The required rate of simple interest is 1.75%.
Here, we have,
(Principal + Interest) is a straightforward interest equation.
A = P(1 + rt)
Where: A is the sum of the accrued principal and interest.
Principal Amount is P.
I is the interest rate.
r is the annual percentage rate of interest, or R/100.
R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.
Since I = Prt,
the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,
which may be represented as A = P(1 + rt).
Given: Principal is $1,300
Rate is 7% and the amount earned that is A-P is $159.25.
A = P(1 + rt)
Therefore substituting the values in the above mentioned equation, we get:
159.25= 1300(1+r×7)
On solving we get,
r= 1.75%
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complete question:
At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.
What rate of simple interest is offered at the
Blue Bank?
A study is conducted to determine if the age at which an individual can receive a driver's license should be increased. One
hundred people at a local high school are asked to take a survey.
The survey is composed of 5 statements to which people respond on a scale of 1-5. A response of 5 indicates strong
agreement with the statement and a response of 1 indicates strong disagreement with the statement. The results to the
statement, "The age at which an individual can receive a driver's license should not be increased." shows an average
response score of 1.5 and a standard deviation of 0.3.
One conclusion in the report of the study states that there may be a causal relationship between the age of those surveyed and
their responses.
Which statement regarding the report is true?
A)The report inaccurately stated the results of the survey because the majority of those surveyed were likely
teenagers.
B)The report accurately stated the results because the sample size was sufficient.
C)The report accurately stated the results of the survey because the majority obse surveyed were likely teenagers.
Reading Off
D)The report inaccurately stated the results because teenagers are likely to oppose an increase in the age
requirement.
Answer: B) The report accurately stated the results because the sample size was sufficient.
Step-by-step explanation:
The given statement in the report about a possible causal relationship between age and responses cannot be determined solely based on the information provided. However, the statement can be considered accurate because the sample size of 100 people from a local high school was sufficient to provide reliable results. The fact that the majority of those surveyed were teenagers does not make the report inaccurate or unreliable. The mean response score of 1.5 and the standard deviation of 0.3 are valid indicators of the attitudes of the surveyed group towards the age at which an individual can receive a driver's license.
I am truely not sure how to do
Answer:
[tex]x=4.865[/tex]
Step-by-step explanation:
We know the area of a rectangle to be [tex]base*height[/tex]. In this instance, [tex]base=(2x+10)in[/tex], [tex]height=(3x) in[/tex], and [tex]area=288in^2[/tex]
The next step is to plug these known values into the [tex]area=base*height[/tex] equation. It'll look like this:
[tex]288=(2x+10)*(3x)=6x^2+30x[/tex]
This simplifies to:
[tex]48=x^2+5x[/tex]
Next, we want to rewrite the equation so we can apply the quadratic formula to it. We are going to do this by subtracting 48 from each side. The new equation looks like this:
[tex]x^2+5x-48=0[/tex]
Next, we plug this into the quadratic formula:
[tex]x=\frac{-(5)+\sqrt{5^2-4(1)(-48)} }{2(1)}=4.865[/tex]
[tex]x=\frac{-(5)-\sqrt{5^2-4(1)(-48)} }{2(1)}=-9.865[/tex]
The second value of x is negative, and since a side length cannot be negative this leaves us with just the first answer of [tex]x=4.865[/tex].
Answer:
[tex]\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
Step-by-step explanation:
The area of a rectangle is equal to the base × height:
[tex]\large \textsf{$\rm A $ $= (2x+10)\times(3x)$}\\ \\\large \textsf{$\rm \phantom{A}=$ $6x^2+30x$, and since A = 288,}\\ \\\large \textsf{$\therefore 288 = 6x^2+30x$}[/tex]
Rearranging this equation, we get:
[tex]\large \textsf{$6x^2+30x-288=0$}\\\\\large \textsf{$6(x^2+5x-48)=0$}\\\\\large \textsf{$\therefore x^2+5x-48=0$}[/tex]
Here we are left with a quadratic equation, which we can solve using the quadratic formula:
[tex]\Large \boxed{\textsf{$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$}} \textsf{ where $ax+bx+c=0$}[/tex]
Plugging values into the formula, we get:
[tex]\Large \textsf{$x = \frac{-(5)\pm \sqrt{(5)^2-4(1)(-48)}}{2(1)}$} \\\\\Large \textsf{$x=4.87, -9.87$,} \large \textsf{ but length cannot be negative.}\\\\\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
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Solve the following differential equations
3. What is the value of x? (1 point) 45° 10 45° X
5√2 is the value of x in the given triangle. Therefore, the correct option is option A among all the given options.
