4x + 9y = 24
X + y = 10
Help ASAP

I understand that you want to know the consequences of rounding off answers when solving an integer programming problem by treating it as a linear programming problem. Here's my explanation:

When you solve an integer programming problem as a linear programming problem and then round off the answers, you may encounter the following issues:

1. The values of decision variables obtained by rounding off might be sub-optimal: Rounding off can lead to a solution that is not the true optimal integer solution, as linear programming allows fractional values that might not be feasible in the integer problem.

2. The values of decision variables obtained by rounding off might violate some constraints: Rounding off can result in values that do not satisfy the integer constraints, which could render the solution infeasible for the original integer problem.

3. The values of decision variables obtained by rounding off are not always very close to the optimal values: Although it is possible for the rounded solution to be close to the optimal integer solution, there is no guarantee that this will be the case, as the linear relaxation might lead to significantly different values.

In summary, when solving an integer programming problem by treating it as a linear programming problem and rounding off the answers, you might encounter sub-optimal solutions, constraint violations, and values that are not very close to the true optimal integer values.

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9514 1404 393

Answer:

  (d)  528 ft³

Step-by-step explanation:

The shape is that of a trapezoidal prism. The front face is a trapezoid with bases 8 ft and 14 ft, and height 6 ft. Its area is ...

  A = (1/2)(b1 +b2)h = (1/2)(8 +14)(6) = 66 . . . . square feet

Then the volume is given by ...

  V = Bh

where B is the area of the (trapezoidal) base, and h is the height of the prism (8 ft). Filling in the values, we find ...

  V = (66 ft²)(8 ft) = 528 ft³

The pool can hold 528 ft³ of water.

The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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We can substitute the first equation into the second to eliminate \(y\) and solve for \(x\)

\($$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$\)

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution. Infinite represents limitless or unboundedness. It is usually represented by the symbol ” ∞ “.

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

This system of linear equations can be graphed on a \($x-y$\) plane. The first equation represents a line with slope \(\frac{1}{4}\) and \($y$\)-intercept \(-3\). The second equation represents another line with slope \(-1\) and \($y$\)-intercept \(-4\). The intersection point of the two lines is the solution to the system of linear equations.

To find the solution, we can substitute the first equation into the second to eliminate \(y\) and solve for \(x\)

\($$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$\)

We can then use either equation to find the value of \(y\)

\($$\begin{gathered}y=\frac{1}{4} x-3 \\\Rightarrow \\y=\frac{1}{4} \cdot 3-3 \\= \\y=-2\end{gathered}$$\)

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A. The base and height of a parallelogram are not inherently related to a circle. They are properties of the parallelogram itself, while the circle has its own properties such as radius, diameter, circumference, and area.

B. A parallelogram cannot be used to directly justify the formula for the area of a circle, which is A = πr^2 (where A is the area and r is the radius). However, it is possible to use a parallelogram to derive an approximate value of π.

The method involves inscribing a circle inside a regular polygon (such as a hexagon or an octagon), and then approximating the area of the circle as being equal to the area of the polygon. As the number of sides of the polygon increases, the approximation becomes more accurate and eventually converges to the true value of π.

C. Dividing a circle into 16 congruent triangles will form a new shape that resembles a polygon rather than a parallelogram. The area of this shape can be used to estimate the area of the circle, but it is not necessarily a better estimate than using the original parallelogram method. The accuracy of the estimate will depend on the size and shape of the triangles, as well as the accuracy of the calculations used to determine the area of the shape. In general, using a larger number of smaller triangles will provide a more accurate estimate of the area of the circle.

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Answer:

A,B,E

Step-by-step explanation:

Just did completed this on Ed

Solution for given inequality is \(-5\leq x\leq -2\)

                                         or         \(x\) ∈ [ -5 , -2]

 a.) Solve  -24 <= 4x - 4 <= -12

Case I :

                      -24 <= 4x - 4                          

                     \(-24 + 4\leq 4x\)

                                       \(-20 \leq 4x\)

                                             \(\frac{-20}{4} \leq x\)

                                                    \(-5\leq x\)   ........ (I)

Case II :

                     4x - 4 <= -12

                      \(4x\leq -12+4\)

                           \(4x\leq -8\)

                              \(x\leq \frac{-8}{4}\)

                                 \(x\leq -2\)   ......................(II)

combining (I) and (II) we get,

                              \(-5\leq x\leq -2\)

b). graph of

                              \(-5\leq x\leq -2\) , refer the attachment

c). Solution in interval

                                   \(x\) ∈ [ -5 , -2]

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If the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120, then the 95% confidence interval for the average number of calories in cereal is (109.2457, 144.7544).

