Answers
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]
Related Questions
Without graphing, answer the questions for the system of equations below.
2x+y = 7
x+6y= 30
Are the graphs of the given equations identical lines, parallel lines, or lines intersecting at a single point?
Identical lines
Parallel lines
Intersecting lines
Answers
Answer:
intercepting lines
.Solve for x
a) x = 192
b) x = 336
c) x = 8√3
d) x = 4√21
Answers
The value of x for the given Right angled triangle is x= 8√3. So, option c is correct.
What is meant by right-angled triangle?90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°. The bases and perpendiculars are the other two sides that are close to the right angle.
A right triangle is a triangle with one of the internal angles at 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.
Given,
BD=28 and BC=12
CD=BD-BC
=28-12
=16
AB²=BC+AC²
AB²=(12)²+x²
x²=AB²-144 -----(1)
From ΔACD
AD²=AC²+CD²
AD²=x²+16²
x²=AD²-256 -----(2)
From ΔABD
BD²=AB²+AD²
784=AB²+AD²
2x²=AB²+AD²-144-256
2x²=784-144-256
2x²=384
x²=192
x=√192
x=√64×3
x=8√3
Therefore, The value of x for the given Right angled triangle is x= 8√3.
Hence, option c is correct.
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a professor teaches a class of 42 students. if only 34 students show up to take the first exam, then how would we characterize this group who took the first exam?
Answers
Correct this group constitutes a sample of all students in the class.
What are some instances of intuitive reasoning?
As an illustration, when we enter a coffee shop, we immediately recognize a cup as one that we have seen many times before.
We also immediately recognize that it will probably be hot and spill quickly over an uneven surface.
What is the intuitional method?
Intuition is the earliest means of knowing. When we use our intuition, we are putting our trust in our feelings, emotions, and/or instincts to lead the way.
When using intuition, one believes what seems true rather than looking at the facts or using reason.
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Given 3 and one-tenth times negative 6 times seven-twelfths, determine the product.
eighteen and one sixtieth
negative eighteen and 7 over 120
ten and 17 over 20
negative 10 and 17 over 20
Answers
The product of the expression [3 + 1/10] (-6 x 7 / 12) is -10 + (17 / 20) = negative 10 and 17 over 20.
What is multiplication?Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
Example - 2 × 3 means 2 is added three times or 3 is added 2 times.
Given that the expression { 3 + (1/10) } {-6 x (7 / 12) }
Simplifying the expression using PEMDAS,
{ 3 + (1/10) } {-6 x (7 / 12) }
= ( 31 / 10 ) × ( -7 / 2 )
= - 217 / 20
= -10 + (17 / 20)
= negative 10 and 17 over 20
Therefore, the value of the expression [3 + 1/10] (-6 x 7 / 12) is -10 + (17 / 20) = negative 10 and 17 over 20
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A line of fit for a data set is -3x+4y=-5. Describe the correlation of the data.
Answers
The correlation of the data set is positive
How to describe the correlation of the data?From the question, we have the following parameters that can be used in our computation:
Line of fit for a data set: -3x+4y=-5
Write out the equation of the line
So, we have
-3x + 4y = -5
Make y the subject of the equation
So, we have the following representation
y = 3/4x - 5/4
A linear equation is represented as
y = mx + c
Where
slope = m
This means that the slope of the equation is
m = 3/4
The above number is a positive number
Hence. the correlation is positive
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need help on this! thank you in advance!
Answers
The value of the angle x will be equal to 36°.
What is an arc of the circle?A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.
Given that the minor arc is 144. The value of angle x will be calculated by the ratio of the difference between the major arc and the minor arc to the 2.
The angle x will be calculated as,
x = ( Major arc - Minor arc) / 2
x = ( 360-144-144) / 2
x = 72 / 2
x = 36
Therefore, the value of the angle x will be equal to 36°.
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A moving company has one large truck for furniture and one small truck for boxes.During one move, it took the large truck 4 hours to travel 180 miles. It took the small truck 3 hours to make the same trip.How much faster did the small truck travel in miles per house.?
Answers
Answer:
15
Step-by-step explanation:
180 / 4 = 45
180 / 3 = 60
Answer: 15
Step-by-step explanation:
I need help to solve this!
