Answer:
[tex]D = 1[/tex] --- Determinant
[tex]M = \frac{N+1}{2}th[/tex] --- Median
Step-by-step explanation:
Given
[tex]5m^2 - m = 0[/tex]
Required
Calculate the determinant (D)
This is calculated using
[tex]D = b^2 - 4ac[/tex]
In [tex]5m^2 - m = 0[/tex]
[tex]a = 5[/tex], [tex]b = -1[/tex] and [tex]c = 0[/tex]
So, we have:
[tex]D = b^2 - 4ac[/tex]
[tex]D = (-1)^2 - 4 *5*0[/tex]
[tex]D = 1 - 0[/tex]
[tex]D = 1[/tex]
(b) Median Formula.
Median (M) is calculated using:
[tex]M = \frac{N+1}{2}th[/tex] item
The perimeter of the rectangular base of a monument is 230.5 feet. If the width is equal to its length, what are the dimensions of the base?
The width of the base is ____ feet
The length of the base is ____ feet
The width of the base is __57.625__ feet
The length of the base is __57.625__ feet
What is rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given,
Perimeter of the rectangular base of a monument is 230.5 feet.
width is equal to its length
Perimeter of rectangle = 2 (length + width)
230.5 = 2 (length + length)
4 length = 230.5
length = 230.5/4
length = 57.625 feet
thus, width = 57.625 feet
Hence,
57.625 feet is the length of rectangular base.
57.625 feet is the width of rectangular base.
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problem 1.9. (know your theory) write the precise definition of the following: (1) {xn}nn0 is a sequence of reals. (2) give an example of a sequence of rational numbers. (3) (give the recursive definition of) p ` i
1) A sequence of real numbers is an ordered list of real numbers where each number in the list is assigned a specific position or index, usually denoted by n. The sequence is denoted by {xn} n>n0, where xn represents the nth term of the sequence and n ranges from 0 to infinity.
2)An example of a sequence of rational numbers is {2, 1.5, -0.5, -1.25, ...}, where each term in the sequence is a rational number.
3) The recursive definition of the summation of ai is a mathematical formula that defines the nth term of the summation in terms of the previous terms. It is typically denoted as:
∑(i=1)^ni = a1 + (a2 + (a3 + ....(an-1 + an)...)),
Where a1 is the first term of the summation, a2 is the second term, and so on and so forth. This recursive definition is used to calculate the nth term of the summation by adding the previous term to the current term. It is generally used in mathematical induction and recursion.
4)The associative property of summation notation states that the order in which the summation is performed does not affect the final result. In other words, for any three indices a, b, and c, and any sequence of numbers {xn}, the following equation holds:
∑(a=b)c xn = ∑(a=c)b xn = ∑(a=b)c xn
This property allows us to group the terms in a summation in different ways without changing the final result.
5) The translation invariance property of summation notation states that the value of a summation is unchanged when the index of summation is translated (shifted) by a constant value. In other words, for any indices a and b, any constant k, and any sequence of numbers {xn}, the following equation holds:
∑(a=b)xn = ∑(a+k=b+k)xn
This property allows us to shift the index of summation without affecting the final result of the summation.
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What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y-ma+bwhere m is the slope and b is the y-intercept
Enter your answer in the box
Answer: y = 3x - 8
Step-by-step explanation: Given slope m = 3, and point x = 3, y = 1
y -1 = 3(x-3)
y = 3x - 9 + 1
y = 3x - 8
Nya rode her bike about 2 ½ miles in ¼ hour. What was her average speed in miles per hour?
Nya's average speed was 10 miles per hour.
What is the speed, distance, and time?
Speed, distance, and time are related concepts in physics that are used to measure and describe motion.
Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed can be calculated using the formula:
Speed = Distance / Time
To find Nya's average speed in miles per hour, we need to divide the distance she traveled by the time it took her to travel that distance.
Average speed = distance/time
We know that Nya rode her bike 2 ½ miles in ¼ hour. To use these measurements in the formula, we need to convert the units to the same unit of measurement. In this case, we need to convert the distance to miles and the time to hours.
Average speed = (2.5 miles) / (0.25 hour)
To find out the speed in miles per hour, you need to multiply by the conversion factor 1 hour/60 minutes, so
Average speed = (2.5 miles) / (0.25 hour) * (1 hour/60 minutes)
Average speed = (2.5 miles) / (0.25 hour) * (4)
Average speed = 10 miles per hour.
