The temperature at 3 AM is about 53 degrees Fahrenheit.
How would you define temperature?The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.
A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.
We are aware that a sinusoidal function models temperature, and the following information is crucial:
A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.
The day's average temperature is 60 degrees.
We're looking for the temperature at three in the morning, or three in 24-hour time.
We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:
B = 2π/24 = π/12
To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:
C = (8/24) * 2π = (1/3)π
To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:
A = 10
Finally, we can use the formula to find the temperature at 3 AM:
f(x) = A sin(B(x - C)) + D
f(3) = 10 sin(π/12(3 - (1/3)π)) + 60
f(3) ≈ 53.4
So the temperature at 3 AM is about 53 degrees Fahrenheit.
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is 27 goldfish to 15 frogs a equivalent ratio
a bakery sells blueberry muffins for 2.50 each. it costs c dollars to make each muttij the profit for selling m muffins is described by the expression below in the expression what is the meaning of (2.5-c)
Answer:
7.8
Step-by-step explanation:
What is the value of x
Answer:
The value of x is 12.
Greetings!!!
Firstly, recall the Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'. The hypotenuse is the longest side and it's always opposite the right angle. In this triangle a² = b²+ c² and angle is a right angle.
a, b, and c represent the lengths of sides of a triangle, then: a2+b2=c2 if and only if the triangle is a right triangle.
Thus, on this question
the hypotenuse is a= 20
the value of b= 16
so the required value is c
[tex]a {}^{2} = b {}^{2} + c {}^{2} [/tex]
substitute known variables into the equation
[tex](20 ){}^{2} = (16) {}^{2} +( c) {}^{2} [/tex]
evaluate both sides
[tex]400 = 256 +( c) {}^{2} [/tex]
minus 256 from both sides
[tex]400 - 256 = (c) {}^{2} [/tex]
[tex]144 = (c) \frac{2}{} [/tex]
write bothe sides under radical in order to erase the square
[tex] \sqrt{144} = \sqrt{c {}^{2} } [/tex]
solve for c
[tex]c = 12[/tex]
Hope it helps
Answer:
x = 12
Step-by-step explanation:
Pythagoras Theorem
= Hypotenuse² = adjacent² + opposite²
From the question
Hypotenuse = 20
Adjacent = x
Opposite = 16.
The value for x
= 20² = x² + 16²
= 400 = x² + 256
= 400-256 = x²
= 144 = x²
[tex] \sqrt{144} = { \sqrt{x} }^{2} \\ \sqrt{144} = x \\ 12 = x[/tex]
Therefore adjacent (X) = 12
The seats in a theater are arranged in rows with an equal number of seats in each row. The graph shows the relationship between the number of rows and the total number of seats. How many seats are in each row (The variables can only be positive numbers.)
The number of seats in each raw by the given graph is 30.
How do we make graph of a function?Suppose the considered function whose graph is to be made is
f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f(x)
are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x
Total number of seats = x x x = x²
From the given information,
2x(x-10)= x²+ 300
2x²-20x = x²+300
x²-20x-3000
(x-30) (x+10) = 0
x = 30, -10
Since, by the function number of rows or seats cannot be negative. So, x = 30.
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please help with show work. urgent
Answer:
51
Step-by-step explanation:
Assume d varies directly as t and d = 180 when t = 3. Find t when d = 390.
The value of t is 6.5. The value of the constant is 60
What varies directly?
The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant).
Given that d varies directly as t.
The relation between d and t is
d = kt.
Given that d = 180 when t = 3.
Putting d = 180 and t = 3 in d = kt
180 = 3k
Divide both sides by 3:
k = 180/3
k = 60
Putting k = 60 in d = kt:
d = 60t
Now putting d = 390 in d = 60t:
390 = 60t
60t = 390
Divide both sides by 60
t = 6.5
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8. A In rectangle ABCD, AC and BD are diagonals. If m/1 = 55, find ABD.
The value of m∠ABD is equals to 125 degrees.
What is a rectangle ?
Rectangle can be defined in which opposite sides are equal.
AC and BD are diagonals of the rectangle ABCD.
Angle ABD is adjacent to angle 1 and angle ABO, where O is the intersection of diagonals AC and BD.
We know that m∠1 = 55, and we can find m∠ABO using the fact that the diagonals of a rectangle bisect each other. Since angle AOB is opposite to side AB, which is congruent to side CD, we have:
m∠ABO = 180 - m∠AOB
= 180 - (180 - m∠1) / 2
= 180 - (180 - 55) / 2
= 62.5
Therefore, we can find m∠ABD by adding m∠ABO and m∠DBO, where DBO is congruent to ABO:
m∠ABD = m∠ABO + m∠DBO
= m∠ABO + m∠ABO
= 2m∠ABO
= 2(62.5)
= 125
Hence, The value of m∠ABD is 125 degrees.