Answers
Answer:
C. neither B. exponentialStep-by-step explanation:
You want to know the nature of the sequences ...
1, 4, 9, 161/3, 1, 3, 9, 27DifferencesTo determine if a sequence is linear, you look at the differences between terms. If they are all the same, then the sequence is linear.
Here, the differences are ...
3, 5, 72/3, 2, 6, 18Neither sequence is linear
Common factorA sequence that is exponential will have adjacent terms with the same ratio.
Here, the ratios are ...
4/1, 9/4, 16/93, 3, 3, 3The first sequence is not exponential. The second sequence is.
The sequences can be characterized as ...
neitherexponential__
Additional comment
You may have noticed that the differences of the first sequence have a common difference of 2. This constant 2nd difference means the sequence can be described by a 2nd-degree (quadratic) polynomial. In fact, each term is the square of its term number.
the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. the thickness of the rind is always one tenth of the radius. the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week. assume that the radius is initially zero.
Answers
The volume of a sphere is V = 4/3 x pi x r^3 .
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
V' equals (4 pi x r' x r'2) (4 pi x (.9 3) x r2 x r')
This equation expresses how quickly the rind volume changes over time.
As stated in the issue, r' = 2.
Additionally, the radius will be r = 2 * 5 = 10 after 5 weeks.
V' equals (4 pi x 102 x 2) (Pi x (.93) x 10 x 2) = -
V' is equal to (800 pi) - (800 pi x (.729)).
V' = (800 x pi) (1 - .729) (1 - .729)
V' = (800 x pi)(.271) (.271)
681.09 cubic centimeters make up V'.
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a store has a 20% off sale on pants
Answers
The original price would typically be less expensive than the current price, though it is possible for the two to be equal in specific circumstances. The original price of the pants is $ 19
What was the original price of the pants?A store has 20% off sale on pants. With this discount, the price of one pair of pants before tax is $15.20.
n is the total price, 0.2n is the discount: n - 0.2n
n - 0.2n = 15.20
Step 2: Combine like terms
n - 0.2n = 15.20
0.8n = 15.20
Step 3: Divide both sides by 0.8
0.8n / 0.8 = 15.20 / 0.8
n = 19
$19 is the original price
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the ftoli (fundamental theorem of line integrals) says: (select all correct answers) group of answer choices none of these the work done by a gradient vector field is always zero. the work done by any vector field is independent of path. the line integral of a gradient vector field depends only on the initial and terminal points of the path. the work done by a gradient vector field is independent of path.
Answers
Fundamental Theorem of Line Integral, also called the Gradient theorem, tells us that line integrals through gradient fields are path independent and depend only on the initial and final values. correct answer is option 4 and 5
What does the Line Integrals Fundamental Theorem teach us?
In general, this theorem, like the Fundamental Theorem of Calculus, states that if we integrate a "derivative-like function" (f′ or f), the outcome depends only on the values of the original function (f) at the endpoints.
It is referred to be a conservative vector field if a vector field F is the gradient of a function, F=f.
The line integral of a gradient vector field depends only on the initial and terminal points of the path.
The workdone by gradient vector field is independent of path..
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Mark, taylor, & brian's ages are consecutive whole numbers. Mark is the youngest, and brian is the oldest. The sum of their ages is 111. How old is mark?.
Answers
The age of Mark, Taylor, & Brian's ages will be Whole numbers 36,37, and 38 respectively.
What exactly is a whole number?
Whole numbers are a collection of positive integers and zero that do not contain any fractions.
It is denoted by the letter "W," and its corresponding set of numbers are "0," "1, 2, 3,,","5,,"6,,"7,","8,"..."
It is given that Mark, Taylor, & Brian's ages are consecutive whole numbers, Mark is the youngest, and Brian is the oldest and the sum of their ages is 111.
Suppose the age of mark is x as a result the age of Taylor and brian will be x + 1 and x + 2 respectively.
