Answer:
Step-by-step explanation:
The answer is 3.
X=2X-3
X+3=2X
3=2X-X
3=X
Answer:
3x < 2x + 8
Step-by-step explanation:
Mary Beth Marrs, the manager of an apartment complex, feels overwhelmed by the number of complaints she is receiving. Below is the check sheet she has kept for the past 12 weeks. Develop a Pareto chart using this information. What recommendations would you make?WEEK GROUNDSPARKING/DRIVES POOLTENANTISSUESELECTRICAL1333 33 3 33323 333 33 33 33333 333 33 343 3333 3 3 33533 333 3333 3363 3333 337333 33 3383 3333 33 333 393 33 3103 3333 33 3311333 33 312 33 333 333 3Problem S6.11
Mary Beth Mars, develops a Pareto chart using the information. The recommendations that you would make is as follows:
A graph containing both bars and a line, the bars representing individual values in descending order and the line representing the cumulative total, is known as a Pareto chart. The Pareto chart allows us to concentrate on it when we need to. The Pareto chart is built upon the 80%-20% run of the show. The Pareto chart states that 20% of arrangements assist in resolving 80% of issues. The complex manager, Mary Beth Marrs, must concentrate on issues with the pool, the ground, and the stopping part in order to satisfy the majority of residents and reduce complaints.
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Three out of 5 students at Maria's school participate in a school club or sport. There are 175 students at the school. How can equivalent fractions be used to find the s, the total number of students participating in a school club or sport?
The total number of students participating in a school club or sport is 105.
How to calculate the number of students?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
Given that three out of 5 students at Maria's school participate in a school club or sport and there are 175 students at the school.
In this situation, the number of people that participate will be:
= Fraction utilized × Total number of students
= 3/5 × 175
= 105
The number of people is 105.
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The value of China’ export of automobile and part i approximately F of X equal 1. 8208 to the E to the 0. 3387. Ak her ak equal zero correpond in 1998 and what year did will the oxford reach 5. 3 billion
In the year 2002 the exports of Chinese's automobile parts will $5.3 billion.
Explain the term exponential function?The formula for an exponential function is f (x) = a^e, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.The exponential function for the given export of Chinese's automobile parts is-
5.3 = 1.8208 e^0.3387x
5.3/1.8208 = e^0.3387x
Taking ln both sides-
ln(5.3/1.8208) = ln e^0.3387x
ln(5.3/1.8208) = 0.3387x
Further simplifying
x = ln(5.3/1.8208)/0.3387
x = 3.15
x ≈ 3 year ad some months
Add 3 years to 1998 to get the required year.
Year = 1998 + 3
Year = 2001 and months
Year = 2002
Thus, in the year 2002 the exports of Chinese's automobile parts will $5.3 billion.
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The correct question is-
The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x) = 1.8208e^.3387x, where x = 0 corresponds to 1998.
In what year did/will the exports reach $5.3 billion?
find the measure of a negative angle co terminal with 95°
Line j has an equation of y= 1 /5 x+7. Perpendicular to line j is line k, which passes through the point (– 1,– 3). What is the equation of line k
Answer:
y = -5x -8
Step-by-step explanation:
The slope must be the negative reciprocal(-5). So we have y = -5x + b, where we need to find b. To do that, we will plug in the known point. This gives us [tex]-3 = -1 * -5 + b[/tex], or[tex]-3 = 5 + b[/tex]. We subtract 5 from both sides to get b = -8.
In a tug-of-war, Team A is pulling to the left with 6 Newtons and Team B is pulling to the right with
4 Newtons. What is the net force?
Answer: 2n!
Step-by-step explanation:
6N -4 N =2N
test worth 50 points; test score of 40%
Answer:
20/50
Step-by-step explanation:
40% is equal to 40/100
40/100 is equal to 20/50
A high school offers math placement exams for incoming freshmen to place students into the appropriate math class during their freshman year. Three different middle schools were sampled and the following pass/fail results were found. Run a test for independence at the 0.10 level of significance. School A School B School C Pass 42 29 45 Fail 57 35 61 Hypotheses: Pass/fail rates are dependent on/independent of school. Pass/fail rates are independent of/dependent on school. Enter the expected matrix - round to 4 decimal places. School A School B School C Pass Fail After running an independence test, can it be concluded that pass/fail rates are dependent on school? Yes/No
The pass numbers are independent of the school of study.
