Answer:
False. The center of a semisimple Lie algebra is usually not trivial.
Step-by-step explanation:
The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.
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A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 25%.
If the regular box has dimensions l, w, and h, then the dimensions of the family value box would be 1.25l, 1.25w, and 1.25h. This means that the volume of the family value box would be 1.25 * 1.25 * 1.25 = 1.953125 times the volume of the regular box. Since the family value box is 25% larger in each dimension, its volume is nearly double the volume of the regular box.
Choose answers that describe the quadrilateral STUV if ST|| UV,TU||VS
and diagonals are congruent: SU≅TV
Parallelogram
Triangle
Rhombus
Square
Trapezoid
By using properties of quadrilateral, it can be concluded that-
Square describes the quadrilateral STUV
What is a quadrilateral?
Quadrilateral is a two dimensional four sided figure.
Here the properties of quadrilateral STUV is
Pair of opposite sides are parallel
Diagonals are congruent.
In a parallelogram, the pair of opposite sides are parallel but diagonals are not congruent
Triangle is not a quadrilateral
In Rhombus, the pair of opposite sides are parallel but the diagonals are not congruent
In square, the pair of opposite sides are parallel and the diagonals are congruent
In Trapezoid, one pair of opposite sides are parallel and one pair of opposite sides are non parallel.
So Square describes the quadrilateral STUV
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g has two real eigenvalues . find these eigenvalues, their multiplicities, and the dimensions of their corresponding eigenspaces.
The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue
What is Eigen Value?
Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.
It is not possible to determine the eigenvalues, their multiplicities, and the dimensions of the corresponding eigenspaces of the matrix g without more information about the matrix itself.
In order to find the eigenvalues of a matrix, you need to determine the values of the variables in the matrix and then solve the characteristic equation, which is obtained by setting the determinant of the matrix equal to zero.
The eigenvalues are the roots of the characteristic equation, and the multiplicity of an eigenvalue is the number of times it appears as a root.
The dimension of the eigenspace corresponding to an eigenvalue is the number of linearly independent eigenvectors associated with that eigenvalue.
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The data given to the right includes data from 41 candies, and 9 of them are red. The company that makes the candy claims that 31% of its candies are red. Use the sample data to construct a 90% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 31%?
The population percentage of candies that are red: (0.141,0.447)
What do you conclude about the claim of 29%?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]
Given:
- Number of samples: 34
10 red candies total.
The formula for the population proportion's confidence interval is: pz/2[p (1-p)/n]
Given:
- Number of samples: 34
10 red candies total.
Red candy prevalence in sample: p = 10/340.294
Level of significance: =1-0.95=0.05
Critical value: 1.96 for z / 2
The population percentage of red candies will now have the following 95% confidence interval estimate: 0.294 (1.96) [0.294(1-0.294)/34] 0.294 0.153, 0.294+0.153) (0.141.0. 447)
The population percentage of candies that are red: (0.141,0.447)
The complete question is : The data given to the right includes data from 34 candies, and 10 of them are red. The company that makes the candy claims that 29% of its candies are red. Use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. What do you conclude about the claim of 29%? Construct a 95 % confidence interval estimate of the population percentage of candies that are red.
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Write an equation of the line below.
Answer: Recommended to simplify to y=1/4x+3
y=2/8x+3
*Note slope may need to be simplified to (1/4 depends)
Step-by-step explanation: Formula y=mx+b
Slope m=2/8 >>>>simplify to 1/4 up 1 over 4 (the x goes beside this)
Look on y-axis count up to the dot y=3
the graph of a line is shown on the grid. the coordinates of both point indicated on the graph of the line are integer
Answer:
-5/6
Step-by-step explanation:
By the application of Analytical geometry the rate of change of y with respect to x is -5/6.
what is Analytical geometry?
Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.
The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.
