a)
3 x a x 2 x b
b)
с^5 х с
c) 2y^4 x 5y^3
d) 3gh? x 4g^3h^3

To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

learn more about dimensions here : brainly.com/question/28688567

#SPJ11

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

Learn more about LP model here : brainly.com/question/33051152

#SPJ11

Answer:

x < 10

set builder notation: (-∞ , 10)

Step-by-step explanation:

2(x - 4) < 12

multiply left side out:

2x - 8 < 12

add 8 to both sides:

2x - 8 + 8 < 12 + 8

2x < 20

divide both sides by 2:

2x/2 < 20/2

x < 10

in set builder notation: (-∞ , 10)

Answer:

n = 3 Year (Approx)

Step-by-step explanation:

Given:

Growth rate (r) = 45% = 0.45

Find:

Number of year for 3 times of population (n)

Computation:

Assume;

Current population = P

So,

New population = 3P

A = p(1+r)ⁿ

3P = P(1+0.45)ⁿ

3 = (1.45)ⁿ

n = 2.96 year

n = 3 Year (Approx)

The strophoid is a curve represented by the polar equation r = sec(θ) − 2cos(θ), where -2 < θ < 2. In Cartesian coordinates, the strophoid equation can be written as (x^2 + y^2)^2 = 4y^2(x + 2).

The strophoid has a unique shape characterized by its looped structure.

The strophoid is symmetric with respect to the y-axis, as changing θ to -θ gives the same value of r. It has two branches that intersect at the origin (0, 0). As θ increases from -2 to 2, the curve starts from the rightmost point of the loop, extends to the left, and then returns back to the rightmost point.

The loop of the strophoid is created by the interplay of the secant function, which stretches the curve away from the origin, and the cosine function, which pulls it towards the origin. The strophoid exhibits interesting geometric properties and is often used in mathematical modeling and visualization.

To learn more about intersect click here:

brainly.com/question/14217061

#SPJ11

The simple exponential smoothing forecast for the 3rd week, given α = 0.3, cannot be calculated as the time series values for the preceding weeks are not provided.

 To calculate the error for the 3rd week using the Naïve forecast, the forecasted value for the 3rd week needs to be determined. However, since the previous time series values are not given, the Naïve forecast and subsequent error calculation cannot be performed.

  To calculate the simple exponential smoothing forecast for the 3rd week, we would need the time series values for the preceding weeks. The simple exponential smoothing method requires historical data to compute the forecast. As the values for the previous weeks (Weeks 1 and 2) are not provided, it is not possible to calculate the forecast for the 3rd week using α = 0.3.

   The Naïve forecast is a simple forecasting technique where the forecasted value for a given period is equal to the observed value of the previous period. However, in this case, only the time series value for Week 1 is provided, and the values for Weeks 2 and 3 are missing. Therefore, it is not possible to determine the forecasted value for the 3rd week using the Naïve method.

Since we cannot determine the forecasted value, we cannot calculate the error for the 3rd week using the Naïve forecast. The error calculation requires a comparison between the forecasted and actual values, which cannot be done without the necessary data.

LEARN MORE ABOUT  time series HERE:

https://brainly.com/question/29743783

#SPJ11

Answer:

The domain is: (-∞,∞)

The range is: (0,∞)

Step-by-step explanation:

Answer:

The domain of y = x2 is

✔ all real numbers

The range of y = x2 is

✔ y >= 0

Step-by-step explanation: Hope this helps!

Answer:

2^4x

Step-by-step explanation:

4^x+2^2x

=(2)^2x+2^2x

=4^2x

=(2)2*2x

=2^4x

Answer:

4^x+2^2x

Step-by-step explanation:

There is really not much to do here but multiply 1*2^2x which stays the same

giving an answer of 4^x+2^2x

Answer:

Factor 3 out of the variable terms

Answer:

Factor 3 out of the variable terms.

Step-by-step explanation:

To complete the square the coefficient on the x^2 term must be 1

Therefor

Factor 3 out of the variable terms.

Its C I think

Step-by-step explanation:

turn the line that shows twelve and make it match the line that shows X and then the first line will be shorter

The value of x is 15.

What is Right triangle?

A triangle in which one of the interior angle is 90° is called a right triangle.

Given that;

Sides of a right triangle are 12, 9 and x.

Now,

By the Pythagoras theorem;

x² = 12² + 9²

x² = 144 + 81

x² = 225

x = √225

x = 15

Thus, The value of x is 15.

Learn more about the right triangle visit:

https://brainly.com/question/15249087

#SPJ5

Answer:

123.1323

Step-by-step explanation:

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

for similar questions on sandbox.

https://brainly.com/question/31290675

#SPJ8

that other answer is a virus dont click it

cell wall : gives plant cell its shape, rigid

cell membrane: more selectively controls what goes in and out of the cell, acts like a skin

dunno about grid

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

To know more about mean here

https://brainly.com/question/22871228

#SPJ4

The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

For more questions like interest visit the link below:

https://brainly.com/question/18096283

#SPJ11

Answer & Step-by-step explanation:

1. (3g−2) (2g+3)

2. 9(x−1)^2

Sorry if wrong ;(

Hope this helps ;)

Answer:

(3g-2)(2g+3)

9(x-1)^2

Hope this helps

Solution

Let y represent the length of the other leg

If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35  .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385  ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53  .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

Learn more about Yearly Cost here

https://brainly.com/question/14272357

#SPJ4

Answer:

-6 and 11

Step-by-step explanation:

The only factors of 66 are 11, 6, 2 and 3

11*6 is the only pair whose product is 66

The difference betwen 11 and 6 is 5

11 must be positive and 6 negative since the sum is positve

Answer:

C) The graph opens down and the vertex is a maximum.