Given that a high school offers math placement exams for incoming freshmen to place students into the appropriate math class during their freshman year
Set up hypotheses as
H₀ : Pass independent of school
Hₐ : Pass independent on school
Two tailed chi square test for independence)
Contingency table is shows as below
School A B C Total
Pass 42 29 45 116
Expected 38.6667 38.6667 38.6667 116.0000667
Obs-exp)^2/observed 0.2874 2.4167 1.0373 3.74138208
df 2
p value = 0.154
Since p > alpha(0.1) we accept null hypothesis
The pass numbers are independent of the school of study.
Hence we get the required answer.
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given that $x$, $\frac{1}{x}$, $y$, $\frac{1}{y}$, $z$ and $\frac{1}{z}$ are all integers, how many distinct values of $x y z$ are possible?
Distinct value of x, y, z are will be 3
Consider the function will be f(x) = x3 - x2 - 2x +2 = ( x - 1 ) (x2 - 2 )
we have three real roots and ,
x + y + z = - 1/ (-1)
= 1 ,
1/x + 1/y + 1/z = -2 /(-2)
= 1
Consider the function
f(x) = x3 - x2 - 40 + 20.
Set the derivation equal 0 we get x = 4 and x = -10/3
are two local extrema. When x= 4 , f(x)<0,when x = -10/3 . f(x) >0 there are three real roots . we have x + y + z = 1 and 1/x + 1/y + 1/z = - (-40)/ 20 = 2
consider the function
f(x) = x3 - x2- 40x + 40/3 .
we still have same local extrema as (2) and we have x= 4 , f(x) < 0 and we
x= -10/3 , f(x) > 0 so there are three real roots. We have x+ y + z = 1 and 1/x + 1/y + 1/z = -(-40)/40/3 = 3
So, there are 3 distinct values
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For each of the following ML functions, could the activation record for the function be deallocated as soon as the function returns? Explain why or why not.a) fun f x = x + 1;b) fun f x = fn y => x + y;c) fun f x = fn y => y + 1;d) fun f x = map ~ x;
The explanation for each condition of the question is given below in which the activation record for the function is deallocated for Option (A).
What is an activation record?
Information required for just one execution of a procedure is managed by an activation record. When a procedure is called, an activation record is pushed into the stack, and it is popped when the control is returned to the calling function.
From the question, Languages typically group all activation-specific function validation under the umbrella of an activation record.
Whenever the block is entered, extend the function activation record.
a. fun f x = x + 1;
In this situation, the activation record concludes after the function "f" exits.Extend the function activation record if the block is entered; otherwise, revert.The activation record was terminated after execution at x=x+1. So, we. The activation record has to be reallocated.Because f(x)=x+1.11f is called, the local function is returned. The activation record is therefore deallocated.b. fun f x = y =>x y;
Take fun f
x=fun y
x+y
Here, f(x) and f are two functions (y).The execution of f(x) requires f(y).Therefore, until f(x) and f(y) is performed, the activation record will remain active. When the control returns to the first function, the activation record is exited.Therefore, during the function return, we need to reallocate the activation record.c. fun.f x = fn y => y+ 1;
fun f
x => fn
y => y+1
In this case, the activation record is expanded to include the second function, f(y), whose execution is reliant on f(x).The record will remain active till the execution of the two functions.After the activation record has been allocated, it is reactivated as the method returns.d. fun f x = map ~ x
Here, the map is used to connect the list to the function f(x) and the activation record is for the function f(x). As a result, the activation record is changed independently and then returned.As a result, a new activation record is not necessary.To learn more about an activation record
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Fred deposits $6,500 in a saving account that pays 0.5% interest, compounded quarterly. Round each answer to the nearest cent.
a. Find the first quarter's interest.
b. Find the first quarter's ending balance.
c. Find the second quarter's interest.
d. Find the second quarter's ending balance.
e. Find the third quarter's interest.
f. Find the third quarter's ending balance.
g. Find the fourth quarter's interest.
h. What is the balance at the end of one year?
i. How much interest does the account earn in the first year?
The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;
a. Interest for the first quarter = $8.125
b. First quarter ending balance = $6,508.125
c. Interest for the second quarter = $8.13515625
d. Second quarter ending balance = $6,516.26015625
e. Interest for the third quarter = $8.1432520325
f. Third quarter closing balance = $6,524.40548145
g. Interest for the fourth quarter = $8.15550685975
h. The amount of interest earned in a year is about $32.56
What is an interest earned on an amount?An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.
