Answer:
let 5= a and b = 3^1/3
(a+b) ( a-b)
a^2-b^2
putting the value of a and b we get
(5)^2-(3)^2/2
25-3
22
Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance. She wants the ends of the strings where the stars will be attached to be 7 feet from the floor. Use the diagram to determine how long she should make the strings
12/5 yards is the length she should use to make the string.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance
She wants the ends of the strings where the stars will be attached to be 7 feet from the floor.
BD is perpendicular to AC.
∠BDA+∠2+∠3=180
∠2+∠3=90 degrees.
∠1=∠3 (the equivalent substitution)
ΔABD=ΔBCD
AD/BD=BD/DC
(Similar triangles have sides that are proportional)
AD.DC=BD²
PC⊥AC
∠ACP=90 degrees.
∠ACM+∠MAC+∠∠CAM=180
∠ACM=∠APC
Therefore ΔAMC~ΔPCA
CM/CD=AC/AD
CM=12/5 yards
Hence, 12/5 yards is the length she should use to make the string.
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Answer: 18
Step-by-step explanation:
First, find x for x-2. So you would use one of the Geometric Mean Theorems using 5 and a height of 10. For this problem, we will use "y" as a placeholder for finding the whole total of that side.
[tex]\frac{5}{10} =\frac{10}{y} \\[/tex] Solve. --> [tex]5y = 100\\[/tex] --> [tex]\frac{5y}{5} =\frac{100}{5} \\[/tex] --> y = 20
Then subtract 20 from 2 to find x. You get 18 as an answer.
Consider the points A = (0, 0), B = (1, 0) and C = (0, 1). Now choose a random point (X, Y ) uniformly from the union of the line segments AB and AC. Find Cov(X, Y )
The answer is cov(x,y) = 0.059, if we choose a random point (X, Y ) uniformly from the union of the line segments AB and AC.
As given, A = (0, 0) ,B = (1, 0) and C = (0, 1)
and we have the select x and y from line segment AB and AC respectively.
So, x can be 1.0, 0.8, 0.6, 0.4, 0.2
and y can be 1.0, 0.8, 0.6, 0.4, 0.2
Now we have to find,
cov(x,y) = ∑(Xi - μ) (Yj - v) / n
where,
Cov(X, Y) represents the covariance of variables X and Y.Σ represents the sum of other parts of the formula.(Xi) represents all values of the X-variable.µ represents the average value of the X-variable.Yj represents all values of the Y-variable.v represents the average value of the Y-variable.Σ represents the sum of the values for both (Xi-µ) and (Yj-v).n represents the total number of data points across both variables.Now µ = 1.0 + 0.8 + 0.6 + 0.4 + 0.2 + 0.0 ÷ 6
µ = 3 ÷ 6
µ = 1/2 = 0.5
Now v = 1.0 + 0.8 + 0.6 + 0.4 + 0.2 + 0.0 ÷ 6
v = 3 ÷ 6
v = 1/2 = 0.5
Now, we have to find
(Xi - µ) = (1.0 - 0.5), (0. 8- 0.5), (0.6 - 0.5), (0.4 - 0.5), (0.2 - 0.5),
(0.0 - 0.5)
(Xi - µ) = 0.5, 0.3, 0.1, (-0.1), (-0.3), (-0.5)
(Yj - v) = (1.0 - 0.5), (0. 8- 0.5), (0.6 - 0.5), (0.4 - 0.5), (0.2 - 0.5),
(0.0 - 0.5)
(Yj - v) = 0.5, 0.3, 0.1, (-0.1), (-0.3), (-0.5)
Now calculate (Xi - μ) (Yj - v): multiply them with their respective one
(Xi - μ) (Yj - v) = (0.5×0.5), (0.3×0.3), (0.1×o.1), (-0.1)(-0.1), (-0.3)(-0.3),
(-0.5)(0.5)
therefore,
∑(Xi - μ) (Yj - v) = (0.25+ 0.09 + 0.01 + 0.01 + 0.09 + 0.25)
∑(Xi - μ) (Yj - v) =0.35
Now, cov(x,y) = ∑(Xi - μ) (Yj - v) / n
cov(x,y) = 0.35 / 6
cov(x,y) = 0.059
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3. Consider two dots, X and Y, 7cm apart horizontally.
a. Draw the locus of points equidistant from X and Y.
b. A third dot Z is 6cm below X. Mark clearly the point equidistant from X, Y, and Z on your diagram in part a.
According to the information, the center line would be 3.5 cm from points X and Y.