A polygon having three edges & three vertices is called a triangle. It can be considered one of the fundamental geometric shapes. A unique triangle and plane (i.e., the two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry. In other words, every triangle has a location in a plane, and there is just one level that contains that triangle.
√2×√50 = √100 = 10.
1×√50 = √50 = 5√2
5√2 since √50 = √25×√2 = 5√2
Therefore, the correct option is option A among all the given options.
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Your question is incomplete but most probably your full question was,
Choosing from the binomial factors shown below, write the equation of the parabola to the left in factored form. (please help)
The equation of the parabola to the left in factored form is y = (x - 2)(x - 7).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;
y = (x - 2)(x - 7)
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A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
HELO
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
We have,
3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.
Now, first convert all quantity in same unit.
3 ½ cups of flour
= 3 cups + 0.5 cups
= 3 cups and 8 ounces.
and, 2 ⅔ cups of sugar
= 2 cups + 0.67 cups,
= 2 cups and 10.72 ounces.
and, 1 ¾ cups of cocoa
=1 cup + 0.75 cups
= 1 cup and 12 ounces.
So, the total amount
= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
= 7 cups
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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Help pldssssssss………………..
The missing value for the quadratic function is given as follows:
y = -3.
How to obtain the quadratic function?As a function of it's roots x* and x**, the quadratic function is defined as follows:
y = a(x - x*)(x - x**)
In which a is the leading coefficient.
The roots of the function are the values of x when y = 0, hence:
x* = -4, x** = -2.
Thus:
y = a(x + 4)(x + 2)
y = a(x² + 6x + 8).
When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:
8a = -8
a = -1.
Hence:
y = -x² - 6x - 8;
The missing value is the value of y when x = -1, hence:
y = -(-1)² - 6(-1) - 8
y = -3.
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Find the length of the radius r
Answer:
[tex]r = \sqrt{ {8.6}^{2} - {5}^{2} } [/tex]
[tex]r = \sqrt{73.96 - 25} = \sqrt{48.96} = 6.997[/tex]
The closest answer is b.
Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
Complete the equation describing how x
and y are related.
X
-3
-2
-1
0
1
2
Y
24
16
8
0
-8
-16
y = [? ]x
Enter the answer that
belongs in [?].
A linear equation that describe how x and y are related include the following: A. y = -8x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 24/-3 = 16/-2 = 8/-1 = -8/1 = -16/2
Constant of proportionality, k = -8.
Therefore, the required linear equation is given by;
y = kx
y = -8x
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.HELPPPPPPPPPPPPPPPPP
Answer:
[tex]\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1[/tex]
Step-by-step explanation:
Slope intercept form of a line equation is
y = mx + b
where
m = slope
b = y-intercept
A perpendicular line to y = mx + b will have a slope of -1/m
Let's first find the equation for line z in slope-intercept form
Slope m for a line = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line
Slope of line z is
[tex]m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}[/tex]
So line z will have an equation of the form
[tex]y = -\dfrac{3}{5}x + b[/tex]
We know that a line perpendicular to this line will have a slope of
[tex]- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}[/tex]
So the equation of the perpendicular line is
[tex]y = \dfrac{5}{3}x + b[/tex]
Only one of the 4 choices, name choice A has this slope of 5/3
Therefore the correct answer choice is A
There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:
The perpendicular line passes through (3, 6). This means when x = 3, y =6
Substitute these values of x, y into the equation for the perpendicular line and solve for b
[tex]y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1[/tex]
This corresponds to Choice A
Rhys takes out a loan of £200, which gathers
interest at a rate of 3% per year. How much
interest will he have to pay after the first year?
Rhys will have to pay £6 interest after the first year.
To calculate the interest, we can use the formula:
Interest = Principal x Rate
Where:
Principal = £200
Rate = 3% = 0.03 (in decimal form)
So, the interest Rhys will have to pay after the first year is:
Interest = £200 x 0.03 = £6
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King of Diamonds Industries has bonds on the market making annual payments, with 14 years to maturity, and selling for R1 482,01. At this price, the bonds yield 7%. What is the coupon rate?
The coupon rate of the bonds by King of Diamonds Industries would be 7 %.
How to find the coupon rate ?The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:
= (Coupon payment x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value / (1 + rate )^ number of years
1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14
103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x (1 - ( 1 + 0.07) ^ ( - 14) )
Using a calculator, C is $ 70.
This means that the coupon rate is:
= 70 / 1, 000
= 7 %
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A hat contains four slips of paper number 125 and six a slip of paper is selected from the hat, and its number is recorded. The papers returns the hat and a second slip of paper is selected and it’s number is recorded
What is the probability distribution for the variable X
The probability distribution for X is given below:
Probability of no even number, (X = 0)= 1/2
Probability of one even number, (X = 1) = 1/2
Probability of two even numbers, (X = 2) = 1/8
What is a probability distribution?The probability distribution for X is found as follows:
The probability that an even number is not selected i.e. X = O
P(X = 0) = (2/4 * 2/4) + (2/4 * 2/4)
P(X = 0) = 1/2
The probability that an even number is selected once i.e. X = 1
P(X = 1) = (2/4 * 2/4) + (2/4 * 2/4)
P(X = 1) = 1/2
The probability that an even number is selected twice i.e. X = 2
P(X = 2) = 2/4 * 2/4
P(X = 2) = 1/8
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Evaluate the function below it’s a given output value of 2
f(x)=80/4x-3
The evaluation of the function gives 16.
How to evaluate a function?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
To evaluate the function f(x) =80/4x-3, we need to substitute the value of the input (i.e. x = 2). Thus:
f(x) = 80/(4x-3)
f(2) = 80/(4*2 - 3)
f(2) = 80/(8 - 3)
f(2) = 80/5
f(2) = 16
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Which system of equations has a solution of (1, 2, 3)?
A. -2 - 2z = -8
Y+3z = 7
x + y m - -3x= -3
B. x + y + 2z = 9
2x + 2y + 3z = 15
x - z = -2
C. -3x + 2y + z = 4
X + y + 2z
X - y - z = -2
D. X + Y = 3
Y - z = 1
X + y - z = 0
Please I really need this class to graduate and I have no idea how to do this
14. Evaluate the indefinite integral.
The indefinite integral of ∫ (4x⁴ - 5)⁵ . 32x³ dx is (4x⁴ - 5)⁶/3 + C.
What is the indefinite integral?The solution of the indefinite integral is calculated by using substitution method.
Let u = 4x⁴ - 5
du/dx = 16x³
dx = du/(16x³)
Substituting into the integral;
∫ (4x⁴ - 5)⁵ . 32x³ dx = ∫ u⁵ . 32x³ du/(16x³)
∫ u⁵ . 32x³ du/(16x³) = ∫ 2u⁵ du
∫ 2u⁵ du = 2∫u⁵ du
2∫u⁵ du = 2 (u⁶/6 + C)
2 (u⁶/6 + C) = u⁶/3 + C
Substituting back for u;
∫ (4x⁴ - 5)⁵ . 32x³ dx = (4x⁴ - 5)⁶/3 + C
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please hurry and show work (quickest gets brainiest)
Write the expression using only positive exponents. Assume no denominator equals zero.
(−3^4 ^−7)^−3
Answer: (-3^4^-7)^-3 can be expressed with positive exponents as (-1/3^4^7)^3.
Step-by-step explanation:
First, we need to evaluate the exponents of the expression from the highest power to the lowest power. Since the exponent of 7 is negative, we need to apply the rule that a negative exponent indicates a reciprocal. Therefore, we can rewrite the expression as (-3^4^-1/7)^-3.
Next, we can simplify the expression -1/7 by flipping it to 7^-1. Therefore, we now have (-3^4^7^-1)^-3.
We can now evaluate the exponent of 4, which gives us (-3^16384^-1)^-3.
Finally, we can simplify 16384^-1 by flipping it to 1/16384, which gives us (-1/3^1/16384)^3.
This expression can be written using only positive exponents as (-1/3^4^7)^3.
I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer:
Let x be the number of additional outfits.
5 + x < 11
Which Box And Whisker Plot Has GREATEST interguartile range? picture below
The box and whisker plot that has the greatest interquartile range is option 3..
What is the Interquartile Range of a data Displayed in a Box and Whisker Plot?The interquartile range of a data set can be found by finding the difference of the data at the beginning and end of the edges of the rectangular box in a box and whisker plot.
It is also the difference between the third and first quartile.
The box and whisker plot in option 3 has the greatest interquartile range because the difference of the Q3 and Q1 is close to 9, which is the highest compared to the other data.
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Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x? 30° only 90° only 30° or 150° 30°, 90°, or 150°
Answer:
Answer = 30° , 90° , 150°
Step-by-step explanation:
Hope it helps you
What does 96 tell you about the volume of one small cube(1/4)
The larger cube is made up of 384 small cubes, each with a volume of 1/4.
We have,
If we assume that 96 is the total volume of a larger cube made up of smaller cubes, and each small cube has a volume of 1/4.
