The measure of angle C of the given triangle is 42.8°.
Solve for measurement(s) of angle c?To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,
sin A / a = sin B / b = sin C / c
where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.
Given ∠A = 61°, c = 35, a = 45
∴( sin A)/a = (sin C)/c
(sin 61° )/ 45 = (sin C) / 35
sin c = ((sin 61°) / 45) × 35
sin c = 0.68
c ≈ 42.8°
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Complete question:
You have given a triangle ΔABC, where ∠A = 61°, c = 35, a = 45. Solve for measurement(s) of angle c.
-4t + 14 = -9t + 24
what value of t makes the equation true
Answer: t=2
Step-by-step explanation:
-4t+14= -9t+24
+9t =+9t
5t+14=24
-14=-14
5t=10
5t/5 10/5
t=2
Need help with 1-6 pls
1. The value of n in 3n + 19 = 28 will be 3.
2. The value of b in 34 - 4b = 18 will be 4.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The value of n in 3n + 19 = 28 will be:
3n + 19 = 28
Collect the like terms
3n = 28 - 19
3n = 9
Divide
n = 9 / 3
n = 3.
The value of b in 34 - 4b = 18 will be:
34 - 4b = 18
4b = 34 - 18
4b = 16
Divide.
b = 16 / 4
b = 4
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the towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. the cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. what is the height of the cabl...
As the cable between the towers has the shape of a parabola, the height of the cable 200 feet from a tower is 40 feet.
Consider the origin of coordinate system at the bridge level midway between the towers and the cable has the shape of a parabola. It is the vertex of the parabola. The general equation of a parabola is given by y = a(x – h)^2 + k where (h, k) denotes the vertex. Hence, based on the provided information, the equation is;
y = a^x^2
The height of the tower above the road is 160 feet which is 400 feet from the vertex. Hence, x = 400 feet and y = 160 feet.
Substituting the values,
160 = a^(400)^2
a = 0.001
Hence, the equation of the given parabola is:
y = 0.001x^2
In order to calculate the height of the cable at 200 feet from the tower, the value of x = 400 – 200 = 200 feet
y = 0.001(200)^2 = 40 feet
Note: The question is incomplete. The complete question probably is: The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 feet from a tower?
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You borrowed $95 for 1 year at 5. 2% interest that is compounded semi annually. What will you pay back in full
You will pay back $100.00
We know that the formula for the compound ineterst:
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
where, A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
n = number of compounding periods
t = time in years
First, convert R as a percent to r as a decimal
r = 5.2/100
r = 0.052 rate per year,
Now we solve the equation for A
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
[tex]A = 95\times (1 +\frac{0.052}{2})^{2\times 1}[/tex]
A = 95.00 × (1 + 0.026)²
A = 100.004
A ≈ 100
Therefore, the total amount accrued with compound interest on a principal of $95.00 at a rate of 5.2% per year compounded semi annually is $100.00.
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Ken Made $14,500 in five months at his new job.How much can he expect to make in two years if his pay remains constant.
If Ken's pay remains constant, he should expect to earn $69,600 in two years.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represents the wages.x represents the time in months.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 14,500/5
Constant of proportionality, k = 2,900
In two (2) years, Ken's wages is given by:
y = kx
y = 2,900(24)
y = $69,600.
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Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously. How much would Serenity need to invest, to the nearest hundred dollars, for the value of the account to reach $670 in 11 years?
Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously therefore Serenity would need to invest $400 to the nearest hundred dollars, for the value of the account to reach $670 in 11 years.
This is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
We can solve the problem by :
1+(0.044÷365)= 1.0001205479
Yearly impounding factor, 1.0001205479^365=1.0449795838
For a period of 11 years, maturity factor,1.0449795838^11 = 1.6225043167.
$1 becomes $1.6225043167.
If Maturity value is to be,$670 which is amount to be invested,
670÷ 1.6225043167 = 412.942
To the nearest 100 dollars is $400.
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A dozen long stemmed roses cost $48 What is the cost per rose?
Answer:
$4
Step-by-step explanation:
Given;
Dozen long stemmed roses cost $48
Question:
What is the cost per rose?
Solve:
Based on the given, we can see that it states that a dozen long stemmed roses cost $48.
Knowing that - Dozen = 12
Since, we know that dozen equal 12. Hence, 12 long stemmed roses cost $48.
Now, divide the cost by the amount to find the cost per rose.
Thus,
48 ÷ 12 = 4.
Therefore, the cost per rose is $4.