The amount Fred deposited, P = $6,500
The interest paid by the account, r = 0.5% compounded quarterly
a. The first quarter interest can be found by the formula;
[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times \dfrac{1}{4} }- P[/tex]
Therefore;
[tex]C.I. = 6500\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6500 = 8.125[/tex]
The interest after the first period is $8.125
b. The first quarter ending balance is therefore;
A = P + C.I.
A = $6,500 + $8.125 = $6,508.125
c. The second quarter's interest can be found from the formula;
[tex]C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times t} - P[/tex]
Here, P = The balance from the first quarter = $6,508.125
t = 1/4 for one quarter
Therefore;
[tex]C.I. = 6508.125\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6508.125 = 8.13515625[/tex]
The second quarter's interest is $8.13515625
d. The second quarter ending balance is therefore;
A = $6,508.125 + $8.13515625 = $6,516.26015625
The second quarter ending balance is $6,516.26015625
e. The third quarters interest is therefore;
[tex]C.I. = 6516.26015625\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6516.26015625 = 8.1432520325[/tex]
The third quarter's interest is about $8.1433
f. The third quarter's ending balance is therefore;
A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145
The third quarter's ending balance is $6,524.40548145
g. The fourth quarter's interest can be found as follows;
[tex]C.I. = 6,524.40548145 \times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6524.40548145 = 8.15550685975[/tex]
The fourth quarter's interest is; $8.15550685975
h. The balance at the end of one year is therefore;
Balance = C.I. fourth quarter + Principal for the fourth quarter
Therefore;
Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831
i. The interest the account earns in a year is therefore;
$6,532.56098831 - $6,500 = $32.5609883
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3x² + 15x-5) •/. (x + 5)
Divide using synthetic division
NO LINKS! PLEASE HELP ME!
Answer:
4860 bacteria
Step-by-step explanation:
The given scenario can be modelled using an exponential function with base e.
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=Ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]
Define the variables:
Let y be number of bacteria.Let x be the time (in hours)Given the initial number of bacteria is 20, then A = 20.
[tex]\implies y=20e^{kx}[/tex]
If the bacteria triples its number in 16 hours, then when x = 16:
[tex]\implies y=3 \times 20= 60[/tex]
Substitute x = 16 and y = 60 into the equation and solve for k:
[tex]\begin{aligned}y&=20e^{kx}\\\implies 60&=20e^{16k}\\\dfrac{60}{20}&=e^{16k}\\3&=e^{16k}\\\ln 3&=\ln e^{16k}\\ \ln3&=16k \ln e\\\ln3&=16k\\k&=\dfrac{1}{16} \ln 3\end{aligned}[/tex]
Therefore, the equation that models the given scenario is:
[tex]\large\boxed{y=20e^{\left(\frac{1}{16}x \ln 3\right)}}[/tex]
To find how many bacteria there are after 80 hours, substitute x = 80 into the equation and solve for y:
[tex]\implies y=20e^{\left(\frac{1}{16}(80) \ln 3\right)}[/tex]
[tex]\implies y=20e^{\left(5 \ln 3\right)}[/tex]
[tex]\implies y=20e^{\left(\ln 3^5\right)}[/tex]
[tex]\implies y=20e^{\left(\ln 243\right)}[/tex]
[tex]\implies y=20 \cdot 243[/tex]
[tex]\implies y=4860[/tex]
Therefore, there are 4860 bacteria after 80 hours.
-----------------------------------------------------------------------------------------------
Please note that I have solved this question so that you can calculate the number of bacteria for any number of hours, part hours, etc.
However, there is a much simpler way of solving this particular question.
If the number of bacteria triples every 16 hours, then it will triple 5 times within 80 hours since 80 ÷ 16 = 5.
Therefore:
Hour 0: 20Hour 16: 20 × 3 = 60Hour 32: 60 × 3 = 180Hour 48: 180 × 3 = 540Hour 64: 540 × 3 = 1620Hour 80: 1620 × 3 = 4860As you can see, the result is the same as the previous method.
A town's population has been growing linearly. In 2003 the population was 22,000. The population has been growing by 1700 people each year. Write an equation for the population, P, x years after 2003. P = Preview Use the formula to find the population in 2009: Preview
The equation is P = 1700x + 22,000 and the population in 2009 is 32,200.
Here we have to find the equation to get to know the population after x years.
Data provided:
Population in 2003 = 22,000
Year = x year
Population increases every year = 1700
Let P be the population after x year.
So the equation is:
P = 1700x + 22,000
Now we have to find the population in 2009.
