7x + 2y = 17
2x - 2y = 1
=​

The maximum and minimum values for the corn and grain constraints for which the current constraint value does not change are 0.15 and 0.20.

a) To develop the model in Excel, define the decision variables and objective function as follows:

Let x1, x2, x3, and x4 represent the amount of each feed in thousands of kilograms. The objective function is to minimize the total cost, given by:

Minimize: 0.15x1 + 0.2x2 + 0.18x3 + 0.25x4

Subject to:

x1 + x2 + x3 + x4 = 8  (total feed = 8,000 kg)

0.1x1 + 0.15x2 + 0.2x3 + 0.2x4 ≥ 0.8  (minimum 10% corn)

0.2x1 + 0.3x2 + 0.25x3 + 0.25x4 ≥ 2  (minimum 25% grain)

0.2x1 + 0.2x2 + 0.2x3 + 0.3x4 ≥ 1.6  (minimum 20% minerals)

x1, x2, x3, x4 ≥ 0 (non-negativity constraints)

b) Solving the problem using Excel Solver gives the following least-cost feed mix: x1 = 5, x2 = 0, x3 = 3, and x4 = 0. This mix will cost $2.35 per kilogram, or $18,800 in total.

c) The nutritional elements with a surplus are corn and grain, in amounts of 0.5 and 0.2 thousand kilograms, respectively.

d)i) The objective function's value would decrease to $17,400 if Feed 3 is forced to be in the solution.

ii) The shadow prices for the grain and minerals constraints mean the maximum amount of extra cost per kilogram increase in the corresponding constraint value. The maximum and minimum values for the corn and grain constraints for which the current constraint value does not change are 0.15 and 0.20, respectively.

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Answer:

c

Step-by-step explanation:

Answer:

.25

Step-by-step explanation:

.5 times .5 or half of half is .25

(½)²  is 1²/2² so the answer is 1/4.

When we multiply a number by it self once the number is squared.We add 1 to the exponent.We must also remember squares of numbers from 1 - 20 for us to solve questions related to squares and square roots.

For example - (5)² is 25. { 5² is 5 multiplied by it self once (5×5)}.

Also square root of 25 is 5.We can find square root of any given perfect square number by prime factorisation.

According to the given question we have find what is the square of half.

(1/2)²

= (1×1)/(2×2)

= 1²/2²

= 1/4.

So, square of half is one fourth.

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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12 and 3 because 3 divided by 12=4 and 12x3=36

The surface area of a surface parametrized by a function f(s, t), we use the formula:

Surface Area = ∫∫ √[f_s(s,t)^2 + f_t(s,t)^2 + 1] ds dt

The formula above calculates the surface area by integrating the square root of the sum of the squares of the partial derivatives of f with respect to s and t, plus one, over the surface.

Essentially, the formula is finding the magnitude of the gradient of the surface, which gives the rate of change of the surface in all directions.

Surface Area = ∫∫ √[f_s(s,t)^2 + f_t(s,t)^2 + 1] ds dt

The surface area formula can be used to find the surface area of various types of surfaces, such as parametric surfaces, implicit surfaces, and surfaces of revolution.

However, the integration required to evaluate the formula can be quite challenging, especially for complex surfaces. In such cases, numerical methods may be used to approximate the surface area.

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Answer:

2018 I believe.

Step-by-step explanation:

He'll be two times his age in 2032 which is 28 years old. Subtract 28 from 2032 and you get 2018.

Answer:

2018

Step-by-step explanation:

in 2032 he will be 28 years old because he is 2 times older than 14, 2032-14=2018, because 14 years have passed since he was 14

In the given triangle, by using the 30-60-90 Triangle Theorem, the length of the hypotenuse is 14 in.

From the question, we are to use the 30-60-90 Triangle theorem to calculate the length of the hypotenuse of the given triangle.

The 30-60-90 Triangle theorem states that "In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg".

In the given diagram,

The shorter length is a.

And from the given information,

a = 7 in.

Thus,

Length of the hypotenuse = 2 × 7 in

Length of the hypotenuse = 14 in

Hence,

The length of the hypotenuse is 14 in.

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See attachment for the number line that compares the numbers 5.3, 5 1/5 and 5

The numbers are given as:

5.3, 5 1/5 and 5

We start by representing the numbers as decimals (i.e. real numbers).

