Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
(Picture one)
A. 126 cm3
B. 907.5 cm3
C. 605 cm3
D. 55 cm3
Find the surface area of the cylinder in terms of pi.
(Picture 2)
A) 396 pi in^2
B) 522 pi in^2
C) 360 pi in^2
D) 1008 pi in^2
Answers
The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
we know that,
volume of pyramid is:
V = 1/3 B h
here, we have,
B = 11*11
= 121
h = 15
so, we get,
V = 605 cm^3
again, we have,
surface area of the cylinder :
s = 2πr( r + h)
here, we have,
r = 9
h = 20
so, we get,
s = 522 pi in^2
Hence, The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
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The volume of the square pyramid is A) 126 cm³ and the surface area of the cylinder is B) 522π in².
The volume of a square pyramid is expressed as:
Volume = l² × h/3
The surface area of a cylinder is expressed as:
Surface area = 2πrh + 2πr²
From the diagram:
For the square pyramid:
Length l = cm
Height h = 15cm
Volume =?
Volume = l² × h/3
Plug in the values:
Volume = 11² × 15/3
Volume = 121 × 5
Volume = 605 cm³
Option C) 605 cm³ is the correct answer.
Next, we find the surface area of the cylinder:
Radius r = 9 in
Height h = 20 in
Surface area = 2πrh + 2πr²
Plug in the values:
Surface area = (2π × 9 × 20) + (2π × 9²)
Surface area = 522π in²
Therefore, the surface of the cylinder is 522π in².
Option B) 522π in² is the correct answer.
Related Questions
Which expression represents the area of the shaded triangle?
Answers
Answer:
B. [tex]\frac{1}{2}\times (5.7)\times (1.9)[/tex]
Step-by-step explanation:
We have been given an image of a triangle. We are asked to choose the correct option that represents the area of the shaded region.
We know that the area of a triangle is half the product of its height and base.
Upon looking at our given diagram we can that shaded region is in form of triangle and the height of both triangles is 5.7 meters. We can also see that the base of shaded triangle is 1.9 meters.
[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Height *Base})[/tex]
[tex]\text{Area of shaded region}=\frac{1}{2}\times (5.7)\times (1.9)[/tex]
Therefore, option B is the correct choice.
Answer:
b.
Step-by-step explanation:
Simplify 7x + (x – 4)(x + 5) – 5x.
Answers
7x+(X*2+ 5x-4x-20)-5x
7x+(X*2+ x-20)-5x
X*2+3x-20
Answer:
x^2 + 3x – 20
Step-by-step explanation:
I just did the assignment
a pizza delivery shop averages 21 minutes per delivery with a standard deviation of 3 minutes. what is the probability that a pizza takes less than 15 minutes to be delivered?
Answers
We have the mean, μ = 21 and the standard deviation, σ = 3
We want P(X<15)
Standardizing gives:
P(X<15) = P(Z<(15-21)/3)
P(X<15) = P(Z< -2) ⇒ When the value of the z-score is negative, we will
read the value of z<2 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<2)
P(X<15) = 1 - 0.9772
P(X<15) = 0.0228
the probability that pizza takes less than 15 minutes to be delivered is 0.0228
= 2.28%
Round answer as needed
-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step
Answers
-2v < 6 + 10 6v < -6 - 12
-2v < 16 6v < -18
v > -16/2 v < -18/6
v > -8 v < -3
solution is : -8 < v < -3
simplify 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³
a) -4m³ + 8p²
b) 8p² - 4
c) 4m³ - 13p³ + 5p
d) -4m³ + 13p³ - 5p
Answers
= 13p³ - 4m³ - 5p
= -4m³ + 13p³ - 5p
answer
d) -4m³ + 13p³ - 5p
Final answer:
The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).
Explanation:
To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.
Like terms have the same variable raised to the same power.
In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.
Combine terms with p³: 7p³ + 6p³ = 13p³.Combine terms with m³: 2m³ - 6m³ = -4m³.Combine terms with p: 4p - 9p = -5p.Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).
Is it possible for one point to be in two different planes?
Answers
Yes, it is possible for one point to be in two different planes. Imagine this: take the point in the corner of a room. That point is part of 3 planes (both walls and the floor).
To add, in mathematics, a plane is a flat, two-dimensional surface.
Answer:
Yes, it is possible for one point to be in two different Planes.
This can be explained in following way.
The Intersection of two plane is a line.And on a line infinite number of point lies.
So,"yes" one point or Infinite number of points can be common between two different planes.
(15 POINTS) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).
Answers
An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
What is equation of ellipse?"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
What are vertices of the standard ellipse?"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "
What is focus of the standard ellipse?"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "
For given question,
The center of the ellipse is at the origin.
