Answer:
x + 2 (Choice D)
Step-by-step explanation:
The two polynomials are
P1 = 4x² + 5x - 4
and
P2 = 4x² + 4x - 2
P1 - P2
==> (4x² + 5x - 4 ) - (4x² + 4x - 2)
Expanding brackets we get
==> 4x² + 5x - 4 - 4x² - 4x + 2 (signs inside the second parentheses are
reversed because of the - sign preceding it)
Group similar terms and add the coefficients
==> (4x² - 4x²) +(5x - 4x) +(-4 + 2)
==> 0 + x + 2
==> x + 2 (Choice D)
Question 13
Find the equation in standard form of the line with slope -4/7
that passes through the point (5,1).
Put the left side of the equation in the first answer box and the right side of the equation in the second
answer box.
Note that in standard form all the coefficients should be integers and the coefficient on x should be
positive.
Answer:
4x + 7y = 27
Step-by-step explanation:
The slope-intercept form of the equation of a line is
y = mx + b
Here m = slope which is the rate of change of the y-value with respect to x and b is the y-intercept which is the y-value where the line crosses the x-axis. It is therefore the value of y when x = 0
We are given slope = -4/7
So equation of line is
y = (-4/7)x + b
To find b, notice that the given point is (5, 1) which indicates that at this point x = 5, y = 1
If we plug in x = 5 in the equation we should get a y0value of 1
We can rewrite y = (-4/7)x + b as
(-4/7)x + b = y
Substitute x=5 and y = 1
(-4/7)(5) + b = 1
-20/7 + b = 1
b = 1 + 20/7
b = 27/7
So the equation of the line in slope intercept form is
[tex]\quad y=-\dfrac{4}{7}x+\dfrac{27}{7} \cdots (1)[/tex]
The standard form of a line equation is
Ax + By = C
We can convert equation (1) to standard form by tweaking it
Multiply eq (1) throughout by 7:Decide wether the points are vertices of a right triangle. (1,2),(3,0),(3,3)
Please help solve this question!
Answer:
lesser number: 9
greater number:41
Step-by-step explanation:
Given: a+b=50
Use the word problem to create equation: 5a-4=b
We can solve for either variables, we'll solve for b(greater number) first:
a=50-b
Plug a into other equation:
5(50-b)-4=b
250-5b-4=b
246-5b=b
246=6b
b=41
Plug what we found for b into equation to solve for a(lesser number):
a+41=50
a=9
Verify:
5(9)-4=41 ?
45-4=41
41=41 Checks out.
Hope this helps.
the combined weight of the people on a bus is 1316 kilograms. how much is that in metric tons
Here is a list of equations. Circle all the equations that are identities. Be prepared to
explain your reasoning.
1. a = -a
2. a² + 2ab + b² = (a + b)²
3. a² - 2ab + b² = (a - b)²
4. a²b² = (a - b)(a - b)
5. (a + b)(a²- ab + b²) = a³ - b³
6. (a - b)³=a³-b³-3ab(a + b)
7.a²(a - b)4-b²(a - b) = (a - b)²(a + b)
Answer:
2356
Step-by-step explanation:
HELP ME OUT PLEASE!!!!!!
The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The domain means all the possible values of x and the range means all the possible values of y.
The equation is given below.
y = -2x² + 12x - 13
Convert the equation into a vertex form, then we have
y = -2x² + 12x - 13
y = -2x² + 12x - 18 + 18 - 13
y = -2(x² - 6x + 9) + 18 - 13
y = -2(x - 3)² + 5
The range of the function y = -2x² + 12x - 13 will be [5, -∞). Then the correct option is A.
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identify the transformation of the following functions from the parent function f(x)= 1/x
The parent function is the simplest form of the type of function in the graph is g(x) = 1/x
What is graph ?
In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
y = a / x-h + k
Find a, h and k for
g(x)= 1/x
a = 1
h=0
k = 0
The horizontal shift depends on the value of h and The horizontal shift is described as :
f(x) = f(x+h) The graph is shifted to the left h units
f(x) = f(x-h) The graph is shifted to the right h units.
Horizontal shift depends on the value of k and The horizontal shift is described as :
f(x) = f(x+k) The graph is shifted to up k units
f(x) = f(x-k) The graph is shifted down k units.