So 2009 - 2003 = 6
Put x = 6
P = 1700 × 6 + 22,000
= 10200 + 22,000
= 32,200
Therefore the equation is P = 1700x + 22,00 and in 2009 population is 32,200.
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If the bond angle between two adjacent hybrid orbitals is 109. 5°, which is the hybridization?.
109.5° is the bond angle between two nearby hybrid orbitals. sp3 will be the hybridization.
The hybridization would be sp3. This is because the bond angle of 109.5° is characteristic of hybridized orbitals with four sp3 orbitals, which form an angle of 109.5°. sp3 hybridization occurs when one s orbital and three p orbitals mix to form four sp3 hybrid orbitals.
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the state of california has a mean annual rainfall of 22 inches, whereas the state of new york has a mean annual rainfall of 42 inches. assume that the standard deviation for both states is 8 inches. a sample of 30 years of rainfall for california and a sample of 45 years of rainfall for new york has been taken. if required, round your answer to three decimal places. (a) calculate the sampling error of the sample mean annual rainfall for california.
Sample error is ±2.9872 from the sample mean of 22 inch and standard deviation of 8 inch and sample size of 30 inch.
What is sample error?An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data. As a result, the sample's findings do not accurately reflect the findings from the total population.
Here,
mean=22 inch
standard deviation=8 inch
sample size=30 inch
degree of freedom=29 inch
The sampling error is calculated by dividing the standard deviation of the population by the square root of the size of the sample, and then multiplying the resultant with the Z-score value, which is based on the confidence interval.
By using this,
sampling error=±2.9872 inch
With a sample mean of 22 inches, a standard deviation of 8 inches, and a sample size of 30 inches, the sample error is 2.9872 inches.
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which of the following hypotheses can be tested with the data that was collected? group of answer choices the average number of consumers that prefer catalogs in spanish is large the average number of consumers that prefer catalogs in english is large the percent of hispanics that are likely to buy from an l.l. bean catalog is higher than 30% the percent of hispanics that prefer to read catalogs in spanish is equal or higher than 30%
The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%
What is percentage ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
The percent of Hispanics that prefer to read catalogs in Spanish is equal or higher than 30%
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Which equation is the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7.
Answer:
y=5x+53
Step-by-step explanation:so all i did was go into the demos app and typed in y=5x-7 and then i entered y=5x+30 and i kept going up until i found the right answer
if a baseballs cost $4.50 how much will 5 cost
Answer:
22.5
Step-by-step explanation
22.5 is the correct answer because 4.50 times 5 is 22.5 :))))
Answer:
22.5
if one baseball cost $ 4.50 , we multiply it by 5 , or add 4.50+4.50+4
.50+4.50+4.50 same thing.
Solve 6-5x/10 2x+1/5 +x/3=2x/15
What is an equation of the line that passes through the point (1,7)(1,7) and is perpendicular to the line x+6y=42x+6y=42?
The equation of the perpendicular line to x + 6y = 42 is: y = 6x + 1.
What are Perpendicular Lines?The lines that are perpendicular to each other will have slope values that have a product of -1, which means one is a negative reciprocal of the other.
Given the equation, x + 6y = 42, it can rewritten in slope-intercept form as shown below:
6y = -x + 42
6y/6 = -x/6 + 42/6
y = -1/6x + 7
The slope of the line is -1/6. The negative reciprocal of -1/6 is 6. Therefore, the slope of the line that is perpendicular to x + 6y = 42 is 6.
Substitute m = 6 and (x, y) = (1, 7) into y = mx + b to find the y-intercept (b):
7 = 6(1) + b
7 = 6 + b
7 - 6 = b
b = 1
Tp write the equation of the perpendicular line, substitute m = 6 and b = 1 into y = mx + b:
y = 6x + 1
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in randomized, double-blind clinical trials of a new vaccine, were randomly divided into two groups. subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. after the second dose, of subjects in the experimental group (group 1) experienced as a side effect. after the second dose, of of the subjects in the control group (group 2) experienced as a side effect. does the evidence suggest that a higher proportion of subjects in group 1 experienced as a side effect than subjects in group 2 at the level of significance? question content area bottom part 1 verify the model requirements. select all that apply. a. the data come from a population that is normally distributed. b. the samples are independent. your answer is correct.c. the sample size is more than 5% of the population size for each sample. d. the samples are dependent. e. and your answer is correct.f. the sample size is less than 5% of the population size for each sample. your answer is correct. part 2 determine the null and alternative hypotheses. : equals : greater than part 3 find the test statistic for this hypothesis test.\
Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find the exact length of c from the origin to the point 5, 25 2 , 125 6.
