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The size sample should be obtained in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5% is at least 385 adults.

Assume that the estimated proportion of the population with sleep deprivation is p and the desired level of precision is d, the sample size needed can be calculated using the following formula:

n = (Zp(1 - p) / d²)

where Z is the z-score corresponding to the desired level of confidence (e.g. for 95% confidence, Z = 1.96).

So, in this case, if you want to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%, and you don't know what the true proportion is, you can use a value of 0.5 for p (since this is the midpoint of the range 0 to 1). Plugging these values into the formula above gives:

n = (1.96)(0.5)(1 - 0.5) / (0.05²) = 384.16

Therefore, you would need a sample size of at least 385 adults to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%.

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Answer:

1 sheet costs 1.6 cents

Step-by-step explanation:

The total cost of the toner is 40 dollars which is good for 10000 pages.

The cost of 500 sheets of paper is 6.00 dollars or 600 cents

500 sheets / 600 cents = 1 sheet /x         Cross Multiply

500 sheets  x = 600 cents                        Divide by 500

x = 600/500

x = 1.2 cents.

10000 sheets cost 40 dollars. = 4000 cents

1 sheet      costs x

10000/1 = 4000/x                          Cross multiply

10000*x = 1 * 4000                        Divide by 10000

x = 4000/10000

x = 0.4 cents.

Total Cost for 1 sheet = 0.4 cents + 1.2 cents

Total Cost for 1 sheet = 1.6 cents.

Answer:

8.7 so either 8 or 9 tenth of a year

Step-by-step explanation:

Is it compounded per month? I assume

1. Compound interest formula

FV = PV(1+r/100k)^kn

FV is the future value,

PV is the present value,

n is the number of years,

k is the number of compounding periods per year

r% is the nominal annual rate of interest

2. Plug in numbers

3550 = 2400(1+4.6/100*12)^12*n

71/48 = (6023/6000)^12n

12n = logBase(6023/6000)*(71/48)

n = answer/12

n ≈ 8.70

Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.

If a cheque remains uncashed for option C, 6 months, it becomes stale-dated and can no longer be cashed.

Stale-dating refers to the period after which a cheque is considered expired or no longer valid for cashing. In this case, the correct answer is option C: 6 months. After a cheque has been issued, it is typically expected to be cashed within a reasonable timeframe to ensure prompt payment. If the recipient fails to cash the cheque within the specified period, it becomes stale-dated.

The specific duration for a cheque to become stale-dated may vary based on local regulations or banking practices. However, the general rule of thumb is that cheques are typically considered stale-dated after 6 months. After this time frame, banks may refuse to honor the cheque, and the payee would need to contact the issuer for a replacement or alternative payment method. It's important to note that policies may vary among different financial institutions and jurisdictions, so it's advisable to consult the specific terms and conditions provided by the relevant bank or legal authorities.

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If the estimate of the population standard deviation is 8, the sample size is 62

In this question, you want to estimate the population mean with 95% confidence with a margin of error of 2.

if the estimate of the population standard deviation is 8, we need to find the sample size.

here, α = (1 - 0.95)/2

         α = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - α

so, z = 1.96

Now, to find the margin of error M we have formula

M = z * σ/√n

2 = 1.96 * 8/√n

√n = 1.96 * 4

√n = 7.84

n = 61.47

n ≈ 62

Therefore,  if the estimate of the population standard deviation is 8, the sample size is 62

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The solution of the given problem of quadratic equation  comes out to be factoring the binomial is the correct response.

Regression modelling uses the polynomial solution x = ax² + b + c=0 for one-variable equations. The First Hypothesis of Algebra claims that since this equation has a second order, there can only be one solution. There are simple and complex solutions available. Even as the name suggests, a "non-linear formula" has four variables. According to this, there might be just one squared word.

Here,

In Step 2, it appears that the binomial ax2 + bx in the equation -c = ax² + bx is being factored. The student has specifically factored out a "a" from the words ax2 and bx to get:

=>  a(x² + b/a x) = -c

The student's attempt to factor this same quadratic expression

ax² + bx by eliminating the two terms' "a" largest common factor serves as the best rationale for Step 2, as a result.