How to graph the instructions described?To graph the instructions described we must perform the following procedure:
First of all we must carefully read the instructions and identify what the first step is. In this case we must draw a horizontal line 7 cm long.
Secondly, we must draw a line at the point equidistant from the points X and Z, that is, halfway between these two points. If we take into account that the first line measures 7 cm, this point will be 3.5 cm from each point.
Thirdly, we must give a length of 6 cm to this central line and it must also be equidistant. Therefore, we must give it 3 cm upwards and 3 cm downwards in length so that it is equidistant.
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A and B are two similar 2D shapes. The area of shape A is 200cm^2. Calculate the area of shape B.
The area of shape B which is of 15 cm, is 312.5 cm²
Let us assume that the area of the shape B is x square units.
The dimensions of shape A is 12 cm
The area of the shape A is 200 cm²
The dimensions of shape B is 15 cm
The area of the shape B is x cm²
Since A and B are two similar 2D shapes their dimensions must be in proportion.
So, we get an equation,
A² / B² = 200 / x
12² / 15² = 200 / x
144 / 225 = 200 / x
x = 312.5 cm²
Therefore, the area of shape B is 312.5 cm²
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The complete question is:
A and B are two similar 2D shapes. The area of shape A which is 12cm is 200cm squared. Calculate the area of shape B which is 15cm.
If f(x)=5x+12, what is f(2)
Answer:
To find f(2), we simply substitute 2 for x in the function f(x)=5x+12 and simplify:
f(2) = 5(2) + 12
= 10 + 12
= 22
Therefore, f(2) = 22.
Step-by-step explanation:
1 3/8 divided by 1 4/9
Answer:
99/104
Step-by-step explanation:
1 3/8 divided by 1 4/9
1 3/8 = 11/8
1 4/9 = 13/9
11/8 divided by 13/9
= 11/8 times 9/13
= 99/104
De las 2000 vacunas que llegaron a bolivia para el covid-19 la mitad se usará en vacunar a médicos, la tercera parte se la usará en pacientes con patología de base y la sexta parte lo guardad en refrigeración, ¿cómo representarías eso en forma algebraica? representaremos por x el valor que no conocemos
ayuda
Answer:
pues quien sabe
Step-by-step explanation:
Can someone help me with this. Under lines are: ║ p and q. The statement is: ∠1 and ∠3 are vertical to ∠s. The reasons are: given, vertical angels theorem, transitive property, and def. of vertical ∠s.
The proof for the the lines p and q are parallel is given below.
What are Alternate Exterior Angles?Alternate exterior angles are the angles formed on the two opposite sides of the transversal which are on the outer side of the parallel lines.
Given that,
∠1 ≅ ∠2 or ∠2 ≅ ∠1.
Now ∠1 ≅ ∠3, by the vertical angles theorem.
(By the vertical angles theorem, vertical angles formed by two intersecting lines are congruent).
Then ∠2 ≅ ∠3, by the transitive property.
(Transitive property states that, if a = b and b = c, then a = c)
By the corresponding angles converse postulate, two lines p and q are parallel.
(If the corresponding angles of two lines cut by a transversal are equal, the lines are parallel).
Hence it is proved.
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If the sum of six consecutive odd integers is 504, what is the smallest of the six
integers?
Answer:
79
Step-by-step explanation:
You want the smallest of 6 consecutive odd integers that have a sum of 504.
AverageThe average of the integers will be the even integer between the middle two odd integers. The smallest odd integer is 5 less than this average.
The average is the sum divided by the number of integers:
504/6 = 84
The smallest of the 6 integers is 84 -5 = 79.
__
Additional comment
The integers are 79, 81, 83, 85, 87, 89.
Consecutive integer problems are often easily worked by considering the average of the integers, as here.
If you feel like you need an equation, you can let x represent the smallest. Then the sum is ...
x +(x+2) +(x+4) +(x+6) +(x+8) +(x+10) = 6x +30 = 504
6x = 474 ⇒ x = 474/6 = 79
una caja de refrescos cuesta 104.40 y esta contiene 24 refrescos ¿m cual es el costo de cada refresco?
El precio de cada refresco es de 4.35$
⭐Explicación paso a paso:
En este caso lo que hay que hacer es el precio unitario de cada refresco.
El precio unitario se obtiene al dividir el total de dinero entre la cantidad de refrescos que trae cada caja:
Precio de cada refresco = Precio total/Cantidad de refrescos
Precio de cada refresco = 104.40$/24
Precio de cada refresco = 4.35$ Por lo tanto, el precio de cada refresco es de 4.35$
Do any whole numbers have a cube root between 0 and 1? Explain your reasoning
No, there are no whole numbers with a cube root between 0 and 1. A cube root of a number is a value that, when multiplied by itself three times, gives the original number.