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100 POINTS PLEASE HELP!!!1
use the compound interest formula A=P(1+r/n)^nt to solve. Round to two decimal places
find the accumulated value of an investment of $4,000 at 5% compounded semiannually for 8 years
a.$4,873.61
b.$5,600.00
c.$5,909.82
d.$5,938.02
The accumulated value of an investment of $4,000 at 5% compounded semiannually for 8 years is $5,938.02.
What is Compound Interest?When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.
Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit.
Given:
Investment amount= $4000
Rate of Interest, R= 5%
Time= 8 years semiannually
So, r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 4,000.00[tex](1 + 0.05/2)^{(2)(8)[/tex]
A = 4,000.00[tex](1 + 0.025)^{(16)[/tex]
A = $5,938.02
Hence, the accumulated value of an investment is $5,938.02.
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Pranav and Paul each improved their yards by planting grass sod and shrubs. They bought their
supplies from the same store. Pranav spent $90 on 10 ft² of grass sod and 5 shrubs. Paul spent
$50 on 5 ft² of grass sod and 3 shrubs. Find the cost of one ft² of grass sod and the cost of one
shrub
The cost of one ft² of grass sod is $3 and the cost of one shrub is $10.
How to solve Algebra Word Problems?Let the cost of grass be g and the cost of shrubs be s.
Pranav spent $90 on 10 ft² of grass sod and 5 shrubs. Thus, the equation that portrays this is;
10g + 5s = 90 -----(1)
Paul spent $50 on 5 ft² of grass sod and 3 shrubs. Thus, the equation that portrays this is;
5g + 3s = 50 ------(2)
Multiply eq 2 by 2 to get;
10g + 6s = 100 -----(3)
Subtract eq 1 from eq 2 to get;
s = 10
Put 10 for s in eq 1 to get;
10g + 5(10) = 90
10g = 40
g = 4
Thus, we conclude that the cost of grass sod and shrubs are the values of s and g above.
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What is the y/x ratio?
the ratio of is x: yin reverse
6 pounds of coffee costs $14.99what is the cost per ounce
The cost per ounce is $0.156
What is ounce?An ounce is a unit of weight and mass in the Imperial and United States customary systems of measurement. It is commonly used to measure the weight of precious metals such as gold, silver, and platinum. In the US, the ounce is equal to 28.35 grams. The ounce is also used to measure the weight of food items, liquids, and other substances. In the UK, the ounce is equal to 28.4 grams. The ounce is also used to measure the weight of postage stamps, coins, and other small items. The ounce can also be used to measure the volume of a liquid. One fluid ounce is equal to 29.57 milliliters. A dry ounce is equal to 28.35 grams. An ounce is also one-sixteenth of a pound.
Solution:
1 pound is equal to 16 ounce
6 pounds of coffee = 6 x 16 = 96 ounce
So take $14.99 and divided it into 96
the cost of per ounce is equal to 14.99 / 96 = 0.156
The cost of one ounce is $0.156
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Determine how large the number aa has to be so that ∫a[infinity]1/(x^2+1)dx<0.001.
The number a has to be greater than or equal to 1000.
As per the given data we have to determine that how large the number a has to be so that [tex]$$\int_a^{\infty} \frac{1}{1+x^2} \cdot d x < 0.001$$[/tex]
[tex]$$\Rightarrow \quad\left[\tan ^{-1}(x)\right]_a^{\infty} < 0.001$$[/tex]
[tex]$\Rightarrow \quad \tan ^{-1}(x)-\tan ^{-1}(a) < 0.001$[/tex]
[tex]$$\begin{array}{ll}\Rightarrow & \frac{\pi}{2}-0.001 < \tan ^{-1}(a) \\\\\Rightarrow & 1.5698 < \tan ^{-1}(a)\end{array}$$[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad \tan ^{-1}(a) > 1.5698 \\& \Rightarrow \quad a > \tan (1.5698)\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& \Rightarrow \quad a > 999.999 \\& \Rightarrow \quad a \geqslant 1000\end{aligned}$$[/tex]
Therefore the answer is [tex]\quad a \geqslant 1000[/tex]
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A room in an attic has a sloping wall that makes an angle of 55° with the floor, which is parallel to the ceiling.