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The phrases exponential growth and exponential decay appear quite often in media reports these days, referring to environmental, technological, and scientific changes.
In your own words, how would you describe exponential growth and exponential decay to someone unfamiliar with these phrases?
Exponential growth is a pattern of data that shows a rapid increase over time, while exponential decay is a pattern of data that shows a rapid decrease over time.
What is xponential growth and exponential decay?An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
The fundamental distinction between the two is that in an exponential decay relationship, the output values rise quickly as the input value rises, whereas in an exponential growth relationship, the output rises noticeably faster as the input value rises.
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4.21 game of dreidel. a dreidel is a four-sided spinning top with the hebrew letters nun, gimel, hei, and shin, one on each side. each side is equally likely to come up in a single spin of the dreidel. suppose you spin a dreidel three times. calculate the probability of getting
The probability of getting at least one nun in three spins of a dreidel is approximately 0.578
The probability is the ratio of number of favorable outcomes to the total number of outcomes
The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.
The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.
So the probability of getting at least one nun in three spins is
= 1 - (3/4)^3
= 1 - 0.421875
= 0.578125
Therefore, the probability of getting at least one nun is 0.578
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The given question is incomplete, the complete question is:
A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?
Joule Heating
Consider a metal at uniform temperature in a static uniform electric field E. An electron experiences a collision, and then, after a time t, a second collision. In the Drude model, energy is not conserved in collisions, for the mean speed of an electron emerging from a collision does not depend on the energy that the electron acquired from the field since the time of the preceding collision (assumption 4. Page 6).
(a) Show that the average energy lost to ions in the second of two collisions separated by a time t is (eEt)2 2m. (The average is over all directions in which the electron emerged from the first collision. )
(b) Show, using the result of Problem 1(b), that the average energy loss to the ions per collision is (eEt)2/m, and hence that the average loss per cubic centimeter per second is (ne2τ/m)E2=σE2. Deduce that the power loss in a wire of length L and cross section A is I2R, where I is the current flowing and R is the resistance of the wire
A) The average energy lost to ions in the second of two collisions separated by a time t is (eEt)2 2m is (1/3) (eEt)2 / m
B) The average energy loss to the ions per collision is (eEt)2/m is (ne2 / m) E2
In the Drude model, collisions between electrons and ions can cause energy loss, and this loss can be calculated using the average energy lost per collision. Specifically, if an electron experiences two collisions separated by a time t, the average energy lost to the ions in the second collision can be calculated.
We can use the formula for the energy gained by an electron in a uniform electric field: ΔE = eEt, where e is the charge of an electron, E is the electric field strength, and t is the time during which the electron experiences the field.
To do this, we can use the fact that the mean free path of an electron in a metal, before it experiences a collision, is given by λ = vτ, where v is the mean speed of the electron and τ is the average time between collisions.
The average energy lost in the second collision, over all directions of motion, is then given by:
(1/4π) ∫∫ ΔE2 (cosθ) dΩ
where θ is the angle between the direction of motion before the first collision and the direction of motion after the second collision, and dΩ is an element of solid angle. The factor (cosθ) accounts for the projection of the energy loss along the direction of motion.
After some calculations, we obtain the result:
(1/3) (eEt)2 / m
where m is the mass of an electron. This is the average energy lost to the ions in the second collision, over all possible directions of motion.
To answer part (b) of the question, we need to use the result of Problem 1(b), which states that the average time between collisions is given by τ = m/(ne2), where n is the number density of electrons in the metal. Using this formula, we can express the average energy loss per collision as:
(eEt)2 / mτ = (eEt)2 / (m^2 / ne2) = ne2 (eEt)2 / m
This is the average energy lost to the ions per collision, and we can use it to calculate the average loss per unit volume of the metal, which is given by:
(ne2 / m) E2
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A phone sells for $230. It is now on sale for 30% off. How much money will April save if she buys the phone on sale?
If the phone is in sale of 30% off, the money April save if she buys the phone on sale is $69.
A sale is a reduction of the basic price of a good or a service. It can occur on any stage in the process of production.
It is given that a phone sells for $230. It is now on sale for 30% off.
Now, Cost price = $230
sale percentage = 30%
so, the sale price = [tex]230 \times 30\%\\[/tex]
or [tex]230 \times \frac{30}{100}[/tex] = $69
therefore, the money April will save if she buys the phone on sale is $69.