We can make the following calculation:
Let x be the number of small cubes that make up the larger cube.
The volume of the larger cube = Volume of each small cube x Number of small cubes
96 = (1/4) x
Solving for x.
Multiply 4 on both sides.
96 x 4 = x
x = 384
Therefore,
The larger cube is made up of 384 small cubes, each with a volume of 1/4.
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In ABC, AB = 24.1, AC = 15.7, and BC = 25.3. What is LA?
The measure of angle A in triangle ABC is approximately 113.8 degrees.
To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:
c² = a² + b² - 2ab*cos(C)
where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.
In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:
cos(A) = (b² + c² - a²) / 2bc
Plugging in the values we have:
cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)
cos(A) = -0.3694
Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:
A = cos⁻¹(-0.3694)
Using a calculator, we get:
A ≈ 113.8 degrees
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What is the sum of the rational expressions below?
2x-1
7x+x=2
X-2
OA. 9x²-5x+2
7x²-2
OB. 9x²-5x+2
7x²-14x
O C.
O D.
2x²-5x+2
7x²-14x
3x-1
8x-2
Answer:
C
Step-by-step explanation:
To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:
(2x-1)/(7x+x+2) + (x-2)/(8x-2)
Simplifying the denominators, we get:
(2x-1)/(8x+2) + (x-2)/(8x-2)
Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:
[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)
Simplifying the numerator, we get:
[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)
Combining like terms, we get:
(24x²-2) / (64x²-4)
Factoring out a 2 from the numerator and denominator, we get:
2(12x²-1) / 2(32x²-2)
Simplifying further, we get:
(12x²-1) / (16x²-1)
Therefore, the sum of the rational expressions is:
12x²-1
-----------
16x²-1
So, the answer is option C.
How does increasing the distance between charged objects affect the electric force between them?
The electric force increases because the distance has an indirect relationship to the force.
The electric force increases because the distance has a direct relationship to the force.
The electric force decreases because the distance has an indirect relationship to the force.
The electric force decreases because the distance has a direct relationship to the force.
The effect of increasing the distance e between charged object is that , the electric force decreases because the distance has an indirect relationship to the force.
What is coulomb's law?Coulomb's law states that the force between two charged bodies is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.
Coulomb's law can therefore be expressed mathematical as;
F = Q1Q2/r²
where r is the distance between charge Q1 and Q2
This means that since the force is inversely proportional to the square of distance, force will decrease as distance is increasing.
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A fair spinner has eight sides. They are labelled 1, 1, 3, 3, 4, 5, 5, 5. The diagram below shows a probability scale. 0 Which arrow shows the probability of a) scoring a 4? 5 5 5 1 4 3 1 3
Find y.
I will give Brainliest to correct answer !
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
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Solve for x.
x+6= √2x+29 +9
The solution to the equation is x = 10 or x = -2.
What is an equation?An equation refers to a mathematical expression showing that two expressions are equal.
It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).
To solve for x, we shall start with the given equation:
x + 6 = √(2x + 29) + 9
Subtract 9 from both sides:
x - 3 = √(2x + 29)
Square both sides:
[tex](x - 3)^2[/tex] = 2x + 29
Expand the left side:
[tex]x^2[/tex] - 6x + 9 = 2x + 29
We then subtract 2x and 9 from both sides:
[tex]x^2[/tex] - 8x - 20 = 0
Next, actor the quadratic equation:
(x - 10)(x + 2) = 0
Therefore, the equation x = 10 or x = -2
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L={d,e,g} J ={b,c,h} what is the union of L and J
Step-by-step explanation:
well, the combination of all set elements.
FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).
the combination of both sets is then
{b, c, d, e, g, h}
What is the surface area of the square pyramid?
The surface area of the square pyramid using given dimensions is given by option a. 3,456m².
In the square pyramid,
Using Pythagoras theorem,
Height of the square pyramid is equal to,
In a right angled triangle,
Base = 18m
Hypotenuse = 30m
Height = √ Hypotenuse ² - base ²
Substitute the values we have,
⇒ height = √ 30² - 18²
⇒ height = √576
⇒ height = 24m
Dimensions of square pyramid are,
Base edge 'b' = 36m
height of the pyramid 'h' = 24m
Surface area of square Pyramid = b² + 2b√(b²/4) + h²
Substitute the values we have,
⇒Surface area of square Pyramid
= 36² + 2(36)√((36)²/4) + (24)²
= 1296 + 72√324 + 576
= 1296 + 2160
= 3,456m²
Therefore, the surface area of square Pyramid is equal to option a. 3,456m².
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