What is the measure of an angle that forms a pair of same-side interior angles with that angle?
The table of ordered pairs shows the coordinates of the two points on the graph of a line. Which equation describes the line?
ก. y=x+7
c. y=-5 x+2
b. y=x-7
d. y=5 x+2
Please seiect the best answer from the choices provided
P.
8
C.
The equation of the line is y = x + 7
What is the equation of a line?The equation of a line is an equation that describes the line. It is given by y = mx + c where
m = gradient and c = y - interceptHow to find the equation that describes the line?Since the equation of a line is given by y = mx + c and we have the points from the table (-5, 2) and (0, 7)
Substituting these evalues into the equation, we have
y = mx + c
2 = m(-5) + c
2 = -5m + c (1)
Also, the point (0,7),we have
y = mx + c
7 = m(0) + c
7 = 0 + c
c = 7
Substituting c = 7 into equation (1), we have that
2 = -5m + c
2 = -5m + 7
2 - 7 = -5m
-5 = -5m
m = -5/-5
m = 1
Substituting m = 1 and c = 7 into the equation for the line, we have
y = mx + c
y = (1)x + 7
y = x + 7
So, the equation is y = x + 7
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A polygon's interior
angles add up to 4320°.
How many sides does the
polygon have?
Answer:
24 sides
Step-by-step explanation:
The interior angles of a polygon add up to 180(n-2) degrees, where n is the number of sides the polygon has. This means that to find the number of sides a polygon has, we can set up the following equation:
180(n-2) = 4320
Solving for n, we get:
n = (4320 + 360) / 180 = 24
Therefore, the polygon has 24 sides.
32.68-4.15q
a. for q = 0
b. for q = 10
c. for q = -3
a. The value of 32.68-4.15q when q = 0 is 32.68.
b. The value of 32.68-4.15q when q = 10 is -8.82
c. The value of 32.68-4.15q when q = -3 is 45.13.
What is an expression?
Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Given expression is 32.68-4.15q
Putting q = 0 in the given expression:
32.68-4.15 × 0
= 32.68
Putting q = 10 in the given expression:
32.68-4.15 × 10
=32.68 - 41.5
=-8.82
Putting q = -3 in the given expression:
32.68 - 4.15 × (-3)
=32.68 +12.45
=45.13
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The sales price for a sweater was $21. The sweater was 40% off. What was the originalprice of the sweater?
PA BRAINLIEST
Answer:
The original price of the sweater was $35Step-by-step explanation:
To calculate the original price of the sweater, we first need to determine the amount of the discount. Since the sweater was 40% off, the discount was 40/100 * $21 = $8.40.
To find the original price of the sweater, we then need to subtract the discount from the sales price. Since the sales price was $21 and the discount was $8.40, the original price of the sweater was $21 - $8.40 = $<<21-8.4=12.60>>12.60.
However, since the problem states that the original price of the sweater was $35, we can conclude that the calculation above must be incorrect. To find the correct original price of the sweater, we need to divide the sales price by the discount percentage, rather than subtracting the discount amount from the sales price.
Using this method, we can calculate the original price of the sweater by dividing the sales price of $21 by the discount percentage of 40/100, which gives us $21 / (40/100) = $35. This is the correct original price of the sweater
Marie Josee makes famous custom shirts that are sold all over the world from Canada. She wants to make sure her revenue (sales price) for the shirts is equivalent to $45 CAD in every country. What should be the sales price for the shirts in the following countries? (hint: convert to the local currency!)
1. European Union
2. Japan
3. Australia
4. Without considering any other costs (shipping, taxes, tariffs, etc…), which country would it be the best market for Mariee Josee’s shirts? Which one gives her the most revenue? Explain your answer.
The sales price for the shirts in different countries are the following
Country. Price of shirt
European Union , 62.469 EURJapan , 0.477 JPYAustralia, 41.913 AUD4. European Union, is the best market for Mariee Josee’s shirts and this country also gives her most revenue.