As per the question statement, the number of calories in one serving of various cereals are 110, 98, 140, 145, 150, 90, 150, 140 and 120,

And we are required to determine the following:

(a) 95% confidence interval for the average number of calories in cereal

(b) If the average is 115 calories or not.

Here, given that sample size, (n = 9)

And we know that, [Mean (M) = {(Σx)/n}],

That is, Mean [(M) = (1143/9)],

Or, [(M) = 127]

Also, we know that, Standard Deviation (s) = [{√Σ(xi - M)²}/(n - 1)]

Or,  (s) = [{√Σ(xi - 127)²}/(9 - 1)]

Or, [(s) = 23.0976]

Now solving for part (a) at 95% confidence interval,  (α = 0.05)

Or, [d = (n - 1) = (9 - 1) = 8]

And, (t-critical) = t[(α/2),d] = t(0.025, 8)

Also, (t-critical) = (±2.306)... [given in the students t-distribution table]

Therefore, the 95% confidence interval (CI) for (μ) goes as,

CI = [(M) ± {(t-critical) * (s/√n)}]

Or, CI = [127 ± {(2.306) * (23.0976/ √9)}]

Or, [CI = (127 ± 17.7543)]

Or, [CI = (109.2457, 144.7544)]

And for part (b), since 115 lies in the range of 95% confidence interval for the average number of calories in our concerned cereal, we cannot reject 115 calories as the average.

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Answer: Equivalent equations are equations with identical solutions. You can find them by simply simplifying an equation.

EXAMPLE:

1 + 2 + 3 = 5x

An equivalent equation would be 3 + 3 = 5x

The probability of selecting a blue marble is 3/14. Hence, option D is the right choice.

The probability of any event is the chance of the occurrence of that event. It is given as the ratio of the number of favorable outcomes to the event to the total number of outcomes possible in the experiment.

If we consider an event A, the number of favorable outcomes to event A be n, and the total number of outcomes be S, then the probability of event A is given as:

P(A) = n/S.

Let us take the event of selecting a blue marble from the experiment of selecting a marble randomly from the bag be A.

The number of outcomes favorable to event A (n) = 3 {3 blue marbles}.

The total number of outcomes (S) = 14 {Total number of marbles in the bag = 4 red + 3 blue + 7 green = 14 marbles}.

Therefore, the probability of selecting a blue marble is,

P(A) = n/S = 3/14.

Hence, option D is the right choice.

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Answer:

Step-by-step explanation:

Let the  number be 'x'

x*8 + 6 = 7

8x + 6 = 7

   8x   = 7 - 6

  8x = 1

    x = 1/8

Answer:

\( = >( x \times 8) + 6 = 7\)

\( = > 8x= 7 - 6\)

\( = > 8x = 1\)

\( = > x = \frac{1}{8} \)

Answer:

50 m

Step-by-step explanation:

Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.

A quadratic function is given according to the following rule:

y = ax² + bx + c

\(\Delta = b^2 - 4ac\)

The solutions are:

\(x_1 = \frac{-b + \sqrt{\Delta}}{2a}\)

\(x_2 = \frac{-b - \sqrt{\Delta}}{2a}\)

In which:

\(\Delta = b^2 - 4ac\)

For this problem, the equation that models the income as function of age is given by:

I(x) = -425x² + 45500x - 650000.

The income is of 250,000 when I(x) = 250000, hence:

250000 = -425x² + 45500x - 650000.

425x² - 45500x + 900000 = 0.

Hence the coefficients are a = 425, b = -45500 and c = 900000, then:

The youngest age for which the average income of the lawyer is of $250,000 is of 26 years. (the oldest is of 81 years).

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Answer:

16

Step-by-step explanation:

math is my nickname

Geophysics survey methods aid in geometric road design by identifying soil layers with varying properties, such as strength, bearing capacity, compressibility, and deformation. This information helps engineers determine the best location, optimal design, and material requirements. Geophysical survey methods also help identify sinkholes and subsurface features, ensuring solid ground for road construction.

Geophysics survey methods are essential in geometric road designs, as they help identify soil layers with varying properties and strengths. These properties include soil strength, bearing capacity, compressibility, and deformation. Understanding these properties helps engineers determine the best location, optimal design, and material requirements for the road. Geophysics survey methods are particularly useful in locating buried utilities and identifying potential sinkholes, underground cavities, and other subsurface features that could affect road construction. This information is crucial for ensuring the road is built on solid ground that supports vehicle weight and withstands environmental factors.

