The probability value for P(B) is obtained to be, Option (c) : 0.83.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
We can use the formula: P(A È B) = P(A) + P(B) - P(A Ç B) to find P(B).
Rearranging the terms, we get -
P(B) = P(A È B) - P(A) + P(A Ç B)
Substituting the given values, we get -
P(B) = 0.72 - 0.55 + 0.66
P(B) = 0.83
The probability of an event A occurring is denoted by P(A) and is a number between 0 and 1, inclusive.
If A and B are two events, then P(A È B) denotes the probability that at least one of A or B occurs.
P(A Ç B) denotes the probability that both A and B occur simultaneously.
The formula used to find P(B) in terms of P(A), P(A È B), and P(A Ç B) is known as the addition rule of probability.
Therefore, the answer is 0.83.
To learn more about probability from the given link
https://brainly.com/question/23286309
#SPJ1
Determine zα for the following:
a.α = .0055 b.α = .09
c.α = .663
a) The value of zα for α = .0055 is -2.62.
b) The value of zα for α = .09 is 1.34.
c) The value of zα for α = .663 is .39 .
In statistics, the letter "z" usually refers to the z-score, which is a measure of how many standard deviations a particular value is from the mean. In order to determine the value of zα, we need to use the standard normal distribution table or a calculator that has this function built-in.
a. To find zα for α = .0055, we need to locate the area of .0055 in the body of the standard normal distribution table. This area is between z-scores of -2.61 and -2.62. Therefore, zα = -2.62.
b. For α = .09, we need to locate the area of .09 in the body of the standard normal distribution table. This area is between z-scores of 1.34 and 1.35. Therefore, zα = 1.34.
c. Finally, for α = .663, we need to locate the area of .663 in the body of the standard normal distribution table. This area is between z-scores of .38 and .39. Therefore, zα = .39.
In summary, zα is the z-score that corresponds to a given value of α (the level of significance). We can find this value using a standard normal distribution table or a calculator.
To learn more about z-scores click on,
https://brainly.com/question/15016913
#SPJ4
Find the solution of the differential equation that satisfies the given initial condition. dy 5xe, y(0) = 0 dx -In + = -5x² 2 X
The solution of the given differential equation that satisfies the initial condition y(0) = 0 is 0 = (5/2)(0)² - (1/4)(ln(0))^2 - (5/3)(0)³ + C.
To find the solution of the given differential equation that satisfies the initial condition y(0) = 0, we will follow these steps,
1. Identify the differential equation: dy/dx = 5x - (ln(x)/2) - 5x²
2. Integrate both sides of the equation with respect to x.
Integral of dy = Integral of (5x - (ln(x)/2) - 5x²) dx
Since y(0) = 0, we have:
y(x) = Integral of (5x - (ln(x)/2) - 5x²) dx
3. Perform the integration:
y(x) = (5/2)x² - (1/4)(ln(x))^2 - (5/3)x³ + C
4. Determine the value of the constant C using the initial condition y(0) = 0:
0 = (5/2)(0)² - (1/4)(ln(0))^2 - (5/3)(0)³ + C
Since ln(0) is undefined, we cannot solve for C using the initial condition y(0) = 0. However, the given initial condition is not consistent with the differential equation, so there may be an error in the problem statement.
Learn more about "differential equation": https://brainly.com/question/1164377
#SPJ11
given that z is a standard normal random variable, find c for each situation. (a) p(z < c) = 0:2119 (b) p(-c < z < -c) = 0:9030 (c) p(z < c) = 0:9948 (d) p(z > c) = 0:6915
The value of c for each situation is as follows: (a) c = -0.80 (b) c = 1.64 (c) c = 2.55 (d) c = -0.50.
We will use the z-table to find the corresponding z-scores.
(a) For p(z < c) = 0.2119, look for 0.2119 in the z-table, and find the closest value.
In this case, it is approximately 0.2118, which corresponds to a z-score of -0.80.
So, c = -0.80.
(b) For p(-c < z < c) = 0.9030, first we need to find p(z < c) since it is symmetrical around the mean.
This means p(z < c) = 1 - (1 - 0.9030) / 2 = 0.9515.