We have given that,
Marie Josee makes famous custom shirts and sold it in Canada. The currency of Canada , CAD.
The price of shirt = $45 CAD
Now, we should find out the price of shirt in different countries.
Country Currency
Canada CAD
European Union EUR
Japan JPY
Australia AUD
1. one CAD = 1.3882 EUR
=> price of shirt in European Union = 45× 1.3882
= 62.469 EUR
2. one CAD = 0.0106 JPY
=> price of shirt in Japan = 45× 0.0106 =0.477 JPY
3. one CAD = 0.9314 AUD
=> price of shirt in Australia = 45× 0.9314
= 41.913 AUD
4. The country Currency which gives highest price of shirt in above list is better option for selling it. So, we see that the European Union country would it be the best market for Mariee Josee’s shirts. It gives best selling price for shirt
i.e 62.469 EUR.
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Jamal spent 6 dollars on snow cones last week. Each snow cone costs s dollars. Choose the expression that shows how many snow cones Jamal bought.
The expression that represents the number of snow cones is 6/s.
Algebraic Expressions:An algebraic expression is an expression that is made up of variables and constants by operations like addition, subtraction, etc. We use Algebraic Expressions to find unknown values or numbers.
Here we have
Jamal spent 6 dollars on snow cones last week
Each snow cone costs s dollars
Let Jamal bought y snow cones
=> Cost of y cones = ys dollars
Given that Jamal spent 6 dollars
=> ys = 6
=> y = 6/s
Therefore,
The expression that represents the number of snow cones is 6/s.
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Monica deposits $400 into a savings account that pays a simple interest rate of 4.3% .Paul deposits $500 into a savings account that pays a simple interest rate of %4.2 Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.
What is simple interest?
Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
[tex]A = P (1 + rt)\\\\A $ = final amount$\\P $ = initial principal balance$\\r $ = annual interest rate$\\t $ = time (in years)$[/tex]
Given that:
For Monica:
Principal (p) = $400
Rate (r) = 4.3% = 0.043
Year (t) = 1 year
Deposit Paul:
Principal = $500
Rate (r) = 4.2% = 0.042
Year (t) = 1 year
Now calculate the interest amount for Monica and Paul, we get
For Monica:
A = P(1 + rt)
A = 400(1 + (0.043 × 1))
A = 417.2
A = $417.20
Now for Monica, Interest will be
I = A - P
= 417.20 - 400
I = 17.20 dollars -----------(II)
For Paul:
A = P(1 + rt)
A = 500(1 + (0.042 × 1))
A = 521
A = $521 dollars
Now for Paul, Interest will be
I = A - P
= 521 - 500
I = 21 dollars ---------------(II)
From (I) and (II), we can say that Paul will earn more interest than Monica.
Hence, Monica was wrong she will get less interest than Paul as Paul has invested a higher Principal amount than Monica.
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Find the area of the circle.
Use 3.14 for T. Do not round your answer.
Hint: A = πr²
18 inches
The area of circle when π is 3.14 is 1017.36 inches².
What is the area of circle?
It is obvious that one of the rectangle's sides will be the radius and the other will be half the circumference's length.Since we already know that a rectangle's area equals its length times its width, which is compounded by "r," As a result, r2 is the circle's area.Although a circle is not a square, the amount of internal space it encloses is measured in square units. Easy formula for calculating a square's area is length times width.However, a circle simply has a diameter, or width. Since a circle (by definition) is the collection of all points that are equally spaced apart from a particular point in the centre, it lacks a clearly discernible length and width.Area of the circle = πr²
= 3.14 * 18 * 18
= 3.14 * 324
= 1017.36 inches²
Hence, the area of circle when π is 3.14 is 1017.36 inches².
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Complete the paragraph by selecting the correct term or phrase from each drop-down meru.