From the origin (6,18,36) to the tip, the exact length of the curve is 42.
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.
According to our question-
let x = t
x^2= 2y
y = t^2
44/3
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calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.
To calculate the probability that there will be at least four accident in no accident occur before the forth month in which at least one accident occurs
If a month with one or more accidents is regarded as success and let the
k = the number of failures before the fourth success, and then k follows a negative binomial distribution and the requested probability is
1. success taken as a month with no accident
2. k = the number of failure before the fourth success
Alternatively the solution is where [tex]Pr[k\leq 3][/tex]
which is derived directly as a negative binomial distribution
Therefore, the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs is 0.2898
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A number t multiplied by negative -4 is at least negative 2/5
Answer:
-4t ≥ -2/5
Step-by-step explanation:
t≥0.1
The sum of a number and 7 times its reciprocal is 16/3. Find the number
Answer:
7/3 or 3
Step-by-step explanation:
Step by step explanation is shown in the picture attached.
Hope it helps
use the graphs of f and g to describe the transformation from the graph of f the the graph of f to the graph of g.
f(x) = -3x + 4 ; g(x) = f(x) + 1
The value of the function f(x) = -3x+4 is -3x+5
What is function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Given a function, f(x) = -3x+4
g(x) is described as f(x) +1
g(x) = -3x+4+1
g(x) = -3x+5
The graph of f(x) will move 1 unit farther when transformed into g(x).
Hence, The value of the function f(x) = -3x+4 is -3x+5
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Mr. Etrada' car can travel no more than 510 mile on one full tank of gaoline. After filling up the tank with gaoline, he traveled 194 mile in the car. Write an inequality that repreent the value of m, the number of mile Mr. Etrada can travel in the car with the remaining gaoline in the tank and olve
After covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign.
It is an illustration of inequity.
This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
Finding the x numbers for which the inequality holds true is what we are most interested in.
So, the inequality that can represent the given situation is:
x = total distance traveled
m = miles that the gas will allow you to go
The maximum number of miles per full tank is 510.
Then,
x + m ≤ 510
194 + m ≤ 510
m ≤ 510 - 194
m ≤ 316
Therefore, after covering 194 miles, Mr. Etrada's car can go a maximum of 316 miles with the gas still in the tank and the inequality that represents the given situation is x + m ≤ 510.
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what is the sum of all integers $n$ that satisfy $$-3n < 7n-20 < 3n~?$$ in other words, what is the sum of all integers $n$ that satisfy both of the inequalities $$-3n<7n-20\text{~~and~~}7n-20<3n~?$$
3+4=7 is the total of all possible integer values of n.
What are integers?Integers include zero, a positive natural number, and a negative integer represented by a minus sign.
The negative numbers are the inverse additions of the comparable positive numbers.
In mathematical notation, the letter Z is widely used to denote a set of numbers.
An integer is a whole number that can be positive, negative, or zero and is not a fraction.
Integer examples include -5, 1, 5, 8, 97, and 3,043.
So, the two inequalities are resolved independently. We add 3n to both sides of the first inequality, -3n7n-20, to find the solution:
Then, we add 20 to both sides to get 010n-20:
20<10n.
Lastly, multiplying both sides by 10 yields 2n, indicating that n must be bigger than 2.
We deduct 3n from both sides of the second inequality, 7n-203n:
Add 20 on both sides of 4n-200 to obtain:
4n<20.
Lastly, n must be less than 5 since the result of dividing both sides by 4 is n5.
Only the numbers 3 and 4 are greater than 2 and less than 5.
Therefore, 3+4=7 is the total of all possible integer values of n.
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two gamblers are playing a coin toss game. gambler a has (n 1) fair coins; b has n fair coins. what is the probability that a will have more heads than b if both flip all their coins
Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.
What is the binomial distribution?
The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.
Let X be the count of successes in the first n flips by A, Y the indicator that the last flip by A is also a success, and Z the count of successes in n flips by B.
Because Y is independent of X and Z, then:
P(X + Y > Z) = P(Y = 1) P(X ≥ Z) + P(Y = 0) P(X > Z)
= 1/2(P(X = Z) + 2P(X > Z))
P(X > Z) = P(Z > X)
Gambler A loses his comparative advantage the more coins that are tossed for both Gamblers. But Gambler A will always maintain the advantage and has quite a heavy advantage when a few coins are tossed.
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