Find all the analytic functions f = u +iv, where
u(x, y) = e^x (xsin y + y cosy), (x,y) € R^2.

The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

For more such information on Algebra and Geometry:
https://brainly.com/question/24696219

#SPJ8

The points in which relative minimums occur for the function are:

b. Point B.

e. Point E.

A relative minimum in a function f(x) is a value of x at which the function changes from decreasing to increasing.

For this problem, these values are:

b. Point B.

e. Point E.

More can be learned about relative minimums at https://brainly.com/question/9839310

#SPJ1

Answer:

The answer is A. 3 3/5   and     B. 2 8/5

:D

explanation:

It couldn't be 5/18 because that is less than the fraction

And it could not be 3 because 5 (the denominator) times 3, is not 18 (numerator), it is 15.

SO.... now that we narrowed those answers down we have to look at the mixed fractions..  

3 3/5 into an improper fraction would be  18/5 because 3/5 is 15, plus 3 is 18.

2 8/5 into an improper fraction would be 18/5 because 2x5 is 10, plus 8 is 18.

therfore A and B are your answers, hope this helps!

Sorry for answering like, 3 years late Hahaha.

We fail to reject the null hypothesis at the 95% confidence level. There is not enough evidence to conclude that the mean of the Gaussian population is different from zero based on the sampled data.

To test the hypothesis H₀: μ = 0, where μ is the mean of the Gaussian population, we can perform a t-test using the given sample data. Here are the steps to conduct the hypothesis test with a 95% confidence level:

State the null hypothesis (H₀) and the alternative hypothesis (H₁):

Null hypothesis (H₀): The mean of the Gaussian population is μ = 0.

Alternative hypothesis (H₁): The mean of the Gaussian population is not equal to μ ≠ 0.

Calculate the sample mean (x) and the sample standard deviation (s) from the given sample data. The sample mean is the average of the data points, and the sample standard deviation is the square root of the sample variance.

Given data: 4, 3, 5, 5, -7, -13, -6, 11, 7

Sample mean (x) = (4 + 3 + 5 + 5 - 7 - 13 - 6 + 11 + 7) / 9 = -0.67 (rounded to two decimal places)

Sample standard deviation (s) = √[Σ(xi - x)² / (n - 1)] = 7.85 (rounded to two decimal places)

Determine the test statistic. Since the sample size is small (n = 9) and the population standard deviation is unknown, we use the t-distribution.

The test statistic (t) is calculated as:

t = (x - μ) / (s / √n)

In this case, μ is the null hypothesis value (0), x is the sample mean (-0.67), s is the sample standard deviation (7.85), and n is the sample size (9).

t = (-0.67 - 0) / (7.85 / √9) = -0.67 / (7.85 / 3) = -0.67 / 2.62 ≈ -0.256 (rounded to three decimal places)

Determine the critical value or p-value. Since we want to test the hypothesis at a 95% confidence level, the significance level (α) is 0.05. Since this is a two-tailed test, we divide the significance level by 2, resulting in α/2 = 0.025.

Using the degrees of freedom (df = n - 1 = 9 - 1 = 8) and the t-distribution table or statistical software, we can find the critical t-value. For a two-tailed test at α/2 = 0.025 and df = 8, the critical t-value is approximately ±2.306.

Compare the test statistic with the critical value. If the test statistic falls outside the critical region (i.e., if |t| > critical t-value), we reject the null hypothesis. Otherwise, if the test statistic falls within the critical region, we fail to reject the null hypothesis.

In this case, |t| = |-0.256| ≈ 0.256, which is less than the critical t-value of ±2.306.

Learn more about distributions:

https://brainly.com/question/4079902

#SPJ4

Applying the Friedman test, we conclude that there is evidence that at least two population locations differ at a significance level of 10%, since our calculated \($\chi^2$\) value (979.5) is greater than the critical value (7.81).

To apply the Friedman test, we need to first rank the data within each block (column) and calculate the average ranks for each treatment (row). The ranks are calculated by assigning a rank of 1 to the smallest value, 2 to the second-smallest value, and so on. Ties are given the average rank of the tied values.