From the given condition the sum of their ages is 111,
⇒x + x + 1 + x + 2 = 111
⇒3x + 3 = 111
⇒3x = 111 - 3
⇒3x = 108
⇒x = 108/3
⇒x = 36
The age of Mark, x =36
Age of Taylor, x+1 = 36+1 =37
Age of Brian, x+2 =36+2=38
Thus, if their age is in consecutive whole numbers. The age of Mark, Taylor, & Brian's ages will be 36,37, and 38 respectively.
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The figure below is a rhombus.
x =[?]°
Answers
Answer:
X = 90°
Step-by-step explanation:
The figures cross sections form 4 90° angles.
A triangle has three angles which add up to 180°.Knowing x is a 90° angle we can do 180 - 90 to find out the other two angles (63 and z/y = 90).90 - 63 = 27.x = 90y = 27z = 27Find an expression for the perimeter of the figure
Answers
The perimeter of the figure is 4d+6c - 6
How to calculate perimeter ?The distance around the outside of a 2D shape is known as its perimeter. Add together the lengths of all the sides to determine the perimeter.
We have been given a figure. We are asked to write an expression for the perimeter of our given figure.
We know that perimeter of a solid is sum of all of its side.
We can see that opposite side of our given figure are equal and our given figure is a rectangle.
We know that perimeter of rectangle is two times the length and width of rectangle, so the perimeter of our given figure would be:
2×(2d- 3+3c)
Use distributive property:
2 × 2d - 2 × 3 + 2 × 3 c
4d -6+6c
4d+6c-6
Therefore, the perimeter of our given figure is 4d+6c - 6
The complete question is : Write and simplify an expression for the perimeter of each figure
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The length of the base of an isosceles triangle is x. The length of a leg is 3x - 2. The perimeter of the triangle is 66. Find x.
X= ?
Answers
Answer: x=5
Step-by-step explanation:
x=5 possibly i put diff numbers
Line segment cd is the perpendicular bisector of line segment ab. Is line segment ab the perpendicular bisector of line segment cd?.
Answers
Point E is closer to point A.
"I have added screenshot of the complete question as well as the
diagram"
What is line segment ?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie within those endpoints. The Euclidean distance between two endpoints of a line segment determines its length.
- In this diagram, line segment CD is the perpendicular bisector of line
segment AB
∴ AB ⊥ CD
∵ CD intersect AB at M
∴ M is the mid-point of AB
∴ The length of AM = the length of MB
- Assume the conjecture that the set of points equidistant from A
and B is the perpendicular bisector of AB is true
∴ Any point lies on the line CD equidistant from A and B
- If point E lies on the line CD
∵ CD is the perpendicular bisector of AB
∵ E lies on CD
∴ The length of EA = The length of EB
- From the figure point E is on the left side of the line CD
∵ Point A is on the left side of the line CD
∵ Point B is on the right side of the line CD
∵ Point E is on the left side of the line CD
∴ The length of AE < The length of BE
∴ Point E is closer to point A
Complete question: In this diagram, line segment CD is the
perpendicular bisector of line segment
AB. Assume the conjecture that the set of
points equidistant from A and B is the
perpendicular bisector of AB is true. Is
point E closer to point A, closer to point B,
or the same distance between the points?
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Kai has a rope that is meter long. Kai cuts off a piece that is meters long. How long, in meters, is the piece of rope after he cuts it?
Answers
Answer: The answer is a meter or nothing, It depends on the answer you want
Step-by-step explanation:
If he has a rope that is a meter long, but then he takes that meter, he still has a meter, but if you plan on throwing that meter away, then you would have nothing
60 divided by 3 = g - 8 divided by 2 what does g equal?
Answers
Answer:
g = 48
Step-by-step explanation:
60/3 = g-8/2
20 = g-8/2
40 = g-8
g = 48
Answer:
g = 28
Step-by-step explanation:
60 ÷ 3 = g - 8 , that is
20 = g - 8 ( add 8 to both sides )
28 = g
Find the standard form of an equation where a=1, and the vertex is at (-1,11). Find the x and y intercepts and graph the equation.
Answers
Answer:
y = [tex]x^2+2x+12[/tex] (x and y intercepts under "Step-by-step explanation" section)
Step-by-step explanation:
We can start by finding the vertex form and then expand it to the standard form.
