Given the exponential function f (x) and the logarithmic function g(x), which of the following statements is true?
Exponential function f of x equals negative 4 to the power of x minus 1 that decreases to the right passing through the point 0 comma negative 2 and logarithmic function g of x equals negative log in base 3 of x plus 3 decreasing from left to right passing through the point 1 comma 3
As x→∞, f (x)→∞ and g(x)→0.
As x→∞, f (x)→ –∞ and g(x)→ –∞.
As x→∞, f (x)→2 and g(x)→0.
As x→∞, f (x)→2 and g(x)→∞.
Answers
The correct statement regarding the end behavior of the functions is given by:
As x→∞, f (x)→∞ and g(x)→0.
What is the end behavior of a function f(x)?It is given by the limits of f(x) as x goes to infinity.
In this problem, the function f(x), the limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} f(x) = -1[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = -\infty[/tex].For function g(x), the limit is given as follows, as it is not defined for negative values:
[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex].
Hence the correct statement is:
As x→∞, f (x)→∞ and g(x)→0.
As it considers both positive infinity and negative infinity just as infinity.
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Related Questions
"clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute cor the last 1 1/3 minute. what is the total number if pins"
Answers
After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins
As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute (Mixed Fraction form)
We are supposed to find the total number if pins by the clown.
Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes
[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.
Therefore total time = 3.84minutes
Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute so, the number of pins in the last [tex]1\frac{1}{3}[/tex] minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)
So total number of bowling pins = [tex]12+25 = 37[/tex] pins
Mixed Fraction: A mixed fraction is one that is represented by both of its quotient and remainder present in a single expression. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.To learn more about such questions, click on the link given below:
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(-4, 12) and (-7, -3) write an equation of the line in slope intercept form that passes through the points.
Answers
Answer:
The equation in slope-intercept form is: [tex]y=5x+32[/tex]
Step-by-step explanation:
To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.
Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.
To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4 and 12, we get [tex]12=5(-4)+b[/tex].
Then we can solve for [tex]b[/tex].
[tex]12=5(-4)+b[/tex]
[tex]12=-20+b[/tex]
[tex]32=b[/tex]
So, our slope is 32.
We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]
The coldest temperature ever recorded in Mathville was -19°F. This happened on January 30th, 1955. The normal low for that day is 10°F.
How much colder was the record temperature than the normal low temperature?
Answers
Answer:
-29⁰F
Step-by-step explanation:
Because -19-10=-29.
subtract x^2+8x from -3x^2-3x-7.
Answers
Answer: -4x²-11x-7
Step-by-step explanation:
[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]
What two im i missing?
Answers
A hamburger and French fries cost $13. A hamburger and two sodas cost $14. A hamburger, French fries, and a soda costs $16. Write the system of equations that describes this situation, then solve to find the price of each. (PLEASE SHOW WORK)
Answers
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:
x + y = 13 (1)
Also:
x + 2z = 14 (2)
And:
x + y + z = 16 (3)
From the three equations:
x = 8, y = 5, z = 3
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
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48 inches long and 36 inches wide. What is the area?
Answers
Answer:
1728
Hope this helps :)
Jenkins Company uses a job order cost system with overhead applied to jobs on the basis of direct labor hours. The direct labor rate is $20 per hour, and the predetermined overhead rate is $15 per direct labor hour. The company worked on three jobs during April. Jobs A and B were in process at the beginning of April. Job A was completed and delivered to the customer. Job B was completed during April, but not sold. Job C was started during April, but not completed. The job cost sheets revealed the following costs for April:
Job A Job B Job C
Cost of Jobs in Process, April 1, Current Year $ 12,000 $ 1,000 $ 0
Direct Materials Used 2,000 8,000 9,000
Direct Labor 10,000 8,000 3,000
Applied Manufacturing Overhead ? ? ?
Required:
If no other jobs were started, completed, or sold, determine the balance in each of the following accounts at the end of April:
work in progress
finished goods
cost of goods sold
Answers
The work in process(Job C) is $14,250
The finished goods(job B) is $23,000
The cost of goods sold(job A) is $31,500
What are work in process, finished goods and cost of goods sold in this case?
