6 ft

5. The figure shows a container, in the shape of

a trapezoidal prism, that Pete filled with sand.

12 cm

5cm

7 cm

10 cm

The line of best fit gives a general outlook on the data while the correlation is the exact points showcased to calculate or show for a data set or table.

It should be noted that between the two variables it is a positive correlation because they both increase in the same direction.  

Positive correlation is a relationship between two variables in which both variables move in tandem that is, in the same direction.

In order to find the residual one would subtract the predicted value from the measured value.

The diagram is attached.

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Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.

(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.

(b) To find the margin of error for the proportion, we use the formula:

ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.

ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245

(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:

0.1536 - 0.0245 <= p <= 0.1536 + 0.0245

0.1291 <= p <= 0.1781

(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:

1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245

0.8209 <= p <= 0.8264

(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.

Confidence interval in part (c): 0.1291 to 0.1781

Confidence interval in part (d): 0.8209 to 0.8264

Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.

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Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.

(a) The point estimate of the proportion of the population of respondents who do think that the country is headed in the right direction is 384 / 2500 = 0.1536.

(b) To find the margin of error for the proportion, we use the formula:

ME = 1.96 * sqrt(p * (1 - p) / n), where p is the point estimate and n is the sample size.

ME = 1.96 * sqrt(0.1536 * (1 - 0.1536) / 2500) = 0.0245

(c) The 95% confidence interval for the proportion of respondents who do think that the country is headed in the right direction is:

0.1536 - 0.0245 <= p <= 0.1536 + 0.0245

0.1291 <= p <= 0.1781

(d) To find the 95% confidence interval for the proportion of respondents who do not think that the country is headed in the right direction, we subtract the proportion from 1:

1 - 0.1536 - 0.0245 <= p <= 1 - 0.1536 + 0.0245

0.8209 <= p <= 0.8264

(e) The confidence interval in part (c) has a smaller margin of error because the sample proportion of respondents who do think that the country is headed in the right direction is closer to 0.5 (the midpoint of the interval) than the sample proportion of respondents who do not think that the country is headed in the right direction.

Confidence interval in part (c): 0.1291 to 0.1781

Confidence interval in part (d): 0.8209 to 0.8264

Therefore, Margin of Error is 0.0245, 0.8209 <= p <= 0.8264 and CI in (C) is 0.1291 to 0.1781 and in (d) is 0.8209 to 0.8264.

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Eval is a function that evaluates an expression and puts the resulting value into a new or existing field.

To calculate the value of an expression using Eval, you must use the correct syntax. The syntax for Eval is Eval(expression, optional_parameter). The expression can take the form of a mathematical equation or a logical expression. For example, if you wanted to calculate the sum of two numbers, you would use the following expression: Eval(A + B). The optional parameter allows you to specify a range of values to evaluate the expression against.

For example, if you wanted to calculate the sum of two numbers within a given range, you would use the following expression: Eval(A + B, range). The range parameter can be used to specify the starting and ending values that the expression should be evaluated against.

Using Eval to calculate an expression is a useful tool for quickly getting the desired value. It is also useful for quickly testing the accuracy of a complex expression before implementing it in your code.

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The limit of (xy⁴)/(x⁴y⁴) is 0.

The limit squeeze theorem (also known as sandwich theorem) states that if a function f(x) lies between two functions g(x) and h(x) and the limits of each of g(x) and h(x) at a particular point are equal (to L), then the limit of f(x) at that point is also equal to L. This looks something like what we know already in algebra. If a ≤ b ≤ c and a = c then b is also equal to c. The squeeze theorem says that this rule applies to limits as well. We define the squeeze theorem mathematically as follows:

"Let f(x), g(x), and h(x) are three functions that are defined over an interval I such that g(x) ≤ f(x) ≤ h(x) and suppose lim ₓ → ₐ g(x) = lim ₓ → ₐ h(x) = L, then lim ₓ → ₐ f(x) = L".

Here:

The function f lies between g and h and hence they are lower and upper bounds of f respectively.

'a' doesn't necessarily need to be within I.

We have to find the limit of (xy⁴)/(x⁴y⁴).

After applying the limit squeeze theorem, we get

[tex]\lim_{x \to \infty} \frac{xy^{4} }{x^{4}y^{4} }\\ = \lim_{x \to \infty} \frac{1}{x^{3} } \\= 0[/tex]

Thus, the limit of (xy⁴)/(x⁴y⁴) is 0.

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The variance for this sample of 5 scores with the sum of squared errors (deviations)  20 is 5.

Variance is a measure of the spread of the data around the mean. It can be calculated from the sum of squared deviations (SSE) as follows:

Variance = SSE / (n - 1)

where n is the number of scores in the sample.

