We are given the following series
-6, -2, 2, 6
Common difference = last term - first term
For the first two terms
The common difference is calculated as
Last term - first term
Last term = -2
First term = -6
Common difference = -2 - (-6)
= -2 + 6
common difference = 4
Common difference = 2 - (-2)
common difference = 2 + 2
Common difference = 4
Last two terms
common difference = 6 - 2
Common difference = 4
The common difference for this sequence is 4
The sequence is arithmetic.
According to a study of the power quality (sags and swells) of a transformer, for transformers built for heavy industry, the distribution of the number of sags per work has a mean of 346 with a standard deviation of72. Of interest is x, the sample mean number of sags per week for a random sample of 216 transformers. Completo parts a through d below.a. Find E(%) and interpret its valueE() -(Type an integer or a decimal. Do not round.)Interpret the value of E(). Select the correct choice below and fill in the answer box to complete your choice(Type an integer or a decimal. Do not round.)O A. For any random sample of 216 transformers, the mean number of sags por wook is always. B. 1 many random samples of 216 transformers are taken, then the mean of the sample variances is sags por wookOC. If many random samples of 218 transformers are taken, then the mean of the sample mean numbers of sags per week isOD. I many random samples of 216 transformers are taken, then the mean of the sample standard deviations is sags por wookb. Find Var()Var) -(Type an integer or a decimal Round to three decimal places as needed.)c. Describe the shape of the sampling distribution of Xwith mean - and standard deviation -(Type intogors or decimal Round to three decimal places as needed)The sampling distribution of xd. Howey is it to observe a sample mean number of sags por wook that exceeds 3007C
Given data:
Population Mean = 346
Standard Deviation = 72
Expected Value of e(x) = population mean = 346
Sample Size = 216
In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)
To solve for the variance of x or var(x), we follow the formula below:
[tex]var(x)=\frac{\sigma^2}{n}=\frac{(s\tan darddeviation)^2}{\text{sample size}}[/tex]In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:
[tex]var(x)=\frac{72^2}{216}=\frac{5184}{216}=24[/tex]One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.
How likely is it to observe a sample mean number of sags per week that exceeds 390?
For this one, we have this formula to use:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.
[tex]z=\frac{390-346}{\frac{72}{\sqrt[]{216}}}=\frac{44}{2\sqrt[]{6}}=8.98[/tex]Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.
question included as a photo
a. The linear Equations :
3x + (x+42)= 90
⇒4x +42 =90
b. ∠ 1 = 36° and ∠2 =54°
How do you find the solution to a linear equation?In one of the equations, separate one of the two variables.In the other equation, substitute the expression that is equal to the isolated variable from Step 1.For the final variable, solve the linear equation.Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.
here
4x+42 = 90 ⇒ x=12
∠1 =4 x 12=36 and ∠2 = 12+42=54
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11) What is the slope of the line below * X
to find the slope of a line select the two points given.
in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)
use the formula of the slope to calculate
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replace the points into the formula
[tex]\begin{gathered} m=\frac{1-(-1)}{3-(-4)} \\ m=\frac{2}{7} \end{gathered}[/tex]the slope of the line will be 2/7
Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles
and 5 white tiles. The tiles cost $0.50 per cm².
What is the total area of the tiles Felix needs
to buy?
A =
? cm²
27
2.4 cm
2 cm
4 cm
Answer:
first one is 80
Step-by-step explanation:
i did it
The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.
What is meant by the area of parallelogram?In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.
Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.
Area of one parallelogram shaped tile = 4cm × 2cm
Area of one parallelogram-shaped tile = 8cm²
Total area for the 5black and 5white tiles = 10 × 8cm²
Total area for the 5black and 5white tiles = 80cm²
Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.
