Using the function rule y = 5 + 5x, we can fill in the table as follows:
x | y
0 | 5
1 | 10
2 | 15
3 | 20
4 | 25
To fill in the table using the function rule y = 5 + 5x, we can substitute different values of x into the equation and calculate the corresponding values of y.
Let's create a table:
x | y
0 | 5 + 5(0) = 5 + 0 = 5
1 | 5 + 5(1) = 5 + 5 = 10
2 | 5 + 5(2) = 5 + 10 = 15
3 | 5 + 5(3) = 5 + 15 = 20
4 | 5 + 5(4) = 5 + 20 = 25
Using the function rule y = 5 + 5x, we can substitute each value of x into the equation to find the corresponding value of y. For example, when x = 0, y = 5. When x = 1, y = 10, and so on.
Therefore, the completed table is:
x | y
0 | 5
1 | 10
2 | 15
3 | 20
4 | 25
These values satisfy the given function rule y = 5 + 5x.
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The rectangular tank shown below was 4/5 filled with water. how many more litres of water were needed to fill up the tank?
The volume of water required to fill up the tank is: 540 cm³
How to find the volume of the cuboid?The formula for the volume of a cuboid is:
Volume = Length * Width * Height
Thus:
Volume of bigger tank = 15 * 15 * 12
Volume = 2700 cm³
Now, we are told that it is 4/5 filled with water.
Thus, volume needed to fill up the tank is:
¹/₅ * 2700
= 540 cm³
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Find the inverse of the function f(x) = e^(x −3) + 7
3. Set up and solve an equation to
find the missing angle
measurements in the following:
H
4x - 20
G
2x
2G=
ZH=
21=
||
2x
I
The missing angle measurements are:
Angle G = 66.67 degrees
Angle H = 113.32 degrees
Angle Z = 66.68 degrees
Angle I = 66.68 degrees
Let's analyze the given information and solve for the missing angle measurements:
From the diagram, we can see that angle H and angle G are adjacent angles, and the line segment HG acts as a transversal. We are given that the measure of angle G is 2x, and we need to find the missing angle measurements, which are the measures of angle H, angle Z, and angle I.
Since angle G and angle H are adjacent angles, their measures add up to 180 degrees. So we can set up the equation:
2x + (4x - 20) = 180
Simplifying the equation:
6x - 20 = 180
Next, we solve for x:
6x = 200
x = 200/6
x = 33.33
Now that we have found the value of x, we can substitute it back into the original equation to find the measures of the missing angles:
Angle G = 2x = 2(33.33) = 66.67 degrees
Angle H = 4x - 20 = 4(33.33) - 20 = 133.32 - 20 = 113.32 degrees
Angle Z = 180 - Angle H = 180 - 113.32 = 66.68 degrees
Angle I = Angle Z = 66.68 degrees
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Please answer this question
It will take the ball 2.12s to the nearest hundredth to hit the ground.
What is quadratic formula?
Quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0 and that is usually written in the form
x = (-b ± √(b2 − 4ac))/(2a)
From the question, the initial height, h, of the ball is 40 ft
When the ball hits the ground, the height, h, is zero
The equation h = - 16t² + 15t + 40 becomes
0 = - 16t² + 15t + 40
16t² - 15t - 40 = 0
Solving the quadratic equation by formula method for t,
t = (-b ± √(b² - 4ac)) / (2a)
Where, a = 16, b = -15, and c = -49
Substitute these values into the quadratic formula,
t = (15 ± √2785) / 32
Therefore, the possible values of t are:
t = (15 + √2785) / 32
t = (15 - √2785) / 32
Which implies t = 2.12 or t = - 1.18
Since time, t, cannot be negative, t = 2.12s to the nearest hundredth.
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please see photo thank you
Answer:
look below
Step-by-step explanation:
formula A=1/3 Bh
1/3 ×8×5×5
8x5x5=200
200/3=66.66666 round to 66.77cubic metets
The relation of a line graph is visualized by drawing
lines between all of the points on a grid.
The relation of a line graph is visualized by drawing lines between all of the points on a grid is false.
What is a line graph?A line graph is a type of graph that uses lines to connect data points. The points are typically plotted on a grid, but the lines do not need to connect all of the points. In fact, it is often more helpful to only connect the points that are relevant to the data that you are trying to visualize.
