A 5-foot piece of aluminium wire costs $21.00. What is the price per inch?

The answer to the given linear programming problem, which is solved using the simplex method, is as follows:

The optimal solution to minimize the objective function Z = X1 + 2X2 is X1 = 20 and X2 = 0, with the objective function value Z = -100.

To solve the problem, we'll first convert the inequalities to equations by introducing slack and surplus variables. Then we'll set up the initial simplex tableau and iterate through the simplex algorithm until we reach an optimal solution.

⇒ Convert the inequalities to equations:

A. X1 + 3X2 + S1 = 90 (where S1 is the slack variable)

B. 8X1 + 2X2 + S2 = 160 (where S2 is the slack variable)

C. 3X1 + 2X2 + S3 = 120 (where S3 is the slack variable)

D. X2 + S4 = 70 (where S4 is the surplus variable)

⇒ Set up the initial simplex tableau:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       | -1 | -2 |  0 |  0 |  0 |  0 |  0  |

----------------------------------------------

S1      |  1 |  3 |  1 |  0 |  0 |  0 | 90  |

S2      |  8 |  2 |  0 |  1 |  0 |  0 | 160 |

S3      |  3 |   2 |  0 |  0 |  1 |  0 | 120 |

S4      |  0 |   1 |  0 |  0 |  0 | -1 | 70  |

⇒ a) Select the most negative coefficient in the Z row, which is -2. Choose the corresponding column as the pivot column (X2 column).

b) Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 70/1 = 70. Thus, the pivot row is S4.

c) Perform row operations to make the pivot element (1 in S4 row) equal to 1 and eliminate other elements in the pivot column:

  - Divide the pivot row by the pivot element (1/1 = 1).

  - Replace other elements in the pivot column using row operations:

    - S1 row: S1 = S1 - (1 * S4) = 90 - 70 = 20

    - Z row: Z = Z - (2 * S4) = 0 - 2 * 70 = -140

    - S2 row: S2 = S2 - (0 * S4) = 160

    - S3 row: S3 = S3 - (0 * S4) = 120

d) Update the tableau with the new values:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       | -1 |  0 |  0 |  0 |  2 | -2 | -140|

----------------------------------------------

S1      |  1 |  3 |  1 |  0 |  

0 |  0 | 20  |

S2      |  8 |  2 |  0 |  1 |   0 |  0 | 160 |

S3      |  3 |  2 |  0 |  0 |   1 |  0 | 120 |

S4      |  0 |  1 |  0 |  0 |   0 | -1 | 70  |

e) Repeat steps a to d until all coefficients in the Z row are non-negative.

  - Select the most negative coefficient in the Z row, which is -1. Choose the corresponding column as the pivot column (X1 column).

  - Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 20/1 = 20. Thus, the pivot row is S1.

  - Perform row operations to make the pivot element (1 in S1 row) equal to 1 and eliminate other elements in the pivot column.

  - Update the tableau with the new values.

f) The final simplex tableau is:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       |  0 |  0 |  0 |  0 |  1 | -3 | -100|

----------------------------------------------

X1      |  1 |  3 |  1 |  0 |  0 |  0 | 20  |

S2      |  0 | -22 | -8 |  1 |  0 |  0 | 140 |

S3      |  0 | -7 | -3 |  0 |  1 |  0 | 60  |

S4      |  0 |  1 |  0 |  0 |  0 | -1 | 70  |

⇒ Read the solution from the final tableau:

The optimal solution is X1 = 20 and X2 = 0, with the objective function value Z = -100.

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Integral ≈ 904

Let's evaluate the integral of the given function:

∫[-5(-x³ - 10x² - 32x - 36)]dx from -2 to 2 First, we can distribute the -5 to each term inside the parentheses: ∫(5x³ + 50x² + 160x + 180)dx

Now, let's find the antiderivative of the function: Antiderivative: (5/4)x^4 + (50/3)x³ + 80x² + 180x + C

Now, we'll evaluate the antiderivative at the limits of integration, 2 and -2:

F(2) = (5/4)(2^4) + (50/3)(2^3) + 80(2^2) + 180(2) F(-2) = (5/4)(-2^4) + (50/3)(-2^3) + 80(-2^2) + 180(-2)

Now, subtract F(-2) from F(2) to get the integral value: Integral = F(2) - F(-2) Perform the arithmetic operations to get the final answer: Integral ≈ 904

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To construct a Huffman tree and find the Huffman code for the given characters and frequencies, we follow these steps:

1. List the characters and their frequencies: b (6), n (32), p (21), S (14), W (37).

2. Create a binary tree with individual nodes for each character and their frequencies.

3. Combine the two nodes with the lowest frequencies into a single node, with the sum of their frequencies as the frequency of the new node.

4. Repeat the previous step until all nodes are combined into a single tree.

5. Assign binary values (0 or 1) to the branches of the tree, with 0 for left branches and 1 for right branches.

6. Encode the characters based on the paths from the root to each character, where the Huffman code is determined by the sequence of 0s and 1s along the path.