Thus, "factoring the binomial" is the correct response.

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The complete question is

" A student is deriving the quadratic formula. Her first two steps are shown. Step 1: –c = ax2 + bx Step 2: -c = a[x^2+b/ax] Which best explains or justifies Step 2? division property of equality factoring the binomial completing the square subtraction property of equality"

The number of eggs, Bridget collect from the chickens this morning is 28.

Given that, Bridget collected the eggs her chickens had laid and gave ½ to her neighbor.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The equation for the given situation is (e/2)-6=8

⇒ e/2 = 8+6

⇒ e/2 = 14

⇒ e = 28

Hence, the number of eggs, Bridget collect from the chickens this morning is 28.

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The number of eggs will be 28, which Bridget collected from the chickens this morning.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that, Bridget collected the eggs her chickens had laid and gave ½ to her neighbor.

The equation below represents Bridget's original collection.

⇒ (e/2) - 6 = 8

⇒ e/2 = 8 + 6

Apply the addition operation,

⇒ e/2 = 14

Multiply by 2 into both sides of the above equation

⇒ 2 × e/2 = 2 × 14

⇒ e = 28

Therefore, the number of eggs will be 28, which Bridget collected from the chickens this morning.

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a. The riders in the "Screaming Swing" experience an acceleration equal to twice the acceleration due to gravity (2g), both in m/s^2 and in units of g.

b. At the bottom of the ride, as they pass each other, the riders are moving at the same speed.

a. The "Screaming Swing" consists of two swings moving in opposite directions. At the bottom of the swing, each rider follows a circular path. Since the riders are moving in circles, they experience centripetal acceleration. The magnitude of the centripetal acceleration is given by a = v^2/r, where v is the velocity and r is the radius of the circle. In this case, the radius is 4 meters, so the acceleration experienced by the riders is a = (v^2)/4. Since the velocity is constant and the radius is fixed, the acceleration is constant as well. Considering that the acceleration due to gravity is g = 9.8 m/s^2, the riders experience an acceleration of 2g, which is approximately 19.6 m/s^2, and it can be expressed as 2 times the acceleration due to gravity (2g).

b. At the bottom of the ride, as the riders pass each other, they are moving at the same speed. Since the swings are symmetrical and moving with the same velocity at the bottom of their arcs, the riders encounter each other at the same speed.

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Go from right to left in such function questions

a. f(g(x))

⇒ f(4x + 1)

⇒ (4x + 1)² - 2

⇒ 16x² + 8x + 1 - 2

⇒ 16x² + 8x - 1

b. g(f(x))

⇒ g(x² - 2)

⇒ 4(x² - 2) + 1

⇒ 4x² - 7

Answer:

\(f[g(x)]=16x^2+8x-1\)

\(g[f(x)]=4x^2-7\)

Step-by-step explanation:

Given functions:

\(f(x)=x^2 - 2\)

\(g(x) =4x + 1\)

\(f[g(x)]\) means to substitute g(x) in place of x in f(x):

\(\begin{aligned}\implies f[g(x)] & =[g(x)]^2-2\\ & =(4x+1)^2-2\\ & = (4x+1)(4x+1)-2\\ & = 16x^2+8x+1-2\\ & = 16x^2+8x-1\end{aligned}\)

\(g[f(x)]\) means to substitute f(x) in place of x in g(x):

\(\begin{aligned}\implies g[f(x)] & =4[f(x)]+1\\ & = 4(x^2-2)+1\\ & = 4x^2-8+1\\ & = 4x^2-7\end{aligned}\)

The relationship between osmotic pressure and osmosis is closely linked. Osmotic pressure is the pressure exerted by a solvent to prevent the flow of water into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution.

To calculate osmotic pressure, we can use the formula: Π = iRT(Cin - Cout)

- Π represents osmotic pressure in atmospheres.
- i represents the number of ions dissociated from each molecule in solution. For non-electrolytes like sugar, i is equal to 1.
- R is the gas constant, which is 0.082 atm/(K×M).
- T represents the temperature in Kelvin. For room temperature, it is 293 Kelvin.
- Cin represents the concentration of the solution inside the dialysis bag in moles per liter (M).
- Cout represents the concentration of the solution outside the dialysis bag.