For example, when graphing temperature over time, there is only need to connect the points that represent the temperature at each hour. There is no need to connect the points that represent the temperature at midnight, 2am, 4am, etc.
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Complete question:
The relation of a line graph is visualized by drawing lines between all of the points on a grid. Is this true or false? Explain your answer.
Given the points A(-2, 1) and B(3, 4), what are the coordinates of point C in the fourth
quadrant such that mZCAB= 90 degrees and AB = AC? Express your answer as an ordered pair.
degree
The coordinates of C are (121/6, -47/15).Therefore, the answer is (121/6, -47/15 )Answer: (121/6, -47/15)
The given points are A (-2, 1) and B (3, 4).
We need to determine the coordinates of point C in the fourth quadrant such that m∠CAB=90° and AB=AC.
In order to determine the coordinates of point C,
The slope of ABThe slope of the line passing through A(-2, 1) and B(3, 4) is given bym = (y₂ - y₁) / (x₂ - x₁)m
= (4 - 1) / (3 - (-2))m
= 3 / 5
The mid-point of A and BMid-point of A and B is given by the following formula:
Mid-point = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Mid-point of AB is: ((-2 + 3) / 2, (1 + 4) / 2)
= (1/2, 5/2)
The slope of the line perpendicular to AB
The slope of the line perpendicular to AB is given by the following formula: m₁ * m₂ = -1
Where m₁ is the slope of AB and m₂ is the slope of the line perpendicular to ABm₁ = 3 / 5m₂ = - 5 / 3 (as the line is perpendicular to AB and the product of slopes of two perpendicular lines is -1)
The mid-point and the slope of the line perpendicular to AB to find the coordinates of C
Let the coordinates of C be (x, y)We know that AC = AB and we know the coordinates of A (-2, 1) and mid-point of AB (1/2, 5/2).
Simplifying this equation, we get:
15b = 47b = 47 / 15
Substituting this value of b in the equation we got earlier:
a = (70 + 20b) / 8
= (70 + 20(47/15)) / 8
= 121 / 6
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Rewrite each fraction with a denominator of 12.
3
4
5
3
The equivalent fractions with a denominator of 12 are
3/4 = 9/125/3 = 20/12How to rewrite the fractionsTo rewrite each fraction with a denominator of 12, we need to find an equivalent fraction that has 12 as its denominator.
3/4 can be rewritten as (3/4) * (3/3) = 9/12.
5/3 can be rewritten as (5/3) * (4/4) = 20/12.
Therefore, the fractions with a denominator of 12 are:
3/4 = 9/12
5/3 = 20/12
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complete questions
Rewrite each fraction with a denominator of 12.
3/4
5/3
Write an algebraic expression to represent the given phrase. Use x as the variable to
represent the unknown quantity.
8. The sum of a number and 20
9. The product of a number and 20
10. The quotient of 20 and a number
11. The difference of a number and 20
Choices for 8-11:
A) 20-x
D) x + 20
B) 20x
20
X
E)
C) X-20
X
20
AB)
Answer:
8) x + 20
9) 20x
10) 20/x
11) x-20
Step-by-step explanation:
8) x + 20
9) 20x
10) 20/x
11) x-20
what is equivalent to 3 radical 6
The equivalent expression to [tex]3\sqrt{6}[/tex] is given as follows:
[tex]\sqrt{54}[/tex]
How to obtain the equivalent expression?Two expressions are defined as equivalent expressions when they have the same result.
The expression for this problem is given as follows:
[tex]3\sqrt{6}[/tex]
For the equivalent expression, we can move the outer term 3 inside the root, with it being squared, as follows:
[tex]3\sqrt{6} = \sqrt{3^2 \times 9} = \sqrt{54}[/tex]
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PLEASE HELP!
See the image below!
Answer:
A ≈ 199.98
Step-by-step explanation:
the area (A) of Δ ABC can be calculated as
A = [tex]\frac{1}{2}[/tex] ab sinΘ ( substitute values for a, b and Θ )
= [tex]\frac{1}{2}[/tex] × 25 × 33 × sin29°
= 12.5 × 33 × sin29°
≈ 199.98 ( to 2 decimal places )
a motorist travels 210 miles in 5 hour n it will take ------ hours to travel 1386 miles
The time needed to travel 1386 miles is given as follows:
t = 33 hours.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The motorist travels 210 miles in 5 hours, hence the velocity is given as follows:
v = 210/5
v = 42 miles.