Vertical shift : none.
The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.
Reflection about the x-axis: None
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function: g(x) = 1/x
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Hence, The parent function is the simplest form of the type of function g(x) = 1/x .
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Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
When m8 = m4
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.
When m8 = m4, the line segments are parallel.
When two line segments have the same slope (m8 = m4), then the line segments are parallel. Therefore, the statement that the line segments are parallel can be deduced if m8 and m4 are equal.
When two line segments have the same slope, then they will be parallel to each other. This can be deduced when the slopes of both line segments are equal, which is represented by m8 = m4. If the two line segments have the same slope, then they will be parallel to each other and will never meet or intersect. This is because parallel lines always have the same slope and never touch each other. In conclusion, the statement that two line segments are parallel can be deduced if m8 and m4 are equal.
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Pls help me with this question, the answer is not 278.63 square units
Answer:
375 square units
Step-by-step explanation:
Area = (1/2) h (a+b)
=1/2 × 10 (49+26)
= 5 × 75
= 375 square units
hope it helps you <3
The radius of a circle is 1 mile. What is the circle's circumference?
Answer:
Circumference = 2π
Step-by-step explanation:
The formula for a circle's circumference is:
C = 2πr
Here is a quick breakdown:
C = circumference
r = radius
Since we are given that the radius is 1 mile, we can plug in r into the formula above:
C = 2π(1)
C = 2π
A constant unit force vector makes angle 30 with the positive x - axis. Find the work done by the force in moving the object 17 units in the direction of the positive x - axis. g
Answer:
The work done by the constant unit force vector in moving the object 17 units in the positive x-axis direction is equal to the magnitude of the force multiplied by the displacement in the direction of the force. Since the force makes an angle of 30 degrees with the x-axis, the magnitude of the displacement in the direction of the force is equal to the displacement in the x-axis direction multiplied by the cosine of 30 degrees. Therefore, the work done is equal to the magnitude of the force multiplied by 17 multiplied by the cosine of 30 degrees. hope this helped
Suppose that you have a square pyramid like the one pictured. Which plane section will produce a triangle? Question 2 options: A) A cross section cut parallel with the bottom B) Cutting off one of the bottom corners C) A cut parallel to the vertical axis, directly through the vertical axis D) A cut parallel to the vertical axis, but off the vertical axis
A cut parallel to the vertical axis, directly through the vertical axis. Option C is correct.
What are axes?Axes for the figure are defined as the imaginary lines that toward which measurement of the figures are taken.
Here,
When cutting the pyramid through axis perpendicular axis to the vertical axis, the shape produced would be a quadrilateral. But when we cut the pyramid through the vertical axis it produces the triangle.
Thus, a cut parallels the vertical axis, directly through the vertical axis. Option C is correct.
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The bullseye on an archery target has a radius of 3 inches. The entire target has a radius of 9 inches. To the nearest hundredth, find the area of the target outside of the bullseye. Use 3.14 for π.
Answer:
226.1 [tex]in^{2}[/tex]
Step-by-step explanation:
Tommy's four dogs, Fido, Jack, Sam, and Lilly, went to the vet to be weighed. Fido weighed 27 pounds, Jack weighed 37.5 pounds, Sam weighed 53 pounds, and Lilly weighed 16 pounds.
What is the total weight of the four dogs?
A.103 pounds
B. 147.9 pounds
C.112.9 pounds
D.122.9 pounds
Answer: 133.5
Step-by-step explanation:
Add the weights together and, for some reason, you get 133.5
Answer:
133.5 pounds------------------------------------
Add the four numbers together to get the total weight:
27 + 37.5 + 53 + 16 = 133.5 poundsIt doesn't match any options, please double check if they are (or given weights) correct.
A true-false question is to be posed to a husband-and-wife team on a quiz show. Both the husband and the wife will independently give the correct answer with probability p. Which of the following is a better strategy for the couple?
a.) Choose one of them and let that person answer the question.
b.) Have them both consider the question, and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to give.
If p = .6 and the couple uses the strategy in part (b), what is the conditional probability that the couple gives the correct answer given that the husband and wife..
c.) agree?
d.) disagree?