Let's calculate the osmotic pressure for each of the given solutions:

1. Osmotic pressure of 70% Sucrose solution:
First, we need to calculate the molarity of the solution inside the bag (Cin). The molecular weight of sucrose is 342 g/mol. So, for a 70% sucrose solution, we have 700 g of sucrose in 1 L of solution. To convert this to moles, we divide by the molecular weight: (700 g / 342 g/mol) = 2.05 mol/L.

Now we can substitute the values into the formula:
Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(2.05 M - 0 M)
Π = 47.79 atm

Therefore, the osmotic pressure of the 70% Sucrose solution is 47.79 atm.

2. Osmotic pressure of 35% Sucrose solution:
Using the same process as above, we find that the molarity of the solution inside the bag (Cin) is 1.02 M.

Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(1.02 M - 0 M)
Π = 23.67 atm

Therefore, the osmotic pressure of the 35% Sucrose solution is 23.67 atm.

3. Osmotic pressure of water (control):
For water, the concentration of solute (Cin) is 0 M, as there is no solute present.

Π = iRT(Cin - Cout)
Π = (1)(0.082 atm/(K×M))(293 K)(0 M - 0 M)
Π = 0 atm

Therefore, the osmotic pressure of water is 0 atm.

The relationship between osmotic pressure and the rate of osmosis is that higher osmotic pressure leads to a faster rate of osmosis. Osmosis is the movement of solvent molecules from an area of lower solute concentration to an area of higher solute concentration through a semipermeable membrane. The higher the osmotic pressure, the greater the driving force for water molecules to move across the membrane.

If the dialysis membrane were impermeable to ions and NaCl was used instead of sucrose at the same molarity (2.05 M), the osmotic pressure would be different. NaCl dissociates into two ions in solution, so the value of i would be 2.

Π = iRT(Cin - Cout)
Π = (2)(0.082 atm/(K×M))(293 K)(2.05 M - 0 M)
Π = 97.98 atm

Therefore, if NaCl were used instead of sucrose, the osmotic pressure would be 97.98 atm. This is because NaCl generates more particles (ions) in solution, increasing the osmotic pressure compared to sucrose.

By understanding the relationship between osmotic pressure and the rate of osmosis, we can predict that a solution with higher osmotic pressure will have a faster rate of osmosis compared to a solution with lower osmotic pressure.

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Answer:

b

Step-by-step explanation:

just move the shape with cordinantes of b

The rule that maps figure 1 onto figure 2 is B. (x,y)→(x-5, y+11)

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, therefore,

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

The correct option is B.

(x,y)→(x-5, y+11)

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Answer:

11.17 ft

Step-by-step explanation:

Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.

Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by

L = Δθ/360 × 2πr where  Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ =  -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.

Substituting r and  Δθ into L, we have

L = -80°/360° × 2π(8 ft)

= -8/36 × 16π ft

=  -32π/9 ft

= -100.53/9 ft

= -11.17 ft

Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft

To compare the 3-month and 12-month moving average forecasts using the mean absolute deviation (MAD) criterion, we need to calculate the MAD for each model and then compare them. The MAD is a measure of the average magnitude of the forecast errors, and a lower MAD indicates a better forecast.

To calculate the MAD for the 3-month moving average model, we need to first calculate the forecasted values for each month by taking the average of the unemployment rates for the previous 3 months. For example, the forecasted value for April 2018 would be the average of the unemployment rates for January, February, and March 2018. We then calculate the absolute deviation between the forecasted value and the actual value for each month, and take the average of those deviations to get the MAD for the 3-month moving average model.

We can repeat this process for the 12-month moving average model, but instead of taking the average of the previous 3 months, we take the average of the previous 12 months.