The information obtained from geophysics survey methods can be used to create a subsurface map of the road site, which is then used to develop the best road design. Overall, geophysics survey methods are crucial in determining the properties of soil and subsurface features in geometric road designs, ultimately ensuring a safe and environmentally friendly road.

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Answer:

27.92 percent

Step-by-step explanation:

Answer:

3.58

Step-by-step explanation:

um yah I know this one

This value of v into the formula for centripetal acceleration, we have:14.7 = (2πr/45)2Solving for r, we get:r = 77 meters (rounded to the nearest whole number). Therefore, the radius of the loop is 77 meters.

A loop is created by having an airplane follow a circular path in a vertical plane. This means that the acrobatic plane has centripetal acceleration, which is directed towards the center of the circular path. The acceleration depends on the speed of the plane, the mass of the plane, and the radius of the circular path. The acceleration can be calculated using the formula a = v2/r where v is the velocity and r is the radius of the circular path.

The given centripetal acceleration, a = 14.7 m/s2, is equal to v2/r. The velocity of the plane is not given, but we can use the fact that the pilot takes 45 seconds to complete the loop to find the velocity. During the loop, the plane travels a distance equal to the circumference of the circular path.

Therefore, the velocity of the plane is given by the formula v = 2πr/t where t is the time taken to complete one loop, which is 45 seconds.

Substituting this value of v into the formula for centripetal acceleration, we have:14.7 = (2πr/45)2Solving for r, we get:r = 77 meters (rounded to the nearest whole number) Therefore, the radius of the loop is 77 meters.

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Answer:

d = 4

Step-by-step explanation:

4d - 4 = 5d - 8

Add -5d and 4 on both sides.

4d - 5d = - 8 + 4

- 1d = - 4

Divide -1 into both sides.

d = -4/-1

d = 4

Evaluate the expression, we find that, d + e - f = 33, when d = −9, e = 36, and f = −6.

What is expressiοn?  

In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)

Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.

We can evaluate the expression using the given values of d, e, and f:

d + e - f

= (-9) + 36 - (-6)  [substitute the given values]

= (-9) + 36 + 6     [simplify the double negative]

= 33                [add the terms]

Therefore, d + e - f = 33 when d = −9, e = 36, and f = −6.

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Answer:

Beam stick out = 2.09 ft

Step-by-step explanation:

Given:

Length of wooden beam = 12 ft

Side of bed =  5.5 ft by 8 ft by 2 ft

Find:

Length of wooden beam needed.

Computation:

\(Length\ of \ diagonal = \sqrt{a^2+ b^+ c^} \\\\\\ Length\ of\ diagonal = \sqrt{5.5^2+ 8^2+ 2^2}\\\\ Length\ of\ diagonal = \sqrt{30.25+64+4}\\\\Length\ of\ diagonal = \sqrt{98.25}\\\\Length\ of\ diagonal = \sqrt{30.25+64+4}\\\\Length\ of\ diagonal = 9.91\)

Length of wooden beam needed = 9.91 ft

Beam stick out = 12 ft - 9.91 ft

Beam stick out = 2.09 ft

Answer:

12 and 6

Step-by-step explanation:

12×6=72

12÷6=2

I hope this may help you

A midpoint has coordinates of \((-2, -1)\) we will call them \((x_m, y_m)\).

The coordinates of a midpoint are constructed from coordinates of enpoints \((x_1,y_1),(x_2,y_2)\), namely as a divided sum.

\(

x_m=\frac{x_1+x_2}{2}\implies x_1=2x_m-x_2 \\

y_m=\frac{y_1+y_2}{2}\implies y_1=2y_m-y_2

\)

Now insert the numbers.

\(

x_1=2(-2)-(-6)=2 \\

y_1=2(-1)-4=-6

\)

The result is an endpoint at \((2,-6)\).

Dot plots are better suited for maintaining the identity of individual observations, especially in smaller data sets, while histograms are useful for visualizing the distribution of larger data sets, even though they lose the identity of each specific data point.

Regarding dot plots and histograms, the true statement is that dot plots do not lose the identity of individual observations. Dot plots display each data point as a dot on a number line or axis, preserving information about individual data points. This is especially useful when dealing with small to moderate-sized data sets, as it allows for easy identification of patterns, clusters, or outliers.

