The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.
What is end behavior?Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.
In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.
In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.
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Given: Line l and line m intersect Prove: Image of perpendicular lines l and m with 1, 2, 3, and 4 as angles at the point of intersection Statements Reasons 1. Line l and line m intersect 1. given 2. is supplementary to 2. linear pair theorem 3. ? 3. ? 4. 4. congruent supplements theorem Which statement and reason best completes the proof? A. 3. is supplementary to 3. linear pair theorem B. 3. 3. definition of supplementary angles C. 3. 3. definition of supplementary angles D. 3. is supplementary to 3. linear pair theorem
An angle will always be formed when two or more lines intersect. These can form a series of complementary or supplementary angles. Complementary angles add upt o a right angle, while supplementary angles are two or more angles formed that add up to [tex]180^{o}[/tex]. Thus two supplementary angles can be referred to as a linear pair.
Therefore the required statements and reasons for the question are stated below:
STATEMENT REASONS
1. Line l and line m intersect Given
2. <1 is supplementary to <2,
<3 is supplementary to <4 Linear pair theorem
3. m<2 + m<3 = [tex]180^{o}[/tex],
m<3 + m<4 = [tex]180^{o}[/tex] Definition of Supplementary angles
4. m<1 + m<2 = m<3 + m<4 = [tex]180^{o}[/tex] Congruent Supplement Theorem
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Answer:
Step-by-step explanation:
<3 is supplementary to <4 Linear pair theorem
I took the plato test and got it right
A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail.
The value of X that number of unit fails are 1/12.
According to the statement
we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.
And we have to find that the how much units that fails in the specifications.
So,
We find the value of X by use of Probability.
The probability that unit fails = number of units that chosen randomly / total units.
So, substitute the values in it then
The probability that unit fails = 5 / 60
The probability that unit fails = 1 / 12.
The probability that unit fails from 60 accelemoters is 1 / 12.
So, The value of X that number of unit fails are 1/12.
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Mia invests $5000 in an index fund after 1 year the funds share price has increased by 8% how much did mia gain
A year later, Mia gained $400.
Calculation of interestMia invests in an index fund= $5000
The share price of the fund has grown by 8% after a year.
So, one year later Mia's investment would also increase by 8% since her invested share value has grown by 8%.
Hence, the amount of share would be = ($5000 + 8% of $5000) =($5000+$5000*8/100) = ($5000+$400) = $ 5400
Therefore, Mia's gain is $400.
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Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process. This is known as _________.
Each element in a population has an equal chance of being chosen is Random selection.
Given that each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process.
Sampling is an umbrella term for all methods used to take samples from populations. The main purpose of sampling is to ensure that a chosen sample reflects the desired characteristics of a population so that a statistical study can produce accurate and reasonable results. Sampling techniques include random sampling, stratified sampling and many others.
As we know, random selection is the process of selecting a small group of people from a larger group to participate in a study. Each person has an equal chance of being selected, giving each person in the group an equal chance to participate.
Hence, Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process is known as random selection.
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A fair six sided die is rolled twice what is the probability it will end on one and then six
Answer:
2.78%
Step-by-step explanation:
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.
Therefore, the probability of rolling one is:
[tex]\implies \sf P(x = 1)=\dfrac{1}{6}[/tex]
The probability of rolling six is:
[tex]\implies \sf P(x = 6)=\dfrac{1}{6}[/tex]
Therefore, the probability of rolling one and then six is:
[tex]\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}[/tex]
Total elements in sample space=6
P(1)
1/6P(6)
1/6P(1 and 6)
(1/6)²1/362.78%Determine the present value of quarterly payments of $450 for 6 years at 7.5% annual interest, compounded quarterly. PV= R[(1+i)^-n]/i
Using it's formula, the present value of the amount is: $288.
What is the present value formula?The present value formula is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
In which the parameters are:
R is the future value.r is the interest rate.n is the number of periods.Considering quarterly compounding, the parameters for this problem are as follows:
R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.
Hence the present value is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]
PV = $288
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The function g(x) is graphed.
to
4
34
24
1
-3+
Mark this and retum
2
Which statements about the function are true? Choose
three options.
g(1) = -1
□g(0) = 0
O
0
g(4) = -2
g(1) = 1
g(-1) = 1
Answer: Options (2), (4), (5)
Step-by-step explanation:
When x = 1, y = 1. So, g(1)=1.
Using similar logic to test the other options, we see that the correct answers are options (2), (4), and (5).
