Cajun Catering Company experiences an insured loss of $850,000 while having insurance coverage beyond its coinsurance requirement. The insurance is divided among Company A with $500,000 coverage and Company B with $750,000 coverage.

Part A: Determine the fractional coverage from Company A. Show your work.

Part B: Determine the fractional coverage from Company B. Show your work.

Part C: Determine the amount paid by each insurance company. Show your work.

Here is the completed piecewise function that models Roland's pay:

[tex]\[f(x) = \begin{cases} 95x & \text{if } x \leq 100 \\1.25(x-100) + 95(100) & \text{if } 101 \leq x \leq 300 \\1.55(x-300) + 95(100) + 1.25(300-100) & \text{if } x > 300\end{cases}\][/tex]

This piecewise function represents Roland's pay based on the different pay rates for the respective ranges of units produced.

To create a piecewise function to model Roland's pay, we need to consider the different ranges of units produced and the corresponding pay rates.

Let's complete the missing portions of each expression:

[tex]\[f(x) = \begin{cases} 95x & \text{if } x \leq 100 \\1.25(x-100) + 95(100) & \text{if } 101 \leq x \leq 300 \\1.55(x-300) + 95(100) + 1.25(300-100) & \text{if } x > 300\end{cases}\][/tex]

In the piecewise function:

- For [tex]\(x \leq 100\)[/tex], Roland receives 95 cents for each unit, so the expression is [tex]\(f(x) = 95x\).[/tex]

- For [tex]\(101 \leq x \leq 300\),[/tex] Roland receives $1.25 for each unit between 101 and 300. The base pay for the first 100 units (at 95 cents each) is added, resulting in the expression [tex]\(f(x) = 1.25(x-100) + 95(100)\).[/tex]

- For [tex]\(x > 300\)[/tex], Roland receives $1.55 for each unit over 300. Both the base pay for the first 100 units and the additional pay for units between 101 and 300 are added, leading to the expression [tex]\(f(x) = 1.55(x-300) + 95(100) + 1.25(300-100)\).[/tex]

This piecewise function models Roland's pay based on the different pay rates for the different ranges of units produced.

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[tex]f(s) = ℒ{(4t+1)(t-1)} = 8/s^3 - 3/s^2 - 1/s[/tex] by using laplace transform for the function.

A mathematical technique for studying linear, time-invariant systems is the Laplace transform. It transforms a time-domain function into a frequency-domain function, making it simpler to analyse the behaviour of the system.

The transform is defined as the function's integral times an exponential that decays, with the integral being assessed from 0 to infinity. The Laplace transform can convert a differential equation into an algebraic equation, which can subsequently be solved more quickly, making it useful for solving differential equations.

Along with other disciplines, the Laplace transform has uses in signal processing, electrical engineering, and control theory. It is an effective technique for deconstructing complicated systems and comprehending their evolution.

To find f(s), we first need to apply the Laplace transform to the function (4t+1)(t-1), denoted by ℒ{(4t+1)(t-1)}. Using the linearity property of the Laplace transform, we can split this into two separate transforms:

[tex]ℒ{(4t+1)(t-1)} = ℒ{4t^2 - 3t - 1} = 4ℒ{t^2} - 3ℒ{t} - ℒ{1}[/tex]

Next, we use the table of Laplace transforms to find the transforms of each term:

[tex]ℒ{t^n} = n!/s^(n+1)[/tex] for any integer n greater than or equal to 0
[tex]ℒ{1} = 1/s[/tex]

Using these formulas, we get:

[tex]ℒ{t^2} = 2!/s^3 = 2/(s^3)\\ℒ{t} = 1!/s^2 = 1/s^2\\ℒ{1} = 1/s[/tex]

Substituting these results back into the original equation, we get:

[tex]ℒ{(4t+1)(t-1)} = 4(2/(s^3)) - 3(1/s^2) - (1/s)\\= 8/s^3 - 3/s^2 - 1/s[/tex]

Therefore, [tex]f(s) = ℒ{(4t+1)(t-1)} = 8/s^3 - 3/s^2 - 1/s[/tex].

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The expression is 4x.

The expression is x + 3.

The expression is 4(x + 3).

The number of sweets she used can be represented by the product of the number of cakes, x, and the number of sweets on each cake, which is 4.

The number of cakes Paul made can be represented by the sum of the number of cakes Jennifer made, x, and 3.

The number of sweets Paul used can be represented by the product of the number of cakes Paul made, which is x + 3, and the number of sweets on each cake, which is 4.

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Answer: 1 mile

Step-by-step explanation:

Well it's 1 because half of 2 is 1, so Zachary ran 1 lap around the lake.