In the early 1900s, many people in the United States were concered that drinking alcoholic beverages was causing many problems in society. This concern led to the passage of the
- Amendment. An unintended effect of the enactment of this amendment was an increase in
The rate of immigration
The amount of organized crime
The number of eligible voters
In the early 1900s, many people in the United States were concerned that drinking alcoholic beverages was causing many problems in society. This concern led to the passage of the Eighteenth Amendment.
An unintended effect of the enactment of this amendment was an increase in The amount of organized crime.
What did the Eighteenth Amendment lead to ?The temperance movement, which believed that prohibiting the sale of alcohol would help alleviate poverty and other societal issues, worked for decades to create the Eighteenth Amendment.
Sadly, there was an unintended effect with the Eighteenth Amendment which was a rise in organized crime. This was because criminal gangs became obscenely rich and powerful from the sale of alcohol on the Black Market.
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Is (5, 10) a solution to this system of equations?
20x 12y = -20
5x - 11y = −1
yes
no
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer: b includes only rational numbers
Step-by-step explanation:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.
b.
The population of a certain single-cell organism doubles every hour, starting with 100 cells. Which COULD be an equation to model th
situation, where f(t) is the number of organisms and t is time in hours?
geometric progression with common ratio 2.
so, f(t) = 100 x [tex]2^t[/tex] be an equation to model the situation.
What is geometric progression ?A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying each preceding term by a fixed number, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers.A geometric progression, also termed a geometric sequence, is a set of integers where each term after the first is obtained by multiplying the one before it by a constant, non-zero quantity known as the common ratio.Given :
starting with 100 cells.
a=100
r = 2
a certain single-cell organism doubles every hour
f(t) is the number of organisms and t is time in hours.
f(t) = 100 x [tex]2^t[/tex]
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which statement comparing the two functions is correct?
A .Function to has a small minimum value of -9.
B. Function to has a smaller minimum value of 4.
C. Function one has the smaller minimum value of -14.
D. Function one has the smaller minimum value of -2.
Answer:
it would be C
hope this helps
Step-by-step explanation:
What is the product of the 4 x and the 3 x cubed y squared minus 2 x y cubed?
Answer: 170678
Step-by-step explanation:
try it and you'll see.
Carl deposits $500 into the bank for 8 years with a 3% interest rate. After 8 years, how much will he have in the account?
After 8 years, the amount of money which Carl would have in the bank account is equal to $620.
How to calculate the future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P represents the principal or starting amount.R represents the interest rate.A represents the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have the following;
S.I = 500 × 3/100 × 8
S.I = $120.
Now, we can calculate the future value (A) as follows;
Future value (A) = P + S.1
Future value (A) = 500 + 120
Future value (A) = $620.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
P = 6000r = 0.059n = 4$10164.30Step-by-step explanation:
Given that $6000 is deposited into an account earning 5.9% compounded quarterly, you want the values of P, r, n used in the future-value formula, and you want the value after 9 years.
(A) Formula valuesThe problem statement tells you the values:
amount deposited = P = 6000
interest rate = r = 5.9% = 0.059
compounding periods in a year = n = 4
(B) Future valueUsing these numbers in the formula, you find (with t=9) ...
S(9) = 6000(1 +0.059/4)^(4·9) ≈ $10164.30
Solve the formula c=pid for d
Answer:
d=c/pi
Step-by-step explanation
divide by pi then d=c/pi
Answer:
C / pi = d
Step-by-step explanation:
The formula for circumference is
C = pi * d
To solve for d, divide each side by pi
C / pi = d
i will mark brainliest determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths. y ≥ 0 y ≤ 0 y is greater than or equal to negative 1 over 40 y is less than or equal to negative 1 over 40
The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.
How to Solve an Inequality?To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.
The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:
4y + 1/5 ≤ 4/5 [given]
Subtract 1/5 from both sides of the inequality:
4y ≤ 4/5 - 1/5 [subtraction property of equality]
4y ≤ 3/5
Multiply both sides by 1/4:
4y × 1/4 ≤ 3/5 × 1/4
y ≤ (3 × 1) / (5 × 4)
y ≤ 3/20
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