Answer: find the solution in the explanation
Step-by-step explanation:
Let's use resolution of forces by resolving into x - component and y- component.
X - component.
Sum of forces = F1 - F3 - F4cos 15
Sum of forces = 0
5 - 5 - 0.97F4 = 0
- 0.97 F4 = 0
F4 = 0
Y - component
Sum of forces = F2 + F4 sin 15
Sum of forces = 0
5 + 0.26F4 = 0
0.26 F4 = -5
F4 = -5/0.26
F4 = -19.23 N
Simulating F4 back into the equation
Sum of forces = F1 - F3 - F4cos 15
- F4cos Ø = 0
- (-19.23) cos Ø = 0
Cos Ø = 0
Ø = 1
Does the angle formed approximate 15 degrees ? NO
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, said that they some what agree, said they some what disagree, and said they strongly disagree with this statement.
Required:
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
Step-by-step explanation:
a. It would provide a quantitative data
b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.
c. 44% of the respondents strongly agree
d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean salary of city 1 librarians
x2 = sample mean salary of city 2 librarians
s1 = sample standard deviation for city 1
s2 = sample standard deviation for city 2
n1 = number of soles for city 1
n1 = number of soles for city 2
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28
z = 2.048
x1 - x2 = 28,900 - 30,300 = - 1400
Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)
= 1647
The upper boundary for the confidence interval is
- 1400 + 1647 = 247
The lower boundary for the confidence interval is
- 1400 - 1647 = - 3047
Which of the given shapes has a larger area?
Answer:
Rectangle
Step-by-step explanation:
Count the units. For the triangle, A=0.5bh. 0.5(4)(6)=A. A=12
Now, for the rectangle, A=bh. A=(3)(5). A=15. The rectangle is larger
Please help me HURRY!!!!!!
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
Answer:
The probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds is P(X<368)=0.011.
Step-by-step explanation:
We have a normal distribution with mean 460 and standard deviation 40 to describe the time for the mile run in its secondary-school fitness test.
We have to calculate the probabiltiy that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
To calculate this, we have to calculate the z-score for X=368:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{368-460}{40}=\dfrac{-92}{40}=-2.3[/tex]
Then, we can calculate the probability:
[tex]P(X<368)=P(z<-2.3)=0.011[/tex]
14 fewer than 12 times the
number of people in my
family is 46.
Answer:
538
Step-by-step explanation:
12 times 46 is 552 then 552 minus 14 is 538
:D
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
V=
Answer: V=4778.4 cm³
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation
[tex]V=\pi (13)^2(\frac{27}{3})[/tex]
[tex]V=169\pi (9)[/tex]
[tex]V=1521\pi[/tex]
[tex]V=4778.4cm^3[/tex]
A team of researchers published an article on the study of how vehicles are dispatched based on an airport-based taxi service. The researchers modeled this system with an underlying assumption that travel times of successive trips to and from the terminal are independent exponentially distributed random variables with β = 15 minutes. (a) Find the mean and standard deviation of trip time distribution (b) How likely is it for a particular trip to take more than 25 minutes? (c) If two taxis are dispatched together, what is the probability that both of them will be gone for more than 25 minutes? (d) what is the likelihood of at least of one of the taxis returning within 25?
Answer:
a. The mean would be 0.067
The standard deviation would be 0.285
b. Would be of 1-e∧-375
c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5
d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375
Step-by-step explanation:
a. According to the given data the mean and the standard deviation would be as follows:
mean=1/β=1/15=0.0666=0.067
standard deviation=√1/15=√0.067=0.285
b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:
p(x>25)=1-p(x≤25)
since f(x)=p(x≤x)=1-e∧-βx
p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375
c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5
d. p(x≥25)=1-e∧-15x25=1-e∧-375
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Find the probability expressions: (Round your answers to 2 decimal places.)
a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).
Answer:
a. P(X=50)= 0.36
b. P(X≤75) = 0.9
c. P(X>50)= 0.48
d. P(X<100) = 0.9
Step-by-step explanation:
The given data is
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Where X is the variable and P(X) = probabililty of that variable.
From the above
a. P(X=50)= 0.36
We add the probabilities of the variable below and equal to 75
b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9
We find the probability of the variable greater than 50 and add it.
c. P(X>50)= 0.38+0.10= 0.48
It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.
d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9
Find f(g(−1)), f(g(−1))=___
Answer:
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
f(g(−1)) is - 8.