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of a positive number is always positive. If a positive number is between 0 and 1, then its cube will be even smaller.
For example, the cube root of 8 is 2, and the cube root of 27 is 3. If we take the cube root of a number less than 1, such as 0.5, the result is less than 1. However, since we are talking about whole numbers, 0.5 is not a whole number and therefore not in the scope of the question.
Therefore, it can be concluded that there are no whole numbers with a cube root between 0 and 1 because any positive whole number raised to the power of 1/3 will result in a value greater than 1.
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The following dot plots show the number of hours of sleep employees got before a major sale at two stores. Each dot represents a different employee.
Complete the comparison of the typical hours of sleep.
In general, the employees at
got more sleep, with
of sleep per employee.
In general, the employees at Store 1 got more sleep, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.
The dot plots for the two stores show that Store 1 had employees who got between 5 and 10 hours of sleep, whereas Store 2 had employees who got between 4 and 8 hours of sleep. The median for Store 1 was 8.5 hours of sleep, and the median for Store 2 was 7.5 hours of sleep. This indicates that, in general, the employees at Store 1 got more sleep than the employees at Store 2. The dot plots also show that there were more employees at Store 1 with 8 hours of sleep than Store 2, and fewer employees at Store 1 with 6 hours of sleep than Store 2. This suggests that Store 1 had more employees getting 8 hours of sleep, and fewer employees getting 6 hours of sleep, than Store 2. This can be further seen by the fact that the average amount of sleep for employees at Store 1 was 8.5 hours, while the average amount of sleep for employees at Store 2 was 7.5 hours. Therefore, in general, the employees at Store 1 got more sleep than the employees at Store 2, with an average of 8.5 hours of sleep per employee, compared to Store 2's average of 7.5 hours.
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How to solve
2x*2 +5x+3/X*2+x-2
On solving the provided question, we can say that the question we have here is [tex]2x\times2 +5x+\frac{3}{X}\times 2-2[/tex], by bodmas [tex]\frac{9x^{3} + 6 - 2x}{x}[/tex]
Describe bodmas.The acronym BODMAS helps children remember the order of mathematical operations (the correct order for solving math problems). The words B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction make up the acronym BODMAS.
In some places, BODMAS is also referred to as PEDMAS.
Exponents, division, multiplication, addition, and subtraction are represented by this. It serves as a parentheses as well. Parentheses must be handled first, then powers or roots (i.e., of), divisions, multiplications, additions, and finally subtractions, according to the BODMAS rule.
In India and the UK, he is referred to as BODMAS, but in the US, he is more commonly called PEMDAS. They are, nonetheless, exact replicas of one another.
the question we have here is
[tex]2x\times2 +5x+\frac{3}{X}\times 2-2[/tex]
by BODMAS
Firstly, division them multiplication,
⇒ [tex]4x + 5x + \frac{6}{x} - 2[/tex]
Now we will add the addends,
⇒ [tex]9x^{2} + \frac{6}{x} - 2[/tex]
⇒ [tex]\frac{9x^{3} + 6 - 2x}{x}[/tex]
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A theater owner is looking to maximize his profits and needs to increase his ticket
prices. The function P(t) = -50t2 + 100t + 14,400 represents his total profit, P, based on
the amount, in dollars, he raises the ticket price, t.
The ticket price that would maximize the profit is $1 and the maximum profit would be $14,450.
How did we get the values?To maximize the profit, we need to find the maximum value of the function P(t) = -50t^2 + 100t + 14,400.
The maximum value can be found by finding the vertex of the parabolic equation. The vertex can be found using the formula:
t = -b / 2a
where a, b, and c are the coefficients of the equation in the form of y = ax^2 + bx + c. In this case, a = -50, b = 100, and c = 14,400.
Substituting the values into the formula, we get:
t = -b / 2a = 100 / (-2 * -50) = 100 / 100 = 1
So, the ticket price that would maximize the profit is $1. To find the maximum profit, we can plug in t = 1 into the function:
P(1) = -50 * 1^2 + 100 * 1 + 14,400 = -50 + 100 + 14,400 = 14,450
So the maximum profit would be $14,450.
