2 1/5 x 1 1/4 as a simplest form?
Answer: 2 3/4.
Step-by-step explanation: To multiply the mixed numbers, we need to first make them into improper fractions. To make 2 1/5 into an improper fraction, we multiply the whole number 2 by the denominator, 5, and add that to the numerator 1, giving us 11/5. We do the same for 1 1/4, giving us 5/4. 5/4 x 11/5 equals 55/20. 55/20 simplifies to 2 3/4.
I need help PLEASE PEOPLE!!
Answer: 3
Step-by-step explanation:
22.5% of 40= 9 which is the amount for cats
30% of 40= 12 which is the amount for dogs.
12-9=3
Special quadrilateral
The following are the respective measures of angles and lengths of the rectangle ABCD:
m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.
How to calculate the angles and lengths for the rectangle.Considering the triangle AEB, angles A and B are base angles of a the isosceles triangle AEB so;
2(m∠ABE) + 98 = 180° {sum of interior angles of a triangle}
m∠ABE = (180 - 98)/2
m∠ABE = 41°
m∠1 = 90° - 41° {complementary angles of a rectangle}
m∠1 = 49°
angles m∠2 and m∠BAC are alternate angles and are equal so;
m∠2 = 41°
m∠ADC is one of the four interior angles of a rectangle so m∠ADC = 90°
Considering the right triangle ∆ABD and the tangent of angle B = 41°, we can solve for the length of AB as follows:
tan 41° = 6/AB {opposite/adjacent}
AB = 6/tan41° {cross multiplication}
AB = 6.9022.
m∠3 and m∠ABD are alternate angles so;
m∠3 = 41°
lines AC and BD are diagonals of the rectangle and they bisect each other, since EB = 5 then;
BD = 2 × 5 = 10
CE = 5
Therefore, the following are the respective measures of angles and lengths of the rectangle ABCD:
m∠1 = 49°, m∠2 = 41°, m∠3 = 41°, m∠ADC = 90°, AB = 6.9, BD = 10, and CE = 5.
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if ₱60,000.00 was deposited in a bank and became ₱61,625.00 at the end of 150 days, find the interest rate using exact and ordinary days.
Days exactly: The rate of interest is 4.17%. The interest rate of amount is 4.21% on regular days.
I = P x R x T/365, where I is the interest, P is the principal, R is the rate, and T is the duration, can be used to determine the interest rate using exact days.
I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows: 625 = 60000 x R x 150/365. By multiplying both sides by 365/150, we may find R. As a result, R = 625 x 365/90000 = 4.17%.
I = P x R x T/360, where I is the interest, P is the principal, and R is the rate of return, can be used to get the interest rate using regular days.T stands for time, and R represents the rate. I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows:
625 = 60000 x R x 150/360. By dividing both sides by 360/150, we may find R. As a result, R = 625 x 360/90000 = 4.21%.
I = P x R x T/365, which means that R = I x 365/P x T = 625 x 365/60000 x 150 = 4.17%. Exact days
I = P x R x T/360 on typical days, which means that R = I x 360/P x T is 625 x 360/60000 x 150, or 4.21%.
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3.5 minutes into meters per second
Answer:
0.583 [the 3 goes on forever]
Step-by-step explanation:
In a large city, taxicabs charge $1.00 for the first mile and $0.30 for each additional mile. Frank has only $3.50. What is the maximum
distance he can travel (not including a tip for the cabbie)?
The maximum distance Frank can travel would be 10 miles.
What is maximum distance?
For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.
From given question,
taxicabs charge for first mile = $1.00
for each additional mile = $0.30
The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.
Therefore, The maximum distance Frank can travel would be 10 miles.
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I NEED HELP ASAP!!
How many boxes would Alan have to sell to earn exactly $700?
Answer: Alan would have to sell exactly 180 boxes.
Step-by-step explanation:
I need Help fjidsfidasfiajiujirufr
The x- intercepts in parabola is (1,0) and (5,0).
What do you mean by parabola?A parabola is a type of symmetrical, U-shaped curve that is a graph of a quadratic function. It is defined by the equation y = ax² + bx + c, where a, b, and c are constants. The shape of the parabola is determined by the value of the coefficient "a". If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.
Parabolas are used in many areas of mathematics and science, including physics, engineering, and economics. For example, they are used to model the trajectory of objects under the influence of gravity, to describe the motion of objects in space, and to analyze the behavior of systems that exhibit parabolic patterns.
The vertex of a parabola is the point that represents the highest or lowest point on the curve, and the axis of symmetry is a line that separates the curve into two congruent halves.
The x-intercepts of a parabola can be found by setting the y-value to 0 and solving for x. In this case, the y-coordinate of the x-intercepts will be 0, so we have:
y = 0
To find the x-intercepts, we can use the information given in the coordinates of the parabola: (1,0), (5,0), and (0,6).
From the coordinates (1,0) and (5,0), we can see that the x-intercepts are at 1 and 5.
From the coordinate (0,6), we can see that the y-intercept is at (0,6).
So, the x-intercepts of the parabola are (1,0) and (5,0).
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In a circle with radius 4, an angle intercepts an arc of length 8\pi8π. Find the angle in radians in simplest form.
The required Angle in radian in simplest form is 2π.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Explain angle in radian with arcs of circle.The centre angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2 radians.
According to question:Radius = 4 unit, arc = 8π
We know that
angle = arc/radius
angle = 8π/4
angle = 2π radian.
Thus, required angle in radian is 2π.
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Find the amount in a continuously compounded account for the following condition.
Principal, $4000; Annual interest rate, 5.7%; time, 2 years
The balance after 2 years is $
(Round the final answer to the nearest cent as needed. Round all intermediate values to five decimal places as needed.)
The balance after 2 years would be $4482.25
What exactly is compound interest?
Compound interest is when you earn interest on both your savings and your interest earnings.
The formula for finding the amount in a continuously compounded account is: A = P * e^(rt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.
Using this formula, we have:
[tex]A = $4000 * e^(0.057 * 2) = $4000 * e^0.114\\\\A = $4000 * 1.12061367\\\\A = $4482.25[/tex]
So the balance after 2 years would be $4482.25
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find the slope of the line passing through the points(-3 -8) and (4 ,6)
Answer:
below
Step-by-step explanation:
For the slope, m, between two lines
m = (y1-y2) / (x1-x2) it does not matter which point you assign as 1 or 2
m = (-8-6) / ( -3 - 4) = -14 / -7 = 2
how many distinct initial possible pairings are there for a single-elimination ping-pong tour- nament involving n players that result in distinct tournament brackets, for n = 2, 4, 8?
The number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).
What is logarithm ?
The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
In a single-elimination ping-pong tournament, each player plays one match in each round until a champion is determined. For n players, there are log2(n) rounds in the tournament, and in each round half the players are eliminated.
For n = 2, there is only 1 player left after the first round, so there is only 1 distinct pairing and 1 distinct tournament bracket.
For n = 4, there are 2 players left after the first round, and they play in the final. There are 2 possible pairings for the first round, which result in 2 distinct tournament brackets.
For n = 8, there are 4 players left after the first round, and there are 4 possible pairings for the first round. These pairings result in 4 distinct tournament brackets.
So the number of distinct initial possible pairings for a single-elimination ping-pong tournament with n players that result in distinct tournament brackets is 2^(log2(n) - 1).
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