Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
what can you infer about angles w and z based on the information in the other triangles?
Answer:
They are supplementary and their sum is 180°
w = 45 + 60 or w = 105
z = 180 - 105 or z = 75
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:length 30, width 18
Step-by-step explanation:
60% +100%=160%
160% × 2 = 320 %
96/320 = 0.3 ×100 =30 ( length)
30 × 0.6 =18 (width)
Check: (18 + 30) 2 = 96
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.
Answer:
(73.845 ; 76.155) ;
(41.633 ; 48.367) ;
1.273 ;
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;
1.717
Step-by-step explanation:
1.)
Given :
Mean, xbar = 75
Sample size, n = 24
Sample standard deviation, s = 3.3
α = 90%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 24 - 1 = 23
Tcritical = 1.714
Margin of Error = 1.714 * 3.3/√24 = 1.155
Confidence interval = 75 ± 1.155
Confidence interval = (73.845 ; 76.155)
2.)
Given :
Mean, xbar = 45
Sample size, n = 37
Sample standard deviation, s = 10.1
α = 95%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 37 - 1 = 36
Tcritical = 2.028
Margin of Error = 2.028 * 10.1/√37 = 3.367
Confidence interval = 45 ± 3.367
Confidence interval = (41.633 ; 48.367)
3.)
Given :
Mean, xbar = 37
Sample size, n = 30
Sample standard deviation, s = 4.1
α = 90%
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 30 - 1 = 29
Tcritical = 1.700
Margin of Error = 1.700 * 4.1/√30 = 1.273
5.)
Sample size, n = 23
Confidence level, = 90%
df = n - 1 ; 23 - 1 = 22
Tcritical(0.05, 22) = 1.717
Is AABC-ADEF? If so, name which similarity postulate or theorem applies.
75
A. Similar - SSS
B. Similar - AA
0
C. Similar - SAS
D. Cannot be determined
Answer:
B. Similar - AA
Step-by-step explanation:
Two angles in ∆ABC are congruent to two corresponding angles in ∆DEF. Thus, it follows that the third pair of angles of both triangles would also be congruent.
Therefore, the three sides of ∆ABC and corresponding sides of ∆DEF will be proportional to each other.
This satisfies the AA Similarity Criterion. Therefore, ∆ABC ~ ∆DEF by AA.
find the sum and difference between the place value and face value of 5 in the number 3508 6941
Answer:
Sum= 5000005
Difference= 4999995
Step-by-step explanation:
The place value of 5 in the number 35086941 is 5000000
The face value is 5
The sum between the face value and place value can be calculated as follows
°= 5000000+5
= 5000005
The difference can be calculated as follows
= 5000000-5
= 4999995
A 3 phase traffic signal is designed with 2 seconds of all red per phase and phase lengths of 25 seconds, 30 seconds, and 15 seconds. The cycle length is ____ seconds.
Answer:
[tex]CL=76secs[/tex]
Step-by-step explanation:
From the question we are told that:
Traffic Phases p=3
Phase time Lengths
25 seconds, 30 seconds, and 15 seconds
Red Per Phase [tex]T=2sec[/tex]
Generally the equation for Cycle Length is mathematically given by
[tex]CL=Phase\ Length+Red\ Per\ Phase[/tex]
[tex]CL=(25+2)+(30+2)+(15+2)[/tex]
[tex]CL=76secs[/tex]
simplify 6 x + 3y /3
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
A.For a group of individuals, the random variable x denotes the number of credit cards per individual with the following distribution. x: 0 1 2 3 4 5 P(x): .27 .28 .20 .15 .08 .02 a. find the mean, variance and standard deviation of x b. find the probability that a randomly selected individual holds at least 1 card.
Answer:
1.55
2.66
1.631
Step-by-step explanation:
Given :
x: 0 1 2 3 4 5
P(x): .27 .28 .20 .15 .08 .02
The expected mean, E(X) = Σ(x*p(x))
E(X) = (0*0.27)+(1*0.28)+(2*0.20)+(3*0.15)+(4*0.08)+(5*0.02)
E(X) = 1.55
The expected variance :
Σx²*p(x) - E(X)
(0^2*0.27)+(1^2*0.28)+(2^2*0.20)+(3^2*0.15)+(4^2*0.08)+(5^2*0.02) - 1.55
4.21 - 1.55 = 2.66
The standard deviation :
√variance = √2.66 = 1.631
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!!