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evaluate 4a - 2b +c over 2 abc when a=5 b=-2 and c=1
Answer:
0.85
Step-by-step explanation:
4a-2b+c/2abc
where a=5,b=2,c=1
4(5)-2(2)+1/2×5×2×1
20-4+1/20
17/20
0.86
Please solve for a and b:
Answer:
42=7
15=0.6
Step-by-step explanation:
It takes Jacob 30 minutes to ride his bike to school at 6 mph. Following the same route, how long would it take him to walk to school at 1.5 mph. (d = st)
The time it would take him to walk to the school at 1.5 mph is given as follows:
2 hours.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
v = 6, t = 0.5 hours.
Hence the distance is of:
d = vt
d = 6 x 0.5
d = 3 miles.
At a velocity of 1.5 miles per hour, the time would be given as follows:
1.5 = 3/t
1.5t = 3
t = 2 hours.
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33) a ten year old is having his birthday party at the roller rink. Explain two different counts that his parents will estimate for the party. One should be an over-estimate and the other can be an under-estimate.
34) an airline pilot is planning a fight from new York’s LaGuardia airport to Boston, mass. Explain two measurements the pilot must not estimate in order to plan a safe flight
35) a construction work needs to build a concrete wall to support a prefabricated ramp that will be used as a handicap access to the public library. (A) explain why this would not be a place to estimate measurements. (B) describe where some estimates might be adequate for the plan
Measurements are important for a safe and secure structure, as they must adhere to local building codes and regulations. Preliminary planning can be used to estimate the height, width, and length of the ramp and the amount of concrete and other materials needed.
What is a measurement?A measurement is a measurable quantity that includes length, breadth, height, area, volume, weight, or time. Measurements are used to measure an object's or area's size, shape, or qualities.
A) Estimating measurements for a construction project such as this is not advisable, as accuracy is essential for ensuring the wall is stable and safe for use. Calculations must be precise in order to ensure the dimensions, material strength, and angles are correct, which is why it is important to use exact measurements in the plans.
B) In some cases, estimates may be acceptable. For example, the approximate number of blocks or pieces of material needed may be estimated based on the overall size and shape of the wall. Additionally, estimates of the time needed to complete the project may be made based on the experience of the construction team and the complexity of the project.
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11. Mr. Lee made finding the zeros of the polynomial function h(x) = x(x-4) (x + 2). He stated that
the zeros of this polynomial are x = 1, x = 4, x = -2. Explain his error. (DOK3)
Answer:
one of the zeros is x = 0 and not x = 1
Step-by-step explanation:
Zeros are found by setting each of the factors to 0 and solving for x
Factors are x, x -4, x + 2
Set each of them to 0:
x =0
x + 2 = 0 ==> x = -2
x -4 = 0 ==> x = 4
So one of the zeros is x = 0 and not x = 1
Which of the following will form the composite functions G(F(x)) shown below
The answer is Option B (F(x) = x + 1 and G(x) = √3x).
Which of the following will form the composite functions G(F(x)) ?The composite function G(F(x)) means we first apply the function F(x) to x and then apply the function G(x) to the result. So, we need to find F(x) and G(x) such that:We can use substitution method to verify that F(x) = x + 1 and G(x) = √3x forms the composite function G(F(x)) = √3(x + 1).Let's start by applying F(x) to x:F(x) = x + 1Next, we apply G(x) to the result of F(x):G(F(x)) = G(x + 1) = √3(x + 1)Since the above result matches with the given composite function G(F(x)) = √3(x + 1), we can conclude that F(x) = x + 1 and G(x) = √3x forms the composite function G(F(x)) = √3(x + 1).G(F(x)) = G(x + 1) = √3(x + 1)So, F(x) = x + 1 and G(x) = √3x.To learn more about composite function refer:
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a father wants to buy toys for his daughter and his son. he wants to spend at least $25 on each child. if his overall budget to spend on both kids no more than $1 50, what is one possible combination of money the father can spend on each of his children for toys?
40 points!!!!! PLease HELP!!!!!!
The ratio between the areas of equilateral triangles $\triangle BXY$ and $\triangle BAC$ is $1:4.$ If $AC=6,$ what is $XY?$
Answer: b y c a x b is the answer
:
A researcher recorded the height of all 217 adult members of a tribe. The average was 5.49 feet.
What term best describes the analysis conducted by the researcher?
The term that best describes the analysis conducted by the researcher is; Observational Study
How to identify the system of research?We are given the parameters as;
Number of all adult members of a tribe = 217
Average height of the adult members = 5.49 ft
Now, there are different methods of research analysis such as experiment
randomized trial
double blind study
observational study
Now, in this case we are only told what the researcher has observed from his analysis and an observational study is used to answer a research question based purely on what the researcher observes.