Hence, Nya's average speed was 10 miles per hour.
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solve the system
2x+y-3z=0
x-4y+z=0
4x+16y+4z=0
Answer:
x=0
y=0
z=0
Step-by-step explanation:
60th term of -28 -45 -62
Answer:
-79
Step-by-step explanation:
First Identify the sequence
-28 to -45 is -17
-45 to -62 is -17
This is an Arithmetic Sequence because it is constant
(Constant ; same throughout)
Two Formulas:
a60=28 -45 -62
or
an= -17(60)-11
↑
A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The
concrete's strength is then measured. The following data represent the strength of nine randomly selected casts (in psi). Compute the mean, median, and mode strength of the
concrete (in psi).
3960 4050 3170 3080 2940 3830 4050 4060 3810
Select the com
below:
the answer box to complete your choice
PSI stands for Pounds per Square Inch, and it's the unit of measurement that reflects the air pressure inside your tire.
What is PSI example?For example, a bicycle tire pumped up to 65 psig in a local atmospheric pressure at sea level (14.7 psi) will have a pressure of 79.7 psia (14.7 psi + 65 psi). When gauge pressure is referenced to something other than ambient atmospheric pressure, then the unit would be pound per square inch differential (psid).Pounds per square inchPounds per square inch or PSI is an imperial unit of pressure. Using the imperial units of pounds and square inches, it is a measure of force per unit area. Therefore, 1 PSI is measured as one pound of force applied per one square inch.Given the data representation of the strength of nine randomly selected casts (in psi) as 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780.
Mean is the average of the samples
[tex]x={3960+4050+3170+3080+2940+3830+ 4050+4060+3810}[/tex]
x=32950/9
x=3661
is thw sum of the given data
N is the sample size
is the mean
Hence the mean of the data is 3,670psi
MEDIAN
Median is the value at the middle of the data after rearrangement.
On rearranging in ascending order
2940, 3100, 3200, 3,780) 3,830 (3,960, 4040, 4090, 4090
It can be seen that the middle value is 3860. Hence the median of the data is 3860psi.
MODE
Mode is the most occurring data in the dataset. It is the data with the highest frequency. From the data, it can be seen that the only data occurring most (twice) is 4090, hence the modal value is 4090psi
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Use tape diagrams to solve these ratio problems.
1. The sport court donated helmets and
footballs to the youth club in the ratio 3:7.
There were 60 pieces of sports equipment
altogether. How many more footballs were
donated than helmets?
24 more footballs were donated than helmets in the given ratio problem.
What is ratio?Ratio refers to the quotient of two values. The expression a:b or a/b can be used to represent the ratio of a to b. A is the antecedent and b is the consequent in both scenarios. Every time we make comparisons, ratios appear.
For simplicity, they are typically expressed in the simplest terms. In a school with 1,000 students and 50 teachers, there are 20 students for every teacher.
The golden ratio of classical architecture is an example of an aspect ratio, which is the ratio of a rectangle's width to height. A proportion is an equation that results from setting two ratios equal to one another.
Lets 3x be the no. of helmet and 7x be football distributed.
total pieces = 3x + 7x
3x + 7x = 60
10x = 60
x = 60/10
x = 6
3x = 3(6) = 18
7x = 7(6) = 42
Difference = 42 - 18
= 24
Thus, 24 more footballs were donated than helmets in the given ratio problem.
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pleasee hellppp
-9=6m+15
solution:
check:
The solution to the equation -9 = 6m + 15 is m = -4.
What is the solution to the given equation?Given the equation in the question;
-9 = 6m + 15
Rewrite the equation as 6m + 15 = -9
Move all terms not containing m to the right side of the equation by subtracting 15 from both sides
6m + 15 - 15 = -9 - 15
6m = -9 - 15
Add -9 and -15
6m = -24
Divide both sides by 6
6m/6 = -24/6
m = -24/6
m = -4
Solution check
Plug m = -4 into the equation and check
-9 = 6m + 15
-9 = 6( -4 ) + 15
-9 = -24 + 15
-9 = -9
Correct.
Therefore, the numerical value of m is -4.
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HELP ME OUT PLEASE!!!!!!!