The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.
Job A:
Cost of job in process=$12,000
direct materials used=$2,000
direct labor=$10,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$10,000/$20=500 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=500*$15=$7,500
cost of goods sold=$12,000+$2,000+$10,000+$7,500
cost of goods sold=$31,500
Job B:
Cost of job in process=$1,000
direct materials used=$8,000
direct labor=$8,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$8,000/$20=400 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=400*$15=$6,000
finished goods=$1,000+$8,000+$8,000+$6,000
finished goods=$23,000
Job C:
Cost of job in process=$0
direct materials used=$9,000
direct labor=$3,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$3000/$20=150 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=150*$15=$2,250
work in progress=$0+$9,000+$3,000+$2,250
work in progress=$14,250
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There are 6 black marbles and 4 red marbles in a jar. If you add 4 red marbles to the jar, how many black marbles do you need to add to keep the ratio of black marbles to red marbles the same?
Answers
You need to add 6 red marbles for the ratio to stay the same
How many black marbles do you need to add?The given parameters are:
Black = 6
Red = 4
Represent as ratio
Ratio = Red : Black
This gives
Red : Black = 4 : 6
When you add 4 red marbles, we have:
4 + 4 : 6 + x = 4 : 6
Where x represents the additional number of black marbles
This gives
8 : 6 + x = 4 : 6
Multiply 4 : 6 by 2
So, we have:
8 : 6 + x = 8 : 12
By comparing both sides, we have
6 + x = 12
This gives
x = 6
Hence, you need to add 6 red marbles for the ratio to stay the same
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A machinist is required to manufacture a circular metal disk with area 600 cm2 . (a) What radius produces such a disk? (b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius? (c) In terms of the limit limx→a f(x) = L, what is f(x)? What is a? What is L?
Answers
The required radius and error in radius is 13.8 cm and ± 0.12cm
Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.
The area of a circle is given by the pie times square of the radius.
Area of circle = πr^2
Here,
a) The given area of disk = 600 cm²
πr² = 600
r = √600/3.14
r = 13.8 cm
b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm
Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.
Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.
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-0.75(12x+60) = -x-8x - 15.
Answers
Answer:
Step-by-step explanation:
-9x - 45 = -7x - 15 (Distribute -0.75 to (12x+60)) (x-8x = -7x)
-30 = 2x (add 15 to both sides and add 9x to both sides)
-15 = x (divide both sides by 2)
Given the function f(x) = |x+3|, find each of the following.
f(6), f(- 10), f(0)
f(6) = ?
Answers
The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
What is a function?A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the function;
f(x) = |x+3|
To determine f(6)
Substitute the value of x as 6
We have;
f(6) = | 6 + 3 |
f(6) = 9
To determine f(-10)
Substitute the value of x as - 10
We have;
f(-10) = | -10 + 3 |
f(-10) = | -7|
f(-10) = 7
To determine f(0)
Substitute the value of x as 0
We have;
f(0) = | 0 + 3|
f(0) = 3
Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
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A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
Answers
The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
According to the question we have been given that
The height of the small plant = [tex]2\frac{1}{2}[/tex] inch
In 1 week the plant grows = [tex]\frac{3}{4}[/tex] inch
We need to find the height of the small plant after 3 weeks.
For that we will first find how much tall it will be in 3 weeks using unitary method that is,
1 week = [tex]\frac{3}{4}[/tex] inch
3 week = [tex]\frac{3}{4}[/tex] * 3 inch
= 9/4 inch
Therefore the height of the small plant after 3 weeks will be
[tex]=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}[/tex]
hence the height is 19/4 inch
And the method which will not give the correct number of inches is the first option which is
multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.
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help me pleaseeeeeeeeee
Answers
Answer:
Step-by-step explanation:
x + x + 16 = 90
2x +16 = 90
2x = 74
x = 37
a cat on a table 960m views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table
Answers
The angle of depression of the meat from the top of the table is 40°
This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle
to know the angle of depression of the meat from the top of the table
we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.