The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6 and if husband wife don't agree is p=0.5, and statement B is the better strategy.
Option B, have them both consider the question, and then either give the common answer if they agree or, if they disagree, flip a coin to determine which answer to give is the better strategy.
c.) The conditional probability that the couple gives the correct answer if the husband and wife agree is p = .6.
d.) The conditional probability that the couple gives the correct answer if the husband and wife disagree is 0.5. This is because in this case, they must flip a coin to decide which answer to give.
Since the probability of both parties giving the correct answer is p = .6, but the probability of either party giving the correct answer is only 0.5,
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Write the equation of the line that passes through the points (-3, 3) and (1, 2).
The system shown has the unique solution (2, y, z). Solve the system and select the values that complete the solution. y = 0 y = 2 y = 3 z = 0 z = 2 z = 3
The required solution of the equations is given as (2, 3, 0).
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
So we are given a system,
3x -2y + 3z = 0
-3x-5y-5z = -21
Substitute x =2, and we get the system,
-2y + 3z = -6
-5y -5z = -15
Multiply equation 1 by -5 and equation 2 by 2 we get the system,
10y - 15z = 30
-10y -10z = -30
Adding the above equations,
z = 0
Now,
-2y = -6
y = 3
Thus, the required solution of the equations is given as (2, 3, 0).
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If the length of a rectangular field is 7 feet less than six times its width, and the perimeter is 140 feet.
Length of a rectangular field is_____
feet.
From the given data, using perimeter of rectangle, Length(L) = 6 × 11 - 7 of the rectangular field.
The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. P = x+x+y+y, where P is the perimeter.
Let length of the rectangular field = L
Width of rectangular field = W
Given,
length of a rectangular field is 7 feet less than six times its width
perimeter is 140 feet,
According to the question,
L = 6W - 7
Perimeter of the rectangle = 2 (L + W)
140 = 2 (6W - 7 + W)
140 = 2 (7W - 7)
70 = 7 W - 7
77 = 7 W
W = 11
L = 6 × 11 - 7
Length = 59
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A desk drawer contains the different-colored markers listed below. . 12 green markers . 4 blue markers . 20 red markers A marker will be randomly selected from the drawer and it is not replaced. Then another marker will be randomly selected from the drawer. What is the probability that a blue marker will be selected then a red marker?
Answer:
Step-by-step explanation 0% because there is more red markers
Answer: (Don't read this if this is a test)
Step-by-step explanation: I might get this wrong because I was kind of confused too (sorry if I am!)
Hello! The first thing you would want to do for these kinds of questions is to write the probability of a green, blue, or red marker being picked as a fraction. To do this, add 12 + 4 + 20 which is 36.
The probability of picking a green marker - 12/36, partially simplified = 3/9
The probability of picking a blue marker - 4/36, simplified = 1/9
The probability of picking a red marker - 20/36, simplified = 5/9
G - 3/9
B = 1/9
R = 5/9
You know that the probability of picking a blue marker is 1/9. Once you know this, you can figure out the new probability of picking a red marker since the blue marker won't be replaced. The answer is 4/35. Multiply 1/9 by 4/35 to find the probability of picking one after the other and you will get 4/315.
Given (b - 3)( 3b + 8)(2b + 5) = 0, which factor(s) must equal zero?
Here b is =0, According to the Zero Product Property, if ab=0, then either a=0 or b=0 (or both). If and only if one or more of the factors in a product are zero, the product is zero. This is very helpful when attempting to solve quadratic problems.