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A kite is shown below. What is the length of LINE AC? (image attached)A. 4B. 6C. 9D. 10
The length of AC is given by AE + EC
According to the Pythagorean Theorem, we know that:
AE² = AD² - ED²
AE² = 5² - 3²
AE² = 25 - 9
AE² = 16
AE = 4
EC² = DC² + ED²
Since DC = BC, we have:
EC² = BC² + ED²
EC² = 45 - 9
EC² = 36
EC = 6
Therefore, AC = 4 + 6 = 10
Answer: D. 10
what % less 60 is 51
To find the percent we are looking for we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 51\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{51\cdot100}{60} \\ x=85 \end{gathered}[/tex]This means that 51 is 85% of 60.
Therefore 51 is 15% less than 60.
Pls help if someone can solve for me 7-15. Thank you!
Given:
Set U: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
Set P: {2, 3, 5 7, 9, 11, 13, 17, 19}
Questin 7.
Complement of set P.
The complement of set P will be the set that contains the elements present in set U but not in P.
Hence, we have:
ANSWER:
P' = {1, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20}
The height of an item falling can be modeling by h^t=-16t^2+h^o. Where h^o is the initial height in feet, and h^t is the height in feet at time t in seconds. If I drop at a height of 18.9 feet,how long will it take the item to hit the ground.A. 2.09B.1.09C.1.19D.0.09
h(t) = -16t^2+h^0
object falls untill height becomes 0, so h(t) =0, h^0 = 18.9feet
0 = -16t^2 + 18.9
-18.9= -16t^2
-18.9/-16 = -16t^2/-16
t^2=1.18125
[tex]\begin{gathered} t\text{ =}\sqrt[]{1.18125} \\ t\text{ = 1.09sec} \end{gathered}[/tex]ANSWER= OPTION B
2. Bob and Joy Salkind want to save $50,000 in 5 years for home improvement projects. If the
Bank of Aventura is paying 8% interest compounded quarterly, how much must they deposit
now to have the money for the project?
The amount of money should be invested to obtain interest of amount 50000$ is 34,000$(approximately)
What is the compound interest?The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. Reinvesting interest, or adding it to the lent capital rather than paying it out or seeking repayment from the borrower, results in interest being received on the principal amount plus interest collected previously.
How to calculate principal amount to get certain amount of interest?[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where,A is the total sum.
P equals the initial principal amount.
The nominal yearly interest rate is r.
The compounding frequency is n.
t is the total amount of time that the interest is charged (expressed using the same time units as r, usually years).
The final value less the beginning investment yields the entire compound interest.
On substituting the values we get that initial investment of approximately 34000$
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Sheldon thought of a natural number, and then he added the next natural number to it.
He got the sum of 75. What was Sheldon's number?
Using a system of equations, it is found that Sheldon's number is of 37.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.
For this problem, we have to consider that:
The natural number is of x.The next natural number is the successor of x, represented by x + 1.The sum of these numbers is given by:
x + x + 1 = 2x + 1 (combining the like terms).
The sum is equals to 75, hence we can solve for the natural number x as follows:
2x + 1 = 75
2x = 74
x =74/2
x = 37. (which is Sheldon's natural number).
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Pls help
Alyssa's algebra test score was 8 points lower than Jennifer's. The total of their two tests was 180. What did each girl receive?
plesehelppppppppppppppppppp!
Answer:
54 x 5
Step-by-step explanation:
the first figure out the brackets, then multiply by 5.
plss mark me as brainlist
Answer:
the answer is 6 ^ 15 you are very welcom
suppose the probability of a horse winning a race is 0.04. what are the odds of winning? express your answer in the form a:b
The probability of a horse winning a race is
[tex]Pr(\text{ win)=0.04}[/tex]The probability of the horse losing will be calculated as
[tex]Pr(\text{lose)}=\text{ 1- Pr(win)}[/tex]By substituting the value, we will have
[tex]\begin{gathered} Pr(\text{lose)}=\text{ 1- Pr(win)} \\ Pr(\text{lose)}=1-0.04 \\ Pr(\text{lose)}=0.96 \end{gathered}[/tex]The formula used to calculate the odds of winning is given below as
[tex]\text{Odds of winning=}\frac{pr(\text{ win)}}{Pr(loose)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Odds of winning=}\frac{pr(\text{ win)}}{Pr(loose)} \\ \text{Odds of winning}=\frac{0.04}{0.96} \\ \text{Odds of winning}=\frac{4}{96} \\ \text{Odds of winning}=\frac{1}{24} \\ \text{Odds of winning}=1\colon24 \end{gathered}[/tex]Hence,
The odds of winning = 1 : 24
Which of the following sets of numbers could represent the three sides of a righttriangle?Submit AnswerO {9, 12, 14}O {48, 55,73}O {11, 59, 61}{8, 40, 41}
Answer:
{48, 55,73}
Explanation:
To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ c\text{ is the longest side, the hypotenuse} \end{gathered}[/tex][tex]\begin{gathered} 14^2=9^2+12^2 \\ 196\neq225 \end{gathered}[/tex][tex]\begin{gathered} 73^2=48^2+55^3 \\ 5329=5329 \end{gathered}[/tex]Therefore, the side lengths that could form a right triangle are {48, 55,73}.
