Answer: 9c²
Step-by-step explanation:
To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.
207c³ 108c²
∧ ∧ ∧ ∧
9·23 c·c·c 9·12 c·c
∧ ∧ ∧
3·3 3·3 3·4
∧
2·2
207c³: 3·3·23 c·c·c
108c²: 2·2·3·3·3·4 c·c
GCF = 3·3 c·c
= 9c²
The GCF of 207c^3 and 108c² is 9c²
Given the expressions [tex]207c^3 \ and \ 108c^2[/tex]
We are to find the GCF of both terms
First, we need to get the factors as shown::
207c³ = 9 * 23 * c² * c
108c² = 9 * 12 * c²
From the factors, we can see that 9 and c² are common to both terms:
The GCF of 207c^3 and 108c² is 9c²
Learn more here: https://brainly.com/question/21612147
A bag contains six balls labeled 1 through 6. One ball will be randomly picked.
What is the probability of picking an odd number?
Write your answer as a fraction in simplest form.
S = sample space = set of all possible outcomes
S = set of whole numbers 1 through 6
S = {1,2,3,4,5,6}
E = event space = set of outcomes we want to happen
E = set of odd numbers between 1 through 6
E = {1,3,5}
We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2
Answer: 1/2A poll reported that 66 percent of adults were satisfied woth the job the major airlines were doing. Suppose 25 adults are selected at random and the number who are satisfied is recorded.
1. Explain why this is a binomial experiment.
A. This is a binomial experiment because there are three mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
B. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a random number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
C. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success changes in each trial.
D. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
2) Find and interpret the probability that exactly 15 of them are satisfied with the airlines.
Answer:
A)Option D
B)P(X = 15) = 0.1325
Step-by-step explanation:
A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
So option D is correct.
B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66
Let X be the number of adults satisfied with the job. Since 25 are selected,
Thus;
P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)
P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378
P(X = 15) = 0.1325
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the building. How many feet away from the building is the base of the ladder?
Answer:
since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,
sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answer:
C
Step-by-step explanation:
The critical value we are asked to state in this question is the value of the z statistic
Mathematically;
z-score = (x- mean)/SD/√n
From the question
x = 11.58
mean = 12
SD = 1.93
n = 80
Substituting this value, we have
z= (11.58-12)/1.93/√80 = -1.946
Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)
Answer:
Step-by-step explanation:
Part A
(m + n)x = 4x + 5 + 8x - 5
(m + n)x = 12x The fives cancel
Part B
(m - n)x = 4x + 5 - 8x + 5
(m - n)x = -4x + 10
Part C
The trick here is to put n(x) into m(x) wherever m(x) has an x.
m[n(x)] = 5(n(x)) + 5
m[n(x)] = 5(8x - 5) + 5
m[n(x)] = 40x - 20 + 5
m[n(x)] = 40x - 15
find the exact value of sin 0
Answer:
12/13
Step-by-step explanation:
First we must calculate the hypotenus using the pythagoran theorem
5²+12² = (MO)² MO = [tex]\sqrt{5^{2}+12^{2} }[/tex] MO = 13Now let's calculate sin0
sin O = 12/13So the exact value is 12/13
Answer:
C.) 12/13
Step-by-step explanation:
In a right angle triangle MN = 12, ON = 5 and; angle N = 90°
Now,
For hypotenuse we will use Pythagorean Theorem
(MO)² = (MN)² + (ON)²
(MO)² = (12)² + (5)²
(MO)² = 144 + 25
(MO)² = 169
MO = √169
MO = 13
now,
Sin O = opp÷hyp = 12÷13
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
I hope this will help uh.....
expand (x+2y)^2 plzzzzzzzz
The vector x is in a subspace H with a basis Bequals{Bold b 1,Bold b 2}. Find the B-coordinate vector of x. Bold b 1equals[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 3 EndMatrix ], Bold b 2equals[Start 3 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column negative 7 3rd Row 1st Column 11 EndMatrix ], xequals[Start 3 By 1 Matrix 1st Row 1st Column negative 10 2nd Row 1st Column negative 17 3rd Row 1st Column 27 EndMatrix ]
Answer and Step-by-step explanation: To find the B-coordinate vector of x:
[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]
The augmented matrix will be:
[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]
Transforming into reduced row-echelon form:
= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]
The values for the vector will be:
x = 2
y = 3
The B-coordinate vector is of the form:
V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
A construction crew is lengthening a road. The road started with a length of 56 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 33 days.
Answer:
Below
Step-by-step explanation:
The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.
so the equation is:
y= mx+56
m is the slope of the function wich is by how much the function grows.
By analogy, m is the distance added to the road each day.
● y= 3x+56
X is the number of days.
■■■■■■■■■■■■■■■■■■■■■■■■■■
To find the length of the road after 33 days, replace x by 33.
y= 3*33+56 = 155
So after 33 days the road is 155 miles.