RevyBreeze
Liquid A and liquid B are mixed together in the ratio 4:11 by volume to make
liquid C.
Liquid A has density 1. 05g/cm
Liquid B has density 1. 27 g/cm
A cylindrical container is filled completely with liquid C.
The cylinder has radius 5 cm and height 20 cm.
Work out the mass, in g, of the liquid in the container.
Give your answer correct to 3 significant figures.
The mass of the liquid in the container is 18.17 g, correct to 3 significant figures
Calculate the volume of the container:
Volume = πr2h
Volume = π x (5 cm)2 x 20 cm
Volume = 3,142 cm3
Calculate the total volume of liquid A and B:
Total volume of A and B = 4:11
Total volume of A and B = 4 + 11 = 15 cm3
Calculate the volume of liquid A:
Volume of A = 4/15 x 15 cm3
Volume of A = 4 cm3
Calculate the volume of liquid B:
Volume of B = 11/15 x 15 cm3
Volume of B = 11 cm3
Calculate the mass of liquid A:
Mass of A = Volume of A x Density of A
Mass of A = 4 cm3 x 1.05 g/cm3
Mass of A = 4.2 g
Calculate the mass of liquid B:
Mass of B = Volume of B x Density of B
Mass of B = 11 cm3 x 1.27 g/cm3
Mass of B = 13.97 g
Calculate the total mass of liquid C:
Total mass of C = Mass of A + Mass of B
Total mass of C = 4.2 g + 13.97 g
Total mass of C = 18.17 g
The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.
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Lucy ha a trawberry lace that i 36cm long. She need piece 18mm long to decorate a cake
The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.
To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.
We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.
To summarize, the formula used to calculate the number of pieces Lucy needs is:
(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.
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If α and β are the zero of the quadratic polynomial p(x)=4x 2 −5x−1, find the value of α 2 ββ2 α
The value of α2ββ2α2 is -20. a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation.
Given,
p(x) = 4x2 − 5x − 1
α and β are the zeroes of the quadratic polynomial p(x).
Therefore,
α + β = -5/4
and
αβ = 1/4
Therefore,
α2ββ2α2 = (α+β)2αβ = (-5/4)2(1/4) = (-5/4)(-5/4)(1/4) = 25/16 = -20
Given a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation. To find the value of α2ββ2α2, we first need to find the sum and product of the two zeroes, which can be done by solving the equation. The sum of the zeroes is -5/4 and their product is 1/4. We can then use these values to calculate the value of α2ββ2α2, which is equal to (-5/4)2(1/4) = 25/16 = -20. Thus, the value of α2ββ2α2 is -20.
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The coordinates of equilateral triangle ABC are A(0,-6) B(0,0) and C(x,y). Find the coordinates of c if the triangle is in the fourth quadrant
The coordinates of point C are C(0,-sqrt(36 - x²))
An equilateral triangle has all sides of equal length and all angles of 60 degrees. Since the triangle is in the fourth quadrant, so we know that both the x and y coordinates of point C must be negative.
We can use the distance formula to find the length of the sides of the triangle:
AB = sqrt((0 - 0)² + (-6 - 0)²) = 6
BC = sqrt((x - 0)²+ (y - 0)²) = AC = sqrt((x - 0)² + (y - (-6))²) = sqrt(x² + (y + 6)² = 6
We may now use the notion that all angles in an equilateral triangle equal 60 degrees. We know that point A is at (0,-6) and point B is at (0,0), therefore we can use the slope of line AB and the length of the side to compute point C's coordinates.
Line AB has a slope of (0 - (-6))/(0 - 0) = 6/0 = undefined.The slope of a line perpendicular to AB is the negative reciprocal of AB's undefined slope; so, line AB is parallel to the x-axis. So C(x,y) has the same x-coordinate as B(0,0) but a different y-coordinate.
The length of the side is 6, so we can use this information to find the y-coordinate of point C:
y = sqrt(6² - x²) = sqrt(36 - x²)= -sqrt(36 - x²)
So, the coordinates of point C are C(0,-sqrt(36 - x²))
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in a school of 330 students,85 of them are in the drama club 200 of them are in a sports team and 60 students do drama and sports
Answer: There would be 345 students because 85+200+60=345
Step-by-step explanation: it equal 245
Solve each trigonometric function IN THE INTERVAL [0, 2).
sin(x) + 1 = cos(x)
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The trigonometric function is given below.
sin(x) + 1 = cos(x)
Simplify the equation, then we have
sin(x) + 1 = cos(x)
(sin(x) + 1)² = cos² (x)
(sin(x) + 1)² = 1 - sin² (x)
sin² (x) + 2sin x + 1 = 1 - sin² (x)
2sin² (x) = 0
sin (x) = sin 0
x = 0
The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.
