A package of tickets for four home games is $180. Write a proportion to find out how much a 12 game package would cost at the same rate.

By applying the Simplex Method or Big M Method to the given problem, the optimal solution for minimizing the objective function Z = 4x₁ + 2x₂ subject to the given constraints is obtained. The optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

To solve the given problem using the Simplex Method or Big M Method, we follow these steps:

Step 1: Convert the problem into standard form:

Introduce slack variables to convert inequalities into equations.

Express any unrestricted variables as the difference of two non-negative variables.

The given problem can be converted into the following standard form:

Minimize Z = 4x₁ + 2x₂

subject to:

3x₁ + x₂ + s₁ = 27

-x₁ - x₂ = 21

x₁ + 2x₂ + s₂ = 30

x₁, x₂, s₁, s₂ ≥ 0

Step 2: Set up the initial Simplex tableau:

Construct the initial tableau using the coefficients of the objective function and the constraints:

  | Cj   | x₁ | x₂ | s₁ | s₂ | RHS |

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

Z  | -4   |  0 |  0 |  0 |  0 |  0  |

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

s₁ |  0   |  3 |  1 |  1 |  0 | 27  |

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

s₂ |  0   |  1 |  2 |  0 |  1 | 30  |

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

Step 3: Perform iterations of the Simplex Method:

We start with the initial tableau and iterate until we reach an optimal solution. I will provide the final tableau directly:

| Cj   | x₁ |  x₂ |  s₁ |  s₂ |  RHS |

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

Z  | -2   | 0  |  0  |  1  | -2  |  -27 |

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

x₁ |  1   | 1  |  0  | -1  |  1  |   6  |

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

s₂ |  0   | 0  |  1  | -0.5|  0.5|   3  |

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

The optimal solution is obtained when all the coefficients in the Z row (except Cj) are non-positive. I

n this case, Z = -27, x₁ = 6, and x₂ = 3. The objective function is minimized when x₁ = 6 and x₂ = 3, resulting in Z = -27.

Therefore, the optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

Note: The steps provided above show the general process of solving a linear programming problem using the Simplex Method or Big M Method. The exact calculations and iterations may vary depending on the specific values and coefficients in the problem.

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Answer:

3 packs of pencils.

Step-by-step explanation:

one pack has 8 pencils

two packs has 16

and three has 24

     </3 PureBeauty

Answer:

You can buy 3 packs, youll have a few lefover.

Step-by-step explanation:

;]

Answer:

A

Step-by-step explanation:

So there are 4 chocolate chips and 12 oatmeal. In total, there are 16 cookies.

The probability of selecting a chocolate chip when you reach in for the first time will be 4/16 or 1/4.

The second time, you reach in, however, there would be one less chocolate chip cookie because you would've pulled one out previously. Thus, the probability is now 3/15 or 1/5.

So, the probability of pulling a chocolate chip cookie consecutively is:

\(\frac{1}{4}\cdot\frac{1}{5}=\frac{1}{20}\)

Our answer is A :)

Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

Answer:

0.0715

Step-by-step explanation:

Not much to explain

To find the value of p(b), we can use the formula for conditional probability:

p(a|b) = p(a ∩ b) / p(b)

Since a and b are independent events, p(a ∩ b) = p(a) * p(b). Substituting this into the formula, we have:

0.60 = (0.60 * p(b)) / p(b)

Simplifying, we can cancel out p(b) on both sides of the equation:

0.60 = 0.60

This equation is true for any value of p(b), as long as p(b) is not equal to zero. Therefore, we can conclude that p(b) can be any non-zero value.

In summary, the value of p(b) is not uniquely determined by the given information and can take any non-zero value.

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The solutions of the equation in the interval [0, 2π) are x=0, π, (2n+1)π/2 (for all integers n and n≠0).

To solve this equation, we need to find all values of x in the interval [0, 2π) that satisfy the equation sinx(2cosx+2)=0.

First, we need to find all values of x where sinx=0. These occur when x=0, π, and any integer multiple of π. We will call these values of x "sinx solutions".

Next, we need to find all values of x where 2cosx+2=0. Solving for cosx, we get cosx=-1. This occurs when x=π and any odd multiple of π/2. We will call these values of x "cosx solutions".

Now, we need to check which of these solutions also satisfy the original equation sinx(2cosx+2)=0.

For the sinx solutions, we have:

x=0: sinx(2cosx+2)=0(2cos0+2)=0(2+2)=0. This solution works.

x=π: sinx(2cosx+2)=sinπ(2cosπ+2)=0(2(-1)+2)=0. This solution works.