An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line.How many different ways can they sit if the elf and the dwarf insist on sitting next to each other
Answer: 24
Step-by-step explanation:
1. Number Them
Elf and Dwarf = 1
Hobbit = 2
Wizard = 3
Man = 4
* Elf and Dwarf are put together so that they are always sitting together
2. Multiply
1 x 2 x 3 x 4 = 24
What's the value of this python expression: (2**2) == 4?
Answer:
Python will return:
True
Step-by-step explanation:
The math function ** is an exponent indicator.
The equation you made was:
[tex]2^2 =4[/tex]
When you run this in python, it will return as true.
It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.
If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.
Which choices are equivalent to the quotient below? Check all that apply. √16 √8
The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
How to find the equivalent of a quotient?We want to find the equivalent quotient of the given expression; √16 / √8
Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4
Thus, applying that to our expression gives;
√16/√8 = 4/√8
Now, square root of 8 which is √8 can also be expressed as; 2√2
Thus;
4/√8 = 4/2√2 = 2/√2
The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
Step 2: Make sure all radicals are simplified.
Step 3: Simplify the fraction if needed.
If we rationalize the denominator of our expression, we have;
2/√2 × √2/√2 = 2√2/ 2 = √2
Also, 2/√2 can be expressed as √4 /√2
Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
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can someone help me!!
i need a detailed explanation
The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)
How to find the equation of the line for the height of a triangle
In this question we must find the equation of the line perpendicular to the segment BC and that goes through the point A(x, y) = (1, 3). First, the slope of the line segment BC is:
m = [1 - (- 3)]/[5 - (- 3)]
m = 4/8
m = 1/2
And the slope of the line is:
m' = - 1/(1/2) = - 2
The intercept of the line is found by using the explicit form of equation of the line, m' = - 2 and (x, y) = (1, 3):
3 = - 2 · 1 + b
b = 5
The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)
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The vertices of polygon ABCD are at A(1,1), B(2,3), C(3,2), and D(2,1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A' B'C'D' to it's coordinates.
The coordinates of the polygon A'B'C'D' following a reflection across the x-axis and a translation 2 units up are;
A'(1, 1), B'(2, -1), C'(3, 0), and D'(2, 1)How can the coordinates of the image be found?The vertices of the polygon are;
A(1, 1), B(2, 3), C(3, 2), and D(2, 1)
Reflection over the x-axis gives;
(x, y) reflection across the x-axis → (x, -y)
Which gives;
A(1, 1) R x-axis → A''(1, -1)
B(2, 3) R x-axis → B''(2, -3)
C(3, 2) R x-axis → C''(3, -2)
D(2, 1) R x-axis → D''(2, -1)
Translation of the points ABCD 2 units up gives;
A''(1, -1) T(0, 2) → A'(1, -1 + 2) = A'(1, 1)
B''(2, -3) T(0, 2) → B'(2, -3 + 2) = B'(2, -1)
C''(3, -2) T(0, 2) → C'(3, -2 + 2) = C'(3, 0)
D''(2, -1) T(0, 2) → D'(2, -1 + 2) = D'(2, 1)
The coordinates of A'B'C'D' are therefore;
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Robert, Richard and David were working on a project to redesign coke cans. First, Robert measured the original coke can and found the circumference to be 8.6 inches. Richard measured the height to be 15.2 cm.
David calculated the volume to be 131.3 cm3.
Choose the true statement(s) below.
Select one or more:
a.David's calculations are incorrect, he needed to convert centimeters to inches before finding the radius then use the area of the base times the height .
b.David is correct.
c.David's calculations are incorrect, he used the circumference and the height to find the volume.
The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.
VolumeCorrect calculation:
Height = 15.2 cmCircumference = 8.6 inchesC = 2πr
8.6 = 2 × 3.14 × r
8.6 = 6.28r
r = 8.6/6.28
r = 1.36942675159235 inches
convert 1.36942675159235 inches to cm
= 3.478343949044569 cm
Approximately,
r = 3.5 cm
Volume = πr²h
= 3.14 × 3.5² × 15.2
= 3.14 × 12.25 × 15.2
= 584.668 cm³
Approximately,
volume = 584.7 cm³
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If a wall is built in a room at a 36 degree angle. The angle formed in the other room by the wall is 144 degrees. What kind of angles are formed when they are added together
They form supplementary angles when they are added together.
Reason for Being Called Supplementary Angles
It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.
This implies that,
∠1 = 36°
∠2 = 144°
∠1 and ∠2 are adjacent angles and,
∠1 + ∠2 = 36° + 144°
⇒ ∠1 + ∠2 = 180°
Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.
What are supplementary angles?
Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.
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Evaluate the expression 21 ÷ 3 + 8 − 4.
A) 19
B) 17
C) 15
D) 11
Answer:
D
Step-by-step explanation:
We will use the order of operations to evaluate the expression.