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In 1985 Mat Biondi set a record for the men's 100 m freestyle event. It took him 49. 17 s to finish the race. What was his average speed to the nearest hundredth?
The average speed is S=2.033 m/s
The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time.
The unit of speed is a meter/second.
Speed formula can be used to find the speed of objects, given the distance and time taken to cover that distance.
To calculate the average speed we have a general formula:
speed = distance ÷ time.
Given distance=100m
time=49.17 s
Plugging the values in the above formula:
speed=100/49.17
speed=2.033
Therefore, the average speed is 2.033 m/s.
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Find the distance between the points ( – 18,11) and ( – 18, – 19).
Answer: 15.4
Step-by-step explanation: d= [tex]\sqrt{(-18)^{2} - 18^{2}) +((-19)^{2} - 11^{2})\\[/tex]
[tex]\sqrt{361 - 121}[/tex]
[tex]\sqrt{240}[/tex]
15.4
mr. brown went grocery shopping to buy meat for his annual office picnic. he bought 7 3 4 pounds of hamburger, 17.85 pounds of chicken, and 6 1 2 pounds of steak. how many pounds of meat did mr. brown buy?
There are 32.1 pounds of meat.
Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.
Add up the pounds of meat.
7.75 + 17.85 + 6.5 = 32.1 pounds
Thus, there are 32.1 pounds of meat.
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Tell whether each function is written in standard form. If not, rewrite it
in standard form.
1. y = 3x
2. 7-y = 5x + 11
Given a gla
3. -2(x+y)+9=1
Answer
1: 3x-y=0
2: 5x+y= -4
3: y=-x+4
Step-by-step explanation:
Which of the following functions maps 3 to -6?
O f(x)=x-3
O f(x)=3-1²
O f(x)=3-x
O f(x)= x + 3
Answer:
A
Step-by-step explanation:
Need help brainliest explination
Rick and his dad are making rock candy. The first step is to pour sugar into boiling water. So, Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water.
What fraction of the bag of sugar does Rick's dad pour into the water?
The fraction of the bag of sugar that Rick's dad pour into the water is 2/3
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Fractions is a part of a whole number. It is the ratio of two numbers. The top number is the numerator while the bottom number is the denominator. Hence:
Fraction = numerator / denominator
Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water. Hence:
Fraction of sugar poured into water = amount of sugar poured in water / total amount of sugar
Substituting:
Fraction of sugar poured into water = 2 cups / 3 cups = 2/3
Ricks dad pour 2/3 of the sugar into the water
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Please i need urgent help here right now
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
What is the discriminant?The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given as,
2(c² + d²)x² + (c - d)x + 9 = 0
Then the discriminant is given as,
D < 0
(c - d)² - 4 × 2(c² + d²) × 9 < 0
(c - d)² > 72 (c² + d²)
The expresssion (c - d)² must be positive. Then we have
(c - d)² > 0
c - d > 0
c > d
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
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A cheetah travels
90 feet in 7 seconds.
How fast is that?
??? feet per second
The speed of the cheetah based on the information provided is 12.85 feet per second.
How to calculate the speed of the cheetah?The speed of a body in movement can be expressed using different units such as:
kilometers per hour = km/hfeet per second= ft/smeter per minute = m/mBased on this, it is necessary to find how much distance the cheetah covers every second by dividing the distance given by the time given as it follows:
90 feet / 7 seconds=12.85 feet per secondTherefore, the speed of the cheetah is 12.85 feet per second
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Pleaseee help 20 points
Maria read 9 books over summer vacation. Jim read b more books than Maria. Choose the
expression that shows how many books Jim read.
A) 9
B) b - 9
C) 9 + b
D) 9 - b
Answer:
c
Step-by-step explanation:
it wouldnt just be 9, thats marias books, to get what jim ahs and hers its 9+b
b representing the amount jim read
a survey for kindergartners asked about their favorite color. the children were asked to check the box corresponding to blue, red, green, yellow, or orange. what is the scale of measurement for this question? group of answer choices ordinal interval nominal ratio
Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.
Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.
Ratio scales are interval scales where lengths are expressed in relation to a rational zero.
Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.
Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.