For the sinx solutions where x is an integer multiple of π, we have:

x=nπ: sinx(2cosx+2)=0(2cos(nπ)+2)=0(2(-1)ⁿ+2)=0. This solution works when n is odd (since (-1)ⁿ =-1), and does not work when n is even (since (-1)ⁿ=1).

For the cosx solutions, we have:

x=π: sinx(2cosx+2)=sinπ(2cosπ+2)=0(2(-1)+2)=0. This solution works.

x=(2n+1)π/2: sinx(2cosx+2)=sin((2n+1)π/2)(2cos((2n+1)π/2)+2)=0(2(0)+2)=0. This solution works for all integers n.

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Answer:

The Value of 9a+6b is 27. and the value of 4x+3y is 30.

Explanation

1)

3a+2b=9

multiplying both by side by 3

or, 3×( 3a+2b)=3×9

Hence, 9a+6b=27

2)

8x+6y=60

Dividing both by side by 2

or, (8x+6y)/2 = 60/2

Hence, 4x+3y=30

1. The correct answer is A. Rights and obligations. An artificial legal persona, such as a corporation or a company, is a separate legal entity that is distinct from its owners or shareholders. As such, it has its own rights and obligations, which include the ability to enter into contracts, own property, sue or be sued, and engage in various legal activities.

2. The correct answer is A. Copyright law. Intellectual Property law encompasses various legal frameworks that protect creations of the human intellect, such as inventions, literary and artistic works, symbols, names, and designs. Copyright law specifically deals with the protection of original creative works, such as books, music, films, and computer software. 3. The correct answer is D. All of the above. Contracts are considered contrary to public policy if they have a negative impact on society, interfere with the public's welfare, or compromise public safety. Public policy represents the legal principles and values that underpin societal norms and interests, and contracts that run counter to these principles are generally unenforceable or void. 4. The correct answer is D. Payment of wages. Employment duties typically include obedience to lawful instructions, maintaining good faith and loyalty towards the employer, and providing services as agreed upon in the employment contract. Payment of wages, although an essential aspect of the employment relationship, is not classified as a duty but rather as an obligation of the employer to compensate the employee for their services rendered.

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Answer:

0

Step-by-step explanation:

Its equal to something multiplied by 0 so it is 0

The area of the L-shaped prism is 360 cm^2.

To find the area of the L-shaped prism in cm^2, we need to add up the areas of all six faces.

First, we can find the area of the two rectangular faces by multiplying the length and width of each face. From the diagram, we see that one rectangular face has dimensions 8 cm by 12 cm, while the other has dimensions 6 cm by 12 cm. Therefore, the total area of the rectangular faces is:

8 cm x 12 cm + 6 cm x 12 cm = 144 cm^2 + 72 cm^2 = 216 cm^2

Next, we can find the area of the four square faces by multiplying the length of one side by itself and then multiplying by the number of faces. Each square face has dimensions of 6 cm by 6 cm. Therefore, the total area of the square faces is:

6 cm x 6 cm x 4 = 144 cm^2

To find the total area of the L-shaped prism, we add up the areas of all six faces:

216 cm^2 + 144 cm^2 = 360 cm^2

Therefore, the area of the L-shaped prism is 360 cm^2.

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Answer:

x = 22, The length of BC is 22

Step-by-step explanation:

It is shown that angle ACB and angle ABC are congruent (The measure of angles are the same) in the picture. Since the angles are congruent, we can say that AC = AB because of base angle theorem converse. We can then substitute the given numbers in for AC and AB. We would then get 2x - 24 = x - 2. If you solve, you would get that x = 22 (The length of BC is 22).

9514 1404 393

Answer:

  666 ft

Step-by-step explanation:

The circumference of the wheel is given by the formula ...

  C = 2πr

For a radius of 106 ft, the circumference is ...

  C = 2(3.14)(106 ft) = 665.68 ft

Sabrina traveled about 666 feet in one revolution.

Answer:

the unite rate is 20 rows per hour or 20:1

Step-by-step explanation:

120/6= 20 rows per hour

let x be the cost of jwellery sold by you.

The equation for option A is given by:

The equation for option B is given by:

So the equality is given by:

Hence the sales should be 100000$ for you to make the same salary on both options.

Answer: $14.10

Step-by-step explanation:

11.25 * 9 = 101.25

101.25/100 = 1.0125

11.25 + 1.0125 = 12.2625

--
12.2625 * 26 = 282.0375

282.0375/100 = 2.820375

11.25 + 2.820375 = 14.070375
--

14.070375 rounded = 14.10

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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Answer:

7x-5

Step-by-step explanation:

The probability that the jury makes the correct decision that the defendant is guilty is 0.7063.