1,936 divided by 8 in long division
Answer:
242.
Step-by-step explanation:
Basically, you have to put the 2 numbers "1936" and "8" down. After you put the 2 numbers down, you have to figure out how many times 8 goes into 19 which is 2 times.
You put the 2 above the 1 in 1936. After you put the 2 up there, you have to figure out 2 x 8 which is 16. You have to put the 16 below the 19 and subtract 19 by 16 which is 3.
After you finish that equation, you must bring the 3 down next to the 3 you wrote down on 19 - 16. The number turns into 33 and you have to figure out how many times 8 goes into 33 which is 4 times. You put the 4 next to the 2 above and then do 4 x 8 which is 32. You do 33 - 32 which is 1.
You bring the 6 down in 1936. It turns into a 16. You now have to figure out how many times 8 goes into 16 which is 2 times. You put 2 next to the 2 and the 4 above and that turns the number into 242.
You then have to do 2 x 8 which is 16 and put 16 under the 16 from 33 - 32. That'll make an equation which is 16 - 16 which is 0. There is no remainder and all the numbers were added above so 242 is your answer.
Hopefully, this has helped, tried my best!
=================================
Long Division - Solution and Process
=================================
We are given the Divisor 8 and the Dividend 1,936.
242 ← Our Final Solution
8 | 1936
16
___
33
32
____
16
16
0
The quotient of the given problem would be 242 with a remainder of 0, or simply 242.
Hope this helps!
Please help asap brainlyest to the best answer
Answer:
All of them work.
Step-by-step explanation:
An invertible function can be tested for by the horizontal line test. An function is not invertible is a horizontal line drawn anywhere crosses two or more points. A straight line is an invertible function as long as the slope is not equal to 0. With that, let's check A. From x = -6 to -4, the horizontal line test does not cross two points anywhere. A works. Let's check B. B also works because it passes the horizontal line test. C also works.
A triangle has sides of lengths 11 in., 59 in., and 61 in. Is the triangle a right triangle?
O yes
O no
O There is not enough information to tell.
Finding slope and y-interceptfor this equation.-5x - y = 14
Finding slope and y-intercept
for this equation.
-5x - y = 14
we know that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope
b is the y-intercept
In this problem we have
-5x-y=14
Isolate the variable y
y=-5x-14
therefore
slope is -5y-intercept is -14A wireless company offers two cell phone plans. For the month of September Plan A charges $35 plus $0.25 per minute for calls. Plan B charges$20 plus $0.50 per minute for calls. ?
EXPLANATION
Let's see the facts:
Plan A --> $35 + $0.25/minute
Plan B --> $20 + $0.5/minute
Let's call "x" to the number of minutes that a person could talk.
Here we have two equations as follows:
(1) 35 + 0.25x
(2) 20 + 0.5x
Where x represents the number of minutes a person talks on the phone.
We need to equal both equations in order to obtain the same cost.