What is a composite function ?A composite functions is a function where two or more than two functions are combined.The output of the previous function is the input of the next function.
According to the given question we have to find a composite function.
Assuming f(x) = x² + 9x and g(x) = x³.
To find f(g(-1)) first we have to put x = -1 for g(x) which is
= g(-1) = (-1)³ = -1.
Now we put this value of g(-1) in f(x).
∴ f(g(-1))
= f(-1)
= (-1)² + 9(-1)
= 1 - 9
= - 8.
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Please help . I’ll mark you as brainliest if correct! Only the one marked with an X is wrong . I don’t get it
Answer:
(x+7)² = 9
Step-by-step explanation:
x² + 14x + 40 = 0
(x² + 14x) + 40 = 0
(x² +14x +49) + 40 - 49 = 0
(x+7)² - 9 = 0
(x+7)² = 9
Hope this helps!
Answer:
(x+7)² = 9
Step-by-step explanation:
Describe the steps you would use to solve the
following inequality
2x - 3
Answer: No answer
Step-by-step explanation:
Not an inequality, inequalities are of the form 2x - 3 > something.
If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.
Hope that helped,
-sirswagger21
Jose makes custom bicycles. He sells each bicycle for $400.
A)How much revenue does he make if he sells 1 bicycle?
B)How much revenue does he make if he sells 2 bicycles?
C)How much revenue does he make if he sells X bicycles?
D)What is her revenue equation?
A) $400
B) $800
C) 400*X
D) revenue=400x
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
Because the slope is -0.09 the answer is the second option. A negative slope means a decrease.
A typical classroom is a rectangle with dimensions of 20 feet wide by 25 feet long, and the area needed for each person in the room is approximately 28 square feet, what fraction of the total area in a classroom is needed for each person? What is the largest number of people that would fit in an average sized classroom while practicing good social distancing?
Answer:
A fraction of 0.056 of the classroom is needed for each student.
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
Step-by-step explanation:
We have a classroom that is a recatngle with dimensions of 20 feet wide by 25 feet long.
The total area of the classroom is:
[tex]A=w\cdot l=20\cdot25=500[/tex]
As the area of the classromm is 500 square feet and we need 28 square feet for each student, the fraction that is needed for each student is:
[tex]f=\dfrac{A_{\text{student}}}{A_{\text{classroom}}}=\dfrac{28}{500}=0.056[/tex]
A fraction of 0.056 of the classroom is needed for each student.
The largest number of students that would fit in an average sized classroom while practicing good social distancing can be calculated dividing the area of the classroom by the area needed for each student. This is equal to the inverse of the fraction calculated previously:
[tex]n=\dfrac{1}{f}=\dfrac{1}{0.056}\approx17.86[/tex]
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
WHAT IS A VOLUME OF THE BOX WITH A HEIGHT OF 3\2 WIDTH OF 5\2 AND LENGHT OF 7\2
Answer:
13.125 or 105/8u^3
Step-by-step explanation:
To find the volume of the box, you can use the formula of length times width time height.
3 * 5 = 15
2*2=4
15/4*7/2=105/8 which can be divided to become 13.125
Please answer this correctly
Answer:
Set the height up to 4
Step-by-step explanation:
Since there are 4 numbers between 1-5, set the height up to 4
Answer:
4 temperature recordings.
Step-by-step explanation:
2, 2, 4, 5
There are 4 recordings in the range of 1-5°C.
A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.
Answer:
Due to the higher z-score, he did better on the SAT.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Determine which test the student did better on.
He did better on whichever test he had the higher z-score.
SAT:
Scored 1070, so [tex]X = 1070[/tex]
SAT scores have a mean of 950 and a standard deviation of 155. This means that [tex]\mu = 950, \sigma = 155[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1070 - 950}{155}[/tex]
[tex]Z = 0.77[/tex]
ACT:
Scored 25, so [tex]X = 25[/tex]
ACT scores have a mean of 22 and a standard deviation of 4. This means that [tex]\mu = 22, \sigma = 4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 22}{4}[/tex]
[tex]Z = 0.75[/tex]
Due to the higher z-score, he did better on the SAT.
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
After the accounts have been adjusted at December 31, the end of the fiscal year, the following balances were taken from the ledger of Pioneer Delivery Services Co.:
Kerry Buckner, Capital. $9,556,300
Kerry Buckner, Drawing 80,000
Wages Expense 1,878,400
Rent Expense 1,415,500
Supplies Expense 125,000
Fees Earned 30,600
Miscellaneous Expense 22,100
Journalize the two entries required to close the accounts.