Using the standard form of equation of the ellipse,
[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
A vertex at (13, 0)
⇒ (a, 0) = (13, 0)
⇒ a = 13
And a focus at (12, 0).
⇒ (c, 0) = (12, 0)
⇒ c = 12
We know, [tex]c^{2}= a^{2}- b^{2}[/tex]
Now, we find the value of b i.e., minor axis
[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]
Substituting these values in the standard form of equation of ellipse with center (0, 0),
[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
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anna owes home antiques Whose value is 160000 today assuming normal growth. however anna believes the value will grow at 16% per year for the next three years she wants to take this rapis growth ibto consideration when valuing the buisness for potential sale find the future value of the buisness in three years then use that future value to find the present value at a rate 8% compounded annually
Answers
A=p (1+r)^t
A future value?
P present value 160000
R interest rate 0.16
T time 3years
A=160,000×(1+0.16)^(3)
A=249,743.36
Use that future value to find the present value at a rate 8% compounded annually
To find p (present value) solve the formula for p
P=A÷ (1+r)^t
Where r is 0.08
P=249,743.36÷(1+0.08)^(3)
p=198,254.33
The product of three and a number is thirty-three. What is the number? N = 11 N = 30 N = 36
Answers
Answer:
Step-by-step explanation:
N=11
HELP ME PLEASE !! IM SO CONFUSED
Answers
2. 2.2 x10^6
3. 2.0 x 10^4
Just covert each until you reach the end, like you know that there are 356 days in a year and 100 years in a century.
PS They're in scientific notation
If you were to add all odd numbers between 1 and 11 (both inclusive), the result would be
Answers
1,3,5,7,9,11
This is an arithmetic sequence with common difference of d=2
The first term is a₁=1.
The number of the term 11 (without counting) is found from
1 + (n-1)*2 = 11
1 + 2n - 2 = 11
2n -1 = 11
2n = 12
n = 6
The sum of the first n terms of an arithmetic sequence is
[tex]S_{n} = \frac{n(a_{1}+a_{n})}{2} [/tex]
Therefore, the sum of the sequence is
S₆ = [6*(1 + 11)]/2
= (6*12)/2
= 36
Answer: 36
Final answer:
By adding all the odd numbers from 1 to 11 inclusive (1, 3, 5, 7, 9, 11), the sum is 36.
Explanation:
If you were to add all odd numbers between 1 and 11 (both inclusive), the odd numbers are: 1, 3, 5, 7, 9, and 11. To find the result of adding these numbers together, you simply add each one sequentially:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16
16 + 9 = 25
25 + 11 = 36
So, the result of adding all the odd numbers from 1 to 11 inclusive is 36.
Merlin industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.
Answers
f=ir^t, f=final value, i=initial value, r=common ratio or "rate", and t=times rate is applied or "time".
In this case i=2100 and r=(100-14)/100=0.86 so the equation is:
f=2100(0.86^t) and in five years...
f(5)=2100(0.86^5)
f(5)≈$987.90 (to nearest whole cent)
C: -5/2 D: 5/2 help please
Answers
what is the exact solutions of x2=5x+2
Answers
x²-5x-2 = 0
Solve with x₁,₂ = (-b±√Δ)/2a
Δ = b²-4ac
call a (1)x², b -5 and c -2
x1,2 = (-(-5)±√(-5)²-4*1*(-2))/2*1
x1,2 = (5±√25+8)/2
x1,2 = (5±√33)/2
x1 = (5+√33)/2
x2 = (5-√33)/2
Answer:
The answer has a positive 5 and 33.
Step-by-step explanation:
I used a calculator.
Choose the point on the terminal side of -45°. (-3, -3) (4, -4) (5, 5) (-2, 2)
Answers
-45° is in quadrant IV and the point (4, -4) is the only point out of the points given that is also in quadrant IV
The point (4,-4) is the only one that satisfies that condition
hope that helps
PLEASEEEEE HELPPPP ASAP NEED TO GET RIGHT!!!! WILL GIVE THANKS
Answers
r² = x² + y²
(√34)² = x² + 3²
34 = x² + 9
x² = 25
x = 5
the coordinates is placed as (x,y) and you already solved these values and so (5, 3)
Which statement is true about the equations –3x + 4y = 12 and x – y = 1? The system of the equations has exactly one solution at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
Answers
The system of equations has exactly one solution, but it is located at (16,15), not (–8, 3), (–4, 3) or any other points. So, none of the provided options are true.
Explanation:The task is to identify the statement that is correct about the system of equations –3x + 4y = 12 and x – y = 1. To discover this, we must solve the system which consists of these two linear equations. Adjust equation two to be in the same format as equation one by adding y to both sides which gives x = y + 1. Substitute it into the first equation: -3(y + 1) + 4y = 12, which simplifies to -3y - 3 + 4y = 12, giving y = 15. Substitute y = 15 to the second equation, it gives us x = 16. Hence, none of the provided solutions is correct, because the system has exactly one solution at (16,15).