Finding the line of best fit is something a Machine Learning Model would do.
This particular ML model is called "Linear Regressor" or "Linear Regression Model". Look it up and there are definitely calculators for it, as it is relatively simple.
You can also, if you know how to use ML libraries and code, use Python to determine the value of [tex]b[/tex].
Hope this helps.
Use the P (A + B) = P (A) x P (B) rule to find the probability of system failure. Let A and B be the events that the first alarm and second alarm, respectively, fail. Do you get the same answer you did in the earlier question?
Answer:
answer is in the pic Mark me brainliest plz
Step-by-step explanation:
Answer:
The probability of the first alarm failing is (1 - 0.8) = 0.2
The probability of the second alarm failing is (1−0.9)=0.1.
Using the multiplication rule (since A and B are independent), the probability of failure is 0.2 * 0.1 = 0.02
Step-by-step explanation:
I need at least two more sentences in regards with this assignment. Note the included photo. Please come up with two proper sentences following the assignments instructions. Ps. Don’t try to steal points from this or you will be reported
Answer:
A={x: x is a cat}
B={x: x likes climbing on trees}
My little cat Louis likes climbing on trees (Louis is in the intersection of the two sets)
A={x: x is a town in the USA}
B={x: x is a town in the UK}
To improve my English I'd like to go on holiday to a town in the USA, but a town in the UK would work too (the town shall be in the union of the two sets)
Find each product
-4 (41)
4 (-41)
-4 (-41)
Please help me!!
Express 20% as a decimal number
Answer:
.20
Step-by-step explanation:
take the two digit % and move the decimal two places to the left
Answer: 0.2
Step-by-step explanation: 20/100 is 1/5 and 1/5 means 1 divided by 5 so the answer is 0.2
You are installing new carpeting in a family room. The room is rectangular with dimensions 2012feet × 1318feet . You intend to install baseboards around the entire perimeter of the room except for a 312 -foot opening into the kitchen. How many linear feet of board must you purchase?
Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
HELP WILL MARK BRAINLIESG
Write an equation that represents the line,
Use exact numbers.
Answer:
3/2 + 7
Step-by-step explanation:
Tell whether ADEF and AGHI can be proven
congruent.
A.No, ADEF and AGHI aren't congruent
because they don't share a side.
B.Yes, ADEF and AGHI can be proven
congruent by HL.
C.No, there isn't enough information
because the triangles aren't right
triangles.
D.Yes, ADEF and AGHI can be proven
congruent by SSS.
Answer:
A. No, ADEF, and AGHI aren't congruent because they don't share a side.
----------------------------
hope it helps...
have a great day!!
PLEASE HELP ME ASAP GIVING 10+ POINTS
The actual height of the building shown in the model is 150 feet What is the actual width of the building shown in the model?
Answer:
60 ft
Step-by-step explanation:
The answer has to be in feet units
Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units
5 cm = 150 ft
Rule: multiply cm by 30 to get the ft
2 cm = ?
2 cm × 30 = 60 ft
2 cm = 60 ft
Question 23 (5 points)
A triangle has two interior angles with the measurement of 68° and 54º. What's the
measurement of the third interior angle?
55°
620
58°
65°
Answer:
58°
Step-by-step explanation:
Given that,
The measure of two interior angles are 68° and 54º.
We need to find the measurement of the third interior angle.
We know that, the sum of angles of a triangle is equal to 180°. Let the angle is x. So,
x+68+54 = 180
x+122 = 180
x = 180-122
x = 58°
So, the measure of the third interior angle is equal to 58°.
Find the slope of the line y= -3x+7
Answer:
If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".Answer:
-3
Explanation:
The given equation is in slope-intercept form. The format of slope-intercept is y = mx + b, where m is the slope and b is the y-intercept.
The slope is the coefficient of x.