So, we have:

5.3, 5.2 and 5

Reorder the numbers in ascending number (i.e. from least to greatest)

So, we have

5, 5.2 and 5.3

Next, we plot the numbers on a number line using a scale of 0.1

This can be visualized as

5        5.2      5.3

See attachment for the number line that compares the numbers 5.3, 5 1/5 and 5

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If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.

Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.

Mathematical operations help us to determine unknown values, given a known domain.

Increase in school enrollment over last year's = 6%

Enrollment for the current year = 1,378

Let last year's enrollment = 100%

And the current year's = 1.06 (100 + 6)

Therefore, the enrollment last year = 1,300 (1,378/1.06)

Thus, the enrollment (number) last school year was B. 1,300.

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The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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Answer:

140

Step-by-step explanation:

The sum of one interior angle and one exterior angle is 180

180-40=140 so an interior angle of the regular polygon would be equal to 140

Answer:

Median is 3

Step-by-step explanation:

Answer:

             The smaller number:  a = 10

             The larger number is 32

Step-by-step explanation:

a - the smaller number

2a - twice the smaller number

2a+12   - twelve more than the twice smaller number (the larger number)

a + 2a+12  - the sum of the numbers

a + 2a+12 = 42

     -12              -12

          3a  =  30

          ÷3       ÷3

            a = 10

2a+12 = 2×10+12 = 20+12 = 32

Check:   10+32=42

Answer: 13.50

Step-by-step explanation: Add all the ages and divide it by the number of bears

Answer:

5x−5+11x^2+4x−6x^2+8

5x^2 + 9x + 3

Step-by-step explanation:

Answer: 5x^2 + 9x + 3 .

Step-by-step explanation: i took the test !

Answer:

Step-by-step explanation:

you have 7 reds of 14 total.

the 1st marble has 7 of 14 probability of being red

the 2nd has 6 of 13 of being red

the 3rd has 5 of 12 of being red

multiplying this out you have:

(7/14)*(6/13)*(5/12)=210/2184

THAT will condense down to 5/52 or 9.615%

this does assume not placing the balls back in between draws

if you do put them back in between draws you would have 7 of 14 chance each draw

that would give you by multiplying out

(7/14) * (7/14)* (7/14) = 343/2744

Found it online lol

that condenses to 1 of 8 or 12.5%

Found it online lol

If the order of selection does not matter, then there are 14 color combinations of the three marbles are possible.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given that the 1st marble has 7 of 14 probability of being red.

And the 2nd has 6 of 13 of being red and the 3rd has 5 of 12 of being red

Now multiplying this out we have:

(7/14) x (6/13) x (5/12)=210/2184

=  5/52 or 9.615%

Now if we do put them back in between draws then we would have 7 of 14 chance each draw

(7/14) x (7/14) x (7/14) = 343/2744

= 12.5%

If the order of selection does not matter, then there are 14 color combinations of the three marbles are possible.

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It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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The perimeter of the rhombus is 4√117 feet.

What is rhombus?

A rhombus is a special type of quadrilateral (a polygon with four sides) where all four sides are equal in length. It is also known as a diamond shape because of its symmetrical appearance.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles.

Let's denote the length of one diagonal as d1 and the length of the other diagonal as d2. In this case, d1 = 18 feet and d2 = 12 feet.

Each right triangle formed by the diagonals has legs equal to half the lengths of the diagonals. Therefore, the lengths of the legs are d1/2 = 18/2 = 9 feet and d2/2 = 12/2 = 6 feet.

Using the Pythagorean theorem, we can find the length of the hypotenuse of each right triangle, which is also a side of the rhombus.

\(h^2 = (leg1)^2 + (leg2)^2\\\\h^2 = 9^2 + 6^2\\\\h^2 = 81 + 36\\\\h^2 = 117\)

Taking the square root of both sides:

h = √117

Since the rhombus has four congruent sides, the perimeter is given by:

Perimeter = 4 * h = 4 * √117

Thus, the perimeter of the rhombus is 4√117 feet.

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Answer:27 cm squared

Step-by-step explanation: we take both numbers(3,4) and multiply them by the scale factor of 1.5 giving you 4.5 and 6, then you find the area of the new colorado by multiplying 4.5 and 6 giving you 27 centimeters squared.

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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The best type of scale to assess how happy UNC students are on a 7-point scale (1 not very happy to 7 extremely happy) is an ordinal scale.

