after so-called play-in games, the ncaa men’s basketball tournament is a 64-team single-elimination tournament. after the teams are assigned, in how many ways can the tournament unfold? how many (base-10) digits does this number have?

Answers

Answer 1

This is a total of 2^32×2^16×2^8×2^4×2^2×2^1 possible outcomes that is 2^63 outcomes.

What is counting principle?

The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. It indicates that there are nm methods to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.

Here,

Since I don't know anything about NCAA's March Madness, I'll assume that you're talking about a 64-team single-elimination tournament.

In the first round, there are 32 games, each with 2 possible outcomes. This provides for a total of 2^32 possibilities.

In the next round, there are only 16 games, again each with 2 possible outcomes, for a total of 2^16 possibilities.

You keep going, eliminating half of the players each round and taking half as long as the previous round to play the games out, until the finals, at which point there is 1 game with 2 possible outcomes.

This is a total of 2^32×2^16×2^8×2^4×2^2×2^1 possible outcomes that is 2^63 outcomes.

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Related Questions

Please answer this ASAP.

Answers

Answer:

y = 0.8x

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts

Bottom line slope can be found by noting that it passes through points

(0, -3.2) and (4,0)

Then find the difference in y values which is called  the rise

Find the corresponding difference in x values called the run

rise/run = slope

For the bottom line
Rise = 0 - (-3.2) = 3.2

Run = 4 - 0 =4

So slope m = 3.2/4 = 0.8

Slope of top line is also 0.8

Since it passes through origin there is no y-intercept

So equation of top line is simply
y = 0.8x

Which fraction is equivalent ?

Answers

Answer:

Option A

Step-by-step explanation:

→ Simplify all the options

a. 5/6 and b is 2/3

Which of the following options have the same value as 60% and 94?
A: 0.06⋅94
B: 0.6⋅94
C: 5/3⋅94
D: 60⋅94
E: 60/100⋅94

Answers

Answer:

0.6 x 94

Step-by-step explanation:

You can convert 60% into a decimal, by moving the decimal place twice to the left, and it will still be the same. So, we have 0.60. Then, usually the term "and" means addition, but that is not in one of the answers, so I suppose they mean multiplication. So, we can set up this equation:

0.6 x 94

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3.
(07.04)
1 over 3b = 4 over 5 . Which of the following equals b in this equation? (4 points)

1 over 4
1 1 over 8
2 2 over 5
2 over 5

Answers

Answer:

c) 2 2 over 5 = 2 2/5

Step-by-step explanation:

Forming the equation,

→ (1/3)b = 4/5

Now the value of b will be,

→ (1/3)b = 4/5

→ b = (4/5) ÷ (1/3)

→ b = (4/5) × (3/1)

→ b = (4 × 3)/(5 × 1)

→ b = 12/5

→ [ b = 2 2/5 ]

Hence, value of b is 12/5.

Need help asap now please!!!!!!!!

Answers

Answer:

C. 150

Step-by-step explanation:

Divide 1,350 by 9, which gives you 150 (with no remainders)

Answer:

150

Step-by-step explanation:

1350 divided by 9

A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed asfunctionsequation editorcups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.

Answers

The quantity can also be expressed as a function equation in cups of coffee per hour is; f(x) = 5x

How to Solve function word problems?

We are told that a gas station is open for the 365 days of the year and 24 hours each day.

Thus,

Total number of hours in the year = 365 * 24 = 8760 hours

Now, the number of cups they served for the year = 40000 cups

Now, the rate of cups per hour = 40000/8760 = 4.566 ≈ 5 cups per hour

The quantity can also be expressed as a function equation in cups of coffee per hour; f(x) = 5x

where;

x is the number of hours

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the base of a right triangle is 6 and the perpendicular height is 8, what is the length of a hypotenuse

Answers

The length of hypotenuse is 10. It can be obtained by using Pythagorean Theorem.

What is Pythagorean theorem?

It is a theorem which gives the relationship between the length of base, perpendicular height, and hypotonus. This relationship is valid only for a right angled triangle.

The length of hypotenuse is given by the following formula:

[tex]h=\sqrt{b^2+p^2}[/tex]

Here, h is the length of hypotenuse, b is the length of base, and p is the length of perpendicular.

Substitute 6 for b and 8 for p in the above equation.

[tex]h=\sqrt{6^2+8^2}\\=\sqrt{36+64}[/tex]

Now, take the square root of 100.

[tex]h=\sqrt{100}\\=10[/tex]

Hence, the length of hypotenuse is 10.

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according to a recent survey 85 percent of high school students own a personal media player. what is the probability that 6 out of 10 random highschool students own a personal media player

Answers

The probability is 0.04.