Look for 0.9515 in the z-table, and the closest value is 0.9517, which corresponds to a z-score of 1.64.
So, c = 1.64.
(c) For p(z < c) = 0.9948, look for 0.9948 in the z-table, and find the closest value.
In this case, it is approximately 0.9949, which corresponds to a z-score of 2.55.
So, c = 2.55.
(d) For p(z > c) = 0.6915, we need to find p(z < c) first.
p(z < c) = 1 - 0.6915 = 0.3085.
Look for 0.3085 in the z-table, and the closest value is 0.3085, which corresponds to a z-score of -0.50.
So, c = -0.50.
Learn more about mean:
https://brainly.com/question/1136789
#SPJ11
use partial fractions to find the power series of the function for 3/((x-2)(x 1))
The power series of the function 3/((x-2)(x+1)) is:
-3/4 - 1/4(x-2) + 1/4(x-2)² - 1/4(x-2)³- 1/2 - 1/2(x+1) - 1/2(x+1)² - 1/2(x+1)³ + ...
How to find the power series?To find the power series of the function 3/((x-2)(x+1)), we first need to find the partial fraction decomposition of the function:
3/((x-2)(x+1)) = A/(x-2) + B/(x+1)
To solve for A and B, we need to find a common denominator on the right-hand side:
3 = A(x+1) + B(x-2)
Setting x = 2, we get:
3 = A(3)
A = 1
Setting x = -1, we get:
3 = B(-3)
B = -1
Therefore, we have:
3/((x-2)(x+1)) = 1/(x-2) - 1/(x+1)
Now we can use the formula for the geometric series:
1/(1 - t) = 1 + t + t²+ t³ + ...
to write the power series of each term in the partial fraction decomposition. Substituting t = x-2 for the first term and t = -x-1 for the second term, we get:
1/(x-2) = -1/4 - 1/4(x-2) + 1/4(x-2)² - 1/4(x-2)³ + ...
1/(x+1) = -1/2 - 1/2(x+1) - 1/2(x+1)² - 1/2(x+1)³ - ...
Combining the two series, we have:
3/((x-2)(x+1)) = -3/4 - 1/4(x-2) + 1/4(x-2)² - 1/4(x-2)³ - 1/2 - 1/2(x+1) - 1/2(x+1)² - 1/2(x+1)³ + ...
Therefore, the power series of the function 3/((x-2)(x+1)) is:
-3/4 - 1/4(x-2) + 1/4(x-2)² - 1/4(x-2)³- 1/2 - 1/2(x+1) - 1/2(x+1)² - 1/2(x+1)³ + ...
Learn more about power series
brainly.com/question/29896893
#SPJ11
A survey asked college students the number of week days they go to a live class on campus, # of days in class (x) 0 1 2 3 4 5 (P(x) 0.34 0.22 0.22 0.10 0.08 0.04 What is the probability a student attends a live class at least 2 days a week? What is the probability a student attends a live class less than 2 days a week?
The probability that a student attends a live class at least 2 days a week is 0.58 and the probability that a student attends a live class less than 2 days a week is 0.56.
To find the probability that a student attends a live class at least 2 days a week, we need to add up the probabilities of attending class for 2, 3, 4, and 5 days. This is because attending 0 or 1 day a week means attending less than 2 days, so we need to exclude those probabilities.
P(attending at least 2 days) = P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)
= 0.22 + 0.22 + 0.10 + 0.04
= 0.58
Therefore, the probability that a student attends a live class at least 2 days a week is 0.58.
To find the probability that a student attends a live class less than 2 days a week, we need to add up the probabilities of attending 0 or 1 day a week.
P(attending less than 2 days) = P(x = 0) + P(x = 1)
= 0.34 + 0.22
= 0.56
Therefore, the probability that a student attends a live class less than 2 days a week is 0.56.
To learn more about probability, refer:-
https://brainly.com/question/11234923
#SPJ11
How many numbers did Bill write? Bill wrote all the natural numbers between 9 and v (where v is greater than 9)
The number of numbers that Bill wrote (v-8) numbers.
How to form inequalities?
A mathematical phrase that states the order relationship between two integers or algebraic expressions as greater than, greater than or equal to, less than, or less than or equal to.