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Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F + G) (2) =
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F G) (2) =
Answers
Answer with Step-by-step explanation:
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F+G)(2)=F(2)+G(2)
= 4+5
= 9
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F - G) (6) =F(6)-G(6)
=8-9
=-1
F = {(0, 1), (2, 4), (4, 6), (6, 8)}
G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
(F.G) (2) =F(2).G(2)
= 4×5
= 20
Susie and Amelia solved the same equation using two separate methods. Their work is shown in the table below:
Answers
Answer:
(C)
Step-by-step explanation:
Explanation of Susie's method:
The given equation is:
[tex]2x-3=4x-2[/tex]
[tex]2x-2x-3=4x-2x-2[/tex]
[tex]-3=2x-2[/tex]
[tex]-3+2=2x[/tex] ( she made a mistake when she subtracted 2)
[tex]-1=2x[/tex]
[tex]x=-\frac{1}{2}[/tex]
Susie made a mistake in step 4 when she subtracted 2,
Thus, option C is correct.
Eduardo bought a refrigerator with a sticker price of $2400. If he paid $35 a week for two years, what was the approximate markup rate on the refrigerator?
A. 65.9%
B. 51.7%
C. 34.1%
D. 75.8%
Answers
In 2 years there are 104 weeks
Total paid
35×104=3,640
markup rate
((3,640−2,400)÷2,400)×100=51.7%
It's b
Answer:
The correct answer is option B
Step-by-step explanation:
Payment done per week [tex]= 35 dollar\\[/tex]
Total number of weeks in a year [tex]= 52 weeks\\[/tex]
Total number of weeks in two year [tex]= 104 weeks\\[/tex]
Total amount paid in two weeks
[tex]= 35 * 104\\=3,640\\[/tex]
The make up rate is basically the amount paid over and above $2400
[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]
A company performs linear regressions to compare data sets of two similar products. If the residuals for brand A form an increasing curve, and the residuals for brand B form a U-shaped pattern, what can be concluded?
A. Brand A's data are probably linear, while brand B's data are probably not. B.Neither data is likely to be linear.
C.Both data sets are probably linear.
D.Brand B's data are probably linear, while brand A's data are probably not.
Answers
Brand A's data are probably linear, while brand B's data are probably not.
What can be concluded from a graph?A graph shows how much a set of data fits into a pattern. This data is defined by the regression line.
Now, when we have the graph for brand A as an increasing curve, and the residuals for brand B form a U-shaped pattern, we can conclude that Brand A's data are probably linear, while brand B's data are probably not.
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Please help me ASAP.
David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didn’t use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.
Based on the information in the graph, if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
a.$64
b. $65
c. $67
d. $68
Answers
Answer:
d. $68Step-by-step explanation:
First, let's find the equation of the line.
The slope is defined by
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where we are gonna use points (2,0) and (9,7).
[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]
Then, we use the point-slope formula to find the equation.
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].
Replacing this value in the equation, we have
[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]
Therefore, the price without coupon is $68.
15 * 4 2/3 please help
Answers
4 2/3 = 14/3
15 = 15/1
14/3 * 15/1 = 14*15=210, 3*1 = 3
210/3 = 70
answer is 70
Christine buys 7 hamburgers and 3 sodas for $27.95. Laura buys 5 hamburgers and 4 sodas for $23.40. How much does a hamburger cost?
A. 1 .85
B. $3.20
C. $6.80
D. $6.55
E. $3.50
Answers
3s=27.95-7h divide both sides by 3
s=(27.95-7h)/3
Then we are told:
5h+4s=23.4, using s found above makes this equation become:
5h+4(27.95-7h)/3=23.4 multiply both sides by 3
15h+4(27.95-7h=70.2 perform indicated multiplication on left side
15h+111.8-28h=70.2 combine like terms on left side
-13h+111.8=70.2 subtract 111.8 from both sides
-13h=-41.6 divide both sides by -13
h=$3.20
Calculate each unit rate
$11.49 for 3 packages
Answers
Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
Answers
[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
The parameters a, b and c represent the coefficients of the standard form of the quadratic equation: y = ax^2 + bx + c. Thus, for the equation y = x2 − 8x + 7,
a = 1
b = -8
c = 7
The mistake Joyce made was in Step 1. Because Step 1 is wrong, the rest of the equation is wrong consequently. The mistake was made by Joyce when she assigned b = 8. She forgot to include the negative sign of -8x.
Her mistake is in the first step, she wrote the equation incorrectly.