Define probability sampling.

The sampling probability of an element or member of the population in statistics, in the theory relating to sampling from finite populations, is its likelihood of being included in the sample during the drawing of a single sample.

Probability sampling refers to the selection of a sample from a population when this selection is based on the principle of randomization, that is, random selection or chance. When compared to non-probability sampling, probability sampling is more difficult, time-consuming, and typically more expensive.

Solution Explained:

Given,

x = 7, n = 10, p = 0.85 and q = 0.15

Using the formula,

P(X=6) = [tex]_{n}C_{x} (0.85)^{n} (0.15)^{x}[/tex]

           = [tex]_{10}C_{6} (0.85)^{6} (0.15)^{4}[/tex]

           = 210(0.377)(0.0005)

           = 0.04

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the diameter of a tree was 14 in. during the following​ year, the circumference increased 4 in. about how much did the​ tree's diameter​ increase? about how much did the​ tree's cross-section area​ change?

Answers

The diameter of the tree increased by 0.27in. (approximately) and the change in tree's cross section area is 27.5 in.².

As given in the question,

Diameter of the tree 'd' = 14in.

Radius = 7in.

Circumference of the tree = πd

                                            = 3.14 × 14

                                            = 43.96 in.

New circumference increased by 4 in. = 43.96 + 4

                                                                = 47.96in.

New diameter = 47.96 / 3.14

                        = 15.27 in. (approximately)

New Radius ≈ 7.6 in.

Increase in diameter= 15.27 - 15

                                  = 0.27 in.

Area of cross section original tree = 3.14 × 7²

                                                         = 153.9 in.²

New area of cross section original tree = 3.14 × 7.6²

                                                                 = 181.4 in.²

Change in area = 181.4 - 153.9

                          = 27.5 in.² ( approximately)

Therefore, increase in diameter is 0.27in. and change in cross - section area is 27.5 in.²

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when severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated?

Answers

The fundamental regression assumption that the error terms are independent of one another is broken when substantial autocorrelation is shown following the estimation of a regression model. Here option C is the correct answer.

The two error factors must be somewhat co-correlated in order for there to be autocorrelation. Having it indicates that the correlation between the two error factors is not equal to zero. It goes against the fundamental tenet of the traditional linear regression approach.

Autocorrelation measures the relationship between a variable's current value and its historical values. A perfect positive correlation is represented by an autocorrelation of 1, whereas a perfect negative correlation is represented by an autocorrelation of 1.

An explanation of how one or more independent variables relate to the target variable, response variable, or dependent variable that the regression model predicts.

Complete question:

When severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated? A - The dispersion of population data points around the population regression line remains constant everywhere along the line

B - The population of values is normally distributed about the population regression line.

C - Heteroscedasticity

D - The error terms are independent of each other.

E - A linear relationship exists between X and Y in the population

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Evaluate each expression for the given value of the variable. 4(x-4);x=7

Answers

Answer:

(28-16)

Step-by-step explanation:

x=7

4x-16

If x is 7

then it is 4x7 = 28

Therefore we can say 28-16 is our final answer.

Thank you.

what value of aa would indicate no association between gender and voting pattern for the people in the sample?

Answers

The value of ' a 'indicating no association between gender and voting pattern for the people in the sample is 500.

What is sample?

A sample is a result of a random experiment. We sample a random variable when we select a specific value from among its possible possibilities. A exact value is that of a sample. The potential values and likelihood of each are determined by the random variable's probability distribution. They should be picked at random from a broader group or population in order to assist you understand more about the population as a whole. Samples are employed in statistical testing when population sizes are too big for all prospective participants or observations to be included in the test.

Here,

Considering Split ticket,

a + b = 600  ---(1)

Considering No Split ticket,

c + d = 400    ---(2)

Considering Men,

a + c = 800      ---(3)

Considering Women,

b + d = 200       ---(4)

Applying (1) - (4),

a + b -  b - d= 600 - 200

a - d = 400    ---- (5)

Applying (2) - (4),

c + d - b - d = 400- 200

c - b = 200  ----(6)

a - c = 200 --- (7)

Applying (3) + (7)

2a = 1000

a = 500

For those in the sample, the value of "a" showing there is no correlation between gender and voting behavior is 500.

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You make a total of 16 two-point and three-point shots in a basketball game. You score a total of 35 points. Which system can be used to find the number p of two-point shots and the number q of three-point shots you make? Responses p+q=35 2p+3q=16 p plus q is equal to 35, , 2 p plus 3 q is equal to 16, p+q=16

Answers

2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

We need to find the number p of two-point shots and the number q of three-point shots you make.

a total of 16 two-point and three-point shots in a basketball game.