If Bill wrote all the natural numbers between 9 and v, then the number of numbers he wrote would be equal to the difference between v and 9 plus one (since he included both 9 and v).
v > 9
(where v is greater than 9 i.e., (v-9)+1. )
=(v-9) + 1
= v - 9 + 1
= v - 8
Therefore, the number of numbers he wrote would be (v - 8) numbers.
To know more about numbers check the below link:
https://brainly.com/question/25734188
#SPJ1
work out the value of (3squared)squared times (10cubed)squared
Answer:
Scientific Notation:
[tex]8.1*10^7[/tex]
Expanded form:
81000000
Hope this helps :)
Pls brainliest...
The value of ''(3squared)squared times (10cubed)squared'' is,
8.1 × 10⁶
We have,
Expression is,
= (3squared)squared times (10cubed)squared
It can be written as,
(3squared)squared times (10cubed)squared
(3²)² × (10³)²
9² × 1000²
81 × 1000000
8,10,00,000
8.1 × 10⁶
Thus, The value of ''(3squared)squared times (10cubed)squared'' is,
8.1 × 10⁶
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ6
transversal problems pls hlp
The solution to the transversal problem is determined using the alternate exterior angles theorem, therefore, x = 15.
How to Solve Transversal Problems?The diagram shows two given alternate exterior angles, to solve this transversal problem, apply the alternate exterior angles theorem, which states that alternate exterior angles are congruent.
Thus, we have:
6x + 8 = 7x - 7
Combine like terms:
6x - 7x = -8 - 7
-x = -15
x = 15
The value of x is: 15.
Learn more about the transversal problem on:
https://brainly.com/question/28393152
#SPJ1
calculate the final thickness of the silicon dioxide on a wafer
The final thickness of the silicon dioxide on a wafer is given by: Initial thickness + (growth rate x oxidation time)
To calculate the final thickness of the silicon dioxide on a wafer, you will need to know the initial thickness of the oxide layer and the duration of the oxidation process.
The growth rate of silicon dioxide is dependent on temperature and can be determined from the literature. Once you have this information, you can use the following formula to calculate the final thickness:
Final thickness = initial thickness + (growth rate x oxidation time)
It is important to note that the final thickness may be affected by any post-oxidation processing steps, such as etching or cleaning, that may remove some of the oxide layer.
To learn more about silicon dioxide, refer below:
https://brainly.com/question/20571315
#SPJ11
-7x - 2 ≥ -3(x -6) need help
a sort of o(nlogn) is always preferable to a sort of o(n 2). true false
The statement " a sort of o(nlogn) is always preferable to a sort of o(n 2)" is true because sorting algorithms with O(n log n) time complexity have a lower rate of growth and are generally more efficient than sorting algorithms with O(n^2) time complexity
In general, it is true that a sorting algorithm with a time complexity of O(n log n) is preferable to a sorting algorithm with a time complexity of O(n^2), assuming other factors such as memory usage and stability are comparable.
This is because the time complexity of an algorithm describes the rate at which the algorithm's running time increases as the input size grows. In the case of sorting, O(n log n) algorithms, such as merge sort or quicksort, have a much lower rate of growth than O(n^2) algorithms, such as bubble sort or insertion sort.
This means that as the input size grows larger, the time required to sort the input using an O(n^2) algorithm can become prohibitively long, while an O(n log n) algorithm can still be practical.
Learn more about sorting algorithm here
brainly.com/question/31385166
#SPJ4
What is the circumference of a circle with a diameter of 50 units? Use π = 3.14 and round your answer to the nearest hundredth.
Here are the step-by-step workings:
Circumference = π * Diameter
Circumference = 3.14 * 50 units
Circumference = 157 units
Rounded to the nearest hundredth:
Circumference = 157.00 units
Answer:
ask your teacher
What is the circumference of a circle with a diameter of 50 units? Use π = 3.14 and round your answer to the nearest hundredth
URGENT!! Will give brainliest :)
Question 4 of 25
Describe the shape of the distribution.