Then the time needed to travel 1386 miles is given as follows:
42 = 1386/t
42t = 1386
t = 1386/42
t = 33 hours.
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A 16 ounce bottle of spring water is $2.08. A 20 ounce bottle of fresh water is $2.40. Which statement is true ?
A 16 ounce bottle of spring water is $2.08. A 20 ounce bottle of fresh water is $2.40 Therefore, this statement "A 20 ounce bottle of fresh water is $2.40" is true.
To determine which statement is true, let's compare the prices of the two water bottles:
16 ounce bottle of spring water: $2.08
20 ounce bottle of fresh water: $2.40
To find the price per ounce for each water bottle, we can divide the total price by the number of ounces:
Price per ounce of spring water: $2.08 / 16 ounces = $0.13 per ounce
Price per ounce of fresh water: $2.40 / 20 ounces = $0.12 per ounce
Comparing the prices per ounce, we can see that the price per ounce of fresh water ($0.12) is less than the price per ounce of spring water ($0.13).
Therefore, the statement "A 20 ounce bottle of fresh water is $2.40" is true.
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List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.)
T(x) = 9x4 − 3x2 − 7
Answer:
The rational zeros theorem states that all possible rational zeros of a polynomial with integer coefficients are of the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.
In this case, the constant term is -7 and the leading coefficient is 9. Thus, the possible rational zeros are:
p/q = ±1, ±7, ±9
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Given statement solution is:- The statement that best explains whether the data in the table represents a linear or nonlinear function is:
The table represents a nonlinear function because the graph does not show a constant rate of change.
When x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.
The statement that best explains whether the data in the table represents a linear or nonlinear function is:
The table represents a nonlinear function because the graph does not show a constant rate of change.
In the given table, the values of y do not change at a constant rate as x increases or decreases. For example, when x increases from -4 to -1, y changes from 4 to 2.5, which is a rate of change of -1.5. However, when x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.
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The price of an item has risen to $119 today yesterday it was $85 what is the percentage Increase
The price has increased by approximately
40%.How to find the percentage increaseTo calculate the percentage increase, we use the following formula:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
given data:
New Value = $119
Old Value = $85
Percentage Increase = (($119 - $85) / $85) * 100
= ($34 / $85) * 100
≈ 40%
Therefore, the price has increased by approximately 40%.
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Find the coordinates for the midpoint of the segment with the endpoints given.
(5, 6) and (8, 2)
What is the length of side s of the square shown below?
45
90°
OA. 1
OB. 2
OC. 2.2
OD. 4
OE. E
F. 4.2
Answer:
E
Step-by-step explanation:
using Pythagoras' identity on the lower right triangle , with legs s and hypotenuse 2 , then
s² + s² = 2²
2s² = 4 ( divide both sides by 2 )
s² = 2 ( take square root of both sides )
s = [tex]\sqrt{2}[/tex]
Which description does NOT guarantee that a quadrilateral is a parallelogram?
a quadrilateral with consecutive angles supplementary
a quadrilateral with the diagonals bisecting each other
a quadrilateral with both pairs of opposite sides congruent
quadrilateral with two opposite sides parallel
The description that does NOT guarantee that a quadrilateral is a parallelogram is:
a quadrilateral with consecutive angles supplementary.Why the statement is not a guaranteeWhile it is true that consecutive angles in a parallelogram are supplementary (their sum is 180 degrees), the converse is not true. In other words, having consecutive angles that are supplementary does not necessarily imply that the quadrilateral is a parallelogram.
There are other types of quadrilaterals, such as trapezoids or irregular quadrilaterals, that can also have consecutive angles that are supplementary.
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Find the sizes of the three unknown angles in
the image below.
Give your answers in degrees (°).
b
с
a
34°
Answer:
Step-by-step explanation:
The diagram shows a model of a pyramid mounted on a base in the shape of a cuboid.
The length and width of the cuboid are both 25cm and its height is 4cm. Each of the
four faces of the pyramid is an equilateral triangle with side length 18cm. The model is
to be painted all over, except for the underside of the base, which will not be visible.
Fill in the gaps, giving your answers to three significant
figures where appropriate.