The constructed Huffman tree and the corresponding Huffman codes are as follows:

Huffman Tree:

          130

         /    \

       51      79

      /  \    /   \

     20   31 21   58

    /  \     \

   6   14     17

Huffman Codes:

b - 000

n - 10

p - 001

S - 011

W - 1

Therefore, the Huffman codes for the given characters are:

b - 000

n - 10

p - 001

S - 011

W - 1

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At a price of $44, 30 units of good x are exchanged. This can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50).

At a price of $44, the quantity of good x that is exchanged can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50). The quantity supplied at price $15 is 10 units, the quantity supplied at price $31 is 30 units, and the quantity demanded at price $44 is 50 units. Therefore, the quantity exchanged at price $44 is 50 units minus 10 units (q0) minus 30 units (q*) which equals 10 units. Thus, the quantity of good x exchanged at price $44 is 10 units.

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a) The probability that Z is less than 1.08 is 0.8599.

b) The probability that Z is greater than -0.21 is 1 - 0.4168 = 0.5832.

c) The probability that Z is less than -0.21 or greater than the mean is 1 - 0.4168 = 0.5832.
d) The probability that Z is less than -0.21 or greater than 1.08 is 1 - 0.4168 - 0.8599 = 0.7233.

A) The probability that Z is less than 1.08 can be found by using the standard normal distribution table or a calculator with a normal function. Using the table, we find the value corresponding to 1.08 which is 0.8599.

B) The probability that Z is greater than -0.21 can be found by using the standard normal distribution table or a calculator with a normal function.

Using the table, we find the value corresponding to -0.21 which is 0.4168. Since we want the probability that Z is greater than -0.21, we need to subtract this value from 1.

C) The probability that Z is less than -0.21 or greater than the mean can be found by using the standard normal distribution table or a calculator with a normal function.

Since the mean is 0, we can find the probability that Z is less than -0.21 and subtract it from 1 to find the probability that Z is greater than the mean.

Using the table, we find the value corresponding to -0.21 which is 0.4168.

D) The probability that Z is less than -0.21 or greater than 1.08 can be found by using the standard normal distribution table or a calculator with a normal function.

Using the table, we find the value corresponding to -0.21 which is 0.4168, and the value corresponding to 1.08 which is 0.8599.

We can then subtract these values from 1 to find the probability that Z is less than -0.21 or greater than 1.08.

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The probability of flipping heads and rolling a three is zero. These are two independent events, and the probability of each event occurring is 1/2 for flipping heads and 1/6 for rolling a three. Therefore, the probability is 1/12, which can be written as a fraction.

To calculate the probability of two independent events occurring simultaneously, we multiply the probabilities of each event. In this case, flipping heads and rolling a three are two independent events. The probability of flipping heads is 1/2 because there are two possible outcomes (heads or tails), and assuming a fair coin, each outcome has an equal chance of occurring. Similarly, the probability of rolling a three on a fair six-sided die is 1/6 because there are six possible outcomes (numbers 1 to 6), and each outcome has an equal chance of occurring.

When we want to find the probability of both events happening, we multiply the individual probabilities. In this case, (1/2) * (1/6) = 1/12. This means that out of all the possible outcomes of flipping a coin and rolling a die, only one out of twelve outcomes satisfies the condition of getting heads and rolling a three simultaneously.

Therefore, the probability of flipping heads and rolling a three is 1/12.

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Answer:

y = 3x + 1

Step-by-step explanation:

The slope is 3 (rise over run)

It cross the y axis at 1

Answer:

y=3x+1

Step-by-step explanation:

Given the system of equations:

x - y + 3z = 8

3x + y - 2z = -2

2x + 4y + z = 0

Let's solve the system of equations using elimination method.

Take the first two equations:

x - y + 3z = 8

3x + y - 2z = -2

Since the y variables are opposite of each other, let's eliminate y by adding both equations:

x - y + 3z = 8

+ 3x + y - 2z = -2

__________________

4x + z = 6

Rewrite the equation for z.

Subtract 4x from both sides:

4x - 4x + z = 6 - 4x

z = 6 - 4x

Also, eliminate y in the second and third equations:

3x + y - 2z = -2

2x + 4y + z = 0

Multiply the equation 2 by -4:

-4(3x + y - 2z = -2)

2x + 4y + z = 0

-12x - 4y + 8z = 8

2x + 4y + z = 0

______________

-10x + 9z = 8

We now have the results:

4x + z = 6

-10x + 9z = 8

Multiply the top equation by -9:

-36x - 9z = -54

-10x + 9z = 8

____________

-46x = -46

x = 1

Substitute 1 for x into any of the equations:

4x + z = 6

4(1) + z = 6

z = 6 - 4

z = 2

Substitute 2 for z, and 1 for x in any equation and solve for y:

2x + 4y + z = 0

2(1) + 4y + 2 = 0

4 + 4y = 0

4y = -4

y = -1

Therefore, we have the solutions:

x = 1, y = -1, z = 2

So the minimal transportation cost is $8,700, and it can be achieved by renting 6 buses and 27 vans.