A. It is uniform.
B. It is skewed.
C. It is symmetric.
D. It is bimodal.
The shape of the distribution of the box plot is described as: B: It is Skewed
What is the shape of the distribution?The box plot shape is used to indicate if a statistical particular set is either normally distributed or skewed.
There is a property of the box plot i.e. When the median is in the center of the box, and the whiskers are about the same on both flanks of the box, then the distribution is symmetric. However, when the median is anywhere to the box except the center, and if the whisker is more concise on the left or right end of the box, then the distribution is skewed.
In this question, we can clearly see that the whisker is more concise on the right end of the box, and as such we can say that the distribution is skewed.
Read more about shape of distribution at: https://brainly.com/question/23706420
#SPJ1
a population has a mean μ=80 and a standard deviation σ=7. find the mean and standard deviation of a sampling distribution of sample means with sample size n=49.
The population mean is equal to 80 for the mean of a sampling distribution of sample means with n=49, and the standard deviation is equal to 1/√(n).
What does standard deviation mean?The standard deviation is a statistician's gauge of a group of values' degree of dispersion or variation. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the expected value) of the set.With a sample size of 49, the mean of a sampling distribution of sample means is equal to the population mean of 801.
With a sample size of n=49, the standard deviation of a sampling distribution of sample means is identical.
n=49 is equal to σ/√(n)
= 7/√(49) = 1¹
To know more about standard deviation visit:
brainly.com/question/23907081
#SPJ1
the exponential mode a=979e 0.0008t describes the population,a, of a country in millions, t years after 2003. use the model to determine the population of the country in 2003
The population of the country in 2003 was 979 million.
We are given that;
a=979e 0.0008t
Now,
To find the population of the country in 2003, we need to plug in t = 0 into the model, since 2003 is the starting year.
a = 979e^(0.0008t)
a = 979e^(0.0008(0))
a = 979e^0
a = 979(1)
a = 979
Therefore, by the exponential mode the answer will be 979 million.
Learn more about exponential growth and decay here:
https://brainly.com/question/2193820
#SPJ1
The population of the country in 2003 was 979 million.
We are given that;
a=979e 0.0008t
Now,
To find the population of the country in 2003, we need to plug in t = 0 into the model, since 2003 is the starting year.
a = 979e^(0.0008t)
a = 979e^(0.0008(0))
a = 979e^0
a = 979(1)
a = 979
Therefore, by the exponential mode the answer will be 979 million.
Learn more about exponential growth and decay here:
https://brainly.com/question/2193820
#SPJ1
Answer the question in the picture below.
Answer:
i believe it is D. because you need multiple sets of data. :)
Rectangle X is enlarged to give rectangle Y. Both shape are shown below but some rectangle Y is missing
What is the title width of rectangle Y
The width of rectangle Y is 8 units.
How to find the width of rectangle Y?The width of rectangle Y is obtained applying the proportions in the context of the problem.
The dimensions of rectangle X are given as follows:
Height of 3 units.
Width of 2 units.
The dimensions of rectangle Y are given as follows:
Height of 12 units.
Width of x units.
The height was enlarged by a scale factor of 4, hence the width is given as follows:
2 * 4 = 8 units.
Learn more about rectangle on:
https://brainly.com/question/2607596
#SPJ1
Complete Question
Check attached image
There are 12 DVDs, 7 video games, 14 CDs, and 3 videotapes on Jamie’s bedroom shelf. If Jamie selects an item at random from the shelf, what is the probability that it is a DVD or video tape?
Answer:
41.6666%
Step-by-step explanation:
12. You drive your car for 2 hours while traveling at a speed of 40 mi/hr. How many miles do you
travel?
Answer: you travel 80 miles in 2 hours while driving at a speed of 40 miles per hour.
Answer: 80 mi/hr
Step-by-step explanation: If you are traveling at a speed of 40 mi/hr for 2 hours, you need to do 40x2 which is equal to 80.