(a) The visible surface area of the cuboid is
(b) The visible surface area of the pyramid is
(c) The total surface area to be painted is
cm².
cm².
cm².
18
25
The surface areas are given as;
a. 2700 cm²
b. 280. 6 cm²
c. 815. 3 cm²
How to determine the surface areaThe formula for calculating the surface area of a cuboid is expressed as;
Surface area (SA) = 2lw+2lh+2hw
Such that l is the length, w is the width and h is the height
Substitute the values, we have;
a. Surface area = 2(25×25) + 2(4 ×25) + 2(25 ×25)
expand the bracket, we have;
Surface area = 1250 + 200 + 1250
Surface area = 2700 cm²
b. Surface area of the pyramid = √3/ 2a²
Substitute the value
Surface area = √3 /2 × 18²
Find the square, we have;
Surface area = 280. 6 cm²
c. The total surface area to be painted ;
= 675 + √3/4a²
= 675 + 140.3
= 815. 3 cm²
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If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.
If the bank is open, then people may make withdrawals or deposits.
Therefore, if …
Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits at the bank.
This conclusion is based on the given premises that the bank is open during the time between 8:00 a.m. and 3:00 p.m. and that when the bank is open, people may make withdrawals or deposits. By combining these premises with modus ponens (a valid form of deductive reasoning), we can infer that if the time is within the bank's operating hours, then people may make withdrawals or deposits at the bank.
what is the volume of the rectangular prism length =9m width = 12m height =5m
The volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.
To find the volume of a rectangular prism, we multiply its length, width, and height.
Given that the length is 9m, the width is 12m, and the height is 5m, we can calculate the volume as follows:
Volume = Length x Width x Height
Substituting the given values:
Volume = 9m x 12m x 5m
To perform the multiplication, we can multiply the numerical values first and then consider the units:
Volume = (9 x 12 x 5) m³
Multiplying the numbers:
Volume = 540 m³
Therefore, the volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.
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-1
-2
The lengths of movie files that are available for streaming are modeled using the normal distribution shown below.
The mean of the distribution is 170.8 min and the standard deviation is 19.7 min.
100
in the figure, Vis a number along the axis and is under the highest part of the curve.
And, U and Ware numbers along the axis that are each the same distance away from V.
Use the empirical rule to choose the best value for the percentage of the area under the curve that is shaded, and find the values of U, V, and W.
Continue
3
0
U
120
Percentage of total area shaded: (Choose one)
140
160
180
V
Time (in min)
200
220
0 240
W
3
Answer:
the best value for the percentage of the area under the curve that is shaded is 68%.
Step-by-step explanation:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 170.8 min and the standard deviation is 19.7 min, we can calculate the values of U, V, and W.
U: U is one standard deviation below the mean.
U = Mean - 1 * Standard Deviation
U = 170.8 - 1 * 19.7
U ≈ 151.1
V: V is the mean.
V = Mean
V = 170.8
W: W is one standard deviation above the mean.
W = Mean + 1 * Standard Deviation
W = 170.8 + 1 * 19.7
W ≈ 190.5
Now, let's determine the best value for the percentage of the area under the curve that is shaded. Based on the empirical rule, the highest percentage that can be shaded is approximately 68% since it represents the data within one standard deviation of the mean.
Therefore, the best value for the percentage of the area under the curve that is shaded is 68%.
The graph represents the piecewise function: f (x) ={ , if -3
The domain and the range of the function are
Domain = (-∝, ∝)Range = (0, ∝)How to determine the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph is a piecewise function
When combined gives an absolute function
The rule of a function is that
The domain is the set of all real numbers
This means that the input value can take all real values
However, the range is greater than the constant term
In this case, it is 0
So, the range is y > 0
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Question
The graph represents the piecewise function:
f(x) =
What is the domain and range of the function
The shape is being enlarged using a scale factor of 2 and centre (6,3).
The coordinates of A' and B' include the following:
A' (4, 7).