In this case, n = 5 and SSE = 20, so the variance is:

Variance = 20 / (5 - 1) = 20 / 4 = 5

So the variance for this sample is "5".

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The width of the sticker will be  8 3/4 inches.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The given logo has a height of 2 inches and a width of 5 inches.

Bumper stickers usually have a height of 3 1/2 inches which has a

= (7/2)/2 = 7/4 scale factor.

Therefore, The width of the sticker will be,

= 5×(7/4).

= 35/4.

= 8 3/4 iches.

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This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.

Proof:

Let S(n) = n + 1 log n

We will prove S(n) = 2 by induction.

Base Case:

Let n = 1. Then S(1) = 1 + 1(log 1) = 1 + 0 = 1 = 2.

Inductive Step:

Assume S(k) = 2 for some arbitrary integer k ≥ 1. We must show that S(k + 1) = 2.

S(k + 1) = (k + 1) + 1(log(k + 1))

= k + 1 + 1(log k + log 1)

= k + 1 + 1(log k + 0)

= k + 1 + 1(log k)

= k + 1 + log k

= 2 + log k

= 2 (by induction hypothesis)

Therefore, S(n) = 2 for all positive integers n.

This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.

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The interior volume of the tent where the cross sections are triangles is given is 120ft³.

There are two cross sectional triangles

The  one smaller triangle with the height and base of 2ft

The other bigger triangle has a base and height of 4 ft

And the total length of the Tent is given as 6 ft.

Therefore,

Area of smaller triangle = 2 x 2 = 4m²

Area of bigger triangle = 4 x 4 = 16 ft²

So the Volume of the tent is given by ,

Total length x (Area of smaller triangle + Area of bigger triangle)

= 6 x ( 4 + 16 )

=6 x ( 20 )

= 120 ft ³

A measurement of three-dimensional space is volume.  Numerous imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The capacity of a container is typically regarded to be its volume.

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P ↔ Q is a tautology because if P and Q are equivalent propositional forms, they have the same truth value in every possible interpretation, making the bi-conditional proposition P ↔ Q always true.

A tautology is a proposition that is always true, regardless of the truth values of its component propositions.

When two propositions, P and Q, are equivalent, it means that they have the same truth value in every possible interpretation. That is, P and Q are logically equivalent.

Therefore, if P and Q are equivalent propositional forms, then P ↔ Q, the bi-conditional proposition, is a tautology. This is because the truth value of P ↔ Q will always be true, as both P and Q have the same truth value in every possible interpretation.

This can be shown through the truth table for P ↔ Q. The bi-conditional proposition is true if and only if both P and Q have the same truth value. If P and Q are equivalent, then they will always have the same truth value, and so P ↔ Q will always be true.

In general, for any equivalent propositions P and Q, P ↔ Q will always be a tautology.

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The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.

If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.

There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.

Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.

So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.

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The total number of different committees possible is 6 * 3 * 2 * 56 = 3456.

If 2 of the men refuse to serve together, then we have to choose the first man for the committee first and then choose the other two men one by one, making sure that the two men who refuse to serve together are not chosen together.

There are 6 possible choices for the first man. After the first man is chosen, there are 4 remaining men, and we have to choose 2 more men from these 4. However, one of these 2 men must be the one who refused to serve with the first man. So, there are only 3 possible choices for the second man. After the second man is chosen, there are only 2 possible choices for the third man.

Next, we have to choose 3 women from 8. There are C(8,3) = 56 ways to do this.

So, the total number of different committees possible is 6 * 3 * 2 * 56 = 3456.

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The distance between David's house and school is definitely greater than 8.5miles as his school is more than 8.5 miles.

The answer must not be 8 , because as David stays 8.5 miles distance more from his school. An Inequality for a is a>8.5.

The illustration of two expressions by inequal symbol is known as inequality mathematical statement in algebra. It has non equal expressions on both sides. The inequality shows the values on the left side should be bigger or smaller than the expression on the right. The relationships between two algebraic expressions that are expressed using inequality symbols are literal inequalities. An algebraic expression is an expression built up from constant algebraic variables, numbers and the operators.

So the distance between David's house and school must be the value greater than 8.5

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Categorical data is data that can be divided into different categories. Examples of categorical data include hair color, number of suitcases on a plane, tree height, and amount of rainfall.

Hair color would be classified as categorical data because it can be divided into categories such as black, brown, blonde, and red. Number of suitcases on a plane would also be classified as categorical data because the amount of suitcases can be divided into categories such as 0, 1, 2, 3, etc. Tree height would be classified as categorical data as it can be divided into categories such as small, medium, and large. Amount of rainfall would also be classified as categorical data as it can be divided into categories such as light rainfall, moderate rainfall, and heavy rainfall.

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Adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example.