Ordinal scales are used to measure variables that have an inherent order or ranking, such as the level of happiness in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale, on the other hand, is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

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In the consumption-based asset pricing model, an increase in future dividends can result in a decrease in the current stock price due to the income and substitution effects which prompts stockholders to sell their shares, and the substitution effect, which increases the supply of other assets and the demand for stocks.

The income effect refers to the impact of changes in income on an individual's consumption choices. In this model, an increase in future dividends implies higher expected future income for the stockholders. As a result, stockholders may choose to consume more in the future, reducing their current consumption. To finance this increased consumption in the future, stockholders may decide to sell their shares in the present, leading to a decrease in the stock price.

The substitution effect relates to the trade-off between different assets. An increase in future dividends makes holding stocks more attractive compared to other assets. As a result, investors may choose to reallocate their portfolios by selling other assets and buying more stocks. This increased supply of other assets and increased demand for stocks can lead to a decrease in the price of stocks.

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Answer:

Step-by-step explanation:

(a)

Step 1. Find the middle of BC:

\(M_{BC}=\left(\dfrac{x_B+x_C}2\,,\ \dfrac{y_B+y_C}2\right)=\left(\dfrac{4+1}2\,,\ \dfrac{-1+7}2\right)=\left(\dfrac{5}2\,,\ 3\right)\)

Step 2. Calculate the lenth of AM:

\(AM=\sqrt{(x_M-x_A)^2+(y_M-y_A)^2}\\\\AM=\sqrt{(2.5+5)^2+(3+2)^2}= \sqrt{56.25+25}=\sqrt{81.25}\approx9.01\)

(b)

Step 1.  Calculate the lenths of sides:

\(AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\AB=\sqrt{(4+5)^2+(-1+2)^2}=\sqrt{81+1}= \sqrt{82}\approx9.06\\\\AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2} \\\\AC=\sqrt{(1+5)^2+(7+2)^2}=\sqrt{36+81}= \sqrt{117}\approx10.82\\\\ BC=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\\\ BC=\sqrt{(1-4)^2+(7+1)^2}=\sqrt{9+64}= \sqrt{73}\approx8.54\)

Step 2.  Add them:

\(P=9.06+10.82+8.54=28.42\)

the 90 percent confidence interval for μ is (49.427, 50.573).

To find a 90 percent confidence interval for the population mean (μ), assuming that the sample is from a normal population, you will need the sample mean, sample size, and standard deviation.

1. Collect the necessary information from the sample: sample mean (x(bar)), sample size (n), and standard deviation (s).

2. Determine the critical value corresponding to a 90 percent confidence level. Since the sample is from a normal population, we will use the t-distribution. The critical value can be found using a t-table or calculator. Round the t-value to 3 decimal places.

3. Calculate the standard error (SE) using the formula: SE = s / √n. Round the standard deviation (s) to 4 decimal places.

4. Compute the margin of error (ME) using the formula: ME = t-value * SE.

5. Finally, calculate the confidence interval by subtracting and adding the margin of error from the sample mean: Lower Bound = x(bar) - ME and Upper Bound = x(bar) + ME. Round the answers to 3 decimal places.

For example, let's say the sample mean is 50, the sample size is 100, and the standard deviation is 3.4567.

1. x(bar) = 50, n = 100, s = 3.4567
2. The critical value for a 90 percent confidence level with 99 degrees of freedom (n - 1) is 1.660 (rounded).
3. SE = 3.4567 / √100 = 0.3457 (rounded to 4 decimal places).
4. ME = 1.660 * 0.3457 = 0.5732 (rounded to 4 decimal places).
5. Lower Bound = 50 - 0.5732 = 49.4268 (rounded to 3 decimal places).
  Upper Bound = 50 + 0.5732 = 50.5732 (rounded to 3 decimal places).

Therefore, the 90 percent confidence interval for μ is (49.427, 50.573).

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Solution

Since

Yes, it's a special product.

Its type is a Perfect square

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

To check whether the ordered pair (-5, -4) is a solution of the system of equations:

1) 3x - y = -11

2) 2x - 2y = -3

We substitute x = -5 and y = -4 into both equations and check if the equations hold true.

For equation 1:

3(-5) - (-4) = -11

-15 + 4 = -11

-11 = -11

The equation is satisfied.

For equation 2:

2(-5) - 2(-4) = -3

-10 + 8 = -3

-2 = -3

The equation is not satisfied.

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

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Answer:

Acute

Step-by-step explanation:

the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°