List the prime factors of 50
Answer:
[tex]2[/tex] × [tex]5^{2}[/tex]
Step-by-step explanation:
2 X 5 X 5 = 50
Hope this helps
the mean of all the sample means obtained from all random samples of a certain sample size in a sampling distribution is an example of a biased statistic. true or false
The mean of all the sample means obtained from all random samples of a certain sample size in a sampling distribution is an example of a biased statistic is False.
sampling distribution:
The mean of all the sample means obtained from all random samples of a certain sample size in a sampling distribution is an example of an unbiased statistic. This is because the sampling distribution of the mean is centered at the true population mean, and the mean of all sample means provides an estimate of that true population mean without any systematic over- or under-estimation.
However, individual sample means can be biased if there are any issues with the sampling process or if the sample is not representative of the population.
To know more about Sampling distribution:
https://brainly.com/question/13501743
#SPJ11
Can anyone help me on this? I’m pretty sue wits base x height
Answer:
It's 84
Step-by-step explanation:
To calculate the area of a triangule you need to use this formula:
B * H / 2
So:
12 * 14 / 2 = 84
Hope this helps :)
Pls brainliest...
8.G.C.9
Which formula will find my volume?
The formula to find the volume of attached figure: V = πr²h
The correct answer is an option (d)
In the attached image we can observe that the figure is of cylinder with radius 'r' and height 'h'
This means that we need to find the volume of cylinder.
We know that the formula for tha cylinder is:
Volume of cylinder = Base area × height of cylinder
As we know that the base of cylinder is circular in shape.
so, the base area of cylinder would be,
A = πr²
when we say height of the cylinder then it means the perpendicular distance between two parallel bases of cylinder. It is also known as length of the cylinder.
So, the formula for volume would be,
V = πr²h
Therefore, the correct answer is an option (d)
Learn more about volume of cylinder here:
https://brainly.com/question/16134180
#SPJ1
Point B has coordinates (1,2). The x-coordinate of point A is a -5. The distance between point A and B is 10 units. What are the possible coordinates of point A?
Answer:
There are two possible coordinates for A: Either A (-5, 10) or A (-5, -6)
Step-by-step explanation:
To find the possible coordinates of A, we will need to find the possible y-coordinate.
We can do this using the distance (d) formula, which is
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where (x1, x2) are one set of coordinates and (y1, y2) are the other set of coordinates
We can allow point B (1, 2) to be our x1 and x2 coordinates and A (-5, y2) to be our x2 and y2. Thus, we must plug into the formula 10 for d and solve for y2:
[tex]10=\sqrt{(-5-1)^2+(y_{2}-2)^2}\\ 10=\sqrt{(-6)^2+(y_{2}-2)^2}\\ 10=\sqrt{36+(y_{2}-2)^2}\\ 100=36+(y_{2}-2)^2\\64=(y_{2}-2)^2\\[/tex]
To finish solving, we must take the square root of both sides. Whenever you take a square root, there is both a positive answer and a negative answer, since squaring a negative number also yields a positive number (e.g., 5 * 5 = 25 and -5 * -5 = 25):
Positive answer:
[tex]8=y_{2}-2\\10=y_{2}[/tex]
Negative answer:
[tex]-8=y_{2}-2\\-6=y_{2}[/tex]
To check our answers, we can plug in both 10 for y2 into the formula and -6 for y2 into the formula and check that we get 10 each time:
Plugging in 10 for y2:
[tex]10=\sqrt{(-5-1)^2+(10-2)^2}\\ 10=\sqrt{(-6)^2+(8)^2}\\ 10=\sqrt{36+64}\\ 10=\sqrt{100}\\ 10=10[/tex]
Plugging in -6 for y2:
[tex]10=\sqrt{(-5-1)^2+(-6-2)^2}\\ 10=\sqrt{(-6)^2+(-8)^2}\\ 10=\sqrt{36+64}\\ 10=\sqrt{100}\\ 10=10[/tex]
Thus, the two possible coordinates of A are (-5, 10), where 10 is the y-coordinate or (-5, -6), where - 6 is the y-coordinate.
Bookwork code: L64 Calculator allowed a) What is the circumference of the shaded face? b) What is the width, w, of the rectangle? Give each answer to 1 d.p. 5 mm (0 W O Not drawn accurately
The circumference of the shaded face is 62.8 mm while the width of the rectangle is 62.8 mm
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The radius (r) of the circle is 10mm. Hence:
Circumference = 2π * radius = 2π * 10 = 62.8 mm
The width of the rectangle = Circumference of circle = 62.8 mm
The circumference of the shaded face is 62.8 mm
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Assume that a study of 300 randomly selected school bus routes showed that 274 arrived on time. is it unusual for a school bus to arrive late?
