Answers
Answer:
[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]
Step-by-step explanation:
We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:
[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]
[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]
[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]
[tex]r_4 = 30[/tex]
We can now find the area of each red band by subtracting:
the area of the circle within the white band just inward of the red band
-- from --
the area of the circle within the red band.
Finding the area of the outer red band:
[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]
[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]
↓ using 3.14 for [tex]\pi[/tex]
[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]
[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]
Finding the area of the inner red band:
[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]
[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]
↓ using 3.14 for π
[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]
[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]
Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.
[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]
[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]
[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]
Related Questions
Kevin said that if you triple his age the result will be 1 less than his mother age Graph
Answers
Answer:
Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.
According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:
3K = M - 1
We can simplify this equation by adding 1 to both sides:
3K + 1 = M
This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.
Write 3.5 as a mixed number and as an improper fraction.
Write your answers in simplest form.
Answers
3.5= 35/10
35/10= 7/2
which is equal to 3 1/2
Therefore: 3 1/2 and 7/2
what is x?
a. 100
b. 120
c. 60
d. 50
Answers
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Answers
The value of x if the line BD is the perpendicular bisector of AC is 11.5
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure where the line BD is the perpendicular bisector of AC.
To calculate the value of x, we use the following equation by setting the line segments equal to each other
3(2x - 8) = 45
Divide both sides of the above equation by 3
2x - 8 = 15
So, we have the following equation
2x = 23
Divide both sides of the above equation by 2
x = 11.5
Hence, the calculated value of x is 11.5
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helppp me its need to be done quick
Answers
Answer:
100
Step-by-step explanation:
The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.
Therefore, the answer is 100.
Ned has 55 marbles in his collection. He has twice as many white marbles as red marbles. He has five more blue marbles than white marbles. How many white marbles does Ned have?
Answers
Answer:
Ned has 20 white marbles.
Step-by-step explanation:
Let's call the number of red marbles "r".
We know that Ned has twice as many white marbles as red marbles, so the number of white marbles would be 2r.
We also know that he has five more blue marbles than white marbles, so the number of blue marbles would be 2r + 5.
The total number of marbles in Ned's collection is 55, so:
r + 2r + (2r + 5) = 55
Simplifying this equation, we get:
5r + 5 = 55
Subtracting 5 from both sides:
5r = 50
Dividing by 5:
r = 10
So Ned has 10 red marbles.
We can use this to find the number of white marbles:
2r = 2(10) = 20
So Ned has 20 white marbles.
The two-way frequency table shows the results of a survey of students.
Right-handed
Left-handed
Total
In music program Not in music program Total
43
394
437
15
33
48
58
427
475
How many left-handed students are in the music program?
OA. 15
OB. 48
OC. 43
OD. 58
Answers
The left-handed students in the music program are option A 15 students.
What is two-way frequency table?A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.
From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.
Thus, he left-handed students in the music program are 15.
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Find the value of x.
Answers
The value of x in the circle is 4.2
Calculating the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Using the intersecting chords equation, we have
(5x - 8) * 4 = (x + 1) * 10
When solved for x, we have
x = 4.2
Hence. the value of x is 4.2
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I need help pleaseee
Answers
The result of the row 1 multiplication by 1/4 is determined as [¹/₂ 0 ].
What is the result of the row multiplication?The resultant of the row multiplication in the surd is calculated by applying the following method;
row 1 in the given surds = [2 0]
To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;
[2 0] x 1/4 = 1/4(2 0)
= [¹/₂ 0 ]
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.
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SOMEONE, PLEASE HELP!
Answers
3=proportional
Wouldn't be 29 and 1/1.5? becaus ethen it would be 60 + 27 + 2
Answers
If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.
How to solve
In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.
Thus, we do this below:
1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3
So, John has 29 full buckets and another bucket that is 2/3 full.
If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.
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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?
I don’t know how to do this question if anyone does please put the steps thank you.
Answers
If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.
31 + 3 = 34
34 / 2 = 17
17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.
17 + 3 = 20
20 / 2 = 10
Answer: the first term is 10
Hope this helps!
surface area of a square prism 3ft 3ft 15ft
Answers
Answer:
198 ft^2
Step-by-step explanation:
l = 3
w = 3
h = 15
2(3*3) + 4(3*15) = 18 + 180
18 + 180 = 198 ft^2
90w/m sq when the distance is 5m
Answers
The total power being emitted by the source, given the radiant flux density, is 28,274.3 watts of power.
How to find the total power emitted ?The inverse square law can be used with the formula :
I = P / ( 4 π r ²)
We are given the radiant flux density I = 90 W/m² and the distance r = 5 m.
The power being emitted is therefore :
P = 90 W/ m ² x (4 π ( 5 m) ² )
P = 90 W / m ² x ( 4 π x 25 m ² )
P = 90 W / m² x 100 π m²
P = 28, 274.3 watts
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Full question is:
How much power is a source emitting with an amount of radiant flux density of 90w/m sq when the distance is 5 m
AABC-ADEC. 1 and 2 have the same measure. Find DC and
DE. (Hint: Let DC = x and AC=x+4, Use the figure shown to the right.)
DC is unit(s) long.
(Round to the nearest tenth as needed.)
D
4
A
14
E
B
Answers
Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.
Using the properties of similar triangles, we can set up the following proportion:
$\frac{CE}{CA}=\frac{CD}{CB}$
Substituting the given values:
$\frac{CE}{x+4}=\frac{x}{14}$
Cross-multiplying:
$14CE = x(x+4)$
$14CE=x^2+4x$
We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:
$\frac{DE}{AB}=\frac{AE}{AC}$
Substituting the given values:
$\frac{DE}{18}=\frac{AE}{x+4}$
Cross-multiplying:
$AE = 18\frac{DE}{x+4}$
Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:
$14CE=x^2+4x$
$14\frac{DE}{x+4}=x^2+4x$
$14DE=x^2+4x(x+4)$
$14DE=x^2+4x^2+16x$
$18x^2+16x-14DE=0$
We can now use the quadratic formula to solve for $x$:
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$
$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$
Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:
$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$
$DC\approx 2.3$ or $DC\approx -3.1$
Since distance cannot be negative, we choose the positive solution:
$DC\approx 2.3$ units.
To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:
$\frac{CE}{x+4}=\frac{x}{14}$
$\frac{CE}{2.3+4}=\frac{2.3}{14}$
$CE\approx 1.34$ units
Now we can use the second similarity proportion to find $DE$:
$\frac{DE}{18}=\frac{AE}{x+4}$
$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$
$DE\approx 3.64$ units
Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.
Step-by-step explanation:
The table below gives data from a linear function. Find a formula for the function.
Price per shirt, p($) 15 20 25
Number of shirts sold, q = f(p) 1000 750 500
a. f( p) = 1750p − 50 b. f( p) = 1000 − 50p c. f( p) = 1000 + 50 p
d. f( p) = 1750 + 50 p e. f( p) = 1750 − 50p
Answers
The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.
To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.
Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:
slope = (change in y)/(change in x)
= (500 - 1000)/(25 - 15)
= -50
Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:
y - y₁ = m(x - x₁)
y - 1000 = -50(x - 15)
y - 1000 = -50x + 750
y = -50x + 1750
Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.
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A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 9. Compute the raw, x-value associated with a Z-score of 0.21. Round to two decimal places, as needed.
Answers
The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.
To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:
Z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = Zσ + μ
Substituting the given values, we get:
x = 0.21(9) + 144
Simplifying the expression, we get:
x = 145.89
A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.
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Please help discrete math question.
Answers
The number of ways you can tile your walkway if you choose single tiles and double tiles is 3,992,781,803 ways.
How to find the number of ways ?To tile a 1x20 walkway using red, blue, and yellow single tiles (1x1) and green and white double tiles (1x2), we can consider the number of ways to combine the single and double tiles to fill the entire 1x20 space.
The exact number of ways to tile the 1x20 walkway using red, blue, and yellow single tiles and green and white double tiles:
= 3^20 + 3^18 x 2 + 3^16 x 4 + 3^14 x 8 + 3^12 x 16 + 3^10 x 32 + 3^8 x 64 + 3^6 x 128 + 3^4 x 256 + 3^2 x 512 + 1, 024
= 3486784401 + 258280326 + 172186884 + 38263752 + 8503056 + 1889568 + 419904 + 93456 + 20736 + 4608 + 1024
= 3,992,781,803 ways
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I know is blurry just pls help
Answers
12 - 2^2 x 2
---Remember: PEMDAS
---In this case exponents are first, then multiplication, then subtraction
12 - 4 x 2
12 - 8
4
Answer: 4
Hope this helps!
the volume of the indian ocean is about 2.1 X 10^17 cubic meters. How many years would it take for the Narmada River to fill the Indian, assuming it has a water flow of 6.3 X 10^11 cubic meters per year? Answer in scientific notation
Answers
132300000000000000000000000000
Find the area of the regular polygons and degree of central angle when given either the apothem or side length.
Answers
The length of the apothem is 10. 99cm
How to determine the valuesTo determine the apothem of a polygon, we have to use the formula;
a = s/2 tan (180/n)
Such that the parameters are;
a is the length of the apothem.s is the side length of the polygonn is the number of sides of the polygonNow, substitute the values, we have;
a = 8/2tan(180/9)
divide the values
a = 8/2tan 20
Find the values
a = 8/0. 7279
Divide the values
a = 10. 99cm
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Determine any horizontal or slant asymptotes of the rational function: f(X)= 3x^2-x/2x^2-1
Answers
The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.
How to express the asymptoteWe need to compare the degrees of the numerator and denominator.
The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2
Furthermore, f(x) = 3/2 + x/(2x² - 1)
This expression shows that the function has a slant asymptote given by the line: y = x/2
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Is this correct for problem 15?
Answers
The solution to the given inequality is: 10 > x ≤ 12
How to solve Inequality expressions?Inequalities are defined as mathematical expressions that involve the symbols >(greater than), <(less than), ≥(greater than or equal to) and ≤(less than or equal to).
In order for us to 'solve' an inequality, we have to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
We are told that the angle (9x + 7)° is greater than 97° and at most 118°
Thus:
9x + 7 > 97
9x > 90
x > 10
Similarly:
9x + 7 ≤ 115
9x ≤ 108
x ≤ 12
Thus, the solution to the inequality is: 10 > x ≤ 12
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PLEASE HELP WILL MARK BRAINLY What is the area of a regular pentagon with a side of 5 ? Round the answer to the nearest tenth. TYPE THE NUMBER ONLY
Answers
Hope this helps.
ces
Which sequence below would best model the
following description?
A newly planted tree releases 250 pounds of
oxygen over the period of its first year. The amount
of oxygen released by the tree grows at a rate of
12% per year, but the tree cannot generate more
than 6000 pounds of oxygen per year.
Answers
The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.
The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).
However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:
(1- f(n-1/6000)).
To understand this better, let's calculate the oxygen released by the tree in the second year using the formula
f(n) = 1.12f(n-1)(1- f(n-1/6000)).
f(2) = 1.12f(1)(1- f(1)/6000)
= 1.12(250)(1- 250/6000)
= 295.67 pounds of oxygen
Hence, option (b) is correct.
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The correct question is:
Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.
a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)
b. f(n) = 1.12f(n-1)(1- f(n-1/6000)
c. f(n) = 1.12f(n-1) {6000/f(n-1)}
d. f(n) = 1.12f(n-1)(f(n-1) -6000)
A cone has a volume of 48 cubic feet and a height of 9 feet. find the radius.
Answers
Step-by-step explanation:
V = 1/3 x π x r² x h
48 = 1/3 x π x r² x 9
48÷3π = r²
√48÷3π =r
so, r= 2.26 (3.s.f)
write the standard equation of a circle with its centre in the fourth quadrant tangent to x=7, y=-4 and x=17
Answers
Answer:
Step-by-step explanation:
To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.
Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).
So the center of the circle is (12, -4).
Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.
The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).
So the standard equation of the circle is:
(x - 12)^2 + (y + 4)^2 = 25
the mean radius of the earth is 6371.0 kilometers and the mean radius of earths moon is 1737.5 kilometers. what is the approximate difference in the mean circumferences in kilometerse of the earth and earths moon
Answers
the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.
Describe circle.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.
A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. T
he line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius.
The difference in the mean circumferences of the Earth and the Moon can be found by subtracting the circumference of the Moon from the circumference of the Earth.
The circumference of the Earth is:
C earth = 2π * 6371.0 km = 40075.04 km (rounded to two decimal places)
The circumference of the Moon is:
C moon = 2π * 1737.5 km = 10921.16 km (rounded to two decimal places)
The difference in the mean circumferences of the Earth and the Moon is:
C earth - C moon = 40075.04 km - 10921.16 km ≈ 29153.88 km
Therefore, the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.
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what are the answers to these questions?
Answers
The length of wire used for the square is 0.25 meters and the length of wire used for the circle is 1 meter. To maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.
To minimize the total area of both figures and minimize the length of wire used, the wire should be cut in half, giving each piece a length of 1 meter.
For the square frame, we know that each side of the square is equal to the length of wire used to make it, so we can divide the 1 meter of wire in half to get 0.5 meters for each side of the square.
The perimeter of the circle is the length of wire used to make it, so we can use the remaining 1 meter of wire to find the radius of the circle:
2πr = 1
r = 1/(2π)
Using this radius, we can find the circumference of the circle and the length of wire used:
C = 2πr = 1 meter
Therefore, the length of wire used for the square is 0.5 meters and the length of wire used for the circle is 1 meter.
To maximize the total area, we need to cut the wire into two equal pieces, each with a length of 1 meter.
For the square frame, each side will have a length of 0.25 meters, which will give us a total area of 0.0625 square meters.
For the circle, the radius will be 1/(4π) meters, which will give us a circumference of 1/(2π) meters and a total area of π/(16) square meters.
Therefore, to maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.
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The answer is B I just don't know the percentage.
Answers
The correct choice is: B. The statement is false because the reference values for the decrease and increase are not the same. The true improvement over the past two years is 8.56%.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
Mathematically, percentage increase can be calculated by using this mathematical equation (formula):
Percentage increase = [Final value - Initial value]/Initial value × 100
Based on the information provided about the high school test scores, we have the following:
True improvement = (100% - 8%) × (100 + 18)
True improvement = (92%) × (100 + 18)
True improvement = (0.92) × (118)
True improvement = 108.56 ⇒ 8.56%.
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