Step-by-step explanation:

Just took the quiz on K12, good luck! :)

Option (C) will be the correct option.

         f(x) = ax² + bx + c

         Vertex of the parabola is represented by \([-\frac{b}{2a}, f(\frac{b}{2a})]\)

         And the sign of the leading coefficient decides the opening of the

         parabola.

         For positive sign of 'a' → Parabola will open upwards

         For negative sign of 'a' → Parabola opens downwards

Quadratic function given in the question is,

f(x) = -4x²+ 6x - 7

Leading coefficient → (-4)

Negative sign represents the opening of the parabola downwards.

And the vertex will be a maximum.

           Therefore, Option (C) will be the correct option.

Learn more about the quadratic function here,

https://brainly.com/question/1979559?referrer=searchResults                                          

Answer:

86% or a difference of 743/3

Step-by-step explanation:

The equation for a volume of a sphere is 4/3pi r^3 where r is the radius. Plugging in, we get 288pi for a radius of 6, and 121/3pi for a radius of 5.5. The ratio would be 288:121/3 without pi. Subtracting these two values we get 743/3 which is in simplest terms. As for the decrease in percentage, calculating the percentage of decrease would be the original value subtracted by the new value divided by the original value. This means 288 -121/3 is 743/3, and this divided by 288 is approximately 0.86. This means the percentage decrease is approximately 86% rounded to the nearest hundredths.

Answer:

Below.

Step-by-step explanation:

Angle 1 = (3/(3+4+5) * 180 = 3/12 * 180

= 45 degrees.

Angle 2 = 4/12 * 180 = 60 degrees.

Angle 3 = 5/12 * 180 = 75 degrees.

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

The measure of angle X is given as follows:

40º.

We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of x is half the difference between the angle measure of the largest arc by the angle measure of the smallest arc.

The arc angles are given as follows:

125º and 45º.

Hence the value of x is given as follows:

X = 0.5 x (125 - 45)

x = 40º.

More can be learned about angle measures at brainly.com/question/30820033

#SPJ1

Answer:

\(y = -\frac{2}{5}x\)

Step-by-step explanation:

We already know the slope of the line: -2/5. So, we can make an equation like this:

\(y =- \frac{2}{5}x + b\)

In the question it gives us both x and y in the point (-5,2). You can plug this back into the equation like this:

\(2 = -\frac{2}{5}(-5) + b\)

Now, just solve for b to find the y-intercept:

\(2 = \frac{10}{5} + b\\2 = 2 + b\\0 = b\)

Because b equals 0 there is you can write the final equation like this:

\(y = -\frac{2}{5}x\)

I hope this helps!!

- Kay :)

Answer:

Step-by-step explanation:

First you get X. X has been given as 5 already so it is answered. Now finding Y.

Y=(5*5)-3

It is times 5 because x is 5.

Y=25-3

Y=22

To find a particular solution of the differential equation y'' - 2y' - 8y = 3e^(-2x), we can use the method of variation of parameters.

The particular solution can be found by assuming a solution of the form y_p(x) = u(x)e^(-2x), where u(x) is a function to be determined.

The given differential equation is a linear homogeneous second-order ordinary differential equation with constant coefficients. To find a particular solution using the method of variation of parameters, we first find the solutions of the associated homogeneous equation, which is obtained by setting the right-hand side to zero.

The characteristic equation of the homogeneous equation is r^2 - 2r - 8 = 0, which factors as (r - 4)(r + 2) = 0. Therefore, the fundamental solutions are y_1(x) = e^(4x) and y_2(x) = e^(-2x).

Next, we assume a particular solution of the form y_p = u_1(x)y_1(x) + u_2(x)y_2(x), where u_1(x) and u_2(x) are functions to be determined. We differentiate y_p to find its first and second derivatives, and substitute these derivatives into the differential equation. Equating the coefficients of like terms, we obtain a system of equations for u_1'(x) and u_2'(x).

To find u_1(x) and u_2(x), we can solve this system of equations. Once u_1(x) and u_2(x) are determined, the particular solution y_p(x) can be expressed as y_p(x) = u_1(x)e^(4x) + u_2(x)e^(-2x).

Solving the system of equations, we can find the values of u_1(x) and u_2(x). Finally, we substitute these values back into the particular solution expression to obtain the specific form of the particular solution y_p(x) for the given differential equation.

Learn more about differential equation here:

https://brainly.com/question/32645495

#SPJ11

The subset of the data set with x2, x3, and x4 would include 6 missing values.

The subset of the data set with x2, x3, and x4 would include 6 missing values.

1. Subset the data set to include only x2, x3, and x4.

2. Count the number of missing values in each variable.

3. Add the number of missing values for each variable together.

4. The total number of missing values in these three variables is 6.

The subset of the data set with x2, x3, and x4 would include 6 missing values.

Subset the data set to include only x2, x3, and x4.

The complete question is :

Subset the data set to include only x2, x3, and x4. How many missing values are there in these three variables?

Learn more about data here

https://brainly.com/question/14893265

#SPJ4

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

To know more about dividend, here

brainly.com/question/3161471

#SPJ11