The vertex form of the quadratic equation is
[tex]y=a(x-h)^2+k[/tex], where a is a constant and (h, k) is the vertex.
By plugging in 1 for a, -1 for h, and 11 for k, we have:
[tex]y=1(x-(-1))^2+11\\y=(x+1)^2+11[/tex]
Now we simply expand this vertex form to get the standard form:
[tex]y = (x+1)^2+11\\y=(x+1)(x+1)+11\\y=x^2+x+x+1+11\\y=x^2+2x+12[/tex]
We can find the x and y-intercepts using the vertex form.
To find the x-intercept, we plug in 0 for y:
[tex]0=(x+1)^2+11\\-11=(x+1)^2\\\sqrt{-11}=x+1;-\sqrt{11}=x+1\\ x_{intercepts}:(-1+\sqrt{-11}, 0); (-1-\sqrt{-11})[/tex]
The x-intercepts are non-real answers, so the quadratic equation never intersects the x-axis.
To find the y-intercept, we plug in 0 for x:
[tex]y=(0+1)^2+11\\y=1^2+11\\y_{intercept} =(0,12)[/tex]
or According to his running log, Zachary averaged 4 miles per week last month and 25% less this month. How much did he average this month?
Answers
Answer:3
Step-by-step explanation:
Please help me:
find M∠T explain your reasoning
Answers
Explanation:
Angle R = angle A = 41 since both angles involve a single arc marking.
Angle S = angle B = 74, both involve a double arc
For any triangle, the inside angles always add to 180 degrees.
R+S+T = 180
41+74+T = 180
115+T = 180
T = 180-115
T = 65
Please Help. which of the following set notation describes the shaded region above?
Answers
B) X union Y complement
How should a set notation function be written?
The set of all functions f: X Y is denoted by the following notation: The set of all functions f: X Y is labeled Y X for any sets X and Y. Another helpful example of standard notation is as follows: Notation: The term |X|, or occasionally #X, is used to represent the number of elements in finite sets X.
In the above diagram we can see that the shaded region occupy the x and X ∩ Y so the correct option is B
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A 7.5 hg bag of bananas costs 35 Swedish krona ( money ) . If the cost is proportional, how much would 1 kg bag of bananas cost
Answers
Answer:
Step-by-step explanation:
First of all we do conversion.
We have 7.5hg which equals to 0.075kg or 75grams.
Then we use direct proportion where if one value increases so does the other which in this case is the weight of the item is directly proportional to the price of it. Therefor we get this.
Weight Money
75(grams) 35(Swedish Krona)|
1000(grams) x
We cross mutiply.
35,000 divided by 75
so x = 466.67 Swdish Krona
(I Think)
If false explain why. |-7| is greater than -7
Answers
Answer:
True
Step-by-step explanation:
|-7| (absolute value) removes the negative sign, and 7 is greater than -7 so the statement is true.
When we reject the null and the null is true, we have a made a _________ __________.
Answers
When we reject the null hypothesis and the null hypothesis is true, we have made a Type I error.
What is a Hypothesis?In statistical hypothesis testing, the null hypothesis is a statement that represents the anticipated or "normal" outcome of a specific experiment. Unless there is evidence to the contrary, the null hypothesis, which is generally represented by the symbol "H0," is taken to be true.
A Type I mistake, sometimes known as a "false positive," arises when the null hypothesis is correct but is rejected based on the evidence. Applying a statistical test with a strong significance level increases the likelihood of rejecting the null hypothesis even when it is correct, which frequently leads to this mistake.
Making a Type I error can have major repercussions since it can result in judgments being formed based on flawed information and wrong inferences being drawn.
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Mike had $201.58 in his bank account. He paid some bills and now his account balance is -$57.18 Which equation can be used to find x, the amount of his bill payments?
A) 201.58 + x = -57.18
B.) 201.58 - x = -57.18
C.) -201.58 - x = -57.18
D.) 201.58 - x = 57.18
Answers
The equation that can be used to find the amount of bill payments Mike makes, from the $201.58 and the balance in the account of -$57.18, after making the payments is specified in option B.