Treatment Block 1 Block 2 Block 3 Block 4 Ranks

1 2 1.5 3 3.5 10

2 1 3 5 5 14

3 3 2.5 4 2 11.5

4 2 4 2 1 9

5 1 4.5 1 4.5 11

The Friedman test statistic is calculated as:

\($ \chi^2 = \frac{12}{n(k-1)} \left[ \sum_{j=1}^k \left( \sum_{i=1}^n R_{ij}^2 - \frac{n(n+1)^2}{4} \right) \right] $\)

where \($n$\) is the number of blocks, \($k$\) is the number of treatments, and \($R_{ij}$\) is the rank of the \($j^t^h\) treatment in the \($i^t^h\) block.

In this case, \($n=4$\) and \($k=5$\), so:

\($ \chi^2 = \frac{12}{4(5-1)} \left[ \sum_{j=1}^5 \left( \sum_{i=1}^4 R_{ij}^2 - \frac{4(4+1)^2}{4} \right) \right] $\)

\($ \chi^2 = \frac{3}{2} \left[ (10^2 + 14^2 + 11.5^2 + 9^2 + 11^2) - \frac{4(5^2)}{4} \right] $\)

\($ \chi^2 = \frac{3}{2} \left[ 727 - 50 \right] = 979.5 $\)

The critical value for the Friedman test with \($k=5$\) treatments and \($n=4$\)blocks, at a significance level of \(\alpha = 0.1$,\) is:

\($ \chi_{0.1}^2 = 7.81 $\)

Since our calculated \($\chi^2$\) value (979.5) is greater than the critical value (7.81), we reject the null hypothesis that there is no difference between the population locations, and conclude that there is evidence that at least two population locations differ at a significance level of 10%.

Know more about Friedman test here:

https://brainly.com/question/31588473

#SPJ11

Answer:

a) 2.5 x 10^5

b) 8.1 x 10^4

c) 9.06 x 10^8

d) 1.034 x 10^10

Given:

The system of equations is:

\(x+3y=-13\)

\(4x+4y=-12\)

To find:

The solution for the given system of equations.

Solution:

We have,

\(x+3y=-13\)            ..(i)

\(4x+4y=-12\)          ...(ii)

Multiply equation (i) by 4, to make common coefficient of x.

\(4x+12y=-52\)            ..(iii)

Subtract (ii) from (iii).

\(4x+12y-4x-4y=-52-(-12)\)

\(8y=-40\)

\(y=\dfrac{-40}{8}\)  

\(y=-5\)  

Putting \(y=-5\) in (i), we get

\(x+3(-5)=-13\)

\(x-15=-13\)

\(x=-13+15\)

\(x=2\)

Therefore, the solution of the given system of equations is \(x=2,y=-5\).

The term 3x² in the quotient is the result of dividing 3\(x^{4}\) by x²

On dividing 3x^4 by x² we get the following by the long division method

x² | 3x^4 | 3x² --------> quotient

    -(3x^4)

    ______

         0

Thus the quotient is 3x² as mentioned in the question and the remainder is 0. Long division is a method to find out the quotient and remainders on dividing number, algebraic expression by another. As shown above, on the right-hand side we get the quotient and at the bottom, the remainder is obtained.

Another problem with long division:

brainly.com/question/12342242

#SPJ4

Notice that between the tree (represented by a vertical segment), the ground (represented by a horizontal segment), and the rays of the sun (that go from the top of the tree to the ground), we are in the presence of a right angle triangle that has a short leg of size 15 yards (verticel segment), and a long leg of size 17 yards.

Then the angle of elevation is assicuated with the tangent function in that right angle triangle:

This is the quotient of the side opposite to the angle divided the side adjacent to the angle. Then we can solve for the angle by using the arctangent the following way:

arctan(15/17) (this is what you type in your calculator, but make sure your answer comes in DEGREES. (you need to set your calculator for that)

As I do it in my calculator, I get that the angle is: 41.42366 degrees

And since they want us to round it to the nearest tenth, we give:

angle of elevation = 41.4 degrees.

The final charge of the spheres when they are touching after calculated using Coulomb's law , is 1.24 * 10^-6 C

According to the given information, two charged spheres with charges |q1| > |q2| attract each other with a force of magnitude 90.4 mn when separated by a distance of 4.64 m. When the spheres are brought together until they are touching, they attain the same final charge q.

We can use Coulomb's law to find the final charge q. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb's law is expressed as:

F = k * (q1 * q2) / r^2

Where F is the force between the charged particles, k is Coulomb's constant (8.99 * 10^9 N*m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.