Once we have calculated the MAD for both models, we can compare them to determine which model yields better results. Generally, a lower MAD indicates a better forecast. However, it is important to note that the MAD criterion only considers the magnitude of the forecast errors and does not take into account the direction of the errors (i.e., overestimation versus underestimation).

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Full Question ;

The accompanying dataset provides data on monthly unemployment rates for a certain region over four years. Compare 3- and 12-month moving average forecasts using the MAD criterion. Which of the two models yields better results? Explain. Click the icon to view the unemployment rate data. Find the MAD for the 3-month moving average forecast. MAD = (Type an integer or decimal rounded to three decimal places as needed.) A1 fx Year D E F G H I 1 2 3 1 с Rate(%) 7.8 8.3 8.5 8.9 9.4 9.6 9.4 9.5 9.7 9.9 9.8 10.1 9.9 9.7 9.8 9.91 9.7 9.4 9.6 9.4 9.3 9.5 9.9 9.5 9.2 9.1 8.9 A B Year Month 2013 Jan 2013 Feb 2013 Mar 2013 Apr 2013 May 2013 Jun 2013 Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2014 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Aug 2014 Sep 2014 Oct 2014 Nov 2014 Dec 2015 Jan 2015 Feb 2015 Mar 2015 Apr 2015 May 2015 Jun 2015 Jul 2015 Aug 2015 Sep 2015 Oct 5 7 3 ) 1 2 3 1 5 7 9.1 ) 9. 1 2 3 1 5 7 ) 9.1 8.9 8.9 8.9 8.9 8.7 8.4 8.3 8.3 8.4 8.1 8.1 8.4 8.2 8.3 7.7 7.9 7.9 7.8 1 2 2015 Dec 2016 Jan 2016 Feb 2016 Mar 2016 Apr 2016 May 2016 Jun 2016 Jul 2016 Aug 2016 Sep 2016 Oct 2016 Nov 2016 Dec 3 1 5 3 2 2

for a second i thought you were talking about the kim kardashians lma.o

and btw the answer is 4

Answer:

Line m, because if you put a mirror on m, one figure will be truly reflected in another

We have a circle that has an area of 36π square units.

We have to find the radius.

The area in function of the radius is πr², so we can find the radius r as:

Answer: the radius is 6 units.

x = -1

y = -4

2x - y = 2

5x + y = -9

Using the elimination method, we can find the value of x.

2x - y = 2

5x + y = -9

_________+

7x = -7

x = -1

Then, we can use substitution method to find the value of y

5x + y = -9

5(-1) + y = -9

-5 + y = -9

y = -9 + 5

y = -4

So in conclusion, the value of x and y is -1 and -4

integral diverges for the value of c = 6.

The value of the constant c for which the given integral converges is c=6.

When c=6, the integral can be evaluated as follows:

[integral symbol from 0 to infinity] 7x(x^2-1-7c)/(6x+1) dx

= [integral symbol from 0 to infinity] 7x(x^2-43)/(6x+1) dx

To evaluate this integral, we can use long division to divide 7x(x^2-43) by 6x+1. The result is:

7x(x^2-43) ÷ (6x+1) = (7/6)x^2 - (301/36)x + (43/6) - (10/36)/(6x+1)

Therefore,

[integral symbol from 0 to infinity] 7x(x^2-43)/(6x+1) dx

= [integral symbol from 0 to infinity] (7/6)x^2 - (301/36)x + (43/6) - (10/36)/(6x+1) dx

= [(7/6)x^3 - (301/72)x^2 + (43/6)x - (10/36)ln|6x+1|] evaluated from 0 to infinity

= infinity - 0

Thus, the integral diverges.

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Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

Answer:

the right answer is 87,5%

Answer:

\(→0.875 \times 100 = \boxed{ 87.5\%}✓ \\ \)

Answer:

Inverse property

Step-by-step explanation:

3/4 is the reciprocal of 4/3 which means they would cancel each other out. So you would only be left with x=x

The amount that Pham has paid back after 6 years will be $8,511.11.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Pham borrows $6,000 to buy a car. The loan has 6% interest, compounded annually.