Simplify
Answer:
I believe it is -2a⁶b¹² (the first option)
as cordenadas do vertice da funcao y=x2-2x-3
Para encontrar as coordenadas do vértice de uma função do tipo y = x² - 2x - 3, podemos seguir os seguintes passos:
Calcular o valor da coordenada x do vértice: para isso, precisamos encontrar o valor de x quando o coeficiente do x na função é igual a zero. Neste caso, temos x² - 2x - 3 = 0. Então, para encontrar x, podemos factorizar esse polinômio e encontrar as raízes: (x-3)(x+1) = 0. Isso nos dá x = 3 ou x = -1. Como estamos procurando o vértice, que é o ponto mais alto ou mais baixo da parábola, descartamos x = -1 e ficamos com x = 3.
Calcular o valor da coordenada y do vértice: agora que temos o valor de x, podemos substituí-lo na função original e calcular o valor de y. Neste caso, temos: y = (3)² - 2(3) - 3 = 9 - 6 - 3 = 0.
Portanto, as coordenadas do vértice da função y = x² - 2x - 3 são (3, 0).
Answer:
Step-by-step explanation:
(x) = x²-2x-3.
a=1 b=-2 c=-3.
Xv = -b/2a = -(-2)/2 = 1.
Yv = -Δ/4a Δ =(2²-(4.(-3))) = 16 -16/4 = -4
Vertex ( 1 , -4 )
Differentiating
f(x) = x²-2x-3.
f '(x) = 2x-2
2x-2 = 0
x=1. Xv = 1.
f(1) = x²-2x-3.
1-2-3 = -4. Yv = -4.
The doctor has ordered a 5% saline solution to be prepared. How many grams of pure drug will be needed to make 115 mL of solution at the 5% strength?
Answer:
(115 x 5) / 100 = 0.575 grams of the pure drug.
Step-by-step explanation:
To make a 5% solution, the concentration of the pure drug is 5 grams per 100 mL of solution.
To find the amount of pure drug needed for a specific volume, such as 115 mL, you can use the formula:
(volume of solution x concentration of pure drug) / 100
So in this case:
(115 x 5) / 100 = 0.575 grams of the pure drug.
This calculation shows that 0.575 grams of the pure drug would be needed to make 115 mL of a 5% solution.
Answer:
5.75 g
Step-by-step explanation:
First calculate 5% of the total amount of solution, 115 ml:
[tex]\implies \sf 5\%\;of\;115\;ml=\dfrac{5}{100} \times 115=5.75\;ml[/tex]
As we have not been told any information about the drug, assume the standard equivalent that 1 ml equals 1 gram. Therefore, the amount of pure drug needed to make 115 ml of solution at the 5% strength is 5.75 g.
What is the quotient of -4/5-2
Answer:
-1.3
Step-by-step explanation:
Help the picture has everything you need to know 20 points
Answer:
Triangle VWX and triangle IGH are congruent
Step-by-step explanation:
Which sign makes the following statement true? -1/5 _____ -1/2
The sign that makes the following statement -1/5 _____ -1/2 true is <. Option 1
What are inequalities?Inequalities are simply described as a relation that makes a non-equal comparison between two numbers mathematical expressions.
Inequalities are mostly used in comparing two numbers on the number line based on their size.
Mathematically signs used for the representation are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that;
-1/5 is not equal to -1/2
Thjs is so because smaller numbers on the negative side of the number line are greater than the larger numbers.
Thus, the sign is <
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z-2<22 solve the inequality for z
The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex]
.
What is meant by inequality?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if you multiply or divide each side by a negative number.Given inequality:
[tex]$$z^2-11 z+24 < 0$$[/tex]
Factor the left-hand side.
[tex]z^2-11 z+24 & < 0 \\[/tex]
[tex]z^2-8 z-3 z+24 & < 0 \\[/tex]
[tex]z(z-8)-3(z-8) & < 0 \\[/tex]
[tex](z-8)(z-3) & < 0[/tex]
The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex].
The complete question is,
Solve the following inequality:
[tex]$$z^2-11 z+24 < 0$$[/tex]
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match the volume formula to the description
Answer:
145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf
Aria invested $40,000 in an account paying an interest rate of 8\tfrac{3}{8}8 8 3 % compounded daily. Olivia invested $40,000 in an account paying an interest rate of 8\tfrac{1}{8}8 8 1 % compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Olivia's money to triple than for Aria's money to triple?