We can rearrange the equation to solve for q:

q = sqrt(F * r^2 / k)

Plugging in the given values:

q = sqrt(90.4 * 10^-6 N * (4.64 m)^2 / (8.99 * 10^9 N*m^2/C^2))

q = 1.24 * 10^-6 C

Therefore, the final charge of the spheres when they are touching is 1.24 * 10^-6 C

To know more about Coulomb's law, click on the link below :

https://brainly.com/question/506926#

#SPJ11

1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

learn more about consistent: https://brainly.com/question/14633769

#SPJ1

Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent.

In mathematics, the word "graph" has (at least) two distinct meanings. The term "graph" in elementary mathematics refers to a diagram known as a function graph or "function graph." A graph is, in the language of mathematics, a set of points and lines that link a subset (potentially empty) of the points and lines. Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. Bar charts, line charts, histograms, and pie charts are the four types of fundamental statistical charts.

Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent. The x and y axes are the names of the vertical and horizontal axes in bar graphs, respectively. A bar graph can be used, for instance, to compare your classmates' heights.

To know more about graphs visit:
https://brainly.com/question/29467965

#SPJ4

The amount of feet of border that she needs to purchase is given as follows:

20 feet.

The perimeter of a square of side length s is given by the multiplication of four and the side length s, as follows:

P = 4s.

All the sides measure 5 feet, hence the parameter s is given as follows:

s = 5.

Then the perimeter of the square plot is given as follows:

P = 4 x 5

P = 20 feet.

More can be learned about the perimeter of a square at https://brainly.com/question/25092270

#SPJ1

The distribution of the number of members in party ii who will favor prop 88 tomorrow would follow a binomial distribution. The number of members who favor prop 88 tomorrow is the number of "successes" out of a fixed number of "trials", where each trial is the decision of one party ii member.

As per the question given,

The success probability for each trial is not given, but if it is assumed to be the same for all members of party ii, then the binomial distribution can be used to model the number of members who favor prop 88 tomorrow.

The information given about the opinions of party ii members today can be used to estimate the success probability for each trial, if it is assumed that the same proportion of members who favor prop 88 today will favor it tomorrow. However, if there are external factors that could influence the decision of party ii members (such as new information that may come to light), then the success probability for each trial may not be constant and the binomial distribution may not accurately reflect the distribution of the number of members who will favor prop 88 tomorrow.

For such more questions on Distribution

https://brainly.com/question/4079902

#SPJ4

Answer: 1 1/2

Step-by-step explanation:

Step One: 3 / 2 = 1.5000 = 1

Step Two: 3 - (2 x 1) = 1

Step Three: 1 1/2

Please mark me branliest

The 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it can be calculated using a statistical formula. The formula for a confidence interval is: CI = p ± zsqrt((p(1-p))/n)

Where CI is the confidence interval, p is the proportion of interest (in this case, 0.48 or 48%), and z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.645 for 90% confidence), sqrt is the square root function, and n is the sample size (in this case, 331).

Plugging in the values, we get:

CI = 0.48 ± 1.645sqrt((0.48(1-0.48))/331)

CI = 0.48 ± 0.062

Thus, the 90% confidence interval for the proportion of Americans who decide not to go to college because they cannot afford it is (0.418, 0.542). This means that we can be 90% confident that the true proportion of Americans who decide not to go to college because they cannot afford it falls between 41.8% and 54.2%.

To learn more about Confidence interval, visit:

https://brainly.com/question/17034620

#SPJ11

The estimated federal income tax withholding using the percentage method for the given scenario would be $1,940 + $1,680 = $3,620.

To calculate the federal income tax withholding using the percentage method, we need the specific tax rates and brackets for the given income level. The tax rates and brackets may vary depending on the tax year and filing status.

Since you mentioned using the pre-2020 Form W-4, I will assume you are referring to the 2019 tax year. In that case, I can provide an estimate based on the tax rates and brackets for that year.

For a married employee filing jointly in 2019, the federal income tax rates and brackets are as follows:

- 10% on taxable income up to $19,400

- 12% on taxable income between $19,401 and $78,950

- 22% on taxable income between $78,951 and $168,400

- 24% on taxable income between $168,401 and $321,450

- 32% on taxable income between $321,451 and $408,200

- 35% on taxable income between $408,201 and $612,350

- 37% on taxable income over $612,350

To calculate the federal income tax withholding, we need to determine the taxable income based on the employee's earnings and filing status. Assuming no other deductions or adjustments, the taxable income can be calculated as follows:

Taxable Income = Earnings - Standard Deduction - (Withholding Allowances * Withholding Allowance Value)

For the 2019 tax year, the standard deduction for a married couple filing jointly is $24,400, and the value of one withholding allowance is $4,200.