In the equation y = -3x + 7, the slope is -3, because -3 is the coefficient of x.
Hence, the slope is -3.In the diagram, the measure of angle 3 is 76°. A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8. What is the measure of angle 4?
Answer:
104
Step-by-step explanation:
180-76=104
Answer:
104
Step-by-step explanation:
heres my proof. have a nice day :)
A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.
Give your answer rounded to 1 decimal place.
Answer:
height = 3
Step-by-step explanation:
x(x+6) = 27
x^2 + 6x - 27 = 0
(x+9)(x-3) = 0
x = 3
on the provided graph, plot the points where the following function crosses the x-axis and the y-axis g(x) = -5^x + 5, what does the graph look like?
Answer:
see image
Step-by-step explanation:
Z varies directly as Square x and inversely as y. If z = 187 when x = 64 and y = 6, find z if and 9. (Round off your answer to the nearest hundredth.)
Answer:
Z = 50
Step-by-step explanation:
Given the following data;
Z = 187
x = 64
y = 6
Translating the word problem into an algebraic expression, we have;
Z = k√x/y
First of all, we would find the constant of proportionality, k;
187 = k√64/6
187 * 6 = k√64
1122 = 8k
k = 1122/8
k = 140.25
To find z, when x and y = 9
Z = 140.25√9/9
Z = (140.25 * 3)/9
Z = 420.75/9
Z = 46.75 ≈ 50
Note: The values in the latter part of the question isn't explicitly stated, so I assumed a value of 9 for both x and y.
Which system of equations shows a solution of (0.5, -1)?
Need answers asap plzzz
Answer:
The first graph
Step-by-step explanation:
Olivia rides her scooter 3/4 mile in
1/3 hour. How fast, in miles per hour,
does she ride her scooter?
Answer:
2.25 miles per hr
Answer:
2.25 miles per hour
Step-by-step explanation:
speed = distance / time
speed = [tex]\frac{3}{4} / \frac{1}{3}[/tex] (take the reciprocal of [tex]\frac{1}{3}[/tex])
= [tex]\frac{3}{4} * 3[/tex]
= [tex]\frac{9}{4}[/tex] = 2.25 miles per hour
eight times the reciprocal
of a number equals 4 times
the reciprocal of 10.
Answer:
8(1/x) = 4(1/10)
Step-by-step explanation:
lets say the number is x
eight times the reciprocal of a number equals 4 times the reciprocal of 10
8 * 1//x = 4 * 1/10
8/x = 4/10 , cross multiply
4x =8*10, divide both sides by 4
x= 80/4
x= 20
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 110 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
Step-by-step explanation:
L numbers of hours assigned to Lisa
D numbers of hours assigned to David
S numbers of hours assigned to Sara
Objective Function to minimize:
z = 30*L + 25*D + 18*S
Constraints:
Total time available
L + D + S ≤ 110
Lisa experience
L ≥ 0.4 * ( L + D ) then L ≥ 0.4*L + 0.4*D
0.6*L - 0.4*D ≥ 0
To provide designing experience to Sara
S ≥ 0.15*110 then S ≥ 16.5
Time for Sara
S ≤ 0.25 * ( L + D ) S ≤ 0.25*L + 0.25*D or -0.25*L - 0.25*D + S ≤0
Availability of Lisa
L ≤ 50
The Model is:
z = 30*L + 25*D + 18*S to minimize
Subject to:
L + D + S ≤ 110
0.6*L - 0.4*D ≥ 0
S ≥ 16.5
-0.25*L - 0.25*D + S ≤0
L ≤ 50
L ≥ 0 ; D ≥ 0 , S ≥ 0
After 6 iterations optimal ( minimum ) solution is:
z (min) = 2079
L = 26 D = 39.6 S = 16.5
The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.