A squre is cut into three rectangles X, Y and Z
The algebraic expression for the width of rectangle X is:
w = (s - n - 5)/2
Since a square has four equal sides, each side of the square can be represented as s. The area of the square is s². When it is cut into three rectangles X, Y and Z, the area of the square is equal to the sum of the areas of the three rectangles.
So, we have:
s² = 10w + 5n + 5(s-n-5)/2
Simplifying this equation, we get:
s² = 10w + 5n + (5s - 5n - 25)/2
Multiplying both sides by 2, we get:
2s² = 20w + 10n + 5s - 5n - 25
Simplifying this equation, we get:
20w = 2s² - 10n - 5s + 5n + 25
Dividing both sides by 2 and rearranging the terms, we get the algebraic expression for the width of rectangle X:
w = (s - n - 5)/2
Learn more about rectangles
https://brainly.com/question/25292087
#SPJ4
Complete Question:
A square is cut into three rectangles X, Y and Z. Rectangle X has length 10cm. Rectangle Y has length n cm and width 5cm. Write down an algebraic expression for the width of rectangle X.
use your own words to explain what a sequence is. Give an example to illustrate this explanation 
A sequence is a collection of numbers in which a pattern between consecutive numbers is established.
One example is a geometric sequence with first term of 2 and common ratio of 3, which is:
2, 6, 18, 54, ...
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
Considering a geometric sequence with first term of 2 and common ratio of 3, the other terms are given as follows:
2 x 3 = 6.6 x 3 = 18.18 x 3 = 54.And the pattern continues for however many terms are there in the sequence.
More can be learned about geometric sequences at https://brainly.com/question/24643676
#SPJ1
What is the order of 8 + 12Z in the factor group Z/12Z?
The order of 8 + 12Z in the factor group Z/12Z is 3.
This is because the order of an element a in a group G is the smallest positive integer n such that aⁿ = e, where e is the identity element of G. In this case, (8 + 12Z)³ = 8³ + 12Z = 8 + 12Z = 0 + 12Z, which is the identity element of Z/12Z. Therefore, the order of 8 + 12Z is 3.
To find the order of an element in a factor group, we first need to determine the cosets of the group modulo the subgroup. In this case, we have Z/12Z, which is the integers modulo 12. The subgroup is 12Z, which consists of all multiples of 12.
We can write the cosets of 12Z as {0 + 12Z, 1 + 12Z, 2 + 12Z, ..., 11 + 12Z}. Each of these cosets contains an element that is congruent to 8 modulo 12. For example, 8 + 12Z is in the coset 8 + 12Z, and 20 + 12Z is in the coset 8 + 12Z.
To find the order of 8 + 12Z, we need to find the smallest positive integer n such that (8 + 12Z)ⁿ is equal to the identity element of Z/12Z, which is 0 + 12Z. We can compute (8 + 12Z)² as (8 + 12Z)(8 + 12Z) = 64 + 96Z = 4 + 12Z, since 64 is congruent to 4 modulo 12 and 96 is a multiple of 12. Therefore, (8 + 12Z)² is not equal to the identity element.
Next, we compute (8 + 12Z)³ as (8 + 12Z)(8 + 12Z)(8 + 12Z) = 512 + 864Z = 8 + 12Z, since 512 is congruent to 8 modulo 12 and 864 is a multiple of 12. Therefore, (8 + 12Z)³ is equal to the identity element, and the order of 8 + 12Z is 3.
To know more about modulo click on below link:
https://brainly.com/question/6656029#
#SPJ11
Which expression is equivalent to 8+w+5w?
Answer:
2(3w+4)
Step-by-step explanation:
Given:
(W) is a variable with an unknown number
you are multiplying 5 by (w) variable
you are adding the 8 to (w) and 5w
1. Combine like terms:
8+w+5w
8+6w
2. Rearrange terms:
8+6w
6w+8
3. Common factor:
6w+8
2(3w+4)