A tree casts an 8-foot shadow on the ground. The length from the tip of the shadow to the top of the tree is 17 feet. What is the height of the tree?
Answer:
Height of tree = 15 ft
Step-by-step explanation:
Given:
Length of shadow (Base) = 8 ft
Length from the tip to top of the tree (Hypotenues) = 17 ft
Find:
Height of tree = ?
Computation:
Using Pythagoras theorem:
[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]
Height of tree = 15 ft
Answer:
The answer is 15 feet from the ground to the top of the tree.
Step-by-step explanation:
A
B
C
D
Help me out
Answer:
2x^2 + 3/2x -5
Step-by-step explanation:
f(x) = x/2 -2
g(x) = 2x^2 +x -3
f(x)+ g(x) = x/2 -2+ 2x^2 +x -3
Combine like terms
= 2x^2 + 3/2x -5
Design and complete a frequency table for Belinda.
Belinda ask 20 people, how many hours of TV did you watch last week?
Here is the results
3,17,4,4,6,11,14,14,1,20,9,8,9,6,12,7,8,13,13,9.
Belinda wants to show these result in a frequency table.
She will use 4 equal groups.
The first group will start with 1 hour and the last group will end with 20 hours.
Answer:
Step-by-step explanation:
Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours
The class groups would be
1 to 5
5 to 10
10 to 15
15 to 20
The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are
(1 + 5)/2 = 3
(5 + 10)/2 = 7.5
(10 + 15)/2 = 12.5
(15 + 20)/2 = 17.5
The frequency table would be
Class group Frequency
1 - 5 4
5 - 10 8
10 - 15 6
15 - 20 2
The total frequency is 4 + 8 + 6 + 2 = 20
Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This function is used frequently in electrical engineering and signal processing.) Use this list of Basic Taylor Series to find the Taylor Series for f(x) = sinc(x) based at 0. Give your answer using summation notation and give the largest open interval on which the series converges. (If you need to enter [infinity] , use the [infinity] button in CalcPad or type "infinity" in all lower-case.)
Answer:
Step-by-step explanation:
To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that
[tex]\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}[/tex]
which is the taylor series expansion based at 0. Then for [tex]x\neq 0[/tex], by dividing both sidex by x, we have that
[tex]\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}[/tex]
which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.
Complete the synthetic division problem below.
2 1 6 -16
What is the quotient in polynomial form?
Answer: x + 8
Step-by-step explanation:
The required quotient in polynomial form is x + 8.
To determine the synthetic division of 2 | 1 6 -16 and quotient in polynomial function.
It is a method for performing division of polynomials, with little writing and lesser calculations than complex division.
2 | 1 6 -16
+2 +16
1 8 0
Its quotient in polynomial form is given as x + 8
Thus, The required quotient in polynomial form is x + 8.
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Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=15ft^3/min[/tex]
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=[tex]\frac{d}{2}=\frac{h}{2}[/tex]
Volume of pile=[tex]\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3[/tex]
[tex]\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}[/tex]
h=12 ft
Substitute the values
[tex]15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}[/tex]
[tex]\frac{dh}{dt}=0.13ft/min[/tex]
write any two numbers less than 15 , which has exactly four factors
Answer:
4 can be divided by 1 and 2
6 can be divided by 1 and 2
12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4
Step-by-step explanation:
FIND P(NOT 6) WHEN YOU ROLL A STANDARD NUMBER CUBE THEN DESCRIBE THE LIKELIHOOD OF THE EVENT WRITE IMPOSSIBLE ,UNLIKELY , EQUALLY LIKELY , LIKLEY OR CERAIN
Answer: LIKLEY
Step-by-step explanation:
Formula : Probability [tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
A standard cube has six numbers on it (1,2,3,4,5 and 6).
P( NOT 6) =[tex]\dfrac{\text{Numbers that are not 6}}{\text{Total numbers}}[/tex]
[tex]=\dfrac{5}{6}=0.8333[/tex]
We know that when the probability of any event lies between 0.5 and 1then the event is said to be likely to happen.
Since , P(not 6)=0.8333 which lies between 0 and 0.5.
That means, it is likely to happen.
Note :
When probability of having A = 0 , we call A as uncertain event.