Let's start by defining our variables. Let b be the number of buses and v be the number of vans to be rented. We want to minimize the transportation costs, so our objective function is:

C = 1400b + 100v

We also have two constraints:

The total number of students that can be transported cannot be less than 720:

72b + 9v ≥ 720

The total number of chaperones cannot be more than 45:

3b + v ≤ 45

Now we can solve for b and v. Let's solve the second constraint for v:

v ≤ 45 - 3b

Substituting this inequality into the first constraint, we get:

72b + 9(45 - 3b) ≥ 720

Simplifying and solving for b, we get:

b ≥ 6

So we know that we need to rent at least 6 buses. Since we cannot rent a fraction of a bus or van, b must be an integer. Let's try b = 6 and see if it satisfies the second constraint:

3(6) + v ≤ 45

v ≤ 27

Since v must also be an integer, the largest integer that satisfies this inequality is v = 27. Now we can calculate the total cost:

C = 1400(6) + 100(27) = 8700

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Answer:

the answer is c

Step-by-step explanation:

36x36 + 36x60

=3456 and add squared

Answer:

The complex number is;

37 + 55i

Step-by-step explanation:

Here, we want to find the product of the two

We proceed as follows;

(3 + 2i)(17+ 7i)

= 3(17 + 7i) + 2i(17 + 7i)

= 51 + 21i + 34i + 14(i)^2

Recall; i = √(-1)

Thus, we have it that;

51 + 55i -14

= 51-14 + 55i

= 37 + 55i

The triangles formed by the path of the ball and the wall in the given diagram are similar triangles.

The point on the wall she should aim is; A. 7.8 feet away from point B

The possible diagram in the question is attached

Let x represent the distance from point B where the ball lands.

ΔCDE is similar to ΔABE, by Angle-Angle similarity postulate.

By trigonometric ratio, the tangent of the angles ∠CDE and ∠BAE are;

\(tan(\angle CDE) = \mathbf{\dfrac{20 - x}{25}}\)

\(tan(\angle BAE) = \mathbf{ \dfrac{x}{16}}\)

tan(∠CDE) = tan(∠BAE)

Therefore;

\(\dfrac{20 - x}{25} = \dfrac{x}{16}\)

Which gives;

16 × (20 - x) = 25·x

320 = 41·x

x = 320 ÷ 41 ≈ 7.8

The point on the wall she should aim if she's standing at point A is therefore;

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Answer:

Step-by-step explanation:

56n+24 = 24 + 7n

49n + 24 = 24

49n = 0

n = 0

solution

Answer:

n = 0

Step-by-step explanation:

8(7n + 3) = 24 +7n

1. distribute the 8 inside the paranthesis

56n + 24 = 24 + 7n

2. subtract 24 from both sides

56n = 7n

3. subtract 7n from both sides

49n = 0

n = 0

Answer:

24.6 cm^2

Step-by-step explanation:

3.28m = 328 cm

75mm = 0.075 cm

Area of rectangle: L x W

328 times 0.075 = 24.6 cm^2

Answer:

I believe the answer is 0.55

Step-by-step explanation:

divide5/9

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

for my thinking i think the answer is b

Answer:

D

Step-by-step explanation:

Similar question to the one on your quiz

Answer:

Step-by-step explanation:

This would not make sense because width is measured in feet and computers are not. Quantities should be expressed in the same unit. As they are not, 280 does not have meaning

Answer:

y=6x-5

Step-by-step explanation:

The standered form for the equation of a liner line is y=mx+b where m=the slope and b= the y intercept.

First you need to find the slope which is the change in y over the change in x. The change in the y values (7 and -5) is -12 and the change in the x values (2 and 0) is -2. So the slope is -12/-2 which can be simplified to -6/-1 or 6.

Now that you have the slope you just need the y-intercept. Pick one of the two points from the problem and input that into the x and y values and solve for b. For example 7=6(2)-b where 6(2)=12 and you can then subtract 12 from each side to isolate be and end up with b=-5.

In your final answer, x and y remain as variables to get y=6x-5.

Answer: 11

Step-by-step explanation:

Answer:

x+4x+4=0

Combine x and 4x to get 5x.

5x+4=0

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

5x=−4

Divide both sides by 5.

5x/5 = -4/5

x = -4/5

Step-by-step explanation:

Answer:

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Step-by-step explanation:

Answer:

4 dozens of $15 choc chip cookies + 2 dozens of $18 brownies = $96

price

4 x 15 + 2 x 18 = 96

hope it's correct

Answer:

Answer: TRUE

Step-by-step explanation:

12g+21 equals to 3(4g+7) because you have to multiply 3 and 4g which will equal 12g and then multiply 3 and 7 which will equal 21.

So your final answer would be 12g+21 equals to 12g+21.

Hope it helps!!

Answer:

4

Step-by-step explanation: