The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x). The correct option is C.
What is a Straight Line Equation?A straight line equation is represented by y = mx+c, where m is the slope and c is the y-intercept.
m is given by (y₂-y₁)/(x₂-x₁)
From the graph , the y-intercept is 4 and the two points on the line are ( 0,4) and ( 1,1).
m = -3
c =4
The equation of the function g(x) is g(x) = -3x+4
The slope of the function g(x) is greater than f(x) and so g(x) is steeper than f(x).
Therefore, the correct option is C.
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Question 1 of 10
Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated
9 miles back down river before they reached the shore. How far did they get?
A. 135÷9 = 15
B. 15-9=6
C. 15-6=9
D. 9+15=24
Answer:
They get 15×9=135
135÷15=9 is your answer
Consider the polynomial function h(x)= -7x^6+3x^4-5x^2
The end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]
How to determine the end behavior?The function is given as:
[tex]h(x)= -7x^6+3x^4-5x^2[/tex]
Next, we plot the graph of the function (see attachment)
From the attached graph, we can see that:
The function approaches negative infinity, irrespective of the direction of the x value
Hence, the end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]
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Which of the following is equivalent to (8 – 5) ÷ 23 ?
A 3/8
B 19/8
C 27/8
D 1/125
Answer:
none
Step-by-step explanation:
(8-5)=3
8-5÷23
=179/23
a+a+b=14 b+b+c=08 a+b+c=18 b=
The value of b in the expression is -2.
How to find the variable in an expression?a + a + b = 14
b + b + c = 8
a + b + c = 18
Therefore,
2a + b = 14
2b + c = 8
c = 8 - 2b
Hence,
a + b + 8 - 2b = 18
a - b = 18 - 8
a - b = 10
2a + b = 14
a - b = 10
3a = 24
a = 8
8 - b = 10
b = 8 - 10
b = -2
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Answer:
a = 8
b = -2
c = 12
Step-by-step explanation:
a + a + b = 14
2a + b = 14 ⇒ ( 1 )
b + b + c = 8
2b + c = 8 ⇒ ( 2 )
a + b + c = 18 ⇒ ( 3 )
First, let us make a as the subject in equation 1.
2a + b = 14
2a = 14 - b
[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex] ⇒ ( 4 )
Let us make c as the subject in equation 2.
2b + c = 8
c = 8 - 2b ⇒ ( 5 )
Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.
And now let us solve the equation 3 to find the value of b.
[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]
[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]
[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]
And now let us find the value of a
For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.
[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]
Now, let us find the value of c.
For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.
[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]
HELP PLEASE
factor completely.
25d^8−80d^4+64=
Answer:
(5d⁴ − 8)²
Step-by-step explanation:
I hope this is helpful!
2 divided by 9 = 5/2 divided by 5/4
The given equality 2 divided by 9 = 5/2 divided by 5/4 is seen to be; False because LHS ≠ RHS
How to solve equalities?We are given the equality;
2 divided by 9 = 5/2 divided by 5/4
We want to check whether the left hand side of the equality is equal to the right hand side. Thus;
Left hand side can be expressed as;
2 divided by 9 = 2/9
Now, right hand side can be expressed as;
5/2 ÷ 5/4
⇒ (5/2) * (4/5)
⇒ 2
Therefore we can see that LHS is not equal to RHS and so the equality is false.
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A bag contains 2 gold marbles, 9 silver marbles, and 24 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game
The expected value on playing this game is -5/36.
Given: 2 gold marbles, 9 silver marbles, and 24 black marbles.If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
To find: Expected value on playing the game
Chance of occurrence of gold = 1/36
Chance of occurrence of silver = 9/36
Chance of occurrence of black = 26/36
On multiplying the given probability of occurence with the amount you would lose or win
we get,
1/36 * 3 + 9/36 * 2 - 26/36 * 1
3/36 + 18/36 - 26/36
=$ -5/36
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3. What is the distance from (0,0) to (24,10) on the
coordinate plane?
[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]
Answer:
26
Step-by-step explanation:
√(24 - 0)2 + (10 - 0)2
= √(24)2 + (10)2
= √676 and that would equal
26
If f(x) = 5x - 7, what is {3)?
O A. 22
O B. 2
O c. 1
• D. 8
Work Shown:
f(x) = 5x - 7
f(3) = 5(3) - 7 .... every x replaced with 3
f(3) = 15 - 7
f(3) = 8
[tex] \: [/tex]
Given :
f(x) = 5x - 7x = 3To Find :
What is the value of x ?Calculating the value of x :
[tex]\sf : \implies \: 5x - 7[/tex]
[tex]\sf : \implies \: 5(3) - 7[/tex]
[tex]\sf : \implies \: 15 - 7[/tex]
[tex]\bf : \implies \: 8[/tex]
Hence,
[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]
What can be concluded about the line represented in the table? Select 3 options.. x y –6 –7 2 –3 8 0 The slope is 2. The slope is One-half. The y-intercept is –4. The y-intercept is 8. The points (–2, –5) and (8, 0) are also on the line. The points (–5, –2) and (1, 10) are also on the line.
The correct statements regarding the linear function are given as follows:
The slope is 1/2.The y-intercept is -4.The points (–2, –5) and (8, 0) are also on the line.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the line goes through points (-6,-7) and (8,0), hence the slope is given by:
[tex]m = \frac{0 - (-7)}{8 - (-6)} = \frac{7}{14} = \frac{1}{2} = 0.5[/tex]
Hence:
y = 0.5x + b
When x = 8, y = 0, hence the y-intercept is given as follows:
0 = 0.5(8) + b
b = -4.
When x = -2, we have that:
y = 0.5(-2) - 4 = -1 - 4 = -5.
The points (–2, –5) and (8, 0) are also on the line.
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Answer:
B,C,E
Step-by-step explanation:
took the test on edge and got 100
Time Remaining
59:49
Triangle E G F is cut by line H J. Line H J goes from side E G through side G F. Lines E F and H J are parallel.
Using the side-splitter theorem, which segment length would complete the proportion?
StartFraction G H Over H E EndFraction = StartFraction question mark Over J F EndFraction
GF
JH
GJ
EF
Using the side-splitter theorem, the segment length that would complete the proportion is GJ.
How to illustrate the information?It should be noted that the side splitter theorem states that when a line intersects two sides of a triangle and is also parallel to the third side, then it'll divide the sides proportionally.
From the information given, it can be deduced that EF and HJ are parallel while H is on the side EG and J is on GF. Therefore, according to the theorem, GH/HE = GJ/JF
Therefore, the correct option is GJ.
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Answer: C.
Step-by-step explanation: Trust Me! It was correct on the Edge quiz! :)
Jack and Susie want to save to buy a trampoline for their children. They each open a savings account that earns 1.5% a year. Jack opens his account with $1,000, and Susie opens her account with $800.
x = number of years
The following functions represent the value of the savings accounts in x years:
Jack’s savings account: f(x) = 1000(1.015)x
Susie’s savings account: g(x) = 800(1.015)x
Which function represents the total amount Jack and Susie will save in x years?
200(1.015)x
1800(1.015)x
1800(1.015)2x
1800(1.030)x
The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let f(x) and g(x) represent the value in the savings account of Jack and Susie respectively after x years. Hence:
f(x) = 1000(1.015)ˣ, g(x) = 800(1.015ˣ
Hence:
Total savings = 1000(1.015)ˣ + 800(1.015)ˣ = (1.015)ˣ[1000 + 800] = 1800(1.015)ˣ
The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ
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1) a jewelry store sells gold and platinum
rings. each ring is available in ten styles
and is fitted with one of nine gemstones.
a) 187 b) 265
c) 180
d) 195
find the number of possible outcomes
un wd
The number of possible outcomes are 180.
How do you find the number of possible outcomes?To find the total number of possible outcomes for two or more events, multiply the number of outcomes for each event together.
Given that,
We have two types of rings Gold and platinum
For this event (material) we have 2 outcomes.
Each ring is available in 10 style
For this event (style) we have 10 outcomes.
Each ring is fitted with 9 gemstones
For this event (gem) we have 9 outcomes.
Total number of possible outcomes = 2×10×9
= 180
Hence, The number of possible outcomes are 180.
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? Question
Each set of ordered pairs represents two points on a line. Match each set of ordered pairs with the description of the line
they are on.
Tiles
(-5,-3) and (-5,3) (-7,-1) and (-1,-7)
(-6,-2) and (6,-2)
The correct matching of the ordered pairs and the line they are on are:
(-5,-3) and (-5,3) - No slope. (-7,-1) and (-1,-7) - Slope = -1(-6,-2) and (6,-2) - No slope What lines do the ordered pairs belong to?The slope of the first pair is:
= (3 - (-3)) / (-5 - (-5))
= No slope as slope is 0
The slope of the second pair is:
= (-7 - (-1)) / (-1 - (-7))
= -1
The slope for the third pair is:
= (-2 - (-2)) / (6 - (-6))
= 0 or No slope
Rest of the question is:
slope = -1
No slope
No slope
slope = 2
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Answer: vertical line- (-5,-3) and (-5,3)
neither- (-7,1) and (-1,-7)
horizontal line- (-6,-2) and (6,-2)
hopefully this helps
Step-by-step explanation:
Using the function p(t)=5*2^t, estimate the boa constrictor population in 2 years, 3 years, and 4 years. Show your work.
Answer:
2 years: 203 years: 404 years: 80Step-by-step explanation:
There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.
P(t) for different tThe graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:
2 years: 2 × 10 = 20
3 years: 2 × 20 = 40
4 years: 2 × 40 = 80
__
Additional comment
You can always use a calculator to evaluate the function for different values of t.
Scientist released 8 rabbits into a new habitat in a year 0.each year, there were twice as many rabbits as the year before.
The question is incomplete. Below you will find the missing part of the question.
How many rabbits were there after x years? Write a function to represent this scenario.
[tex]8(2)^{x}[/tex] rabbits were there after x years.
The function form is [tex]f(x)=8(2)^{x}[/tex]
The number of rabbits released each year is 8.
During 0 year, there will be 8 rabbits;
During year 1, the number of rabbits will be 8+8 = 16, i.e. 8×2¹ = 16
Similarly, during the year 2, the number of rabbits will be 16+16 i.e. 8×2² = 32
So, according to the pattern we can say that the function would be
[tex]f(x)=8(2)^{x}[/tex]
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how to convert 798 in the base of 2
Subtract the largest power of 2 from 798 such that the difference is not negative.
2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and
798 = 512 + 286 = 2⁹ + 286
Repeat this process with the remainder, 286.
2⁸ = 256, so
286 = 256 + 30 = 2⁸ + 30
⇒ 798 = 2⁹ + 2⁸ + 30
2⁴ = 16 and 2⁵ = 32, so
30 = 16 + 14 = 2⁴ + 14
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 14
2³ = 8, so
14 = 8 + 6 = 2³ + 6
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6
2² = 4, so
6 = 4 + 2 = 2² + 2¹
⇒ 798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹
or more completely,
798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰
Then the base-2 representation of 798 is
11 0001 1110₂
Does the parabola open up or down?
What would the sign of the second differences be?
What are the coordinates of the vertex?
What is the equation of the axis of symmetry?
What is the optimal value?
Is the optimal value considered a max or min?
What are the x-intercepts?
What is the y-intercept?
The parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have given a graph of a parabola.
From the graph:
The parabola opens down.
The sign of the second difference is positive.
The coordinates of the vertex is at (1, 3)
The equation of the axis of symmetry is x = 1
The optimal value of the parabola is at y = 3
The optimal value is considered a max value.
The x-intercepts is at (-1, 0) and (3, 0)
The y-intercept is at (0, 5/2)
Thus, the parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1
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f CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Let us assume that segment AC was dilated by a scale factor of 2 to form C'A', hence:
A'C' = 2 * AC = 2 * 8 = 16 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
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56. Kelly found that the length of the hypotenuse of a triangle was equal to the square root of 125. The length of the hypotenuse was between which two consecutive integers?
A. 10 and 11
C. 30 and 31
B. 11 and 12
D. 62 and 63
Answer: B: 11 and 12
Step-by-step explanation:
- An integer is simply a whole number
- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)
- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12
- So 11.1803398875 falls between 11 and 12, making the answer B
hope this helps :)
need help with these graphs really quickplease
Answer:
Concave up: (0, infinity)Concave down: (-infinity, 0)a. The graph is concave up in the interval 0 ≤ x ≤ +∞
b. The graph is concave down in the interval -∞ ≤ x ≤ 0
To answer the question, we need to know what intervals are
What are intervals?Intervals are range of values in which a function is valid. It can either be the range of values of input or output of the function.
a. Interval where the graph is concave upFrom the graph, we see that the function is concave up in the interval 0 ≤ x ≤ +∞
So, the graph is concave up in the interval 0 ≤ x ≤ +∞
b. Interval where the graph is concave down
From the graph, we see that the function is concave down in the interval -∞ ≤ x ≤ 0
So, the graph is concave down in the interval -∞ ≤ x ≤ 0
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if Ben has 10.4L of deride and Madison has 940 cal of diesel how much does the pair have altogether
Based on the calculations, the total volume which the pair have altogether is equal to 19.8 Liters.
How to calculate the total volume?In Science, volume is a unit of measurement which indicates the capacity of a container and it has the following units:
Liters (L)Centiliter (cL)Cubic meter (m³)Next, we would convert the volume of Madison's diesel in centiliter to liter as follows:
1 centiliter = 0.01 liter
940 centiliter = X liter
Cross-multiplying, we have:
X = 940 × 0.01
X = 9.4 L.
Total volume = 9.4 + 10.4
Total volume = 19.8 Liters.
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The diagram shows AKLM. Which term describes point N?
K
L
A. Orthocenter
N
B. Circumcenter
C. Centroid
D. Incenter
The term that describes point N is centroid. The correct option is C. Centroid
Centroid of a triangleThe centroid of a triangle is the point in which the three medians of the triangle intersect.
The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.
In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.
Point N is the point where the lines intersect.
Hence, the term that describes point N is centroid. The correct option is C. Centroid
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Answer:
B. Circumcenter
Have an Amazing day/night!!
What is the solution to the equation 3 +6=2
Answer: no solution
Step-by-step explanation:
if we simplify this equation, we derive that 9=2.
this is a false statement, which means this equation has no real solutions.
What is the first quartile of the data set: 11, 24, 13, 18, 16, 21, 23, and 29?
Answer: 15, 15, 16, 21, 23, 29
Step-by-step explanation:
Hi I don't know how to do this question
Answer:
7 (option B)
Step-by-step explanation:
the area of a trapezoid can be found using the formula:
[tex]A = \frac{a+b}{2}h[/tex]
where
A: area
a: base
b: other base
h: height
here, we can plug in our known variables to solve for h (height)
A: 119
a: 10
b: 24
h: ??
[tex]A = \frac{a+b}{2}h[/tex]
[tex]119 = \frac{10+24}{2}h[/tex]
{now, simplify!}
[tex]119 = \frac{10+24}{2}h[/tex] {add 10 + 24}
[tex]119 = \frac{34}{2}h[/tex] {divide 34 by 2}
119 = 17 · h
119 = 17 · h
÷ 17 ÷17 {divide both sides by 17to isolate h}
7 = h
So, the height (h) of this trapezoid is 7
hope this helps! have a lovely day :)
Suppose water was being drained at from a conical tank. The radius is decreasing at a rate of 2 inch per minute and the height is decreasing at 4 inches per minute. Find the change in the volume when the height is 5 inches and the radius is 6 inches.
The change in volume is -88π
Volume?The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.
What is volume change?Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement
Given:The radius is decreasing at 2 inches per minute
The height is given as decreasing at 4 inches per minute
So let [tex]\frac{dr}{dt}=-2[/tex] and
[tex]\frac{dh}{dt}=-4[/tex]
and we have radius r=6,
height h=5
The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]
Then
[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]
[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]
[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]
So the volume change is [tex]-88\pi[/tex]
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Do anyone know thissss
Answer: False
Step-by-step explanation:
This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.
A function must have only one output [y-value] for every input [x-value].
However, in the anonymous follow-up survey that re-interviewed the respondents, only 80 percent responded that they would be open to supporting a woman candidate. What could be generating these different results
Social-desirability biases is the sort of response bias that is the tendency of the survey respondent to answer the question in a manner that is favorable to others.
As Maria found that most respondents 98% of the voters were open to support women candidates. The social desirably bias poses a serious problem during the self-reporting as the bias interferes with the interpretations of the average tendencies.
As however during the anonymous survey of the voters or respondents showed only 80% of them would support the women candidate.
Hence the social desirability bias is the main culprit for such a response.
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A girl ran from her home to a store at the rate of 6 mph, and she walked back home at the rate of 4 mph. if it took 15 minutes for the round trip, how far away is the home from the store?
Home is 0.6 miles away from the store
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Given:-
Total time taken by girl to complete the trip = 15 minutes = [tex]\frac{1}{4}[/tex] hours
Speed while riding going = 6 miles per hour
Speed while coming back = 4 miles per hour
Total time taken by girl =
Time taken while going + Time taken while coming back - (1)
Let x be distance from home to store
[tex]\frac{x}{6}[/tex] = Time taken while going
[tex]\frac{x}{4}[/tex] = Time taken while coming back
Substituting in (1) we get
[tex]\frac{1}{4} = \frac{x}{6} + \frac{x}{4}[/tex]
[tex]\frac{1}{4} = \frac{2x + 3x}{12}[/tex]
[tex]\frac{1}{4} = \frac{5x}{12}[/tex]
[tex]x= \frac{12}{20}[/tex]
x = 0.6 miles
Thus home is 0.6 miles away from the store
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