Answer:

yes

Step-by-step explanation:

540 X 2.5 = 1350 calories burned at soccer.

1350 + 800 = 2150 total calories burned.

2150 > 2000.

yes, more energy was used than consumed

The population of interest is all adults in the United States, the sample is 5000 randomly selected adults, the parameter is the proportion of adults with a bachelor's degree or higher, and the statistic is the proportion of adults in the sample with a bachelor's degree or higher.

1 - The population is the entire group of interest, which in this case is all adults in the United States.

2 - The sample is a subset of the population, selected in a random and representative way, in order to make inferences about the larger population. In this scenario, the sample consists of 5000 adults randomly selected from the population of all adults in the United States.

3 - The parameter is a numerical measurement that describes a characteristic of a population. In this case, the parameter of interest is the proportion of adults in the United States with a bachelor's degree or higher. This is because we are interested in making inferences about the entire population of adults in the United States.

4 - The statistic is a numerical measurement that describes a characteristic of a sample. In this scenario, the statistic of interest is the proportion of adults in the sample who have a bachelor's degree or higher. This is because the sample is used to estimate the parameter of the population.

To estimate the population parameter from the sample statistic, we can use statistical inference techniques such as confidence intervals or hypothesis testing. The accuracy of our estimates depends on the sample size, sampling method, and other factors that influence the quality of the data. It's important to ensure that the sample is representative of the population and that any bias or confounding factors are taken into account when making inferences.

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The formulas V=Bh and V=lwh are related because the base area B equals lw

From the question, we have the following parameters that can be used in our computation:

V = Bh

V = lwh

The above formulas are formulas to calculate the volume of a rectangular prism

By substiution, we have

Bh = lwh

Divide both sides by h

B = lw

This means that the base area of the prism is lw

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a. The polynomial function that passes through the points (-3, 15), (1, 11), and (0, 6) is y = -2x² - 3x + 6.

b. The polynomial function that passes through the points (-2,-7), (-1, -3), (0, 3), (1, 5), and (2, -3) is y = -1/2x⁴ - 3/2x³ + 3x² + 7/2x + 3.

c. The polynomial function that passes through the points (4,-1) and (-3, 13) is y = -3x + 11.

d. The polynomial function that passes through the points (-1,-6), (0, 2), (1, 8), and (2, 42) is y = 6x³ + 2x² - 18x

a. Using the given points, we can create a system of three equations:

15 = 9a - 3b + c

11 = a + b + c

6 = c

Solving this system of equations gives us a = -2, b = -3, and c = 6

b. Using the given points, we can create a system of five equations:

-7 = 16a - 8b + 4c - 2d + e

-3 = -2a + b - c + d + e

3 = e

5 = 2a - b + c + d + e

-3 = 16a + 8b + 4c + 2d + e

Solving this system of equations gives us a = -1/2, b = -3/2, c = 3, d = 7/2, and e = 3.

c. Using the given points, we can create a system of two equations:

-1 = 4m + b

13 = -3m + b

Solving this system of equations gives us m = -3 and b = 11.

d. Using the given points, we can create a system of four equations:

-6 = -a + b - c + d

2 = b

8 = a + b + c + d

42 = 8a + 4b + 2c + d

Solving this system of equations gives us a = 6, b = 2, c = -18, and d = 4

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The equation of the attached trigonometric graph is

y = cos (0.4x)

The cos graph in the problem starts at (0, 1)

The equation is represented by y = A cos (Bx + C) + D

The amplitude of the graph is A and this is solved by

= (1 - (-1) / 2

= 2 / 2

= 1

then B is calculated by

B = 2π / period, and the period, form the graph is 5π

B = 2π / 5π = 2/5 = 0.4

The phase shift, C is 0

The vertical shift, D is 0

putting in the values as in the equation above, we have

y = 1 cos (0.4x + 0) + 0

y = cos (0.4x)

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The surface area of the rectangular prism is 1236 in².

We have,

The surface area of the rectangular prism.

= lower surface + top surface + back surface + front surface

+ 2 x side surface

Each surface is in the form of a rectangle.

So,

= 14 x 8 + 14 x 8 + 23 x 8 + 23 x 8 + 2 x (23 x 14)

= 112 + 112 + 184 + 184 + 2 x 322

= 112 + 112 + 184 + 184 + 644

= 1236 in²

Thus,

The surface area of the rectangular prism is 1236 in².

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The volume of the truck bed is simply the product of its three dimensions, which are given as length, width, and height. Therefore, the volume of the truck bed can be calculated as:

Volume = length x width x height

or

Volume = b x w x h

where b, w, and h represent the dimensions of the truck bed in feet, meters, or any other unit of length.