Given :
The company estimates that 110 hours will be required to complete the project.Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers.To provide a label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time.The number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers.Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:
z = 30L + 25D + 18S
The constraints are given by:
1) L + D + S [tex]\leq[/tex] 110
2) L [tex]\geq[/tex] 0.4(L + D)
L [tex]\geq[/tex] 0.4L + 0.4D
0.6L - 0.4D [tex]\geq[/tex] 0
3) S [tex]\geq[/tex] 0.15(110)
S [tex]\geq[/tex] 16.5
Now, to minimize 'z' then use:
[tex]\rm -0.25L-0.25D+S\leq 0[/tex]
L [tex]\leq[/tex] 50
L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0
Now, the minimum z is given by:
z = 2079
L = 26, D = 39.6, S = 16.5
For more information, refer to the link given below:
https://brainly.com/question/23017717
Simplify 2(12-18\3+4)
Question
Simplify
[tex]2(12 - \frac{18}{3} + 4)[/tex]
Answer:-
ATQ->
[tex]2(12 - ( \frac{ \cancel{18}^{ \: \: \: 6} }{3} ) + 4 \\ 2(12 - 6 + 4) \\ 2(16 - 6) \\ 2(10) \\ 20 \: \: is \: your \: ans[/tex]
Answer:
Depends on how the 3 and the 18 are positioned in the fractions on the equation.
47/3
4
Step-by-step explanation:
Step 1. To simplify this, you need to know one of the most basic sayings in math which summarizes the Order of Operations: PEMDAS
Using PEMDAS:
P- Parenthesis
E- Exponents
M- Multiply
D- Divide
A- Add
S- Subtract
P- Parenthesis: We start off by preforming the parts of the equation within the parenthesis.
The 2 on the outside of the parenthesis, will not affect anything until we deal with what is inside the parenthesis.
The next part that we do, is to go through the rest of the steps, looking for either exponents, multiplication or division, skipping over the adding and subtracting until those are done.
The next part that we see, is Division.
D- Division
We find the point of division after the 18. The value we get has to be either:
a. 3/18
b. 18/3
depending on what you were asking for.
The equation, 2(12-18\3+4) at the bolded point, states that the division should be 1/6 because of the way of the division symbol.
Now the equation should either be one of the following:
a. 2(12-1/6+4)
b. 2(12-6+4)
A-Addition
Now, we can add the 4 to the number we got before, which should get us either
A. 1/6+4
B. 6+4
which added together gets us either
A. 25/6<=>4+1/6
B. 10
S-Subtraction
Now, we subtract both parts from the value of 12 getting us:
A. 12-(4+1/6)=12-4-1/6=8-1/6=7+5/6<=>47/6
B. 12-10=2
M-multiply:
Now we move on to the 2 we put aside earlier and multiply both of the answers:
A. 2(47/6)=47/3 or 15+2/3
B. 2(2)=4
Thus the answer is either 47/3 or 4
An ordinary fair die is a cube with the numbers one through six on the sides represented by painted that. Imagine that such a die is rolled twice in succession and that the face values of the two goals are added together. This song is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event a: the sun is greater than six
Answer:
ok so what i think your trying to ask is if we roll two dice that the sum will be more then 6
Two dice
Assuming that the dice are unbiased or not " loaded".
Each side has the same probability, is 1/6 =0.16667, to turn up when rolled, if the die (D) is unbiased. The probability of a side turning up on D1 when 2 dice ( D1,D2) are rolled, is independent of the side turning up in D2. So this is an independent event.
How many ways can one get a sum total of 6 if D1 &D2 are rolled at the same time?
These are the possibilities
Case 1.
D1 =1 & D2=5
Or
D1= 5 & D2=1
Case 2.
D1 =2 & D2=4
Or
D1= 4 & D2= 2
Case 3. D1=3, D2=3
P3 =0.027778
Let's say, P 1 the probability for case 1 and P2 for case 2. There are no other cases.
The final probability P and is the sum total P = P1 + P2 + P3 the probability law of mutually exclusive events.
P1= 0.02778+ 0.02778 =0.055558
P2= 0.02778+0.02778 =0.055558
Same way,
P3=0.027778, when there is only one way to get the sum 6.
So, P = 0.138894
Based on truncating at the sixth decimal place.
A visual representation with two unbiased dice and the possible cases would also give the same result and is a short cut method. I like to derive from the basics.
Hope This Helps!!!