B' (10, 9).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (6, 3) by using the following mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate A', we have;
Coordinate A' = (5, 5) → (2(5 - 6) + 6, 2(5 - 3) + 3)
Coordinate A' = (5, 5) → (2(-1) + 6, 2(2) + 3)
Coordinate A' = (5, 5) → (-2 + 6, 4 + 3)
Coordinate A' = (5, 5) → (4, 7)
For coordinate B', we have;
Coordinate B' = (8, 6) → (2(8 - 6) + 6, 2(6 - 3) + 3)
Coordinate B' = (5, 5) → (2(2) + 6, 2(3) + 3)
Coordinate B' = (5, 5) → (4 + 6, 6 + 3)
Coordinate B' = (5, 5) → (10, 9)
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Simplify the following expression, and then find its value.
The simplified expression is 6 raised to the power of
.
The value of the simplified expression is
.
The simplified expression is 1,675,616. the value of the expression is 1,675,616.
To find the simplified expression and the value of 6 raised to a power, follow the steps given below:
Step 1: Simplify the expression Firstly, the simplified expression is obtained by using the rule of exponents, which states that if a number raised to a power is multiplied by the same number raised to another power, then the resulting power is the sum of the two powers.
6 raised to the power of 2 is 6 × 6 = 36.6 raised to the power of 3 is 6 × 6 × 6 = 216.6 raised to the power of 4 is 6 × 6 × 6 × 6 = 1296.6 raised to the power of 5 is 6 × 6 × 6 × 6 × 6 = 7776.
Step 2: Find the value of the expression
From these results, it can be seen that when 6 is raised to an even power, the resulting number is even, and when 6 is raised to an odd power, the resulting number is odd. This is because 6 is an even number.
In general, if a number is even, then the result obtained when it is raised to an even power is even, and the result obtained when it is raised to an odd power is odd.
If a number is odd, then the result obtained when it is raised to any power is odd. 6 raised to the power of 8 can be written as 6 raised to the power of 4 raised to the power of 2, as shown below 6 raised to the power of 8 = (6 raised to the power of 4) raised to the power of 2= 1296 raised to the power of 2= 1,675,616
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Statements
1
Quadrilateral ABCDwith m/A= (10z), m/B= (8x), m/C= (10z)",
and m/D= (8x)".
2 m/A+m/B+m/C+m/D=360°
3 (10x)+(8x) + (10x) + (8x) = 360°
4
5 x=10
Reasons
Given
Substitution Property
Combine like terms
We can solve for x:
20z + 16x = 360°
16x = 360° - 20z
x = (360° - 20z)/16
Quadrilateral ABCD is given with the measures of angles:
m∠A = 10z
m∠B = 8x
m∠C = 10z
m∠D = 8x
The sum of the measures of the angles of a quadrilateral is 360°:
m∠A + m∠B + m∠C + m∠D = 360°
Substituting the given angle measures:
(10z) + (8x) + (10z) + (8x) = 360°
Combine like terms:
20z + 16x = 360°
Given the equation from step 4, we can solve for x:
20z + 16x = 360°
16x = 360° - 20z
x = (360° - 20z)/16
Reasons:
Step 1: The given angles are labeled with their corresponding measures.
Step 2: The sum of the measures of the angles of a quadrilateral is a geometric property.
Step 3: Substitution of the given angle measures into the equation for the sum of angles.
Step 4: Combining like terms by adding the coefficients of z and x.
Step 5: Solving the equation for x by isolating it on one side.
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find f o g and g o f
f(x)= x^3, g(x)=x^2/3
Answer:
f(g(x)) = f((x^2/3)
(x^2/3)^3
continue solving
A particular restaurant can legally have only 150 people in it at one time. The tables in the restaurant can seat 4 people at a time. The number of tables, t, in the restaurant can be represented by the inequality 4t < 150. What is the maximum number of tables the restaurant can have?
.
The maximum number of tables the restaurant can have is 37. This ensures that the total number of people seated at the tables (37 * 4 = 148) is less than the legal limit of 150 people in the restaurant at one time.
To find the maximum number of tables the restaurant can have, we need to solve the inequality 4t < 150.
Dividing both sides of the inequality by 4, we have:
t < 150/4
Simplifying the right side, we get:
t < 37.5
Since the number of tables must be a whole number, we can conclude that the maximum number of tables the restaurant can have is 37.
Let's verify this by substituting t = 37 into the original inequality:
4t < 150
4(37) < 150
148 < 150
Since 148 is less than 150, the inequality holds true. However, if we increase the number of tables to 38, we get:
4(38) < 150
152 < 150
In this case, 152 is not less than 150, so the inequality is no longer satisfied.
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