In summary, the volume of a right rectangular prism, such as a moving truck bed, can be obtained by multiplying the length, width, and height of the prism.

To provide further explanation, a right rectangular prism is a three-dimensional solid figure with six rectangular faces. The faces opposite each other are congruent, and the parallel faces have equal dimensions. The length, width, and height of the prism are perpendicular to each other, and the product of these dimensions gives the volume of the prism. In the context of a moving truck, the volume of the truck bed determines the amount of space available for loading and transporting goods.

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According to the diagram, the area of the regular polygon is 144√3.

To find the area of a regular polygon, use the formula:

Area = (1/2) × Perimeter × Apothem

In this case, given the length of one side of the polygon (12) and the apothem (2√3). The perimeter of a regular polygon is calculated by multiplying the number of sides (n) by the length of one side (s).

Plug in the values and calculate the area:

Perimeter = n × s = 12 × 12 = 144

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 144 × 2√3

Simplifying further:

Area = 72 × 2√3

Area = 144√3

Therefore, the area of the regular polygon is 144√3.

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The number of different tests the professor can design is 120.

Since the professor has 10 problems and needs to choose 3 for each test, we can use the combination formula to calculate the number of different tests she can design.

The formula for combinations is n choose k = n! / (k! * (n-k)!) where n is the total number of items, and k is the number of items being chosen.

In this case, n = 10 and k = 3, so we have:

10 choose 3 = 10! / (3! * (10-3)!) = 120

Therefore, the professor can design 120 different tests.

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There  is no maximum value of κ on the curve y=3e^x.

To find the point of maximum curvature on the curve y=3e^x, we need to first find the second derivative of y with respect to x, which will give us the curvature of the curve:

y = 3e^x

y' = 3e^x (since the derivative of e^x is e^x)

y'' = 3e^x (since the second derivative of e^x is also e^x)

Now, to find the point of maximum curvature, we need to set y'' equal to zero and solve for x:

y'' = 3e^x = 0

e^x = 0

This equation has no real solutions, which means that there is no point of maximum curvature on the curve y=3e^x.

To find the maximum curvature, we can use the formula:

κ = |y''| / (1 + y'^2)^(3/2)

Since we know that y'' = 3e^x, we can simplify this formula to:

κ = 3e^x / (1 + (3e^x)^2)^(3/2)

To find the maximum value of κ, we can take the derivative of κ with respect to x and set it equal to zero:

dκ/dx = 3e^x (9e^2x - 2) / (1 + 9e^2x)^(5/2) = 0

This equation has no real solutions, which means that there is no maximum value of κ on the curve y=3e^x.

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Answer: 30 costumes

Step-by-step explanation:

Let x be the total amount of costumes.

In order to get 30% , we need to divide 9 by the total amount of costumes (x), but first we need to change 30% to its multiplier:

30% ÷ 100 = 0.3 (multiplier).

[tex]\frac{9}{x} =30[/tex]%

[tex]\frac{9}{x} =0.3[/tex]

[tex]x=\frac{9}{0.3}[/tex]

[tex]x=30[/tex] costumes

Or if that is confusing:

[tex]\frac{9}{x} =30[/tex]%

[tex]\frac{9}{x} =0.3[/tex]

[tex]\frac{x}{9} =\frac{1}{0.3}[/tex]

[tex]x=9 *\frac{1}{0.3}[/tex]

[tex]x=\frac{9}{0.3}[/tex]

[tex]x=30[/tex] costumes

The above equations are exactly the same, they are just written differently.

We can now check if our answer is correct:

[tex]\frac{9}{30} = 0.3\\0.3*100=30[/tex]%

Hope you understand!

Answer:

650

Step-by-step explanation:

calculate 8 [tex]\frac{1}{3}[/tex]% of 600 then add this value to 600 for increase

8 [tex]\frac{1}{3}[/tex] % × 600 ← convert mixed number to improper fraction

= [tex]\frac{25}{3}[/tex] % × 600

= [tex]\frac{\frac{25}{3} }{100}[/tex] × 600 ( % is out of 100 )

= [tex]\frac{25}{300}[/tex] × 600

= 25 × 2

= 50

then increase is 50

so 600 increased by 8 [tex]\frac{1}{3}[/tex] % = 600 + 50 = 650

The measure of the secant tangent angle m∠AXC is equal to 45°

The secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:

θ = 1/2 (arc EB - arc BD)

where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.

m∠AXC = 1/2(arc AC - arc BC)

m∠AXC = 1/2(115 - 25)

m∠AXC = 1/2(90)

m∠AXC = 45°

Therefore, the measure of the secant tangent angle m∠AXC is equal to 45°

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The faster bus is running at a velocity of 67 mph and the sluggish one is proceeding at a speed of 56 mph.