2p+3q=16

Total score is of 35 points.

p+q=35

These two equations 2p+3q=16 and p+q=35 can be used to find the  number p of two-point shots and the number q of three-point shots you make.

Hence, 2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make

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can someone answer this?

Answers

The value of y in the intersected lines is 80.

How to find the angles in the intersected line?

When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles, angles on a straight line etc.

Therefore, the value of y in the angles can be found as follows:

10y - 12 = 3x + 29 (vertically opposite angles)

vertically opposite angles are congruent.

Hence,

10y - 12 = 3x + 29

10y - 3x = 41

6x - 3 + 10y - 12 + 37 = 180 (sum of angles on a straight lines)

6x + 10y = 180 + 3 + 12 - 37

6x + 10y = 158

combine the equation

10y - 3x = 41

10y + 6x = 158

9x = 117

x = 117 / 9

x = 13

6(13) + 10y = 158

10y = 158 - 78

10y = 80

y = 80 / 10

y = 8

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4 1/5 divided by 3 1/2
HELPPPPPPPPPPP

Answers

Exact Form:
6/5
Decimal Form:
1.2
Mixed Number Form:
1 1/5

Simplify the expression to a polynomial in standard form: (x-1)(3x^2+7x+5) (x−1)(3x 2 +7x+5)

Answers

The standard form for the given expression is 3x³ - 3x² - 2x - 5.

How to write a polynomial in standard form?

A polynomial can be written in standard form by writing its terms in descending order of their powers and the constant terms comes at the end.

The given polynomial is (x - 1)(3x² + 7x + 5).

It can be written in standard form as follows,

(x - 1)(3x² + 7x + 5)

= x(3x² + 7x + 5) - 1(3x² + 7x + 5)

= 3x³ + 7x² + 5x - 3x² - 7x - 5

= 3x³ - 3x² - 2x - 5

Hence, the given expression can be written in standard form as,

3x³ - 3x² - 2x - 5

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according to the department of public health, the average age of a new smoker is 13 years old. a researcher working for the tobacco industry wishes to test the claim that the average age is no longer 13 years old. he surveys a sample of 144 new smokers and finds they have an average age of 13.5 years with a standard deviation of 2.5 years. do the sample data support the researcher’s claim? test the relevant hypotheses at a significance level of ????????

Answers

Answer:

Step-by-step explanation:

                                                   ?

Ingrid competed in a triathlon that requires her to run, swim and bike. If she swam at a rate of 3 mph for 1 and a half hour, biked at 12 mph for 3 hours and ran for 6 mph for 4 hours, find the distance of the triathlon.

Answers

The distance of the triathlon, given the time Ingrid spent swimming, biking, and running, is  61.5 miles

How to find the distance?

To find the distance of the triathlon, find the distance of the individual events which are the running, swimming, and biking. Then sum these distances up to find the triathlon distance that Ingrid ran.

The distance for swimming:
= Rate x Number of hours

= 3 x 0.5 hours

= 1.5 miles

The distance for biking:

= 12 x 3

= 36 miles

The distance for running:
= 6 x 4

= 24 miles

The triathlon distance is:

= 1.5 + 36 + 24

= 61.5 miles

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dominic has a family history of hypertension. according to the chronic disease risk reduction intakes (cdrr) for sodium, dominic should lower or maintain his sodium intake to below mg/day to reduce his risk of chronic disease, including hypertension

Answers

Dominic should lower or maintain his sodium intake to below 2,300 mg/day.

Chronic disease :

The Chronic Disease Risk Reduction (CDRR) consumption of 2,300 mg/day was recently developed due to connections between high sodium intake and the risk of hypertension. It is anticipated that sodium intake below this level will lower the risk of chronic diseases.

Adults may be at risk for chronic diseases if their sodium intake exceeds their CDRR intake. The population's cardiovascular health may be improved by efforts to reduce sodium consumption. Among healthy individuals, lowering daily sodium intake to CDRR is anticipated to lower the risk of developing chronic diseases, primarily by lowering blood pressure.

Hence, sodium intake to below 2,300 mg/day can reduce his risk of chronic disease.

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in a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. if 10 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?

Answers

answer: 72 or 1572480 depends on how you do the math

at a deli counter, there are 9 sandwiches with meat and 10 vegetarian sandwiches. dante is at the counter buying sandwiches for a picnic. in how many ways can he choose 9 sandwiches if 8 or more must be vegetarian sandwiches?

Answers

There are two different ways in which he can choose 9 sandwitches. It can be solve by the concept of permutation and combination.

What is permutation and combination?

A permutation is an arrangement of several items taken one at a time or all at once in a specific order.

Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.

Since all vegitarian sandwiches looks like same and all sandwitches with meat looks like same hence, their order will not affect the number of choice.