Using the given information of earning $62,000 and claiming 1 federal withholding allowance, we can calculate the taxable income:

Taxable Income = $62,000 - $24,400 - (1 * $4,200) = $33,400

Now we can apply the tax rates to determine the federal income tax withholding:

10% on the first $19,400 = $19,400 * 10% = $1,940

12% on the remaining $14,000 ($33,400 - $19,400) = $14,000 * 12% = $1,680

Therefore, the estimated federal income tax withholding using the percentage method for the given scenario would be $1,940 + $1,680 = $3,620.

To learn more about federal income tax here:

https://brainly.com/question/30200430

#SPJ4

Answer:

30.8 cm³

Step-by-step explanation:

slant height of small cone =l

using; l²= h²+r²

l²=5²+3²=25+9=34

l=√34=5.8cm

volume of small cone =1/3πrl

=1/3(π×3×5.8)

=1/3(54.67)= 18.2 cm³

slant height of big cone =l

using; l²= h²+r²

l²=5²+6²=25+36=61

l=√61=7.8cm

volume of big cone =1/3πrl

=1/3(π×6×7.8)

=1/3(147.02)= 49.0 cm³

49.0-18.2= 30.8 cm³

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

For more such questions on vector

https://brainly.com/question/3184914

#SPJ8

The interquartile range of the given data set is 2.16.

The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1

The  order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.

Here,

Q1= 1/4 (n+1) = 11/4= 2.75

= 2.22

Q3 = 3/4 (n+1) = 8.25

= 4.38

Q2 =4.38-2.22

= 2.16

Therefore, the interquartile range of the given data set is 2.16.

Learn more about the interquartile range here:

https://brainly.com/question/4135956.

#SPJ1

The required equation is y=90x-80 and slope is 90 and y intercept is -80.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the table we can observe that y represents the number of people abs x represents the number of minutes.

Let us find the equation by taking two points

(1,10) and (2, 100)

m=100-10/2-1=90

Now let us find the y intercept

10=90(1)+b

10=90+b

-80=b

The equation is y=90x-80

The slope is 90 and y intercept is -80.

Hence, equation is y=90x-80 and slope is 90 and y intercept is -80.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

According to the information, the lateral area of the room is 112m²; the area to be painted is 109.4m²; the volume is 185.76m³ and the floor area is 46.44m².

To calculate the area of the lateral surface of the room we must find the area of all the sides and then add it as shown below:

To find the area of the surface to be painted, excluding windows and doors, we must find the area of the doors and windows and subtract it from the total lateral area as shown below:

To find the volume of the room, we must multiply the height, by the length, by the width as shown below:

To find the surface area of the floor we must multiply the length of the width by the length of the length as shown below:

Learn more about area at: https://brainly.com/question/27683633

#SPJ1

Answer:

12/13

Step-by-step explanation:

Pythagorean theorem to find the leg opposite from the angle, x^2+5^2=13^2

x^2+25=169

x^2=144

x=12

sin(x)=12/13

The probability that the time between the next two calls is more than 5 seconds is approximately 0.2865.

To solve this problem, we can use the exponential distribution formula:

\(\[ P(X > t) = e^{-\lambda t} \]\)

where:

\(\( P(X > t) \)\) is the probability that the time between two events is greater than \(\( t \),\)

\(\( \lambda \)\) is the rate parameter of the exponential distribution (equal to \(\( \frac{1}{\text{mean}} \)),\)

\(\( t \)\) is the desired time threshold.

In this case, the mean is given as 4 seconds, so \(\( \lambda = \frac{1}{4} \).\) We need to find the probability that the time between the next two calls is more than 5 seconds, so \(\( t = 5 \).\)

Plugging the values into the formula, we have:

\(\[ P(X > 5) = e^{-\frac{1}{4} \cdot 5} \]\)

Calculating this expression, we get:

\(\[ P(X > 5) \approx 0.2865 \]\)

Therefore, the probability that the time between the next two calls is more than 5 seconds is approximately 0.2865.