Let  "x" speed of the quicker bus

and the slower bus "x - 11",

since we comprehend that it is travelling 11 mph less than the faster one. When both meet, a total distance of 492 miles will have been covered (which is the distance between the two towns). We can utilize the formula:

distance = rate x time

Applicable to each auto:

distance = rate x time

distance = x (mph) x 4 (hours) (for the swifter motorcoach)

distance = (x - 11) (mph) x 4 (hours) (for the slower vehicle)

By adding those equations together, we are given:

492 = 4x + 4(x - 11)

After decreasing the equation, we acquire:

492 = 8x - 44

536 = 8x

Therefore, x = 67

So, the more rapidly running coach is going at an velocity of 67 mph and the sluggish one is proceeding at a speed of (67 - 11)

= 56 mph.

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Surface area of larger triangular pyramid is 49cm².

Given,

Altitude of smaller pyramid = 3 cm.

Altitude of larger pyramid = 7 cm.

Surface area of smaller pyramid = 9cm².

Now,

Relation between altitudes of similar pyramids and surface area :

Surface area of smaller pyramid / Surface area of larger pyramid = (altitude of smaller pyramid / altitude of larger pyramid)²

Let us assume the surface area of larger pyramid be x cm²

Substituting the given values in the relation,

9 cm²/x cm² = (3/7)²

x = 49 cm² .

Thus the surface area of larger pyramid is 49 cm².

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A) The surface charge density on the metal disks is 2.45 μC/m^2.

B) The surface charge density on the Pyrex glass is -2.45 μC/m^2.

To determine the surface charge density on the disks and the glass, we need to use the formula for capacitance of a parallel plate capacitor with a dielectric between the plates:

C = ε0εrA/d

where C is the capacitance, ε0 is the permittivity of free space (8.85 x 10^-12 F/m), εr is the relative permittivity (dielectric constant) of the Pyrex glass, A is the area of the plates, and d is the distance between the plates. We can rearrange this equation to solve for the surface charge density:

σ = Q/A

where σ is the surface charge density and Q is the charge on the plates.

First, we need to calculate the capacitance of the capacitor:

C = ε0εrA/d = (8.85 x 10^-12 F/m)(4.7)(π(0.05 m)^2)/(0.00061 m) = 1.74 x 10^-11 F

The charge on each plate can be calculated using the potential difference:

Q = CV = (1.74 x 10^-11 F)(1300 V) = 2.26 x 10^-8 C

Now we can calculate the surface charge density on the disks:

σ = Q/A = (2.26 x 10^-8 C)/(π(0.05 m)^2) = 2.45 μC/m^2

The surface charge density on the glass is equal in magnitude but opposite in sign:

σ = -2.45 μC/m^2

This means that the disks have a positive surface charge density, while the glass has an equal but negative surface charge density.

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The t-statistic distribution is similar to the normal distribution in shape, but it has heavier tails due to its smaller sample size and greater variability. This means that the t-statistic distribution has more extreme values (both positive and negative) than the normal distribution.

The shape of the t-statistic distribution, compared to the normal distribution, can be described as having thicker tails and a more peaked center. This means that the t-distribution has a higher probability of extreme values than the normal distribution. As the sample size increases, the t-distribution approaches the normal distribution in shape.

The t-statistic distribution is a probability distribution used in hypothesis testing when the sample size is small and the population standard deviation is unknown. It is a family of continuous probability distributions that depend on the sample size and the degrees of freedom.

The t-distribution is similar in shape to the standard normal distribution, but it has heavier tails and is more spread out. The shape of the t-distribution changes as the degrees of freedom change. As the sample size increases, the t-distribution approaches the standard normal distribution.

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After change into inches per second, the number is,

= 16.8 inches per second.

We have to given that;

To convert 14 yards per minute to inches per second.

Since, We know that;

1 yards = 36 inches

1 minutes = 60 seconds

Hence, We can change as;

= 14 yards per minute

= 14 x 36 / 30 inches per second.

= 504/ 30 inches per second.

= 16.8 inches per second.

Thus, After change into inches per second, the number is,

= 16.8 inches per second.