B.) 201.58 - x = -57.18
What is a mathematical equation?An equation in mathematics is a mathematical statement that joins two expressions, with an 'equals to' mathematics symbol.
The initial amount in Mike's account = $201.58
The money in Mike's account after paying his bills = -$57.18
The amount of Mike's bill payment = x
Therefore;
The initial amount of money in Mike's account less the amount Mike paid as bills = The amount Mike has remaining in his account (his account balance)
Plugging in the values of the variables, we get;
The initial amount = 201.58
The amount of bill payments Mike makes = x
The balance in the account = -57.18
The equation, by plugging in the values becomes:
201.58 - x = -57.18The correct option is therefore, option B
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The equation 201.58 - x = -57.18 with option B is the best equation Mike can used to find the amount of bill payments from his bank account of $201.58 and that of -$57.18, after making the payments is specified in
How to find the equation of Bank balance?An equation is a mathematical model stating the equality of two sides.
The given parameters are
The initial balance = $201.58
Balance after paying bills = -$57.18
Mikes payment = x
The equation, by plugging in the values becomes:
201.58 - x = -57.18
The correct option is therefore, option B
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Rachel has 26 dimes. She is getting rolls of
dimes from the bank. She has enough money to get
up to 8 rolls of dime and each roll contains 50
dimes. The bank will not give partial rolls. The
function that models the number of dimes Rachel
will have after leaving the bank is f(r)=50r+26,
where r is the number of rolls of dimes she gets.
What is the practical domain of the function?
What is the practical domain of the function?
Answers
The practical domain of the function :
All integers from 1 to 8 and the set of f(r) is
f(r) = {76, 126, 176, 226, 276, 326, 376, 426}
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
Since Rachel has 26 dimes at the start, this would translate as the y-intercept. Or the value of y when x is zero. In this case, when she has no rolls of dimes., she would still have 26. Since each roll has 50 dimes. each, the function that models the number of dimes. Rachel will have is
f(r) = 50r + 26
If she can only afford 8 rolls, then the maximum number of dimes Rachel will have is:
f(8) = 50(8) + 26 = 426 dimes
The practical domain of the function :
all integers from 1 to 8
Substitute r=1 to 8 into the equation and find f(r).
{76, 126, 176, 226, 276, 326, 376, 426}
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PLEASE ANSWER FAST
Find the missing values in the table below so that it represents a linear function.
active attachment
Answers
Answer:x=-7
Step-by-step explanation:
Hoped this was very useful
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. Y = x2, y = 5 x2 + 4.
Answers
The graph of the equation Y = x² and the 5x² + 4 is attached below.
Equation:
Equation is the combination of variables, numbers and constants.
Given,
Here we have to sketch the region enclosed by the given curves for the equations, Y = x² and Y = 5x² + 4.
Here we have to take some sample value for x to find the value of equations.
And then by using the values, we have to plot the graph through this.
x = -2, -2, 0, 1, 2
Then the corresponding value of y is calculated as,
=> x = -1 => y = 1
=> x = -2 => y = 4
=> x = 0 => y = 0
=> x = 1 => y = 1
=> x = 2 => y = 4
Similarly, the value of Y for the next equation is,
=> x = -2 => y = 24
=> x = -1 => y = 9
=> x = 0 => y = 4
=> x = 1 => y = 9
=> x = 2 => y = 24
Then the graph of the given equation is drawn as.
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A step that has a height of 6 inches. A ramp starts 5 feet away from the base of the step,making a 5.7 angle with ground. what can you say about the angle the ramp would make with the ground if the starts closer to the step?
Answers
Considering all the option and the question, We cannot determine anything about the angle is the right answer.
what is angle?An angle is a geometric shape that is formed by two rays that share a common endpoint, called the vertex.
what is vertex?The vertex of an angle is the common endpoint of the two rays that form the angle. The vertex is also sometimes called the "corner" of the angle.
It is not possible to determine whether the angle of the ramp will decrease or increase without more information. The angle of the ramp is determined by the slope of the ramp, which is the change in height divided by the change in distance. If the ramp starts closer to the step, it will have a different slope, and therefore a different angle, than if it starts 5 feet away from the base of the step.
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