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?
Answer:
y = -3.5x² + 2.7x -8.2
Step-by-step explanation:
the quadratic equation is set up as a² + bx + c, so just plug in the values
Answer:
[tex]-3.5x^2 + 2.7x -8.2[/tex]
Step-by-step explanation:
Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].
So, we can use your values of a, b, and c, and plug them into the equation.
A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].
B is 2.7, so the second term is [tex]2.7x[/tex]
And -8.2 is the C, so the third term is [tex]-8.2[/tex]
So we have [tex]-3.5x^2+2.7x-8.2[/tex]
Hope this helped!
Linda, Reuben, and Manuel have a total of $70 in their wallets. Reuben has $10 more than Linda. Manuel has 2 times what Linda has. How much does each have? Amount in Linda's wallet: $ Amount in Reuben's wallet: $ Amount in Manuel's wallet:
Answer:
Linda has $15Reuben has $25Manuel has $30Step-by-step explanation:
Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.
Linda has $15
Reuben has $25 . . . . . . $10 more than Linda
Manuel has $30 . . . . . . twice what Linda has
Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )
Answer:
[tex]\boxed{x = 9}[/tex]
Step-by-step explanation:
m = -1/3
b = 7
And y = 4 (Given)
Putting all of the givens in [tex]y = mx+b[/tex] to solve for x
=> 4 = (-1/3) x + 7
Subtracting 7 to both sides
=> 4-7 = (-1/3) x
=> -3 = (-1/3) x
Multiplying both sides by -3
=> -3 * -3 = x
=> 9 = x
OR
=> x = 9
Answer:
x = 9
Step-by-step explanation:
m = -1/3
b = 7
Using slope-intercept form:
y = mx + b
m is slope, b is y-intercept.
y = -1/3x + 7
Solve for x:
Plug y as 4
4 = 1/3x + 7
Subtract 7 on both sides.
-3 = -1/3x
Multiply both sides by -3.
9 = x
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
A nut-raisin mix costs $5.26 a pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is A.$16 B.$22 C.$61 D.$80
Answer:
D.$80
Step-by-step explanation:
$5.26 x 15.5= $81.53
The closest amount to $81.53 is D.$80
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2
Answer:
3
Step-by-step explanation:
let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room
A living room is two times as long as the bedroom, so:
A = 2X
A living room is one and one-half times as wide as a bedroom, so:
B = 1.5Y
The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y
So, AB in terms of XY is:
A*B = (2X)*(1.5Y) = 3(X*Y)
It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the bedroom.
Please answer this correctly without making mistakes
66.7
you will get the answer
Answer:
66.7
Step-by-step explanation:
The bicycle shop is 24.1 kilometers west of the train station meaning the distance between them is 24.1 kilometers.
The hardware store is 42.6 kilometers west of the bicycle shop meaning the distance between them is 42.6 kilometers.
Finally, you add both of the distances. (42.6 + 24.1)
You get the answer 66.7 kilometers.
Hope this helps!
Find the number of unique permutations of the letters in each word. SIGNATURE RESTAURANT
Answer:
Ok, we have two words:
"Signature"
The letters are: "S I G N A T U R E"
9 different letters.
Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.
For the first slot, we have 9 options.
For the second slot, we have 8 options (because on is already taken)
For the second slot, we have 7 options and so on.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 9*8*7*6*5*4*3*2*1 = 362,880.
Now, our second word is Restaurant.
The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.
So first we do the same as beffore, 10 slots and we start with 10 options.
The total number of combinations will be:
C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
A lot of combinations, but we are counting only unique words.
For example, as we have two R, we are counting two times the word:
Restaurant (because we could permutate only the two letters R and get the same word)
So we must divide by two for each letter repeated.
we have 3 letters repeated, we divide 3 times by 2.
C = ( 3,628,800)/(2*2*2) = 453,600
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice.
Answer:
.006
:)
Step-by-step explanation:
8 servings can David make with the current amount of spice.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
The rice-to-spice ratio = 15:1
The 75 grams of rice in one serving will require
⇒75/15
⇒5 gram of spice.
David's inventory of 40 gram of spice is enough for
40 g/(5 g/serving) = 8 servings
Hence, 8 servings can David make with the current amount of spice.
Learn more about Ratio
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convert the equation y= -4x + 2/3 into general form equation and find t the values of A,B and C.
Answer:
Standard form: [tex]12x+3y-2=0[/tex]
A = 12, B = 3 and C = -2
Step-by-step explanation:
Given:
The equation:
[tex]y= -4x + \dfrac{2}3[/tex]
To find:
The standard form of given equation and find A, B and C.
Solution:
First of all, let us write the standard form of an equation.
Standard form of an equation is represented as:
[tex]Ax+By+C=0[/tex]
A is the coefficient of x and can be positive or negative.