35 + 0.25x = 20 + 0.5x
Now, we need to solve this equality as shown as follows:
-Subtracting -35 to both sides:
35 + 0.25x -35 = 20 + 0.5x -35
-Adding similar terms:
0.25x = 0.5x - 15
-Subtracting -0.5x to both sides:
0.25x - 0.5x = -15
-Adding similar terms:
-0.25x = -15
-Dividing both sides by -0.25:
x = -15/-0.25
-Simplifying:
x= 60 minutes
So, when a person talks for 60 minutes the cost of both plans is the same.
A car loan totaling 13,456.44 paid off in 36 equal monthly payment can afford no more than $350 per month can she or down explain
She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car
The total amount of the car loan = 13456.44
Number of instalments = 36 monthly payments
Affordable installment per month = $350
EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.
Total payment that can be made using the instalments = Monthly instalments * Number of instalments
= 350*36
Total payment that can be made using the instalments = 12600
The amount remaining after paying instalments = 13456.44 - 12600
= 856.44
Downpayment required = $856.44
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Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given equation.7.(-5, 2), y =1/2x-3
You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)
Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:
Let the given line be:
[tex]y_1=mx+b[/tex]And the perpendicular line
[tex]y_2=nx+c[/tex]The slope of the perpendicular line will be:
[tex]n=-\frac{1}{m}[/tex]So for the line
[tex]y=\frac{1}{2}x-3[/tex]The slope is
[tex]m=\frac{1}{2}[/tex]For the perpedicular line it will be:
[tex]\begin{gathered} n=-\frac{1}{\frac{1}{2}}=-1\cdot\frac{2}{1} \\ n=-2 \end{gathered}[/tex]Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:
[tex]y-y_1=m(x-x_1)[/tex]Replace the with m=-2 and (-5,2)
[tex]\begin{gathered} y-2=-2(x-(-5)) \\ y-2=-2(x+5) \\ y-2=-2x-10 \\ y=-2x-10+2 \\ y=-2x-8 \end{gathered}[/tex]The equation perpendicular to
[tex]y=\frac{1}{2}x-3[/tex]is
[tex]y=-2x-8[/tex]Now you can draw both lines:
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premimum gasolinz is 1. 182 times greater
What is ratio?
A ratio can be described as the ordered pair of numbers, like x and y, written in the form of a rational numbers, x/y with the denominator greater than zero.
It is also described as the number of times a number or element would contain another one.
It is also known to compare two quantities, elements or numbers.
From the information given, we have that;
25 liters of regular gasoline is $58.9825 liters of permimum gasoline for $69.73To determine the value, we have;
Cost of 1 liter of 25 liters in permimum gasoline/Cost of 1 liter of 25 liters in regular gasoline
substitute the values
$69.73/ $58.98
Find the quotient
1. 182
Hence, the value is 1. 182
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Which inequality is represented by the graph?
Answer:
[tex]y < \frac{5}{3} x - 3 \\ [/tex]
Step-by-step explanation:
- General linear equation of a line passing through point (x, y) with a gradient m and y-intercept (0, c) is ;
[tex]{ \rm{y = mx + c}}[/tex]
- As finding gradient, m; consider points (0, -3) and (3, 2) from the graph;
[tex]{ \rm{slope \: m = \frac{2 - ( - 3)}{3 - 0} }} \\ \\ { \rm{m = \frac{5}{3} }}[/tex]
- Then our equation becomes y = 5/3x + c
- Consider point (0, -3), relate it with (0, c) hence c is -3;
[tex]{ \rm{y = \frac{5}{3}x - 3 }}[/tex]
- If you see the format of the coordinates, x coordinates are greater than y coordinates, hence y < x
[tex]{ \rm{y < \frac{5}{3}x - 3 }} \\ [/tex]
Answer:
[tex]y < \dfrac{5}{3}x-3[/tex]
Step-by-step explanation:
All given answer options have the same linear equation:
[tex]y=\dfrac{5}{3}x-3[/tex]
Therefore, there is no need to work out the equation of the line for this question as it is already given.
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.From inspection of the graph there is:
A dashed line.Shading under the line.Therefore, the inequality that is represented by the graph is:
[tex]y < \dfrac{5}{3}x-3[/tex]
00000 Replace the side length of this square with 4 in., and find the area. S
The area of the square is 16 square inches.