If 8 sandwitches are vegitarian then 1 sandwitch must be with meat. So that total sandwithches becomes 9.

If all 9 sindwitches are vegetarian then there is no option to choose another sandwitch. Because he can choose only 9 sandwitches.

Hence, there are two different ways in which he can choose 9 sandwitches.

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The value of a brand new car is $ 40 , 000 $40,000 and the value depreciates 19% every year. Write a function to represent the value of the car after t t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent

Answers

Answer:

Function: V(t) = 40,000(0.81^(4t))

Quarterly rate of change: -19.00%

What type of variable is required to construct a confidence interval for a population​ proportion?.

Answers

The type of variable required is Qualitative with two possible outcomes.

What is a confidence interval?

An estimate level of uncertainty is expressed by a range of values known as a confidence interval.

Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.

Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.

Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.

Hence, the type of variable required to construct a confidence interval for a population​ proportion is Qualitative with 2 possible outcomes.

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Find the values of the variables in each parallelogram

Answers

Adjacent angles of a parallelogram are supplementary.

[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]

a sample of 1600 computer chips revealed that 42% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 39% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.

Answers

Reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.

Explain the term Null hypothesis?The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data or measured phenomena for any given single observed variable.

Let p represent the fraction of the population.

Taking into account the provided data, we have

Null hypothesis: H0 : p ≤ 0.35.

Alternative hypothesis: H1 : p > 0.35, the test is a right-tailed test since the alternative is right-tailed;

For the stated question-

n = 1000; p' = 0.42.

Test statistics for this sample proportion:

z = (p' - p) / √p(1 - p)/n

Put the values-

z = (0.42' - 0.39) / √0.39(1 - 0.39)/1000

z = 1.94

P-value for this right tailed test is;

P(z > 1.94) = 0.0523

Therefore reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.

We draw the conclusion that we have enough data to back up the company's claim at the 0.10 level.

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Data Island is a beautiful beach resort. It has been a premier touristic destination for over 80 years, and the earliest holiday homes have been built just a few steps away from the beach itself. You work for a real estate agency that sells and rents holiday homes in Data Islands. Recently, one of the interns working on the Data Science Team presents you a report. According to the linear regression model they have run, the price of a house is proportional to its age. But this does not make any sense: after all, newer houses should be worth more.
1. Comment the regression output, noticing that the Sig. column is reporting the p-value of the coefficient. What can you tell about the sign of Age’s slope?
2. Why do you think the model forecasts an higher price for old holiday homes? Think carefully about all the information you have concerning Data Island.
3. Assuming that more data and variables are available, what would you suggest your intern to do to fix their report?

Answers

A lovely beach resort is Data Island. Since it first became a popular tourist destination more than 80 years ago, the earliest vacation homes have been constructed just a few steps from the beach. You are a real estate agent for a company that deals in vacation rentals and sales in the Data Islands. A report was recently presented to you by one of the interns on the data science team. The age of a house affects its price, according to the linear regression model they have ran. But this is absurd because newer homes ought to be more valuable.

1.  As the coefficient of Age is positive, so the older the house, the more price it is. Sig. (or p-value) = 0.000 which implies  that the co-efficient of Age is significant.

2.  This may be that the people who live there are reluctant to sell it, so they quote a higher price or the size of old houses are large or they may be located at prime location.

3.  We would ask new interns to consider other independent variables for the regression equation like size of house, location, etc.

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I need help trying to find the area of this triangle please help.

Answers

Answer:

  28 ft²

Step-by-step explanation:

You want the area of a triangle with a base of 7' and a height of 8'.

Area formula

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base of the triangle, and h is the height perpendicular to the base.

Here, it is convenient to use the side marked 7' as the base of the triangle. The distance marked 8' is the perpendicular distance from the base to the top of the triangle. So, the area is ...

  A = 1/2(7 ft)(8 ft) = 28 ft²

The area of the triangle is 28 square feet.

__

Additional comment

As you can see, the vertex opposite the base does not need to lie above the base segment. All that matters is the perpendicular distance from that vertex to the base line.

The letters that form the word
MATHEMATICS are placed in a bowl. Are the
odds favorable or unfavorable that he will
choose a letter that is a vowel followed by a
"T"?

Answers

Answer:

Step-by-step explanation:

The odds arent favorable its a 2/11 chance of happening

is Pavers that cost a set amount per square foot proportional
(This is an imagine math quistion)

Answers

Answer:

Step-by-step explanation:

Yes it is because if the amount of Pavers change so does the cost.

HELP ME PLEASE AS FAST AS POSIBLE

Answers

Answer:

243 inches to the 3 power

Step-by-step explanation:

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