For f(x)=3x+4 and g(x)=x^2 find the following composite functions and state the domain of each.
Answers
The composite functions are:
a) f ∘ g = 3x² + 4, with domain of all real numbers.
b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.
c) f ∘ f = 9x + 16, with domain of all real numbers.
d) g ∘ g = x⁴, with domain of all real numbers.
To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.
a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:
f(g(x)) = 3g(x) + 4 = 3x² + 4
The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:
g(f(x)) = (3x + 4)² = 9x² + 24x + 16
The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:
f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16
The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.
d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:
g(g(x)) = (x²)² = x⁴
The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.
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Related Questions
Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
Answers
$10.25/hour x 40 hours = $410
To earn at least $500, Navid needs to earn an additional $90 ($500 - $410).
To earn 20% more than his basic wage, Navid would earn:
$10.25/hour x 1.2 = $12.30/hour for each overtime hour
So, Navid needs to work:
$90 ÷ ($12.30/hour - $10.25/hour) = 47.4 hours
Since Navid cannot work a fraction of an hour, he needs to work 48 hours to earn at least $500.
Therefore, Navid needs to work for a total of 40 hours + 8 hours of overtime, which is 48 hours in total (rounded up to the nearest hour).
1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
Answers
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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Smart Kitchen sells chocolate nonpareils in 8 oz. containers. Because the candy pieces are not uniform, the weight of each individual container varies slightly. A random sample of nine containers was weighed on a precision scale and the results are shown below:
8.09
8.20
8.03
7.86
7.87
8.06
8.43
7.99
8.08
Determine the interquartile range for this sample. Are there any outliers in this data set?
Answers
The interquartile range of the data will be 0.215.
How to calculate the valueThe lower half is:
7.86, 7.87, 7.99, 8.03
The median of the lower half is:
(Q1) = (7.87 + 7.99) / 2 = 7.93
The upper half is:
8.06, 8.08, 8.09, 8.20, 8.43
The median of the upper half is:
(Q3) = (8.09 + 8.20) / 2 = 8.145
The IQR is the difference between the third and first quartiles:
IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215
Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955
Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795
None of the data points fall outside these thresholds, so there are no outliers in this data set.
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Michael purchased stereo equipment for $2500. His wife claims that was not a smart investment because stereo equipment decreases in value at a rate of 9% per year. How much will his stereo equipment be be worth after 8 years?
Answers
Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.
What is an exponential decay factor?The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.
The decay factor is used in exponential decay functions to determine the depreciated value of an asset.
Current price of stereo equipment = $2,500
Annual decreasing rate = 9%
Decrease factor = 0.91 (100% - 9%)
The number of years = 8 years
Value of the equipment after 8 years = ($2,500 x 0.91^8)
= $2,116.125 ($2,500 x 0.47025)
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what is the
quotient of 62.72+4.9
Answers
Answer:
12.8
Step-by-step explanation:
Quotient means the answer of two things divided.
62.72/4.9=12.8
I need help with the answer to the photo provieded
Answers
Answer:
26
Step-by-step explanation:
For the right triangle below, find the measure of the angle.
Figure is not to scale.
Answers
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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A school purchases boxes of paints for the annual painting competition. The expression below represents the total price for the order including delivery to the school. $11.75x + $20
Answers
Answer:
The expression $11.75x + $20 represents the total price for the order, including delivery to the school.
In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.
The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.
By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.
at football practice, gustavo does push ups for 2 minutes for every 6 minutes playing if he plays for 42 minutes how many of push ups will he do
Answers
Answer:
14 mins
Step-by-step explanation:
2/6 = x/42
6x=84
x=14
A wrestler weighs in on the first day at 162 pounds. To make weight for the first match, the wrestler must lose 1.1 pounds per week. This can be modeled by the equation y=−1.1x+162. Use this model to predict the wrestler’s weight at the first match that is 9 weeks away.
Answers
The wrestler's weight at the first match will be 152.1 pounds. The solution has been obtained by using the substitution method.
What is the substitution method?
The substitution method is a strategy used in algebra to solve simultaneous linear equations. In this process, as the name suggests, the value of one variable from one equation is swapped in the second equation.
We are given that the given situation can be modeled by the equation
y = −1.1x + 162.
Now, we need to find weight at the first match which is 9 weeks away.
So, we get that x = 9.
By substituting this value in the equation, we get
⇒ y = -1.1 (9) + 162
⇒ y = -9.9 + 162
⇒ y = 152.1
Hence, the wrestler's weight at the first match will be 152.1 pounds.
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is 2^7 equal to 2x 7
Answers
Answer: No, 2^7 is not equal to 2x7.