Tan is the ratio of perpendicular and base of the triangle
which is = 96/114.4
tan Ф=0.8392
To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.
Ф = tan-1 0.8392
Ф = 40°
The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.
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Simplify 12/16 to lowest terms and find an equivalent fraction that has a denominator of 32.
10/00
O
0 / 4
Answers
[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]
Need help with this please
Answers
Answer:
HELP WITH WHAT?
Step-by-step explanation:
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
Answers
The INEFFICIENT point of production in the given graph is represented by Point A , the correct option is option (a).
The given graph is for skateboards vs Bikes .
We need to find the point representing the Inefficient Point of Production.
The Production Possibility Curve points are said to be Inefficient when the resources are not utilized to the fullest.
In the given Production Possibility Curve between Skateboards and Bikers the point A is the inefficient point of production .
Therefore , the Inefficient point of production in the given curve is represented by Point A , the correct option is option (a)
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Find the compound interest and the total amount after three years if the interest is compounded half yearly. if principal is ₹1024 rate of interest 100% per annum
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]
please help
please hurry
Answers
The turning point of the equation of the graph f(x) = |x - 4| is (4, 0)
How to determine the turning point of the graph?The equation of the graph is given as
f(x) = |x - 4|
The above equation is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is
Vertex = (h, k)
The vertex also represents the turning point of the absolute value function
From the given equation, we have
(h, k) = (4, 0)
Hence, the turning point of the graph is (4, 0)
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Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances:
DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600
CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260
DEBIT: Cash Dividends: 1,000
CREDITS: Fees Earned: 75,000
DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800.
Total Debits = 135,260; Total Credits = 135,260
You have prepared the Income Statement and the Statement of Retained Earnings, now it is time to prepare the Classified Balance Sheet.
What amount do you report for Plant Assets? Specify as a whole number.
Answers
The amount to report for Plant Assets in the Classified Balance Sheet of the company is $24,600
What are plant assets?
Plant assets are long-term fixed assets used to manufacture or sell products and services for Adventure Travel. These assets are of tangible nature and of monetarily benefits to the company for more than one accounting year.
The only plant assets in this case is the office equipment bearing in mind that it has a contra entry, in other words, the $29,600 is the cost of the office equipment , we need to deduct the accumulated depreciation on it so as to determine its current book value
plant assets=$29,600-$5,000
plant assets=$24,600
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What is the formula used to arrive at x^2-11x+10
Answers
Answer:
Quadratic Formula
Step-by-step explanation:
x^2-11x+10=
x^2-x-10x+10=
x(x-1)-10(x-1)=(x-10)(x-1)
Evaluate the problem
Answers
Answer:
400
Step-by-step explanation:
Change the 16 and the 64 in the numerator to exponents
2^4 x 10^2 x 4^3/2^4 x 4^2
Simplify
10^2 x 4
100 x 4
HELP
The scatterplot for age in months and number of diaper changes per day is shown.
Part A: Estimate and interpret the correlation coefficient. (5 points)
Part B: Create an influential point for this graph that would cause the correlation to decrease. Explain your reasoning.
Answers
Answer:
Here's an answer to part of your question.
Step-by-step explanation:
The older the kids get, the less you have to change their diapers. Therefore, that is why the graph is going down
Last year, Suzie's salary was $76,000. This year, she is getting a 8% raise. What will her new salary be?
Answers
[tex]76000\times1.08=\boxed{82,080}[/tex]
Answer:
82,080
Step-by-step explanation:
To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.
PLS ANSWER 50 POINTS Simplify 6-3/6-4
Answers
The expression 6-3/6-4 after simplification will look like 1.5.
Given that the expression is 6-3/6-4.
We are required to find the value after simplification.
Simplification or simplify fractions basically means to simplify a complicated mathematical expression to get a single or direct answer.