B is the coefficient of y and can be positive or negative.
C can also be positive or negative.
Now, let us consider the given equation:
[tex]y= -4x + \dfrac{2}3[/tex]
Multiplying the whole equation with 3 first:
[tex]3 \times y= 3 \times -4x + 3 \times \dfrac{2}3\\\Rightarrow 3y=-12x+2[/tex]
Now, let us take all the terms on one side:
[tex]\Rightarrow 3y+12x-2=0\\\Rightarrow 12x+3y-2=0[/tex]
Now, let us compare with [tex]Ax+By+C=0[/tex].
So, A = 12, B = 3 and C = -2
A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly
selected from the drawer and set aside. Then another shirt is randomly selected from the
drawer.
What is the probability that the first shirt is white and the second shirt is gray?
Answer:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given that
3 white, 2 blue and 5 gray shirts are there.
To find:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?
Solution:
Here, total number of shirts = 3+2+5 = 10
First of all, let us learn about the formula of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]
[tex]P(First\ White) = \dfrac{3}{10}[/tex]
Now, this shirt is set aside.
So, total number of shirts left are 9 now.
[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]
So, the answer is:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]
You are mandated to pick 45 units per hour. You work 8.5 hours a day (minus a 1/2 hour lunch), Monday to Friday. How many units should you be picking each week?
Answer:
1912.5 unitsStep-by-step explanation:
Firstly let us calculate the amount of hours you will have to work in a week.
Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.
Hence in a week you will work 8.5*5= 42.5 hours in a week
Since in 1 hours you are mandated to pick 45 units
Hence in 42.5 hours you will pick 42.5*45= 1912.5 units
please need help with this math question
Answer:
third option
Step-by-step explanation:
We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.
Answer:
x^2-10x
Step-by-step explanation:
f(x)-g(x)
(2x^2-4x)-(x^2+6x)
carry through the negative
2x^2-4x-x^2-6x
x^2-10x
plzzzzz helpp j + 9 - 3 < 8
Answer:
j < 2
Step-by-step explanation:
Simplify both sides of the inequality and isolating the variable would get you the answer
Evaluate the series
Answer:
the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
C) 59
Step-by-step explanation:
Recall that;
[tex]\sum_{1}^{n}a_n = a_1+a_2+...+a_n\\[/tex]
Therefore, we can evaluate the series;
[tex]\sum_{k=1}^{6}(25-k^2)[/tex]
by summing the values of the series within that interval.
the values of the series are evaluated by substituting the corresponding values of k into the equation.
[tex]\sum_{k=1}^{6}(25-k^2) =(25-1^2)+(25-2^2)+(25-3^2)+(25-4^2)+(25-5^2)+(25-6^2)\\\sum_{k=1}^{6}(25-k^2) =(25-1)+(25-4)+(25-9)+(25-16)+(25-25)+(25-36)\\\sum_{k=1}^{6}(25-k^2) =24+21+16+9+0+(-11)\\\sum_{k=1}^{6}(25-k^2) = 59\\[/tex]
So, the value of the series;
[tex]\sum_{k=1}^{6}(25-k^2) = 59[/tex]
The owner of a shoe store wanted to determine whether the average customer bought more than $100 worth of shoes. She randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below.
Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is greater than $100 and then draw a conclusion in the context of the problem. Use α=0.05.
125 99 219 65 109 89 79 119 95 135
Select the correct answer below:
A) Reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
B) Reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
C) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Answer:
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Step-by-step explanation:
We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;
X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.
Let [tex]\mu[/tex] = average customer bought worth of shoes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100 {means that the mean is smaller than or equal to $100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100 {means that the mean is greater than $100}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78
n = sample of receipts = 10
So, the test statistics = [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 0.991
The value of t-test statistics is 0.991.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean is smaller than or equal to $100.
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
7/44
Step-by-step explanation:
First find the total number of presidents.
2 + 7 + 13 + 12 + 7 + 3 = 44
There were 7 presidents that were 45-49 when elected. Divide this number by the total number of presidents to find the fraction.
7/44 ≈ 0.159
Please help with this question ASAP!
You are studying for the SAT and start the first week spending 2 hours studying. You plan to increase the amount you study by 10% each week. How many hours do you study in the 8th week?
Answer:
8w : 3.8974342 ≈ 3.9 or 4 (hope it help)
Step-by-step explanation:
1w : 2
2w : 2 + 10% = 2.2
3w : 2.2 + 10% = 2.42
4w : 2.42 + 10% = 2.662
5w : 2.662 + 10% = 2.9282
6w : 2.9282 + 10% = 3.22102
7w : 3.22102 + 10% = 3.543122
8w : 3.543122 + 10% = 3.8974342
3.8974342 ≈ 3.9 or 4