To know more about probability visit-

brainly.com/question/28938517

#SPJ11

Answer:

125x - 33x⁴

Pull out like factors :

125x - 27x⁴ = -x • (27x3 - 125)

Factoring: 27x³- 125

Theory : A difference of two perfect cubes, a³ - b³ can be factored into

(a-b) • (a² +ab +b²)

(a-b)•(a²+ab+b²) =

a³+a²b+ab²-ba²-b²a-b³ =

a³+(a2b-ba²)+(ab²-b²a)-b³ =

a³+0+0+b³ =

a³+b³

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : x³ is the cube of x¹

Factorization is :

(3x - 5) • (9x² + 15x + 25)

\( \)

The ideal way to organize electronically the raw data for a study is to use a database management system (DBMS). A DBMS allows the researcher to store, manipulate, and retrieve data in a structured and organized manner. This enables the researcher to easily analyze the data and draw meaningful conclusions from it.

Additionally, a DBMS ensures data accuracy, consistency, and security. Overall, using a DBMS is the most efficient and effective way to manage raw data for a study.
This allows for efficient organization, storage, and retrieval of the data, making it easier to analyze and interpret the results. Additionally, employing proper data cleaning techniques and establishing a clear metadata structure can enhance the overall organization and accessibility of the study's raw data.

To learn more about DBMS : brainly.com/question/28813705

#SPJ11

The dimensions of the fencing that will minimize the cost of the fence are 50 feet by 100 feet.

The area of the total lot with all three pens is 5000 square feet, which means that the total area of the fencing is also 5000 square feet.

Let's say the length of the fencing is x feet and the width of the fencing is y feet. We can write the following equation to represent the area of the fencing:

xy = 5000

The cost of the horizontal fencing (length) is $26 per foot, so the total cost of the horizontal fencing is 26x. The cost of the vertical fencing (width) is $12 per foot, so the total cost of the vertical fencing is 12y. The total cost of the fencing is the sum of these two costs, so we can write the following equation to represent the total cost of the fencing:

26x + 12y = C

Where C is the total cost of the fencing.

We want to minimize the total cost of the fencing, so we want to find the values of x and y that minimize the value of C We can do this by setting up a system of equations and solving for x and y.

xy = 5000

26x + 12y = C

We can solve this system of equations using the substitution method. First, we can solve the first equation for y:

\($y = \frac{5000}{x}$\)

Substituting this expression for y into the second equation, we get:

\($26x + 12(\frac{5000}{x}) = C$\)

Solving for x, we get:

\($x = \sqrt{625} = 25$\)

Substituting this value for x into the first equation, we get:

\($y = \frac{5000}{25} = 200$\)

Therefore, the dimensions of the fencing that will minimize the cost of the fence are x = 25 feet and y = 200 feet, which is a fencing with a length of 50 feet and a width of 100 feet.

To learn more about dimensions, visit:

brainly.com/question/29020359

#SPJ4

The standard deviation of returns is approximately 0.0890.

To calculate the standard deviation of returns, we first need to convert the percentages to decimal form.

Good state: Probability (p₁) = 20% = 0.20, Return (r₁) = 18% = 0.18

Neutral state: Probability (p₂) = 55% = 0.55, Return (r₂) = 9% = 0.09

Bad state: Probability (p₃) = 25% = 0.25, Return (r₃) = -5% = -0.05

Next, we can calculate the expected return (E(R)):

E(R) = (p₁ * r₁) + (p₂ * r₂) + (p₃ * r₃)

E(R) = (0.20 * 0.18) + (0.55 * 0.09) + (0.25 * -0.05)

E(R) = 0.036 + 0.0495 - 0.0125

E(R) = 0.072

Next, we calculate the variance (Var) using the formula:

Var = \((p₁ * (r₁ - E(R))^2) + (p₂ * (r₂ - E(R))^2) + (p₃ * (r₃ - E(R))^2)\)

Var =\((0.20 * (0.18 - 0.072)^2) + (0.55 * (0.09 - 0.072)^2) + (0.25 * (-0.05 -\)\(0.072)^2)\)

Var = 0.005832 + 0.000693 + 0.000399

Var = 0.007924

Finally, we calculate the standard deviation (σ) as the square root of the variance:

σ = √Var

σ = √0.007924

σ ≈ 0.0890

Therefore, the standard deviation of returns is approximately 0.0890.

Learn more about square root here:

https://brainly.com/question/29286039

#SPJ11