We have to use BODMAS rule for the simplification. The full form of BODMAS is Brackets, Open, Division, Multiplication,Addition and Subtraction. Simplication is nothing but to reduce the expression.
The expression is 6-3/6-4.
We have to do division first.
6-3/6-4 =6-0.5-4
Now we have to do subtraction now.
6-0.5-4=5.5-4=1.5
Hence the expression 6-3/6-4 after simplification will look like 1.5.
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this question has 2 parts:
Part A
Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t². Write the expression in factored form.
Part B
What is the height of the soccer ball 1.25 seconds after Callie kicks it?
______ feet
Answers
Part A The quadratic expression in factored form is 2t(19 - 8t)
Part B The height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft
Part A Write the expression in factored form.Since Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t².
So, the expression is a quadratic expression, we have that h(t) = 38t- 16t².
To write the expression in factored form, we find the common factors of both terms and factor them out.
So, h(t) = 38t- 16t²
= 2 × 19 × t - 2 × 8 × t × t
Factoring out 2 and t, we have
= 2 × t × (19 - 8 × t)
= 2t(19 - 8t)
So, the quadratic expression in factored form is 2t(19 - 8t)
Part B What is the height of the soccer ball 1.25 seconds after Callie kicks it?Since the quadratic expression h(t) = 38t- 16t² represents the height of the ball above the ground in feet, to find the height of the ball after 1.25 second,we substitute t = 1.25 s into the expression.
So, h(t) = 38t- 16t²
h(1.25) = 38(1.25) - 16(1.25)²
h(1.25) = 47.5 - 16(1.5625)
h(1.25) = 47.5 - 25
h(1.25) = 22.5 ft
So, the height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft
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Solve the quadratic equation 2h^2 + 100 = 0. If there is more than one solution, separate them with commas. If there are no solutions type DNE.
Answers
Answer:
h=sqrt2*5i, h=-sqrt 2*5i
Step-by-step explanation:
Answer:
DNE
No real solutions
Step-by-step explanation:
This Quadratic Equation: 2h² + 100 = 0
Factor out the common term 2:2(h² + 50) = 0
==> h² + 50 = 0
==> h² = -50
==> h = ±√-50
Since the square roots of negative numbers are not real numbers, we can say that this quadratic equation has no real solutions
Computing a percent mixture
A chemist mixes 225 milliliters of a solution that is 39% acid with 25 milliliters of a solution that is 19% acid.
Answer the questions below. Do not do any rounding.
(a) How many milliliters of acid are in the resulting mixture?
milliliters
(b) What percentage of the resulting mixture is acid?
0%
Answers
Part a: Resulting mixture: 92.2 milliliters.
Part b: Percentage of acid in the resulting mixture = 36.88%.
What is defined as the percentage?A percentage is a segment of a whole represented as a number between 0 or even 100 instead of as a fraction. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the fraction of the total by the total and multiply by 100.Part a: Find the both values from the given percentage;
225 millilitres of a solution contains is 39% acid.
39% of 225 = (39×225)/100 = 87.75 millilitres.
Now, 25 milliliters of a solution contains is 19% acid.
19% of 25 = (19×25)/100 = 4.75 millilitres.
Mixture solution = 87.75 + 4.75
Mixture solution = 92.2 milliliters of acid.
Part b: percentage of the resulting mixture is acid.
92.2 milliliters of the total 250 milliliters is acid.
= 92.2/250 × 100
= 36.88 %
Thus, 36.88% of the the resulting mixture contains acid.
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Find the quotient of The quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.. Write the final answer in scientific notation.
6 x 1048
6 x 1024
6 x 100
6 x 10−48
Answers
The quotient of the given problem using laws of exponents is; 6 * 10⁰
How to use the law of exponents?We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.
This is;
(30 * 10⁻²⁴)/(5 * 10⁻²⁴)
Now, we can break this down into like terms to get;
(30/5) * (10⁻²⁴/10⁻²⁴)
= 6 * 1
Now, 1 can also be written as;
10⁰ = 1
Thus, the solution of the given problem is; 6 * 10⁰
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