On the other hand, histograms are a graphical representation that organizes data into intervals or bins, which can provide an overview of the distribution of a larger data set. While histograms are often easier to construct and can help visualize patterns and trends for large data sets, they lose the identity of individual observations, as the data points are grouped together in bins.

In summary, dot plots are better suited for maintaining the identity of individual observations, especially in smaller data sets, while histograms are useful for visualizing the distribution of larger data sets, even though they lose the identity of each specific data point.

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Answer:

b(-10) = 6

Step-by-step explanation:

B(x)= |x+4|

Let x = -10

B(-10)= |-10+4|

            |-6|

Take the positive value

               6

Answer:

6

Step-by-step explanation:

|-10+4|

|-6|

Remove brackets

6

Answer:

=36n-175

Step-by-step explanation:

The annual change in Production increases at a slower rate than the annual increase in the average salary, as stated in the given option.

Based on the information provided, we can compare the annual change in production to the annual change in average salary.

The statement that accurately compares the annual change in production to the annual change in average salary is: "The annual change in production increases at a slower rate, 105% per year, than the annual increase in average salary, $500 per year."

This statement indicates that the annual change in production, which is approximately 105% per year, is slower compared to the annual increase in the average salary, which is $500 per year.

It is important to note that the graph provided does not specify the exact values or initial production rate, but it does provide the comparison between the two rates. From the graph, we can observe that the annual change in average salary shows a steeper increase compared to the annual change in production. This is represented by the steeper slope of the line depicting average salary compared to the line representing production, which is relatively flatter.

Therefore, we can conclude that the annual change in production increases at a slower rate than the annual increase in the average salary, as stated in the given option.

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Answer: D. The annual change in production increases at a slower rate, 105% per year, than the annual increase in average salary, $500 per year.

The income statement should include all sources of revenue and deduct all applicable expenses to calculate the net income or loss for the period. To create a balance sheet gather information about the company's assets, liabilities, and shareholders' equity as of that specific date. To determine whether there has been an increase or decrease compare the net income figure from a previous period with the net income figure from the current period

1) To prepare a projected income statement for the year ending November 20, sora, you would need to gather information about the revenues and expenses expected during that period. The income statement should include all sources of revenue and deduct all applicable expenses to calculate the net income or loss for the period.

2) To create a balance sheet as of November 30, 2oya, you will need to gather information about the company's assets, liabilities, and shareholders' equity as of that specific date. The balance sheet provides a snapshot of the company's financial position, showing what it owns, owes, and the remaining equity.

3) To determine whether there has been an increase or decrease in the amount of net income, you would need to compare the net income figure from a previous period (presumably November 20, sora) with the net income figure from the current period (ending November 30, 2oya). If the net income has increased, it means the company has generated more profit during the current period compared to the previous one. Conversely, if the net income has decreased, it indicates a decline in profitability.

Overall, the task involves preparing a projected income statement and balance sheet and analyzing the change in net income to assess the company's financial performance.

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Answer:

see below

Step-by-step explanation:

a) see attached chart

b) sum is 10

There are 3 that total to 10  (4,6)  (5,5) and (6,4)  and there are 36 possible outcomes

P(10) = number of outcomes that sum to 10 / total number of outcomes

        =3/36

        = 1/12

c) identical numbers  There are 6 that are identical (1,1) (2,2) (3,3) (4,4) (5,5) (6,6)

p(identical) = number of outcomes that are identical / total number of outcomes

        =6/36

        = 1/6

d product a multiple of 10 ( 5,2)  (5,4) (5,6)  (2,5)  (4,5) (6,5) are the only ones with a product multiple of 10

p(identical) = number of outcomes that are identical / total number of outcomes

        =6/36

        = 1/6

The Svalbard Global Seed Vault is a backup storage facility for seeds In contrast, the World Agricultural Heritage Centre is a research and instructional centre.

Svalbard Global Seed Vault was established to help ensure the survival of important crops in the event of natural disasters, war, or other catastrophic events. The seed vault is located deep inside a mountain on a remote island near the Arctic Circle, where the seeds are stored at a temperature of -18 degrees Celsius.

The World Agricultural Heritage Centre, focuses on the conservation and study of crop diversity. The centre is affiliated with the Food and Agriculture Organization of the United Nations (FAO) and serves as a hub for information and research on the world's crops.

If you want to support the preservation of crop diversity, then the World Agricultural Heritage Centre might be the better choice, while if you want to help ensure the survival of crops in the event of a disaster, the Svalbard Global Seed Vault might be a better choice. Ultimately, both institutions play important roles in the preservation of crop diversity and the future of our food supply.

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The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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