The equation that represent the situation is as follows;
3x + 2y = 34
1 / 2x + 2y = 14
The two number Diego is thinking of are 8 and 5.
How to use equation to represent a problem?He is thinking of two positive numbers.
If we triple the first number and double the second number, the sum is 34.
If we take half of the first number and double the second, the sum is 14.
Therefore, the equation that can be used to solve the situation is as follows:
let
x = first number
y = second number
3x + 2y = 34
1 / 2x + 2y = 14
Therefore,
3x + 2y = 34
1 / 2x + 2y = 14
5 / 2 x = 20
5x = 40
x = 40 / 5
x = 8
3(8) + 2y = 34
2y = 34 - 24
2y = 10
y = 10 / 2
y = 5
Therefore, the two numbers are 8 and 5.
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Write the conditional
statement in if-then form.
The vertices of a triangle
are not colinear.
The conditional statement for "The vertices of a triangle are not collinear" is "if the points are not collinear then they are vertices of triangle."
What is conditional statement?Conditionals are commands used in programming languages to handle choices. Particularly, conditionals carry out various calculations or actions based on whether a boolean condition defined by the programmer evaluates to true or false.
What is if-then?The hypothesis is a prediction of what will transpire in your experiment. The words "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will fail the test if I don't study." Your independent and dependent variables are reflected in the "if" and "then" statements.
"The vertices of a triangle are not collinear" has a conditional statement that reads, "If the points are not collinear, then they are vertices of the triangle."
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standard deviation for binomial distribution n=48 p=3/5
If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.
What is the Standard deviation?Using this formula to determine or find the standard deviation for the binomial distribution
σ =√np(1−p)
Where:
n = 48
p = 3 / 5 or 0.6
σ = ?
Let plug in the formula so as to determine the standard deviation
σ =√ (48) (0.6) ( 1 - 0.6)
σ =√ (48) (0.6) (0.4)
σ =√ 11.52
σ = 3.39
Therefore we can conclude that 3.39 is the standard deviation.
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A survey showed that of college students read internet news on a regular basis and that of college students regularly watch the news on TV. The survey also showed that of college students both follow TV news regularly and read internet news regularly.
(a)What is the probability that a student watches TV news regularly, given that he or she regularly reads internet news? Round your answer to the nearest hundredth.
(b)What is the probability that a randomly selected college student reads internet news regularly, given that he or she watches TV news regularly? Round your answer to the nearest hundredth.
For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.
According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.
Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.
(A) Given that a student reads newspapers frequently,
The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)
= 0.20/0.24 = 0.833
(b) Given that a randomly chosen college student watches TV news frequently
The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)
= 0.20/0.83 = 0.240
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Which words describe the polynomial? (Select all that apply) * (1 Point)
f (x) = x^4 - 2
quartic
trinomial
cubic
quadratic
binomial
A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
What is meant by Quartic polynomial?A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.
A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.
Therefore, the correct answer is option a) quartic.
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So what's in the photo is what I need help with.
Answer:
1 == B No Solutions
2 == A One Solution
3 == C Infinitely Many Solutions
Explanation:
We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.
1.
x
The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w
The area of a rectangle is calculated using the formula:
[tex]A=l\times w[/tex]where l is the length and w is the width.
The functions for the length and width are given to be:
[tex]\begin{gathered} l(x)=2x+1 \\ w(x)=x+4 \end{gathered}[/tex]Therefore, the area of the rectangle will be:
[tex]A=(2x+1)(x+4)[/tex]We can apply the FOIL Method:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Therefore, we have:
[tex]\begin{gathered} \left(2x+1\right)\left(x+4\right)=2x\cdot x+2x\cdot\:4+1\cdot\:x+1\cdot\:4 \\ =2x^2+8x+x+4 \end{gathered}[/tex]Simplifying, the area is:
[tex]a(x)=2x^2+9x+4[/tex]The SECOND OPTION is correct.
Noah operates an orange juice stand. On Monday he used 3 3/10 bags of oranges. On Tuesday he used 1/6 as many oranges as on Monday. How many bags of oranges did Noah use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
The number of bags of oranges Noah used on Tuesday as required to be determined in the task content is; 11/20 bags of oranges.
What is the number of bags of oranges used by Noah on Tuesday?It follows from the task content that Noah used 3 3/10 bags of oranges on Monday.
Hence, by expressing the mixed number, 3 3/10 as a fraction; we have; 33/10.
Therefore, since he uses 1/6 as many oranges as on Monday on Tuesday;
The number of bags of oranges used on Tuesday is; (1/6) × 33/10
= 33/60
= 11/20.
Therefore, the number of bags of oranges Noah uses on Tuesday is; 11/20.