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Use the grouping method to factor the polynomial below completely. 3x³ + 9x² + 5x + 15 O A. (3x²+3)(x + 5) O B. (3x²+5)(x+3) ○ C. (3x² + 3)(x+3) D. (3x² + 5)(x + 5)
The factor of the expression is (3x²+ 5)(x + 3)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
3x³ + 9x² + 5x + 15
Group the terms in two's and factor each term
Using the above as a guide, we have the following:
3x²(x + 3) + 5(x + 3)
Factor out x + 3
So, we have the following representation
(3x²+ 5)(x + 3)
Hence, the solution is (3x²+ 5)(x + 3)
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PLS HELP!!! I NEED IT FOR LESS THAN 20 MINUTES
Answer:
51 stamps
Step-by-step explanation:
since salman's amount is going from 5 to 45 its being multiplied by nine. to keep the ratio true, you need to multiply the other two numbers by 9 too. Nathan then has 12 stamps and Gordon has 63. 63-12=51
At a restaurant, Table A's bill of €72 is split equally
between the people at the table. Table B has two more
people than Table A, and its bill of €108 is also split
equally between the people at the table. Each person at
Table A pays the same amount as each person at Table B.
How many people were at Table A?
There were total 4 people at table A and each of them pay €18.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Table A's bill of €72 is split equally.
and, Table B has two more people than Table A and its bill of €108 is also split equally.
let number of people at table A be x and at table B be (x+2).
So, the number of people
x/ 72 = (x+2)/108
108x = 72x + 144
108x - 72x = 144
36x= 144
x=4
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How many 200 mL glasses can be filled using a 2.2 L bottle of cola?
Answer:
11 glasses
Step-by-step explanation:
There are 200 ml glasses and we have 2.21 liter of bottels. So first of all covert liter into ml so we get 2210 ml of coca cola.now divide 2210 by 200 so we get 11 glasses
Fill in the missing numbers to complete the linear equation that gives the rule for this table.
x y
3 91
4 89
5 87
6 85
The linear equation for the given coordinate points is y=-2x+97.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, the coordinate points are (3, 91) and (4, 89).
Here, slope (m)= (89-91)/(4-3)
m= -2
Substitute m=-2 and (x, y)=(3, 91) in y=mx+c, we get
91=-2(3)+c
91=-6+c
c=97
So, the equation is y=-2x+97
Therefore, the linear equation is y=-2x+97.
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Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.
1. (3x²)(-2x⁴)=3(-2)x²•⁴=6x⁸
2. 4a²•3a⁵=(4+3)a²+⁵=7a⁷
3. x⁶•x•x³=x⁶+³=x⁹
4. 3⁴•2³=6⁴+³
Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".
Step-by-step explanation:
easy
A ladder leans against the wall of a building. The ladder measures
36 inches and forms an angle of 61' with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.
Show your work here
ground to top, in inches:
base to wall, in inches:
Answer:
A ladder leans against the wall of a building. The ladder measures 66 inches and forms an angle of 45 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder?
Step-by-step explanation:
The diagonals of parallelogram ABCD intersect at P. Select all the statements that must be true.
The required true statements are B). BC = AD, D). ∠CAD = ∠LACB, E). ∠BPC = ∠APD
What is parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
According to question:The statements that must be true are:
B. BC = AD (Opposite sides of a parallelogram are equal in length)
D. ∠CAD = ∠LACB (Opposite angles of a parallelogram are equal in measure)
E. ∠BPC = ∠APD (Opposite angles of a parallelogram are equal in measure)
The statements A and C are not necessarily true for all parallelograms.
Statement A (AP = CP) is only true for parallelograms that are rectangles or rhombi, where the diagonals bisect each other.
Statement C (m∠ABC = 90) is only true for parallelograms that are rectangles or squares, where each angle is a right angle.
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In a group of 48 children, 25% have blue eyes. How many children do not
have blue eyes?
Answer:
Step-by-step explanation:
48----------------100%
x------------------75%
x=36
what is the area of this figure?
Answer:
213 km
Step-by-step explanation:
Which expression has the same value as -18-(-9)?
O -18÷2
O −12+(-3)
O -10÷5
O-8+(-4)
Answer: -8 + (-4 )(look at the image for the solution)
Step-by-step explanation:
PLEASE HELP I HAVE 2 MINUTES
PLEASE THIS IS VERY EASY.
The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Nina buys a new rug that matches three colors in her bedroom. The rug is a rectangle. There are eight squares on the rug. Four-eighths of the squares are green. One-fourth of the squares are purple.
The amount of green rug is given as,
⇒ 4/8
⇒ 1/2 square units
The amount of purple rug is given as,
⇒ 1/4 square units
The number of green rugs is more than the number of purple rugs.
The amount of blue rug is given as,
⇒ 8 - 1/4 - 4/8
⇒ (64 - 2 - 4) / 8
⇒ 29/4 square units
The number of green rugs is more than the number of purple rugs. Then the amount of blue rug will be 29/4 square units.
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If 6% of a number is 48, find 1% of that number.
Answer:
8
Step-by-step explanation:
0.06/48=800 0.01x800=8
10. at a pizza shop there is a deal going on that you can get a pizza for $3.00. you can choose thick or thin crust, red or white sauce, and one topping of either pepperoni, sausage, or vegetarian. create a tree diagram to display the sample space on your worksheet. how many total outcomes are there?
The number of total outcomes is 12.
Here is a tree diagram for the pizza options:
Copy code
/ | \
Thick Thin
/ | \
Red White Red White
/ | \ / | \ / | \
Pep Saus Veg Pep Saus Veg Pep Saus Veg
There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:
Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)
Total Outcomes = 12
Therefore, there are 12 total outcomes.
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(10x - 4) + ( -7 + x) = (10x +) + ( -4 + )
The variable gets eliminated, then the equation has no solution.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)
Simplify the equation, then we have
(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)
10x - 4 - 7 + x = 10x + 2 - 4 + x
11x - 11 = 11x - 2
11x - 11x = 9
The variable gets eliminated, then the equation has no solution.
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The correct equation is given below.
(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)
If the diameter of the pie is ten inchefls, what is the approximate arc length of one slice of pie? (A) 1.67 inches (B) 13.08 inches (c) 3.14 inches (D) 5.24 inches
Option (D) is correct. The approximate arc length of one slice of pie is 5.24 inches.
Assuming that the pie is cut into equally sized slices, we can use the formula for the arc length of a circle sector:
Arc length = (angle/360) x 2πr
where r is the radius of the circle, and angle is the central angle of the sector in degrees.
Since the diameter of the pie is 10 inches, the radius is half of that, or 5 inches. To find the central angle of one slice of pie, we need to know how many slices the pie is cut into. Let's assume it's cut into 6 slices, which means each slice is a sector with a central angle of 60 degrees (360 degrees / 6 slices).
Now we can calculate the arc length of one slice:
Arc length = (60/360) x 2π(5) = π(5/3) ≈ 5.24 inches
Therefore, the answer is (D) 5.24 inches.
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2/2^(4-3x)= 8
find x
The equation will be solved x = 2.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
The given equation 2/[tex]2^{(4-3x)}[/tex] = 8
[tex]2^{(4-3x)}[/tex] = 2/8
[tex]2^{(4-3x)}[/tex] = 2⁻²
So we can take 4-3x = -2
3x = 4+2
x = 6/3 = 2
Hence, the equation will be solved x = 2.
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Forest rangers at a state park have observed a decline in the rate of trees per
acre over a 5-year period. At the beginning of their observations, there was an
average of 48 trees per acre. At the end of the 5-year period, there was an
average of 42 trees per acre. If this trend continues, how many trees per acre
will there be 4½ years from the end of the 5-year observation period?
helppp
There will be 36.6 trees per acre after 4½ years from the end of the 5-year observation period. The solution has been obtained by using unitary method.
What is the unitary method?
The value of each individual unit is first determined using the unitary method, and only then is the value of the required number of units determined.
We are given that at the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an average of 42 trees per acre.
So, decline in trees per acre in 5 years is 48 - 42 = 6 trees per acre
So, decline in 1 year = 6/5 = 1.2 trees per acre
Similarly, decline in 4.5 years = 1.2 * 4.5 = 5.4 trees per acre
Thus, trees left per acre = 42 - 5.4 = 36.6 trees
Hence, there will be 36.6 trees per acre after 4½ years.
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the histogram below gives the length of service of members of the department of chemistry at a particular university. the classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty. (a) what percent of the department faculty have 5 or more years of service? (b) if a member of the department is chosen at random to serve on a university committee, what is the probability (in decimal form) that the chosen representative will have between 5 and 35 years of service? (c) what is the probability the representative above will have less than 5 years of service given that the person has less than 15 years of service?
a. The percentage of the department faculty have 5 or more years of service is 76%
b. Probability that a faculty member chosen at random has between 5 and 35 years of service is 0.4.
c. The probability the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.
Histogram:The histogram is used to estimate probability of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.
(a) The per cent of the department faculty have 5 or more years of service is calculated as follows,
The number of department faculty have 5 or more years of service is 38 and total frequency 50, therefore the required probability is:
P(x > 5) = 38/50 = 0.76 = 76%
(b) The probability (in decimal form) of representative will have between 5 and 35 years of service is given as,
P(5 < X < 35) = 20/50 = 0.4 = 40%
(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of service is calculated as follows,
P(X < 5 | X < 15) = 28/40 = 0.7
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