Then the amount after 6 years is given as,

A = $6,000 × (1 + 0.06)⁶

A = $6,000 × (1.06)⁶

A = $6,000 × 1.4185

A = $8,511.11

The amount that Pham has paid back after 6 years will be $8,511.11.

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Answer:

20

Step-by-step explanation:

To find the line of best fit, we can use the equation for a linear regression: y = mx + b, where y is the price, x is the weight in ounces, m is the slope of the line, and b is the y-intercept.

To estimate the price when the weight is 48 ounces, we can plug in x = 48 into the equation: y = mx + b, and solve for y.

The correlation coefficient, denoted by r, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

In this case, the correlation coefficient means that how strong and direction of the relationship between the price and weight of cereal. A correlation coefficient of 1 means that there is a perfect positive correlation between the two variables, which means that as the weight of the cereal increases, so does the price. A correlation coefficient of -1 means that there is a perfect negative correlation between the two variables, which means that as the weight of the cereal increases, the price decreases. A correlation coefficient of 0 means that there is no correlation between the two variables, which means that there is no relationship between the weight of the cereal and the price.

There are 15 employees in the office and 5 need to be chosen, so there are a total of (15 choose 5) possible ways to select the employees. This can be calculated using the formula for combinations:

(15 choose 5) = 15! / (5! * 10!) = 3003

Now, we need to find the number of ways that the specific group of you, Diana, Kyle, Nancy, and Arthur can be chosen. This is simply (5 choose 5), since we want to choose all 5 members of the group.

(5 choose 5) = 5! / (5! * 0!) = 1

Therefore, the probability of this specific group being chosen is:

(5 choose 5) / (15 choose 5) = 1 / 3003 ≈ 0.0003

So the probability of you, Diana, Kyle, Nancy, and Arthur being chosen is very low, at approximately 0.0003 or 3 in 10,000. This is because there are many other possible groups of 5 employees that could be chosen from the pool of 15, and all of these groups have an equal chance of being selected.

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When using the chi-square goodness of fit test, the smaller the value of the chi-square test statistic, the more likely we are to accept the null hypothesis rather than reject it. This statement is false.

The chi-square goodness of fit test is a hypothesis test that measures how well an observed frequency distribution fits a theoretical frequency distribution. It is used to determine whether a sample's categorical data is distributed similarly to the population's categorical data or not.

However, a low chi-square statistic suggests that the observed frequencies are close to the expected frequencies, and thus the null hypothesis should not be rejected. In contrast, a large chi-square value indicates that the observed frequencies are significantly different from the expected frequencies, indicating that the null hypothesis should be rejected.

Therefore, when using the chi-square goodness of fit test, the larger the value of the chi-square test statistic, the more likely we are to reject the null hypothesis, and vice versa.

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The circulation integral of F around the given circle is 2π. To compute the circulation integral using the tangential vector form of Green's Theorem, we first need to parameterize the circle C.

The given circle has the equation x^2 + y^2 = 1, which can be parameterized as follows:

x = cos(t)

y = sin(t)

where t is the parameter ranging from 0 to 2π.

Next, we compute the tangential vector for the parameterization:

r(t) = cos(t)i + sin(t)j

Taking the derivative of r(t) with respect to t, we get:

r'(t) = -sin(t)i + cos(t)j

Now, we can compute the circulation integral using the formula:

∮C F · dr = ∫(F · T) ds

where F is the given vector field, T is the tangential vector, and ds is the differential arc length.

Plugging in the values, we have:

F · T = (-1 yi + 1 xj) · (-sin(t)i + cos(t)j) = -sin(t)y + cos(t)x

ds = ||r'(t)|| dt = dt

Now, we integrate over the parameter t from 0 to 2π:

∫[0 to 2π] (-sin(t)y + cos(t)x) dt

= ∫[0 to 2π] (-sin(t)sin(t) + cos(t)cos(t)) dt

= ∫[0 to 2π] (-sin^2(t) + cos^2(t)) dt

= ∫[0 to 2π] (1) dt

= [t] from 0 to 2π

= 2π

Therefore, the circulation integral of F around the given circle is 2π.

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