Solving quadratic equations:
A general quadratic equation:
ax^2 + bx + c = 0
has the solutions:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, the equation is:
y = x^2 - 8x + 7
And what Joyce writes in each step is:
Step 1:
x = (-8 ± √(8^2 - 4*1*7))/(2*1)
Then we can already see the mistake.
Notice that in the given equation, we have:
b = -8
And the general solution has:
x = (-b ± √(b^2 - 4ac))/(2a)
-b would be equal to 8, then what Joyce must have written here is:
x = (8 ± √((-8)^2 - 4*1*7))/(2*1)
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Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?
Answers
r-value = 0.657 (r)
standard deviation of x-coordinates = 2.445 (Sx)
standard deviation of y-coordinates = 9.902 (Sy)
We are asked to find the slope of the line up to 3 decimal places.
To find the slope of the line, based on the data that we have, we can use this formula:
slope, b = r * (Sy / Sx)
substitute the values to the formula:
b = 0.657 * ( 9.902 / 2.445 )
Solve for the b.
Therefore, the slope of the line is
b = 2.66078, round off to three decimal places:
b = 2.661 is the slope of the line.
Answer: 2.661
Step-by-step explanation:
A P E X
Are the two triangles below similar?
Yes, because there are two pairs of congruent corresponding angles
No, because there are not two pairs of congruent corresponding angles
Yes, because the corresponding sides are proportional
No, because the corresponding sides are not proportional
Answers
Answer :- Yes the two triangles are similar because there are two pairs of congruent corresponding angles.
Explanation:-
In Δ ABC
∠A=30° , ∠C=65 °
By angle sum property of triangle
∠A + ∠B + ∠C= 180°
⇒∠B= 180°-∠A-∠C=180°-30°-65°=85°
⇒∠B=85°
Now in ΔABC and ΔDEF
∠A=∠D=30° and ∠B=∠E=85°
⇒ there are two pairs of congruent corresponding angles.
So by AA-similarity criteria
ΔABC ≈ ΔDEF
Answer:
Yes, because there are two pairs of congruent corresponding angles.
Step-by-step explanation:
Two triangles ABC and DEF are given .
The measure of angles in triangle ABC are:
m<A=30°,m< C=65°,
m<B= 180-(30+65)=85°(measure of sum of angles in any triangle is 180°)
In triangle DEF the measure of the angles are :
m<D=30°,m<E=85°,m<F=180-(30+85)=65°(sum of angles in a triangle add to 180°)
In triangles ABC and DEF,
< A=<D=30°
<B=<E=85°
<C=<F=65°
The two triangles are similar by AAA property.
(06.02)The graph shows the number of weeks a movie has been in theaters and the number of tickets sold each week
Which statement best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold?
As the number of weeks increases, the number of tickets sold decreases.
As the number of weeks increases, the number of tickets sold increases.
As the number of weeks decreases, the number of tickets sold decreases.
No relationship can be determined.
Answers
Therefore, A) As the number of weeks increases, the number of tickets sold decreases would be the correct answer.
As the number of weeks increases, the number of tickets sold decreases so option (A) will be correct.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network. A graph is made up of some points and the distance between two.
In another word, graph is geometrical relation of the analytical variable.
For example to draw the equation y = 6x +8 this will draw a straight line in the coordinate geometry.
In the given question it is clearly visible that as the weeks in theater are increasing the points are going down on the y-axis which is tickets sold.
As the number of weeks increases, the number of tickets sold decreases hence option (A) will be correct.
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Bao Yu is completing the square to solve the polynomial equation.
x2 – x – 3 = 0
What should be her first step?
adding –x to both sides of the equation
adding –3 to both sides of the equation
isolating the first term, x2
isolating the constant, –3
Answers
Solution:
The square of the given equation can be completed as below:
Here we will make the terms on left hand side such that it gets the form of [tex]a^2\pm2ab+b^2=(a\pm b)^2[/tex]
[tex]x^2-x-3=0\\\\\text{Isolate the constant}\\\\x^2-x=3\\\\x^2-2\times\frac{1}{2}\times x +\frac{1}{2}^2=3+ \frac{1}{2}^2\\\\(x-\frac{1}{2})^2=\frac{13}{4}\\[/tex]
Hence the correct option is isolating the constant , -3.
The polynomial equation x^2 – x – 3 = 0 is a quadratic equation, and the first step in completing the square is (d) isolating the constant, –3
What are polynomials?Polynomials are expressions that are represented with variables and coefficients
Below are the steps taken to determine Bao Yu's first step
The equation is given as:
x^2 – x – 3 = 0
Isolate the constant -3 in the equation.
So, we have:
x^2 – x = 3
Hence, the first step in completing the square is (d) isolating the constant, –3
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