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The length of the arc is solved to get the proportion

= x / 12π = 130 / 360

this proves that the proportion would solve the arc length

length of arc is calculated using the formula given below

= (given angle)  / 360 x 2 π r

Where

x is length or arc

r is radius = 6 in

given angle = 130 degrees

then substituting into the formula

x = (given angle)  / 360 x 2 π r

x = 130  / 360 * 2 *  π * 6 in

x = 130  / 360 * 12π

dividing both sides by 12π

x / 12π = 130 / 360 (this equals the given proportion)

but solving for x

x = 13.61 in

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Answer:

18ft

Step-by-step explanation:

6/27= 4.5, 27/4. 4.5x4=18

Answer:

18ft

Step-by-step explanation:

I am taking the test right now and I think this would be the correct answer!

A simple way I found out: 6/4 = 1.5 so I took 1.5 and divided 27 by it.  27/1.5 = 18

Hope this helped!

We do not have enough evidence to suggest that the ammeter used does not meet the marketing specifications.

Statistical inference is the process of making conclusions or predictions about a population based on a sample.

Hypothesis testing is a statistical method used to determine whether there is enough evidence in a sample to support a claim about a population.

To determine if the ammeter used meets the marketing specifications, we need to test if the sample variance is significantly larger than the acceptable standard deviation of 0.2 amp.

We can use a chi-square distribution to test this hypothesis.

The test statistic is given by:

=> x²= (n-1)× s² / σ²

Where n is the sample size, s² is the sample variance, and σ² is the true population variance.

We are given that n = 10, s² = 0.065, and we want to test if the ammeter does not meet the marketing specifications,

Which means that the true population variance is greater than 0.04.

We can calculate the test statistic as follows:

x² = (10-1) × 0.065 / 0.04 = 10.54

The critical value of the chi-square distribution with 9 degrees of freedom (n-1) and a significance level of 0.05 is 16.92.

Since our test statistic is less than the critical value, we fail to reject the null hypothesis that the true population variance is no larger than 0.04.

Therefore,

We do not have enough evidence to suggest that the ammeter used does not meet the marketing specifications.

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Answer:

c

Step-by-step explanation:

The statement given "if 0 is an eigenvalue of the matrix of coefficients of a system of n linear equations in n unknowns, then the system has infinitely many solutions." is true because if 0 is an eigenvalue of the matrix of coefficients of a system of n linear equations in n unknowns, then the system has infinitely many solutions

If a matrix of coefficients of a system of n linear equations in n unknowns has 0 as an eigenvalue, it implies that the homogeneous version of the system (where all constant terms are 0) has non-trivial solutions. This is because the eigenvectors associated with 0 eigenvalue form the null space of the matrix, which represents the set of all solutions to the homogeneous system.

Since the homogeneous system has non-trivial solutions, this means that the original system of equations is linearly dependent, which in turn implies that there are infinitely many solutions. This is because there are linear combinations of the given solutions that are also solutions to the system. Therefore, the statement "if 0 is an eigenvalue of the matrix of coefficients of a system of n linear equations in n unknowns, then the system has infinitely many solutions" is true.

""

if 0 is an eigenvalue of the matrix of coefficients of a system of n linear equations in n unknowns, then the system has infinitely many solutions. true or false

""

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If a and b have the same remainder when divided by m, then a is congruent to b modulo m.

We know that when a positive integer a is divided by a positive integer m, there is a unique quotient q and a remainder r such that a = mq + r and 0 ≤ r < m. This is called the Division Algorithm.

Now suppose a mod m = b mod m. This means that both a and b leave the same remainder when divided by m. So we can write a = mq + r and b = mq + r' for some integers q, r, and r' where 0 ≤ r, r' < m.

Then we have a - b = mq + r - mq - r' = (r - r') which is clearly divisible by m since m divides r - r'. Therefore, we have shown that m divides a - b, or equivalently, a ≡ b (mod m).

To summarize, if two integers have the same remainder when divided by a positive integer m, then they are congruent modulo m. This result is used frequently in number theory and modular arithmetic.

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To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, the company needs to sample sales data for 87 weeks.

To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, we need to determine the sample size required. The standard deviation of the weekly sales figures is given as $1300.

To calculate the sample size, we can use the formula:

n = (z * σ / E)^2

where n is the required sample size, z is the critical value for the 99% confidence level (which is 2.576), σ is the standard deviation of the weekly sales figures, and E is the maximum allowable error or the desired margin of error (which is $300).

Substituting the given values in the formula, we get:

n = (2.576 * 1300 / 300)^2

n = 86.50

Since we cannot have a fractional number of weeks, we round up the value of n to 87. Therefore, the company needs to sample sales data for 87 weeks to estimate the average weekly sales of the new footwear to within $300 with 99% confidence.

To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, the company needs to sample sales data for 87 weeks. This can be calculated using the formula n = (z * σ / E)^2, where z is the critical value, σ is the standard deviation, and E is the maximum allowable error.

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