What is zero product property?The product of two nonzero items is not zero, according to the algebraic definition of the zero product property. In other terms, the following claim:
According to the zero product rule, if the product of any number of expressions is 0, then at least one of them must also be zero.Either p or q must equal zero if pq = 0.The nonexistence of nontrivial zero divisors, the zero product rule, the zero multiplication property, the null factor law, and one of the two zero factor properties are other names for the zero product property.All number systems, including rational numbers, integers, real numbers, and complex numbers, satisfy the zero product rule. A domain is, in general, a ring that meets the zero property.To know more about zero product property,refer to:
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If you need to take out a $80,000 student loan 2 years before duating, which loan option will result in the owest overall cost to you: a subsidized loan with 7.4% Interest for 10 years, a federal unsubsidized loan with 9% interest for 10 years, or a private loan with 5.0% interest and a term of 15 years? How much would you ave over the other options? All payments are deferred for 6 months after graduation and the interest is apitalized. Part: 0/5 Part 1 of 5 (a) Find the total cost of the subsidized loan. The total cost of the subsidized loan is S decimal places, if necessary. 10 Round your answer to two
Answer:
$139,200
Step-by-step explanation:
To find the total cost of the subsidized loan, we need to calculate the total amount of interest that will be added to the loan over the 10-year repayment period. We can use the formula for simple interest:
I = Prt
Where:
I = Interest
P = Principal (the original loan amount)
r = Interest rate (expressed as a decimal)
t = Time (in years)
In this case:
I = 80,000 * 0.074 * 10 = 59,200
The total cost of the loan would be the sum of the principal and the interest:
80,000 + 59,200 = $139,200
So the total cost of the subsidized loan is $139,200.
each question has a proposition r that is a conditional statement. truth values are also given for the individual propositions contained in that conditional statement. indicate whether the conditional statement r is true or false.
Answer: The truth value of a conditional statement can be determined by using the truth table for the conditional operator (->). The truth table for the conditional operator is as follows:
p q p -> q
T T T
T F F
F T T
F F T
To determine the truth value of a conditional statement r, you need to know the truth values of the individual propositions contained in r. Once you have the truth values of the individual propositions, you can use the truth table to determine the truth value of the entire conditional statement. If the conditional statement is true, then it is represented by "T", otherwise it is "F".
Step-by-step explanation:
Which pair of variables is two different scales of measure and why?
Question options:
number of goals scored and penalty minutes
height and IQ
lipstick shades and brands of athletic shoes
laptop price ($) and memory capacity (GB)
The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.
What is the variable?
A variable is a quantity that may be changed according to the mathematical problem. The generic letters which are used in many algebraic expressions and equations are x, y, z. In other words, a variable is a symbol for a number where the value is not known. For example, x + 5 = 10. Here “x” is a variable.
This is because "laptop price" is measured in dollars, which is a monetary unit, and "memory capacity" is measured in GB (gigabytes), which is a unit of data storage.
These are two different types of measurement and cannot be directly compared.
On the other hand, "a number of goals scored" and "penalty minutes" are both measures of performance in a sport and can be directly compared.
"Height" and "IQ" are both measures of human characteristics, although they are different in nature, but they can also be compared.
"lipstick shades" and "brands of athletic shoes" are both consumer products, but they are not directly related and cannot be compared.
Hence, The pair of variables "laptop price ($) and memory capacity (GB)" are two different scales of measure.
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Dr. Hall is studying an endangered fox whose population is declining by 20% every year. If there are currently 3,746 foxes, how many will remain in 4 years?
If necessary, round your answer to the nearest whole number.
Using exponential function, The total number of foxes that will remain after 4 years is 1534.
What is Exponential Function?A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
We employ the exponential function because...
In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
Using exponential function,
P(t) = A . b^t
Formulate: 3746 based on the provided conditions. (1 - 20%) ⁴
Analyze the following formula or expression: 1534.3616
he total number of foxes that will remain after 4 years is 1534
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flu epidemic hits a town. Let P(t) be the number of persons sick with the flu at time t, where time is measured in days from the beginning of the epidemic and P(0)=100. After t days, if the flu is spreading at the rate of P′(t)=120t−3t2 people per day, find the formula for P(t)
The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.
P(t) = 100 + 120t - 3t^2
This formula can be used to calculate the number of people sick with the flu at time t, where time is measured in days from the beginning of the epidemic. The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.
To calculate P(t), the initial number of people sick with the flu, 100, is added to the rate of increase of the number of people sick with the flu over t days, which is 120t - 3t^2. The sum of these two values is the number of people sick with the flu at time t.
For example, at t=2 days, P(2) = 100 + 120(2) - 3(2^2) = 100 + 240 - 12 = 328 people sick with the flu.
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Translate the following sentence into a mathematical equation. Use A to represent the area, and C to represent the circumference. The area of a circle is the product of the number 1/4(pi) and the square of the circumference 
The expression is A = (1/4 pi) * (C^2) when The area of a circle is the product of the number 1/4(pi) and the square of the circumference.
What is Area of circle?
Area of circle can be defined as the product of pi and square of radius of a circle.
Given ,
we have transform the sentence into a mathematical equation
so A is used to represent the area
and C is used to represent the circumference
And condition is
The area of a circle is the product of the number 1/4(pi) and the square of the circumference
SO,
A = (1/4 pi) * (C^2)
Hence, The expression is A = (1/4 pi) * (C^2) when The area of a circle is the product of the number 1/4(pi) and the square of the circumference.
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A manufacturer is shipping a spherical globe that fits exactly in a cube shaped box. The globe is touching all six sides of the box. If the volume of the box is 2197 in³. What is the volume of the globe?
Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic inch only on the end.
The volume of the sphereical globe is 1564in³
What is the volume?We know that when we talk about the volume we have to look at the volume of the box. Let us assume that the box in the problem that we have here is a cubic box, it the follows that the volume of the box is obtained from;
6l^3 = 2197in³
Where l is the length of each side in inches
l = ∛ 2197/6
l = 7.2 inches
This is the radius of the spherical globe
Volume of a sphere = 4/3πr^3
V = 4/3 * 3.142 * (7.2)^3
V = 1564in³
Hence 1564in³ is the volume of the globe.
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DUE SOON please need as much help as possible!!
questions are down below please explain how you got the answer!!
Answer:
Va=4r³π
Step-by-step explanation:
Vb=(4/3)r³π, Vc=r²πh, h is the height of the cylindrical container.
h=12r.
So now the volume of the cylinder is:
Vc=r²π*12r=12r³π.
There are 6 balls so their total volume is:
6*Vb=6*(4/3)*r³*π=(24/3)*r³π=8r³π.
Now we subtract the volume of 6 balls from the volume of the cylinder to get the volume of air Va inside the cylinder:
Va=Vc-6*Vb=12r³π-8r³π=4r³π.
So the volume of air inside of the cylinder is Va=4r³π
Hope This Helps!
Answer:
Volume of air = 4πr³ (units cubed)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Model the squash ball as a sphere.
Assuming the six squash balls are packaged in a cylindrical container where each ball is one on top of the other, the height of the container is 6 times the height of a squash ball.
The height of a squash ball is its diameter, which is twice its radius.
Therefore, the height of the cylinder is 12 times the radius of the squash ball, and the radius of the cylinder is the radius of the squash ball.
Therefore:
[tex]\begin{aligned}\textsf{Volume of the cylinder}&=\pi r^2 \cdot 12 r\\&=12 \pi r^3\end{aligned}[/tex]
where r is the radius of the sphere (squash ball).
To find the volume of air inside the container, subtract 6 times the volume of a sphere from the volume of the cylinder.
[tex]\begin{aligned}\textsf{Volume of air}&=\textsf{Volume of cylinder}-\textsf{6 volume of sphere}\\&=12\pi r^3-6\left(\dfrac{4}{3} \pi r^3\right)\\&=12\pi r^3-8\pi r^3\\&=4\pi r^3\;\; \sf units \; cubed\end{aligned}[/tex]
if the radius is 10 ft,what will be the area of the circle?
The area of the circle having a radius of 10 ft will be 100π.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Given that the radius of the circle is 10 ft. The area of the circle is calculated by the formula written as below,
Area of the circle = πr²
Substitute the value of the radius in the formula and calculate the area of the circle.
Area of the circle = πr²
Area of the circle = π x ( 10 ) ²
Area of the circle = 100π square ft
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Question 6
Find the measure of each angle indicated
The measure of angle ∠B is 44°.
What is the measure of all angles in a triangle?
A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.
We have given,
Triangle ΔABC,
and angles ∠ACB = 90°, ∠CAB= 46°, and ∠ABC = ?
We know that the sum of all angles in the triangle is 180°.
So,
∠ACB + ∠CAB + ∠ABC = 180°
90° + 46° + ∠ABC = 180°,
136 + ∠ABC = 180°,
∠ABC = 180° - 136
∠ABC = 44°,
Hence, the measure of angle ∠B is 44°.
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