A regular expression is a pattern used to match and search for specific strings. To remember the street number "613" and apartment number "apt 57" but not the street name, we can add parentheses to the regular expression to create capturing groups. The parentheses will capture the desired information and allow us to reference it later if needed.

The regular expression would look something like this: (613) (apt 57)

The parentheses indicate that the information inside should be captured as a group. This regular expression will match a string that contains the street number "613" and the apartment number "apt 57", and capture these values in two separate groups.

For example, if we have the following address: "613 Main St, apt 57"

We can use the regular expression to match the desired information:

(613) (apt 57)

In this case, the two groups captured are "613" and "apt 57". The information inside the parentheses can be accessed and used for various purposes, such as formatting or validation.

In summary, adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example. This allows for more precise and flexible matching and extraction of information from strings.

Therefore, Adding parentheses to a regular expression can be used to capture specific information, such as the street number and apartment number in this example.

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log9 72 to four decimal places is 2.8594

To approximate log9 72 using common logarithms, we can use logarithmic properties and logarithmic tables.

First, we can rewrite 72 as [tex]9^3[/tex] to find the exponent that gives us 72:

log9 72 = log9 ([tex]9^3[/tex]) = 3

Now, we can use logarithmic tables or a calculator to find the common logarithm of 9, which is 0.954243:

log10 9 = 0.954243

Finally, we can divide the result by the common logarithm of 10 to find the logarithm to base 9:

log9 72 = (1/log10 9) * log10 72 = 0.954243 * log10 72 ≈ 2.859437

log9 72 to four decimal places is 2.8594.

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Answer:

There are 5 ducks

Step-by-step explanation:

2 ducks behind

1 duck in the middle

2 ducks infront

Answer:

x = 15

Step-by-step explanation:

3/5x - 1/3x = 4

9/15x - 5/15x = 4

4/15x = 4

x = 15

The equivalent expression is 12h - 18/4

It is important to note that algebraic expressions are mathematical expression comprising of factors, constants, coefficients, variables and terms.

These algebraic expressions are also known to be made up of mathematical to arithmetic operations, such as;

From the information given, we have that;

3/4(4h – 6)

To simply this, we need to expand the bracket, we get;

12h - 18/4

Hence, the expression is 12h - 18/4

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Answer:

332126

Step-by-step explanation:

333333+(5+6)-657-(564-3)=332126

The system of equations is given by: y = -2/5x +2 and y = -3x - 4.

Choose two equation pairs at random from the system. Apply the Addition/Subtraction technique to each pair to remove the same variable. Use the Addition/Subtraction method to solve the two new equations as a system. Reintroduce the solution into one of the original equations and find the third variable there.

equations  is:-

y = -2/5x +2 and y = -3x - 4.

when x=0

y= -2/5(0) +2 = 2

y  = -3(0) - 4= 4

when y=0

0= -2/5x +2

x=.80

0= -3x - 4

x=13.33

so from the above value we come to conclusion that system of equations is given by: y = -2/5x +2 and y = -3x - 4.

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14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.

Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).

The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:

3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x

Expanding both sides:

119.75 = 8.04x

Dividing both sides by 8.04:

x = 14.84 pounds

So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.

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14.84 pounds of dried apricots were used and 10.16 pounds of dried prunes were used to produce 25 pounds of the dried fruit mixture.

Let's call the weight of dried apricots used in the mixture "x" (in pounds). Then the weight of dried prunes used in the mixture is 25 - x (in pounds).

The cost per pound of dried apricots is 3.25, and the cost per pound of dried prunes is 4.79. So the total cost of the mixture is:

3.25x + 4.79(25 - x) = 3.25x + 119.75 - 4.79x

Expanding both sides:

119.75 = 8.04x

Dividing both sides by 8.04:

x = 14.84 pounds

So 14.84 pounds of dried apricots were used in the mixture, and 25 - 14.84 = 10.16 pounds of dried prunes were used in the mixture.

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The largest possible value of p can be determined by analysing the ratio of the volumes of the two rectangular boxes.

The volume of the first box is V1 = m*p*n and the volume of the second box is [tex]$V2 = (m2)\cdot (n2)\cdot (p2)$[/tex]. Therefore, we can set up the following equation to solve for p:

[tex]$\frac{V1}{V2} = \frac{mnp}{(m2)(n2)(p2)} = \frac{1}{2}$[/tex]

Solving for p gives us the following:

[tex]$p = \sqrt[3]{\frac{2(m2)(n2)}{mn}}$[/tex]

Since m, n, and p must all be integers, the largest possible value of p is the largest integer such that

[tex]$p \le \sqrt[3]{\frac{2(m2)(n2)}{mn}}$.[/tex]

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Answer: 24 feet

Step-by-step explanation:

Perimeter: 2(length+width)