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800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game? Insert the values given in the problem then scale up or down to find the missing value. attendees percent 100 attempt 3 out of 3 Emilia Salkic Proportional Reasoning, Percents (Level 2) Feb 03, 2:20:32 PM 800 people attended a football game. If 20% of the people who attended were teenagers, how many teenagers attended the game?
Using percentages, we can deduce that 160 of the 800 attendees at the football and math conference were teenagers or 20% of the total.
What are percentages?In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage.
When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100.
Therefore, the proportion refers to a component per 100.
The word percent denotes a percentage of 100.
A percentage (%) is a number that represents how many out of 100 it is and can also be written as a decimal or fraction.
To convert a percentage to a fraction, place the percentage's value in the numerator and 100 in the denominator.
So, we are aware of:
The football game attracted 800 spectators.
20% of the population were teenagers.
The number of teens at that time was:
= 800/100*20
= 8*20
= 160
Therefore, using percentages, we can deduce that 160 of the 800 attendees at the football and math conference were teenagers, or 20% of the total.
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last week we calculated the standard deviation by hand, and then used that to find the standard error. can we find the standard error now?
Yes, you can find the standard error now by taking the standard deviation divided by the square root of the sample size.
The standard deviation in a data set is the mean deviation of the data from their mean.
For sample size n for a data set with data points X1, X2, X3……..Xn for exact standard deviation:
1. Calculates the arithmetic mean M of the set data by adding them all and dividing by n.
M = ( X1+X2+ X3+…..+Xn) / n
2. Calculate the deviation (D) for each data point from the mean M
D = (Xi-M) for all
3. Squaring and sum of all deviations, sum of squares (SS)
4. Divide SS by n.This quantity is the sample variance V
5. Take the square root of V.
6. This quantity is the sample standard deviation, SD.
There are some specific terms and issues to consider. If you are estimating the standard deviation of a population from a sample and the population mean $ is not known, M serves as an unbiased estimate of $. Again, SS is divided by (n-1), not n.
The resulting standard deviation is an unbiased estimate of the population standard deviation based on the sample size, n. If the population mean is known, use that mean instead of the sample mean. , and the SD of the sample is only calculated for n through SS dives.
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Wildlife conservationists want to estimate the deer population in a region. They place an identifying tag on 220 deer. Several months later, researchers investigate 8 samples of 50 deer and record how many have a tag. Based on these results, how many deer should they estimate live in the region?
The number of deer that should be estimated live in the region is:
50.
To estimate the deer population, the method of capture-recapture is commonly used.
This method involves counting the number of tagged animals (in this case 220) and then counting the number of tagged animals in a subsequent sample (in this case 8 samples of 50 deer each).
By comparing the number of tagged deer in the sample to the total number of tagged deer, we can estimate the total population.
Let N be the total population of deer. The estimated population size can be calculated using the formula:
N = (220 * 50) / (the number of tagged deer in the sample)In this case, the number of tagged deer in the sample is 220. So, the estimated population size is:
N = (220 * 50) / 220 = 50Therefore, it is estimated that there are 50 deer living in the region.
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what is the minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible
Any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible.
The minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible is 3. This can be calculated by finding the determinant of the matrix. The determinant is the sum of the products of the entries in the matrix, each multiplied by its corresponding minor. If a 3-by-3 matrix has 3 of its entries equal to zero, the determinant will be equal to 0, which means the matrix is non-invertible. To calculate the determinant of a 3-by-3 matrix, use the formula.
Where a, b, c, d, e, f, g, h, i are the entries of the matrix. If any 3 of those entries are equal to 0, the any 3 of those entries are equal to 0, the determinant will be 0, meaning the matrix is non-invertible determinate will be 0, meaning the matrix is non-invertible.
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The drama club has 72 members. 1/4 of the drama club members are in 5th grade and the rest of the members are in 6th grade. How many drama club members are in 6th grade?
answer choices
72
54
18
3
Answer:
54
Step-by-step explanation:
1/4 of 72 is 18. 72-18=54.
if deja is to perform an appropriate t-test to determine if there is a mean difference between the number of abrasions per leaf produced by the two strains, how many degrees of freedom should she use?
The number of degrees of freedom in a t-test is calculated as the sample size -2.
In this case, if Deja is performing a t-test to determine if there is a mean difference between the number of abrasions per leaf produced by the two strains, she needs to have the sample size of both strains.
Assuming she has n1 and n2 samples for each of the two strains, the degrees of freedom can be calculated as:
df = n1 + n2 - 2
The degrees of freedom represent the number of independent pieces of information in the sample data that are used to estimate the population parameters. The t-test statistic is then compared to a t-distribution with the calculated degrees of freedom to determine the significance of the results.
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