In order to resolve this issue, we must determine the likelihood that the jury would find the defendant guilty. Let's divide the issue into more manageable components.

We are aware that there is a 0.80 chance that a single juror would choose correctly. If the defendant is found guilty, there is still an 80 percent chance that the jury will reach the right verdict. Consequently, if the defendant is found guilty, there is an 80 percent chance that one jury will reach the right verdict.

The likelihood that at least 10 out of 12 jurors will choose the right course of action may be calculated using the binomial distribution formula. The equation is:

\(P(X \geq k) = 1 - \sum (i=0, k-1) [\frac{i!}{(i!(n-i)!)} ]p^i*(1-p)^(^n^-^i^)\)

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Answer:

1310.4

Step-by-step explanation:

26 x 12= 312 x 4.2= 1310.4

The volume of the unused role is 821.34π cm³

Volume is defined as the space occupied within the boundaries of any three-dimensional solid.

Given that is a figure of unused roll of paper towels, we need to find the volume of the unused role,

The volume of a cylinder with radius r and height h is V = π·radius²·height

To find the same we will subtract the volume of the inner cylinder from the outer,

Volume = 6²π(26) - (2.1)²π(26)

= 26(36π - 4.41π)

= 26(31.59π)

= 821.34π cm³

Hence, the volume of the unused role is 821.34π cm³

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The missing reasons/statements are given below

Statement                          |  Reason                                                

                                           |  R2. Vertical angles are congruent  

                                           |  R4. Property of congruence            

S5. 14x + 15 = 13x + 20       |                                                              

                                            |  R6. Subtraction property of Equality

Answer:

Step-by-step explanation:

y + 3 = 1/2(x - 4)

y + 3 = 1/2x - 2

y = 1/2x - 5

In the novel "Brave New World," when Lenina states, "Never put off until tomorrow the fun you can have today," Bernard replies, "Two hundred repetitions, twice a week from fourteen to sixteen and a half"

This comment means that he is promoting individuality. Bernard is the most noticeable of all the characters who consider the worth of individuality. He is small and awkward, and he is unhappy with the system's blind devotion to conformity and pleasure.

His rejection of this way of life is most visible in his reluctance to indulge in promiscuous sex and drugs, which are fundamental components of the citizens' happy lives.A major theme in Brave New World is the rejection of individuality in exchange for happiness.

The residents of the World State are only concerned with their personal comfort and pleasure, which they gain through mind-numbing activities like sex and drugs.

Bernard, on the other hand, rejects these activities and prefers solitude and his own thoughts. He thinks that individuality is essential, and he refuses to give in to the conditioning that the other citizens accept.

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Answer:

x=3/8y

x=Andre

y=kiran

Consumption of Bananas per year = 5, 250, 000 metric tons

We know 1000 kg = 1 metric ton, so

Consumption of Bananas per year (in kg) = 5, 250, 000 x 1000 = 5, 250, 000, 000 kgs

Cost of Banana = $2.10 per kg

So,

Cost of all bananas = 5, 250, 000, 000 x 2.10 = $ 11,025,000,000 (per year)

Taking a year to be 365 days, let's find the cost for a day:

Since there are 317 million [317,000,000] people in the US, the cost per person every day is:

Rounding to the nearest cent,

a. the double integral for the mass of the sheet is given by M = ∬(0 to a) (0 to y) x dxdy. b.  the double integral in part (b), we can find the x-coordinate of the center of mass of the triangular sheet.

a) The mass of the sheet can be found by integrating the surface mass density rho = x over the triangular region.

To set up the double integral, we need to determine the limits of integration for x and y. The triangular region is defined by the vertices (0, 0), (0, a), and (a, 0).

For y, the limits of integration will be from 0 to a, as the y-coordinate varies from 0 to a along the height of the triangle.

For x, the limits of integration will be from 0 to y, as the x-coordinate varies from 0 to the corresponding y-coordinate along each horizontal line.

Therefore, the double integral for the mass of the sheet is given by:

M = ∬(0 to a) (0 to y) x dxdy.

Evaluating this double integral will give us the mass of the sheet.

b) The center of mass coordinate x_cm can be found using the formula:

x_cm = (1/M) ∬(0 to a) (0 to y) x^2 dxdy,

where M is the mass of the sheet found in part (a).

Intuitively, the center of mass coordinate x_cm represents the "balance point" of the triangular sheet. Since the surface mass density rho = x increases linearly from the origin, we can expect the center of mass to be closer to the vertex (0,0). By calculating the integral, we can determine the precise x-coordinate of the center of mass.

Therefore, by evaluating the double integral in part (b), we can find the x-coordinate of the center of mass of the triangular sheet.

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The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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