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ng waffles for breakfast. The recipe calls for 1/2 cups of water for every 2Jemina pancake mix. How many cups water would he need for only oneake mix? Show your work
Ratio:
cups of water / pancake mix = (1/2) / 2
For 1 pancake mix, x cups of water:
x / 1 = (1/2) / 2
Solve for x, cross multiply:
2x = ( 1/2) 1
2x = 1/2
Divide both sides by 2
2x/2 = (1/2) / 2
x = 1/4
Answer:
She would need 1/4 cups of water
what is a root of a parabola?
The roots of a prabola is where the function intersects the x-axis.
In december 2004 35% of student in the high school were satisfied with the lunches supplies through the school of the 856 survey, 265 inducted they were satisfied does this suggests the proportion of student satisfied with the quality of lunches has decreased
What does it means to make a type 2 error for the test
When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.
A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.
The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.
The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.
In essence, a type II error is a false negative.
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Help step by step pleaseeee
The graphic below includes the graph of the provided question.
The horizontal axis is x-axis
The vertical axis is y-axis.
How do collinear points work?Points that are situated along the same straight line but within a single line are known as collinear points. Two or more points in Euclidean geometry are said to be collinear if they are situated on a line that is either close to or far from one another.
In light of the information provided:All the points necessary to solve the equation will be positive and negative in turn, and that point will form a straight line through the origin, indicating that all the points are collinear.
You can change the value to fit your graph in the diagram that corresponds to the graph for the question that is attached below.
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21. Complete the following transactions and explain how they would appear in your register.
(5 points each - 2 points for the correct answers and 3 points for a correct explanation of your
process)
• You open your bank account on April 16 with a tax refund check of $145.00.
You pay Sell Phone $65.34 on April 18. (Check 794)
• You deposit your paycheck on April 23. ($9.76 hour for 35 hours)
• You buy $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24
using your debit card.
Be sure to include in your response:
.
• the steps you followed to complete your computations
the balance as of April 24
• the process for entering the transaction in the registry
(5 points)
After all the transaction, money left in the bank account is $15.8872.
Given that, you open your bank account on April 16 with a tax refund check of $145.00. You pay Sell Phone $65.34 on April 18.
What is a tax refund check?A tax refund is a reimbursement to a taxpayer for any excess amount paid to the federal government or a state government.
On April 16th balance in the account = $145.00 cost of phone = $65.34 on April 18.
Balance on April 18 = 145.00-65.34
= $79.66
Deposited check $9.76 on 23rd April for 35 hours
Balance on 23rd April = 79.66+9.76
=$89.42
Since, the check deposited only for 35 hours, again balance on 24th April will be $79.66
On 24th April you brought clothes from BargainsRUs for
61.32+4% of 61.32
= 61.32+2.4528
= $63.7728
So, the remaining balance in the account = 79.66-63.7728
=$15.8872
Therefore, after all the transaction, money left in the bank account is $15.8872.
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Transforming the graph of a quadratic, cubic, square root, or absolute value function
Explanation:
If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.
If g(x) = f(x) - c, g(x) will be f(x) shifted c units down
If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.
In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then
g(x) = -f(x + 3) - 2
Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.
Answer:
So, the graph for y = -|x + 3| - 2 will be:
a bond issue outstanding that matures in 19 years. The bonds pay interest semiannually. The bonds have a face value of $1,000 and are currently priced at $995.28. The bonds carry a coupon rate of 3.5 percent. What is the aftertax cost of debt if the total tax rate is 22 percent? Multiple Choice
The after tax cost of debt for the bond is 2.73%
Given,
The face value of the bond, FV = $1000
Present value of the bond, PV = $995.28
Maturity period = 19 years
Coupon rate = 3.5%
Total tax rate = 22%
We have to find the after tax cost of debt for the bond.
The bond pays interest semiannually ;
so coupon rate = 3.5/2 = 1.75
Coupon payment , pmt= 0.0175 x 1000 = $17.5
Maturity, nper = 19 years x 2 = 38
Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)
Then,
= RATE(38, 17.5, -995.28, 1000)
Rate or yield is computed as 3.5%
The present value is negative as it is a cash outflow.
The cost of debt is 3.5%
The tax rate is 22%
After tax cost of debt = 3.5 (1 - 0.22) = 2.73%
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what is 5 to the 6 power written in expanded form
5 to the 6th power is:
[tex]5^6[/tex]This, written in expanded form, is:
[tex]5\cdot5\cdot5\cdot5\cdot5\cdot5[/tex]What are the X and Y intercepts for the graph shown in the picture?
Based on the given figure, you can conclude:
x-intercepts:
x = 0
x = number in between 100 and 125, approximately 105
x = number greater than 175, approximately 180
y-intercepts:
y = 0
For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.
I need help solving an answering this practice problems from my pre-calculus prep guide
The general formula of a geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]where,
n = 6
a₁ = -8100
r = -0.1
Replacing on the formula:
[tex]\begin{gathered} a_6\text{ = -8100}\times(-0.1)^{6-1} \\ a_6\text{ = 0.081} \end{gathered}[/tex]Can somebody please help me right now??? i’m stuck and i need help with this bad
Answer:
Is wolfgang Mozart's
Step-by-step explanation:
The central traits of the Classical style are all present in Mozart's music. Clarity, balance, and transparency are the hallmarks of his work, but simplistic notions of its delicacy mask the exceptional power of his finest masterpieces, such as the Piano Concerto No. 24 in C minor, K.