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Joanne made emi-annual depoit of ₱820 into a aving account with an interet of 5% compounded emi-annually. How much i the account balance after eleven year?
The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.
The account balance after eleven years would be ₱14,925.08.
1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.
2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.
3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.
The account balance after eleven years would be ₱14,925.08.
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Aaliyah and her children went into a bakery and will buy donuts and brownies. She must buy a minimum of 11 donuts and brownies altogether. Write an inequality that would represent the possible values for the number of donuts purchased, � d, and the number of brownies purchased, � . b.
The required inequality is d + b ≥ 11 representing the possible values for the number of donuts and brownies purchased.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We can represent the number of donuts purchased as d, and the number of brownies purchased as b. The inequality that represents the minimum number of donuts and brownies that must be purchased altogether is:
d + b ≥ 11
This inequality states that the total number of donuts (d) and brownies (b) purchased must be greater than or equal to 11.
This inequality can be represented graphically on a number line, with point 11 being the boundary between the solutions that satisfy the inequality and those that do not.
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Simplify the expression.
-2. 6f +0. 7f-14-9
- 2. 6f +0. 7f-14-9 =
(Simplify your answer. Use integers or decimals for any numbers in the expression. )
what’s the answer
The simplified form of expression -2.6f +0.7f - 14 - 9 is -1.9f - 23
We know that an expression is nothing but a mathematical statement that consists of at least two terms( variables or constants) along with one algebraic operation.
As we know simplifying an expression means rewriting the same expression in a compact manner with no like terms.
To simplify expressions, we combine all the like terms ; solve all the given brackets, if any.
In the simplified expression, we left with unlike terms which cannot be reduced further.
Consider an expression:
-2.6f +0.7f - 14 - 9
We simplify above expression.
-2.6f +0.7f - 14 - 9
= (-2.6 + 0.7)f - (14 + 9) .........(combine like terms)
= -1.9f - 23
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39-3×12²÷24 please solve and show steps
Answer:
To solve the equation:
39 - 3x12²÷24
Step-by-step explanation:
First, we need to simplify the expression inside the parentheses:
12² = 12*12 = 144
Then we can substitute that value into the equation:
39 - 3x144÷24
Next, we can simplify the expression inside the parentheses:
144÷24 = 6
Then we can substitute that value into the equation:
39 - 3x6
Now we can solve the equation by performing the multiplication and subtraction:
39 - 18 = 21
So the solution is 21.
Steps:
1. 12² = 144
2. 144÷24 = 6
3. 39 - 3x6 = 39 - 18 = 21
So, 39-3*12²÷24 = 21
Answer:
36
Step-by-step explanation:
39 - 3 x [tex]12^{2}[/tex] ÷ 24 First simplify the exponent
39 - 3 (12 x12) ÷ 24
39 - 3 x 24 ÷ 24 Next do multiplication and division going from left to right
39 - 72 ÷ 24
39 - 3 Subtract 3
36
On a certain hot summer's day, 544 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $964.00. How
many children and how many adults swam at the public pool that day?
Answer:
248 children
296 adults
Step-by-step explanation:
Define the variables:
Let x = number of children using the public pool.Let y = number of adults using the public pool.Given information:
A total of 544 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totalled $964.00.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}\;\;\;\;\:\:\:x+y=544\\1.5x+2y=964\end{cases}[/tex]
Rearrange the first equation to isolate x:
[tex]\implies x=544-y[/tex]
Substitute the found expression for x into the second equation and solve for y:
[tex]\implies 1.5(544-y)+2y=964[/tex]
[tex]\implies 816-1.5y+2y=964[/tex]
[tex]\implies 816+0.5y=964[/tex]
[tex]\implies 0.5y=148[/tex]
[tex]\implies y=296[/tex]
Therefore, 296 adults swam at the public pool.
Substitute the found value of y into the equation for x and solve for x:
[tex]\implies x=544-296[/tex]
[tex]\implies y=248[/tex]
Therefore, 248 children swam at the public pool.
What equation do you get when you solve sy-nd= dy/g for y? Please show work thank you!!
nareh ave r.300. hi brother ureh ave r.220. how much money mut nareh gave hi brother o that both of them will have the ame amount of money
Nareh should give his brother $80. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.
Subtract the amount of money that Urch has from the amount of money that Nareh has:
300 - 220 = 80
Nareh should give his brother $80 so that both of them will have the same amount of money.
Nareh currently has $300 and Urch currently has $220, so Nareh should give Urch $80 in order to make them have the same amount of money. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.
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