2^7 means 2 raised to the power of 7, which is 2 multiplied by itself 7 times:
2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
On the other hand, 2x7 means 2 multiplied by 7:
2x7 = 2 x 7 = 14
So 2^7 is not equal to 2x7.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
See, 2 ^ 7 is 2 TO THE POWER OF 7, which is repeated multiplication.
2 x 7 is 2 MULTIPLIED BY 7
2 ^ 7 written out completely is:
2 * 2 * 2 * 2 * 2 * 2 * 2 = 128
See the repeated multiplication above?
2 x 7 is just 14.
See the difference!
14 is NOT equal to 128
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To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase
Answers
Carlos can expect the value of the computer to be $580 three years after purchase.
To model the value of the computer, we can use the formula:
y = abˣ
We know that the initial value of the computer is $1,350, so a = 1350.
We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:
810 = 1350b
b= 0.6
b = 0.6
So our exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3:
y = 1350(0.6)³
y = 583
Hence, Carlos can expect the value of the computer to be $580 three years after purchase.
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If someone wants to call Havana, Cuba from the United States, begins with US three digit exit code 011 followed by the two digit country code for Cuba which is 53, followed by the country code of Havana which is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone number cannot begin with 0. How many different telephone numbers are possible?
Answers
There are possible 4,782,969 different telephone numbers.
We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.
How to calculate the total number of possible telephone numbers?Using the multiplication principle to estimate the number of possible telephone numbers for each digit:
n1 x n2 x n3 x ... x nk
Here:
the first three digits are fixed: 011
The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).
The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).
Therefore, the total number of possible telephone numbers:
9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,
Therefore, 4,782,969 different telephone numbers are possible.
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the following figure, assume that a and b = 3, c = 5, e = 12, and d = 13
Answers
Looking at the information provided, we can guess the triangle is similar to the one attached.
Therefore the area of the joint triangle is 40.825 unit²
How did we find the area of the joint triangle?a = b = 3 is the side lengths of the equilateral triangle c = 5 is the side length shared by both triangles = 12 which is the base of the right triangled = 13 which is the hypotenuse of the right triangle
The height of the equilateral triangle is 4.33 units.
Looking at this information, we solve for the area of the equilateral triangle;
Area = (base × height) / 2 (5 × 4.33) / 2= 10.825
Area = (base × height) / 2
Area of the right angle triangle = (12 × 5) / 2 = 30
The total area 10.825 + 30 = 40.825
The above answer is partly based on the figure provided in the image. The numbers used were the ones provided by you, except for the height of the equilateral triangle.
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Looking at the information provided, we can guess the triangle is similar to the one attached. Therefore the area of the joint triangle is 40.825 unit²
How did we find the area of the joint triangle?a = b = 3 is the side lengths of the equilateral triangle
c = 5 shared by both triangles
12 = the base of the right triangle
13 = the hypotenuse of the right triangle
4.33 = height of the equilateral triangle
To solve the total area, we say
Triangle 1
Area = (base × height) / 2
(5 × 4.33) / 2= 10.825
Triangle 2
Area = (base × height) / 2
Area of the right angle triangle = (12 × 5) / 2 = 30
The total area ∴ 10.825 + 30 = 40.825
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Jeannie designs jewelry. The figure shows a
pendant on a necklace Jeannie is making. It is
composed of three individual beads.
The larger triangular bead cost $1.52. The
rectangular bead costs $0.42, and the smaller
triangular bead costs $0.92.
What is the cost per square millimeter of the
pendant? Round your answer to the nearest
hundredth.
Answers
Answer: ≅ $0.02
Step-by-step explanation:
First, lets find the area of the large triangle
0.5 x 14 x 11 = 77 mm^2
Next lets find the area of the middle rectangle:
4 x 14 = 56 mm^2
Last lets find the area of the small triange:
0.5 x 14 x 3 = 21 mm^2
So the total area is: 77 + 56 + 21 = 154 mm^2
the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86
dividing the cost by the area to find the cost/mm:
2.86/154 ≅ $0.02
Please help me I really don’t get this. ILL GOVE BRAINLIEST TO ANYONE PLEASD I GIVE 18 points
Answers
Answer: C, yes
Step-by-step explanation:
Again you have do the same thing to both sides
They added 1 to both sides
Answer is C , yes they are same
Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answers
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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what is the answer for this question
Answers
Answer:
The yellow region is 13.73 cm squared
Step-by-step explanation:
---
Area of square:
[tex]8 * 8 = 64 cm^2[/tex]
Area of the 4 quarter-circles:
[tex]4(\pi r^2)/4[/tex]
The fours cancel each other, we are left with:
[tex]\pi r^2[/tex]
r = 4, so substitute that, we get:
[tex]\pi 4^2 = 16 \pi cm^2[/tex]
Which can be approximated to 50.27 cm squared
Subtract the area of the circle from the square:
[tex]64 - 50.27 = 13.73 cm^2[/tex]
So the area of the yellow region is 13.73 cm squared
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer: 100.48 cubic feet
Step-by-step explanation:
[tex]8 : 1/3\\[/tex]8 : 1/3
Answers
The ratio of 8 : 1/3 is equivalent to the simplified ratio of 24 : 1.