To the nearest hundredth of a year (period), it will take Olivia's money 0.54 years more to triple than Aria's money to triple.
How the period is determined?The additional period it will take Olivia's money to triple than Aria's is determined as the difference between the two investment periods.
The investment periods are computed using an online finance calculator as follows:
Aria Investment:I/Y (Interest per year) = 8.375%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
Number of Periods (N) = 4,788.531
= 13.119 years (4,788.531/365) or 13 years and 1 month
Total Interest = $80,000.00
Olivia's Investment:I/Y (Interest per year) = 8.125%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
N = 54.633
= 13.65825 years (54.633 quarters/4) or 13 years and 8 months
Total Interest $80,000.00
The difference in investment period:
13.66 - 13.12
= 0.54 years
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−12x−(12x+4)+12=17x−6(3x+56) [Can someone pls tell me what x equal..]
The value of x is 14.957.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign.
The equation is given as,
-12x - (12x + 4) + 12 = 17x - 6(3x + 56)
Since the sign is negative outside the bracket on the left hand side, the signs of terms inside the bracket becomes the opposite of what it has.
-12x - 12x - 4 + 12 = 17x - 6(3x + 56)
Applying the distributive property for the term 6(3x + 56), we get,
-12x - 12x - 4 + 12 = 17x - [(6 × 3x) + (6 × 56)]
-12x - 12x - 4 + 12 = 17x - (18x + 336)
Removing brackets,
-12x - 12x - 4 + 12 = 17x - 18x - 336
Taking all the like terms to separate sides,
-12x - 12x - 17x + 18x = 4 - 12 - 336
-23x = -344
x = -344 / -23
x = 14.957
Hence the value of x for the given equation is 14.957.
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Rewrite (6+3)9 using the distribute property of multiplication over addition
(2)9
6(9)-3(9)
(9)9
6(9)+3(9)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(6 + 3)9}\leftarrow\text{Your given equation}\\\mathsf{= 9(6 + 3)}\leftarrow\text{Convert your equation to this to make it easier to solve}\\\mathsf{= 9(6) + 9(3)}\leftarrow\text{What you are looking for because it is your answer to this question}\\\mathsf{= 54 + 27}\leftarrow\text{Making it more easier to solve for the overall answer} \\\mathsf{= 81}\leftarrow\text{This is your overall answer to the whole equation}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ D. \ 6(9) + 3(9)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Question 39 of 40
Simplify the expression below. If your answer is not a whole number, enter it
as a fraction in lowest terms, using the slash mark (/) as the fraction bar.
8 divided by (4-6) - 15 divided (-5)
Answer: its -1
Step-by-step explanation:
Ridge City is smaller than Peak City. Desert City is smaller than Peak City but larger than Ridge City. Peak City is smaller than Oak City. Which city is the largest?
Answer:
Desert city is the largest city.
Jaden has learned to play 18 1⁄4 of the measures for Fur Elise on the piano. If the song is composed of 108 measures, how many more measures does she have to learn?
Answer:108-8 1/4=89 3/4 Jaden has 89 3/4 measures they still need to learn
Step-by-step explanation:
Answer: 89 3/4
Step-by-step explanation: Jaden played 18 1/4 of the measures and the total of Fur Elise is 108 measures. If you do 108 - 18 1/4 it would be 89 3/4. We did this because the total was 108 and we wanted to know how much of fur elise is left after we played 18 1/4.
How to solve the inequality:
-6 > z/-2 +1
The solution to the inequality is z > 14
What is inequality?Mathematical expressions with inequalities include those in which the two sides are not equivalent. Contrary to equations, we assess and contrast two values in inequality. The inequality signs that are used in place of the equal signs are:
Less than (or less than or equal to), Larger than (or greater than or equal to), or Not equal to.Given:
-6 > z/-2 + 1
Rewrite so "z" is on the left side of the inequality.
z/-2 + 1 < -6
Move the negative in front of the fraction.
-z/2 + 1 < -6
Move all terms not containing z to the right side of the inequality.