The area of a square is calculated by multiplying a side by itself.
In this case, the side S is replaced by 4 in, then:
[tex]\begin{gathered} \begin{cases}A=S\cdot S \\ S=4in\end{cases} \\ A=4in\cdot4in=16in^2 \end{gathered}[/tex]a tiling of the plane occurs when we fill the entire infinite playing with a repeated pattern . the image to the right shows a portion of one such tiling. The pattern extends forever in all directions. A give all angles of rotational symmetry between 0 and 360 degrees about the two marked points. point A: Point B:
EXPLANATION
Let's see the facts:
The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.
The angles of symmetry in point B is 120 degrees.
A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute.
If the reservoir was empty and it is now 35 gallons full, how long has the tanker been filling the reservoir?
The tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute using the estimation concept.
As per the question statement, A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute and the reservoir was empty and it is now 35 gallons full. We are supposed to find out for how long has the tanker been filling the reservoir. We will use the concept of estimation.
Rate of filling gas = 1212 gallons per minute
i.e., 1212 gallon of gas taken 1 minute for transfer.
1 gallon of gas will take = (1/1212) minutes
Hence 35 gallons of gas will take = (1/1212)*35 minutes = 0.0288 min.
So, the tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute.
Estimation: Having an approximate estimate of something's worth, number, size, or extent is referred to as estimation in mathematics.To learn more about Estimation click on the link given below:
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Describe the expression.Cuad2 * 5+7jog vollsynsinontbnilo++7(3 + 13) evollarWhich of the following describes (7 in the expression above?A. factorB.(B, sumC. quotientD. product
Answer:
The expression is given below as
[tex]2\times5+7(3+13)[/tex]Concept:
We will have to explain the options so we can figure out what the final answer is
Sum:
The result is obtained by adding numbers
Quotient:
a quotient is a quantity produced by the division of two numbers.
Product:
A product is the result of multiplication,
Factor:
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
Step 1:
[tex]2\times5=10(represents\text{ the product of 2 and 5\rparen}[/tex]We will then have to deal with the parenthesis
[tex]3+13=16(sum\text{ of 3 and 13\rparen}[/tex]We will then have to multiply 7 by 16 before adding to 10
Hence,
7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16
Therefore,
The final answer is OPTION A
1) Ned started jogging at 2:50. If he jogged for 3 hours and 30 minutes, what time was it when he finished?
Data
Starting hour = 2:50
Time = 3 h 30 min
Addition
1
2:50
+ 3:30
6:20 Use the hexadecimal system to solve this problem.
Select mode<11/11 -10. Write and solve the equation modeled below.Equation:X=Solution:
2=-8-x Equation
x=-10
Explanation
Step 1
the scale is in balance, that indicates that the weights to the right and left are equal
Let
left side=2 squares of 1 each
then
left side=2
Step 2
rigth side=8 times (1) plus -x
rigth side=(8*-1)-x
rigth side=-8-x
Step 3
finally
[tex]\begin{gathered} \text{left side= rigth side} \\ \text{replacing} \\ 2=-8-x\text{ Equation (1)} \end{gathered}[/tex]Step 4
finally solve equation (1) for x
[tex]\begin{gathered} 2=-8-x \\ \text{add 8 in both sides} \\ 2+8=-8-x+8 \\ 10=-x \\ \text{Multiply each side by -1} \\ 10\cdot-1=-x\cdot-1 \\ -10=x \end{gathered}[/tex]I hope this helps you
jayel gas $30. every month she gets 15% interest. how much money does she have after 4 months
The money she will have after 4 months would be 31.50 dollars.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.
Simple Interest = (Principal × Rate × Time) / 100
If the initial amount (also called as principal amount) is given as 30, and the interest rate is 15% annually, and it is left for 4 months for that simple interest, then the interest amount earned is given by:
4 month = 0.333 year
Therefore,
Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = (30 × 15× 0.333) / 100
Simple Interest = 31.50
Hence, the money she will have after 4 months would be 31.50 dollars.
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