How to simplify the ratio?To analyze and describe the ratio 8 : 1/3, we need to convert the fraction to a ratio with a whole number. One way to do this is to express the fraction as a ratio with a denominator of 3:
1/3 = 1:3
Now we can rewrite the ratio 8 : 1/3 as:
8 : 1:3
We can simplify this ratio by multiplying both terms by 3 to get rid of the fractional term:
8 × 3 : 1:3 × 3
24 : 1
Therefore, the ratio 8 : 1/3 is equivalent to the simplified ratio 24 : 1. This means that for every unit in the second part of the ratio, there are 24 units in the first part of the ratio. In other words, the first part of the ratio is 24 times larger than the second part.
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The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answers
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8
 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me
Answers
Need help with this question. Been stuck on this for 20 mins.
Answers
Answer:
see below
Step-by-step explanation:
The Reason for #1 is literally GIVEN to you.
Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.
Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.
Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.
Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.
Can someone please help me do this ?
Answers
Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.
How the pension amount is computed:The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.
Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
Edith's average salary = $65,000
The number of years of service = 4 years
Pension Multiplier = 2%
Pension multiplier factor = 1.02 (100% + 2%)
Vesting percentage = 75%
Pension to be received = $49,725 ($65,000 x 75% x 1.02)
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In 2010, the sea turtle population was twice the amount of turtles as in 2005. How many sea turtles were there in 2010?
Answers
Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.
Let x be the number of sea turtles in 2005.
According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.
We can set up an equation:
2x = number of sea turtles in 2010
We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.
During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
Answers
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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a. Use the graph to approximate the value of the car after 4 years.
b. Use the graph to approximate the value of the car after 5 years.
c. Use the graph to approximate when the car will be worth half its original value. (Determine the number of years.)
Answers
The car will be worth half its original value after 4 years
How to solveA graph for straight-line depreciation for a car is given.
a
The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.
Step 3/7
The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are
(0, maximum car value) and (maximum lifespan,0)
Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600
The intercepts are (0, 25, 600) and (8,0)
Determine the slope of the equation.
Two points determine a line, so only two points are needed to determine the slope of a line.
Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)
Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)
Use the slope ratio as shown below;
The slope of the depreciation equation is.
-3200
The general form for the equation of a straight line is:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept.
The slope is -3,200 and the -intercept is 25,600 as obtained.
Therefore, the straight line depreciation equation is:
y = -3,200x + 25,600
Therefore, the value of the car after 4 years is $12,800
b.
Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.
Therefore, the value of the car after 5 years is $9,600
c.
The half value of the car is half of $25,600 which is $12,800
The car will be worth half its original value after 4 years
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Help me out please y’all
Answers
The piecewise function is
f(x) = { x -3 , x≤3
8, -3 < x ≤ 5
x+10, x>6
For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.
1. For y = x - 2
-5 = -3 - 2= -5
2. For y = x - 3
-5 = -3-3 = -6
The fact that the domain is specified for x less than -3 further demonstrates that the first choice is not an option.
Additionally, we know that the function's value is equal to 8 for the range from x greater than -3 to less than or equal to 5.
Additionally, the equation is given as y = -x + 10 and the line has a negative slope for values greater than 6.
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Natasha is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 20 inches × 15 1 4 inches. She needs to cut another rectangle that is 10 1 2 inches by 10 1 4 inches. How many total square inches of construction paper does Natasha need for her project? Mixed number
Answers
The area of the first rectangle is:
20 inches × 15 1/4 inches = 20 × (60/4 + 1/4) = 20 × 61/4 = 20 × 15.25 = 305 square inches
The area of the second rectangle is:
10 1/2 inches × 10 1/4 inches = (10 × 2 + 1/2) × (40/4 + 1/4) = 21 × 41/4 = 21 × 10.25 = 215.25 square inches
Therefore, the total area of construction paper needed for the project is:
305 + 215.25 = 520.25 square inches
So, Natasha needs 520 1/4 square inches of construction paper for her project.
I have part (a) answered, I just need part (b) if anyone could help with that please?
Answers
(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.
What is range?Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.
According to given information:(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.
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