-z/2 < - 6 - 1
-z/2 < - 7
Multiply both sides by 2
z < -14
Interchange the sign since z cannot be negative;
z > 14
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PLEASEEE HELP I NEED ONE MORE
The solution of the function is as follows:
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
Therefore, let's solve the composite functions as follows:
f(x) = x² + 9x
g(x) = 4x + 1
Therefore,
(f o g)(x) = f(g(x))
Therefore,
f(g(x)) = (4x + 1)² + 9x = (4x + 1)(4x + 1) + 9x = 16x² + 4x + 4x + 1 + 9x = 16x² + 17x + 1
(g o f)(x) = g(f(x))
g(f(x)) = 4(x² + 9x) + 1 = 4x² + 36x + 1
Therefore,
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
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The general strategy for solving an equation of the form x/a=b is to?
We have discussed the general strategy for solving an equation of the form x/a = b.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. An equation is composed of two sides, separated by an equal sign (=), with each side containing one or more variables, numbers, and/or mathematical operations.
The general strategy for solving an equation of the form x/a = b is to:
Multiply both sides of the equation by a, in order to cancel out the fraction on the left side. This will isolate the variable x on one side of the equation.
Simplify the equation by combining like terms if necessary.
Check the solution by substituting it back into the original equation and verifying that it makes the equation true.
For example, consider the equation x/2 = 4
Multiply both sides by 2: x/2 * 2 = 4 * 2
x = 8
To check the solution, substitute it back into the original equation: x/2 = 4, 8/2 = 4. The equation is true, so x = 8 is the correct solution.
It's important to keep in mind that when solving equations, it is important to follow the order of operations, and also to be careful when dividing or multiplying by zero.
Hence, we have discussed the general strategy for solving the equation.
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four granola bars and three drinks cost $12.50. Two granola bars and five drinks cost $15.00. At Snacks To Go, three granola bars and three drinks cost $10.50. Four granola bars and two drinks cost $10.00. Part A Write a system of equations for each concession stand that models the price of its items. Part B Solve each system of equations. What do the solutions represent? Part C You decide to open a new concessions stand and sell granola bars and drinks. Determine a price for each item that differ from the prices at Snacks To Go. Then write a system of equations to model the prices at your snack bar.
Using substitution method to solve the system of linear equations, the granola and drinks cost $1.25 and $2.5 respectively while the modelled system of linear equation is attached below
What is System of Linear EquationA grouping of two or more linear equations that share the same set of variables is known as a system of linear equations. When a, b, and c are constants and x and y are variables, the equations can be written as ax + by = c. Elimination, substitution, and graphing are just a few of the techniques that can be used to solve these problems.
In this given problem, we have to define our variables and then set our system of equations.
a)
Let;
x = granola bardrinks2x + 5y = 15 ...eq(i)
4x + 3y = 12.50 ...eq(ii)
b)
Using substitution method;
From equ(i)
2x + 5y = 15
2x = 15 - 5y
x = (15 - 5y) / 2 ...eq(iii)
Put eq(iii) into eq(ii)
4x + 3y = 12.50
4(15 - 5y) /2 + 3y = 12.50
y = 2.5
Put y = 2.5 into eq(i)
2x + 5(2.5) = 15
x = 1.25
c)
Granola = 1.0
drinks = 3.0
The system of linear equations will be
x + y = 4
2x + 3y = 11
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I need help with this
Answer:
3.Ans
4 is the thousands place value in the number 524,897,123.
The value of the digit 4 would be 4,000,000.
Calculation: 4 x 1,000,000 = 4,000,000
4.Ans
The product of (6*5)*10^3 is 3000. This product has 3 zeroes.
Write in standard form an equation of the line with the given slope through the given point.
Slope=2/5; (6,7)
Answer:
6x+7y=2/5
im not entirely sure if its correct sorry if u get it wrong-
A sequence is shown below.
8.0, 6.5, 5.0, 3.5, . . .
In the recursive formula for the sequence, if an=−4.0 , what is the value of an+1 ?
A
–2.5
B
–5.5
C
–6.0
D
–3.0
The value of the sequence aₙ₊₁ is -5.5
How to determine the value of the sequenceThe definition of the sequence is given as
8.0, 6.5, 5.0, 3.5, . . .
The above definitions imply that we simply subtract 1.5 from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ₊₁ = aₙ - 1.5
From the question, we have
aₙ = -4.0
Substitute the known values in the above equation, so, we have the following representation
aₙ₊₁ = -4.0 - 1.5
Evaluate
aₙ₊₁ = -5.5
Hence, the value of aₙ₊₁ is -5.5
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