When probability of having A = 1 , we call A as certain event.
When probability of having A = 0.5 , we call A as equally likely event.
When probability of having A lies between 0 and 0.5 , we call A as unlikely event.
When probability of having A lies between 0.5 and 1 , we call A as likely event.
Evaluate 1/2 + 1/2 ÷ 18
Answer:
1/18
Step-by-step explanation:
First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18
Answer:
1/18
Step-by-step explanation:
plz mark me brainliest.
Consider the following dice game, as played at a certain gambling casino: players 1 and 2 roll a pair of dice in turn. the bank then rolls the dice to determine the outcome according to the following rule: player i,i=1,2, wins if his roll is strictly
Ii={1 if i wins, 0 otherwise}
and show that I1 and I2 are positively correlated. Explain why this result was to be expected.
Answer:
they are positively correlated.
Step-by-step explanation:
We can calculate the individal expectations first. FIrst player will win if that player's roll is greater than the bank's roll. There are (6 possible rolls of player 1 * 6 possible rolls of bank =) 36 total possible rolls, out of which player 1 will win in 15 cases.
[tex]\therefore E(I_i) = 1\cdot \frac{15}{36} + 0 \cdot \frac{21}{36} = \frac{5}{12} \approx 0.4167[/tex]
For the joint expectation, there are (6 possible rolls of player 1 * 6 possible rolls of player 2 * 6 possible rolls of bank =) 216 total possible rolls.
Cases where both players win: Expectation = $2.
If bank rolls 1, both players will win in 5*5 = 25 cases. P1 is one of {2,3,4,5,6}, P2 is one of {2,3,4,5,6}
If bank rolls 2, both players will win in 4*4 = 16 cases.
If bank rolls 3, both players will win in 3*3 = 9 cases.
If bank rolls 4, both players will win in 2*2 = 4 cases.
If bank rolls 5, both players will win in 1*1 = 1 cases.
If bank rolls 6, both players will win in 0*0 = 0 cases.
Total cases = 25+16+9+4+1+0 = 55 cases.
Cases where player 1 wins $1 and player 2 loses: Expectation = $1.
If bank rolls 1, player 1 will win and player 2 will lose in 5*1 = 5 cases. P1 is one of {2,3,4,5,6}, P2 is {1}
If bank rolls 2, player 1 will win and player 2 will lose in 4*2 = 8 cases.
If bank rolls 3, player 1 will win and player 2 will lose in 3*3 = 9 cases.
If bank rolls 4, player 1 will win and player 2 will lose in 2*4 = 8 cases.
If bank rolls 5, player 1 will win and player 2 will lose in 1*5 = 5 cases.
If bank rolls 6, player 1 will win and player 2 will lose in 0*6 = 0 cases.
Total cases = 5+8+9+8+5+0 = 35
Cases where player 2 wins $1 and player 1 loses: Expectation = $1.
This is the same as above with player 1 and 2 exchanged.
Total cases = 35
Cases where both players lose: Expectation = $0.
If bank rolls 1, both players will lose in 1*1 = 1 cases. P1 is {1}, P2 is {1}
If bank rolls 2, both players will lose in 2*2 = 4 cases.
If bank rolls 3, both players will lose in 3*3 = 9 cases.
If bank rolls 4, both players will lose in 4*4 = 16 cases.
If bank rolls 5, both players will lose in 5*5 = 25 cases.
If bank rolls 6, both players will lose in 6*6 = 36 cases.
Total cases = 1+4+9+16+25+36 = 91 cases.
Total of all cases (we expect this to be 216 as mentioned above) = 55+35+35+91=216
So, joint expectation is:
[tex]E(I_1I_2) = \frac{2\cdot 55 +1\cdot 35+1\cdot 35+0\cdot 91}{216} = \frac{180}{216}= \frac{5}{6} \approx 0.8333[/tex]
So, the covariance is given by:
[tex]\texttt{Cov}(I_1I_2) =E(I_1I_2) -E(I_1)\cdot E(I_2)= \frac{5}{6}-\frac{5}{12}\cdot\frac{5}{12}=\frac{95}{144} \approx 0.6597[/tex]
As this is greater than 0 and closer to 1, they are positively correlated.
The reason why this result is expected is because the same bank roll is being used for both players. So, it is very likely that both players will win if the bank roll is 1 or even 2. Also, it is very likely that both players will lose if the bank roll is 6, 5, or even 4. This shows positive correlation between the events.