From left to right , Multiplication/Division followed by Addition/Subtraction.
21 / 3 + 8 - 4
= 7 + 8 - 4
= 15 - 4
= 11
Therefore, the answer is D
Answer:
D) 11
Step-by-step explanation:
Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.
21 / 3 = 7
Our new expression will be: 7 + 8 - 4
Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.
I'll do the addition first, but order does not matter.
7 + 8 = 15
15 - 4 = 11
So 11 is our final answer.
Looking at the answer choices, D has 11, so D is our answer for this question.
Clarie has $300 in an account. She decides she is going to take out half of what's left in there at the end of the month. (This is for geometric sequence, Math 1 btw and I gotta graph it)
The expected money deposited in Clarie's account in next 12 months is listed below:
300 (Initial value)1507537.5018.759.384.692.341.170.590.290.140.07How to derive and graph a geometric sequence
First, we must derive a formula that will generate the geometric sequence for the money remaining in Clarie's account:
[tex]c = c_{o}\cdot \left(1 + \frac{r}{100} \right)^{t}[/tex] (1)
Where:
[tex]c_{o}[/tex] - Initial money deposited in Clarie's account.r - Decrease rate, in percentage.t - Number of periods, in months.If we know that [tex]c_{o} = 300[/tex] and r = - 50, then the money left for each month is shown in the image attached below.
RemarkThe image quality is poor to the point of being very hard to read. However, it coincides with the complete statement, which is presented in the question.
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need help with the y value
Answer: 12x
Step-by-step explanation:
The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.
For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.
Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,
[tex]y=12x[/tex]
If we use any x on the left, it's corresponding height will be the y.
If im trying to get 20 million dollars and i get 300$ per second how long will it take to reach my goal
Answer:
66666.66 seconds, or 1111.12 minutes
Step-by-step explanation:
Since you are earning 300 dollars per second, and you want to earn 20 million, or 20000000 dollars, you can divide 20 million by 300 to get the time it takes to reach your goal in terms of seconds:
[tex]\frac{20000000}{300}=66666.66[/tex] seconds
It will take you approximately 66667 seconds to reach your goal. If we divide by 60 to get this in terms of minutes, we get that it takes about 1111.12 minutes
Answer:
66.666.6 seconds
1,111.11 minutes
18.518518518499999 hours
Step-by-step explanation:
20,000,000÷300
=66,666.6666666
Change in minutes= 66,666.6666666÷60 =1,111.1111111
Change in hours= 1,111.11111111÷60=18.518518518499999
more math i need help in please nd thank u
The value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36
Inverse variationThe types of variation are;
Inverse variationDirect variationJoint variationy = (k × x²) / z³
where,
k = constant of proportionalityIf y = 12, x = 4 and z = 2
y = (k × x²) / z³
12 = (k × 4²) / 2³
12 × 2³ = k × 4²
12 × 8 = k × 16
96 = 16k
k = 6
Find x when y = 1.728 and z = 5
y = (k × x²) / z³
1.728 = (6 × x) / 5³
1.728 × 5³ = 6x
1.728 × 125 = 6x
216 = 6x
x = 216/6
x = 36
Therefore, value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36
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the accompanying diagram shows a kit that has been secured to skate in the ground with a 20-foot string. the kit is located 12 feet from the ground, directly over point X. what is the distance, in feet, between the skate and point X.
The distance between the skate and point X is 16 feet
Given that the distance between point X and kite is 12 feet
and the distance between stake and kite is 20 feet
We need to find the distance between the stake and point X
Here,
Perpendicular = 12 feet
Hypotenuse = 20 feet
Base = ?
According to Pythagoras Theorem
(Hypotenuse)² = (Perpendicular)²+(Base)²
(20)² = (12)² + (Base)²
∴ (Base)² = 400 - 144
∴ (Base)² = 256
∴ Base = 16 feet
Hence the distance between the Point X and the stake is 16 feet
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IS ANYONE ABLE TO HELP ME PLEASE ASAP
Answer:
36
Step-by-step explanation:
To answer this question, we need to first understand the notation (f · x)(-2). This is a composite function, and another way to write this is f(g(-2)). This means that we have to find g(-2) and apply the function f to whatever this value is. Let's start by finding g(-2):
[tex]g(x)=x-2\\g(-2)=-2-2\\g(-2)=-4[/tex]
Now that we know g(-2) is -4, we can apply this to f:
[tex]f(x)=x^2-4x+4\\f(-4)=(-4)^2-4(-4)+4\\f(-4)=16-(-16)+4\\f(-4)=16+16+4\\f(-4)=36[/tex]
Therefore, our answer is 36
Im one paragraph, summarize the purpose of the graphic and its key findings
The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.
What is Unemployment?This is a situation in which employable individuals look for jobs and are unable to find one.
The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.
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Whats the solution √x-6-x-12
A car is valued at $35400 at the start of the year, and at $25700 at the end of that year. During that year, the car travelled 25000kms.
a) Find the total depreciation of the car in that year in dollars
b) Find the depreciation per kilometre for this car
c) Using (initial value) -> V₀ = 35400, write down a rule for the value of the car Vₙ after ₙ kilometres
d) How many kilometres are travelled when the value of the car is $6688?
e) Including the first year of travel, how many kilometres in total is this car expected to drive before it has a value of 0?
a. Total depreciation = $9700
b. Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = $35400 + ₙt
d. Distance = 4723. 16 kilometers
e. Total distance = 29723. 16 kilometers.
How to determine the depreciation
i. The formula for total depreciation is given as;
Total depreciation = Cost of asset - Residual value
Cost of car = $ 35400
Residual value = $25700
Total depreciation = $35400 - $25700
Total depreciation = $9700
b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers
Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]
Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = V₀ + ₙt
t = time of depreciation
V₀ = $35400
Vₙ = $35400 + ₙt
d. When the car costs $35400, it travelled 25000 kilometers
It costs $6688, it would travel 'x' kilometers
Cross multiply
$35400 × x = $ 6688 × 25000 kilometers
Make 'x' subject
x = [tex]\frac{6688 * 25000}{35400}[/tex]
x = [tex]\frac{167200000}{35400}[/tex]
x = [tex]4723. 16[/tex] kilometers
The car would travel 4723. 16 kilometers
e. To find the total distance
Total distance = 25000 + 4723. 16
Total distance = 29723. 16 kilometers.
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D is the centroid of triangle abc. what is the value of x when bd=2x+40 and bf=18x
The value of x= 20 units
BD = BF
BD =2x + 40
BF = 18x
Equate the expressions thus:
2x + 40 = 2/3(18x)
2x + 40 = 12x
Collect like terms
2x - 12x = - 40
-2x = - 40
Divide both sides by - 2
x = 20
Hence, x = 20 units
The centroid is the center point of the item. The factor in which the 3 medians of the triangle intersect is known as the centroid of a triangle. it is also defined because of the point of intersection of all the 3 medians. The median is a line that joins the midpoint of a facet and the opposite vertex of the triangle.
Then, we can calculate the centroid of the triangle by means of taking the common of the x coordinates and the y coordinates of all of the three vertices. So, the centroid method can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/three).
The centroid of a triangle is the point at which the 3 medians coincide. The centroid theorem states that the centroid is 23 of the space from each vertex to the midpoint of the opposite aspect.
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let n be a natural number such that GCF(n, 70)= 10, and LCM(n, 70)=210. Find N. (Hint: Do you remember that LCM(A,B) x GCF(A, B)= A x B?)
The natural number , n is 30
How to determine the value
Given;
GCF(n, 70) = 10
LCM(n, 70) = 210
We have that;
LCM(A,B) x GCF(A, B)= A x B
Then,
(n, 70) = n × 70 = 70n
10 × 210 = 2100
Equate the two expressions
70n = 2100
n = [tex]\frac{2100}{70}[/tex]
n = [tex]30[/tex]
Thus, the natural number , n is 30
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The ratio of broken ribs to broken collarbones
during last year's rugby season was 2 to 3. If
there were 18 broken ribs, how many broken
collarbones were there?
Given the following formula, solve for a. 8=a+b+c/2
Making "a" the subject of the formula would give us: a = 8 - b - c/2
How to Solve for the Subject of Formula?Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.
8 = a+b+c/2
8 = (2a + 2b + c)/2
2(8) = 2a + 2b + c
16 = 2a + 2b + c
16 - 2b - c = 2a
Divide both sides by 2
16/2 - 2b/2 - c/2 = 2a/2
8 - b - c/2 = a
a = 8 - b - c/2
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Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle 18 units units 36 units units
Answer:
(っ◔◡◔)っ ♥ 36 square root 2 ♥
Step-by-step explanation:
The length of the hypotenuse of the triangle is approximately 48.99 units.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
We can use the Pythagorean theorem to find the length of the hypotenuse of the triangle:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
Substituting the values given in the problem.
c² = 18² + 36²
c² = 324 + 1296
c² = 1620
Taking the square root of both sides.
c = √(1620)
Simplifying.
c = 6 √(90) or approximately 48.99
Therefore,
The length of the hypotenuse of the triangle is approximately 48.99 units.
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