What do the 2 points on the graph mean in terms of the situation
Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.
Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.
Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.
The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).
The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).
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For each graph below, state whether it represents a function.
Graph 1: No, because it fails the vertical line test.
Graph 2: No, because it fails the vertical line test.
Graph 3: Yes, because it passes the vertical line test.
Graph 4: Yes, because it passes the vertical line test.
Graph 5: No, because it fails the vertical line test.
Graph 6: Yes, because it passes the vertical line test.
5x+2y=10 Does the relation represents a function
Answer:
Yes, it is a linear function. For every input there is only 1 output.
Step-by-step explanation:
Use the above data to calculate the correlation coefficient Answer Choices.0.890.94-0.89-0.94
Using the table, we have the following points:
(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)
Let's find the correlation coefficient.
To find the correlation coefficient, apply the formula:
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-\Sigma(x)^2)(n}\Sigma y^2-\Sigma(y)^2)}[/tex]Where:
n = 5
Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5
Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23
Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85
Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75
Σy² = 109.6
Plug in values in the formula and solve for r.
We have:
[tex]\begin{gathered} r=\frac{5(108.85)-(22.5)(23)}{\sqrt{(5(109.75)-22.5^2)(5(109.6)-(23)^2}} \\ \\ r=0.94 \end{gathered}[/tex]Therefore, the coefficient is 0.94
ANSWER:
0.94
Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
What are transformation ?There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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Simplify. DO NOT PUT ANY SPACES IN YOUR ANSWER. - 3\4 (16r-24)
Explanation
[tex]-\frac{3}{4}(16r-24)[/tex]Step 1
eliminate the parenthesis applyng distributive property
[tex]\begin{gathered} -\frac{3}{4}(16r-24) \\ \frac{-3\cdot16r}{4}+\frac{3\cdot24}{4} \\ \frac{-48r}{4}+\frac{72}{4} \\ -12r+18 \end{gathered}[/tex]I hope this helps you
Suppose a triangle has sides a, b, and c, and that a² + b² < c². Let 9 be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
A. The triangle is not a right triangle.
B. cose < 0
C. cose > 0
□ D. a² + b²-c² = 2abcose
SUBMIT
Using trigonometry we know that option (B) "cosθ < 0" is correct.
What is Trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).
Therefore, for a right triangle
a² + b² = c²For the triangle that has a² + b² > c², it shows it is not a right triangle.
Let θ be the measure of the angle opposite the side of length c.We have to find the statements which are must be true.Cosine law:
c² = a² + b² - 2abcosθSubstitute the value then we get:
c² < c² - 2abcosθSubtracting c² on both sides of the inequality:
c² - c² < c²- c² - 2abcosθ0 < -2abcosθAdding 2abcosθ on both sides then we get:
2abcosθ < -2abcosθ + 2abcosθ = 02abcosθ < 0cosθ < 0cosθ is negative in the second quadrant and third quadrants.
Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.
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Question is in the photo.
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
What is a derivative of a function?The derivative of a function f(x) represents its rate of change.
We have,
y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]
Putting log on both sides.
[ log a² = 2 log a ]
log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]
log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]
log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]
Derivation on both sides.
[ d(logx)/dx = 1/x ]
d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx
1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
Thus,
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
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help it’ll be greatly appreciated :(
In population 1:
Pattern is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Describe pattern.A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Given.
Pattern in which population is changing are:
In population 1:
It is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Completing the table:
Population 1 Population 2
42.8 29
38.6 27
33.4 25
27.2 23
Graph is mentioned below.
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Serum albumin levels in adults are distributed approximately Normally with a mean of 35 g/l and a standard deviation of 5 g/l. What is the probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l? (Enter your answer rounded to two decimal places.)
There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.The mean and the standard deviation of the albumin levels are given as follows:
[tex]\mu = 35, \sigma = 5[/tex]
The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (32.5 - 35)/5
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
1 - 0.3085 = 0.6915 = 69.15% probability.
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Solve the inequality and graph the solution on the line provided. 9 + 3x ≥ -6
9 + 3x ≥ -6
9 is adding on the left, then it will subtract on the right
3x ≥ -6 - 9
3x ≥ -15
3 is multiplying on the left, then it will divide on the right
x ≥ -15/3
x ≥ -5
If y = 2x2 – 4, what is its inverse?
The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)
How to find the inverse of a function
In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:
y = x
x = y⁻¹
Now we proceed to clear y⁻¹ by using algebra properties:
x = 2 · (y⁻¹)² - 4
x + 4 = 2 · (y⁻¹)²
(x + 4) / 2 = (y⁻¹)²
√[(x + 4) / 2] = y⁻¹
y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4
The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.
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