2(7+5)

14+10=24

Answer:

50%

Step-by-step explanation:

7 nurses

3 doctors

4 offices

14 in total

7/14 or 50% is the probability

Answer:

0.50

Step-by-step explanation:

[tex]7 + 3 + 4 = 14[/tex]

So, the probability that the nurses are selected to attend the conference is,

[tex] \frac{7}{14} = \frac{1}{2} [/tex]

[tex] \frac{1}{2} = 0.50[/tex]

Answer:

53 1/4

Step-by-step explanation:

55 5/6  - 1 1/3 - 1 1/4  Rewrite with a common denominator

55 10/12 - 1 4/12 - 1 3/12

55 10/12 - 1 4/12 = 54 6/12

54 6/12 - 1 3/12

53 3/12

53 1/4

The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.

What is the differential equations?

A differential equation is an equation that relates an unknown function to its derivatives. It describes the behavior of a physical, biological, or engineering system in terms of changes in variables over time.

A fundamental solution in differential equations is a particular solution to a differential equation that contains arbitrary constants. It is called "fundamental" because it is a building block for constructing more general solutions to the equation. The general solution to a differential equation can be found by adding a linear combination of several fundamental solutions. The coefficients in the linear combination are determined by the initial or boundary conditions of the problem.

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The correct answer fort parallel angles is x = 33° and y = 10°.

The angles created when a transversal intersects two parallel lines are known as corresponding angles. Opening and shutting a lunchbox, completing a Rubik's cube, and an infinite stretch of parallel train lines are common examples of identical angles.

Angle 3y + 20° and angle 5y are parallel angles.

3y + 20° = 5y

2y =  20°

y = 10°

Angles 2x - 16° and 3y + 20° are in direct opposition to one another.

3y + 20° =  2x - 16°

Put the value of angle y in the equation.

3(10) + 20 = 2x - 16

30 + 20 = 2x - 16

50 = 2x - 16

2x = 66

x = 33

As a result, the angles are 33° for x and 10° for y.

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Question:

Find the value of x for which l is parallel to m. The diagram is not to scale. Lines l and m are parallel.

By applying the debt concept, it can be concluded that:

A. He should pay $466.02 to pay off the balance on the account.

B. The balance on his account is $190.68

Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor.

We have the following information:

Ahmad owes $382.45, and because he owes, it means this value is the debt, and we write it:

D = $382.45

Then he returns two items ($25. 10 & $34. 50) so that their values get credited into his accounts.

D = $382.45 - $25.10 - $34.50 = $322.85

Now after this, he makes another two purchases of $45 and $98.17, which increase his debt and makes:

D = $322.85 + $45 + $98.17 = $466.02

Part A: Since the debt or the account balance is $466.02, then he should pay $466.02 to pay off the balance on the account.

Part B: However, instead of paying off the balance, Ahmed makes a payment of $300 and he has to be charged $24.66. It means that his debt is not paid off:

D = $466.02 - $300 + $24.66 = $190.68

So, the balance on his account is $190.68.

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The average speed of the whole journey is 24 kilometres per hour.

The average speed is the total distance travelled by the object in a particular time interval.

A car travels from X to Y at an average speed of 60km/h and returns to X at a speed of 40km/h.

Therefore, the average speed for the whole journey can be calculated as follows:

The total distance travelled is 120 km.

Hence,

total time = 120 / 60 + 120 / 40

total time = 2 + 3 = 5 hours

Therefore,

average speed = total distance / total time taken

average speed = 120 / 5

average speed = 24 km/hr

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30 students are taking none of the classes.

We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.

In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.

So, we can apply PIE as follows:

students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)

Using the given information, we have:

students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)

students taking none of the classes = 100 - (95 - 25)

students taking none of the classes = 100 - 70

students taking none of the classes = 30

Hence, 30 students are taking none of the classes.

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30 students are taking none of the classes.

We can use the Principle of Inclusion-Exclusion (PIE) to determine the number of students taking none of the classes. The PIE states that the total number of elements in the union of several sets is equal to the sum of elements in each set, minus the sum of elements in the pairwise intersections, plus the sum of elements in the three-way intersections, and so on.

In this case, we want to find the number of students taking none of the classes, which is equal to the total number of students (100) minus the number of students taking at least one class.

So, we can apply PIE as follows:

students taking none of the classes = 100 - (students in prob. + students in la + students in comp - students in prob. & comp - students in la & comp - students in prob. & la + students in prob., comp & la)

Using the given information, we have:

students taking none of the classes = 100 - (65 + 45 + 40 - 25 - 20 - 30 + 10)

students taking none of the classes = 100 - (95 - 25)

students taking none of the classes = 100 - 70

students taking none of the classes = 30

Hence, 30 students are taking none of the classes.

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