A Certain Motor Is Able To Perform 6000J Of Work Over The Course Of 2 Minutes. What Power Is Developed By The Motor During

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

84 / 100 so an 84%

Step-by-step explanation:

Answer:

A tire is 24 inches tall. This is an example of height. It has a circumference of 75.36.

Step-by-step explanation:

All you have to do to find the circumference of a circle is times its height by 3.14, or pi.

Beth's rate of travel is 2.2 meters per second and Amy's line is steeper

From the question, we have the following parameters that can be used in our computation:

The table of values

See attachment for the graph

From the graph, we have

Beth's rate of travel = 2.2 meters per second

This is so because from the graph:

As x increases by 1. y increases by 2/2

Here, we have

Amy's rate of travel = 75/30 meters per second

Evaluate

Amy's rate of travel = 2.5 meters per second

The higher the rate, the steeper the line

This means that Amy's line is steeper

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Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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Answer:

4

Step-by-step explanation:

The constants that have to multiply to eliminate one variable from the system are 12 and 5.

The equations are

5x+13y = 232

12x + 7y = 218

Elimination Method

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Both x term and y terms, choose x terms  and apply the elimination method

The coefficient of x in the first equation is 5 and 12 in the second equation

Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.

To make it the same

Prime factorization

Prime factorization is a process of writing all numbers as a product of primes.

5 = 5×1

12 = 2×2×3

LCM (5, 12 ) = 2×2×3×5 = 60

Multiply the first equation by 12 and the second equation by 5

60x + 156y = 2784

60x + 35y = 1090

Subtract equation 2 from equation 1

121y = 1694

Eliminated x term

The constants that we have to multiply to eliminate one variable from the system are 12 and 5

The complete question is:

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232

12x + 7y = 218

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Answer:

y+1

Step-by-step explanation:

4y-3y+6-5

Step-by-step explanation:

= 1/2 ÷ 2/5

= 1/2 × 5/2

= 5/4

Answer:

\( \sf 1 \frac{1}{4} \)

Step-by-step explanation:

\( \sf = \frac{1}{2} \div \frac{2}{5} \)

\( \sf = \frac{1}{2} \times \frac{5}{2} \)

\( \sf = \frac{1 \times 5}{2 \times 2} \)

\( \sf = \frac{5}{4} \)

\( \sf = 1 \frac{1}{4} \)

Answer:

1/4

Step-by-step explanation:

That is because \(\frac{1}{4}x=y\). One each line, you would divide y by x to get the constant, which is 1/4.

Answer:

honestly i got 273.6 so i'm thinking that he would have to pay about 273 times........

Step-by-step explanation:

Answer:

15$

Step-by-step explanation:

Convertible anti-monotone: Adjusting values allowed, but decreasing violates the constraint. Convertible monotone: Adjusting values allowed, increasing satisfies the constraint. Strongly convertible: Adjusting values allowed, increasing and decreasing satisfy the constraint.

Convertible anti-monotone:

In the case of a convertible anti-monotone constraint, the sum of the values (s) must not exceed a given limit (v). "Convertible" means that it is possible to modify the values of s within certain bounds to satisfy the constraint.

"Anti-monotone" refers to a property where increasing the value of one element decreases the overall sum.

In this scenario, the constraint allows for flexibility in adjusting the individual values of s to stay within the given limit. However, as the values increase, the sum decreases.

Therefore, decreasing the value of any element would result in a larger sum, which violates the constraint.

Convertible monotone:

A convertible monotone constraint is similar to the convertible anti-monotone case, with the primary difference being the monotonicity property. In this case, increasing the value of an element also increases the overall sum.

The constraint still requires the sum of the values (s) to be less than or equal to a given limit (v).

The convertible property allows for adjustments to the values of s to satisfy the constraint, while the monotonicity property ensures that increasing the values of the elements increases the sum.

Decreasing the value of any element would result in a smaller sum, which would comply with the constraint.

Strongly convertible:

A strongly convertible constraint combines the properties of both convertibility and monotonicity.

It allows for adjustments to the values of s to satisfy the constraint, and increasing the value of an element increases the overall sum. The sum of the values (s) must still be less than or equal to a given limit (v).

With the strongly convertible constraint, there is flexibility to modify the values of s while ensuring that increasing the values of the elements increases the sum.

Decreasing the value of any element would lead to a smaller sum, which adheres to the constraint. This provides more options for satisfying the constraint compared to the previous two cases.

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Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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Answer:

1

Step-by-step explanation:

The slope intercept form for this problem is y = x - 16

a. The amount remaining in the account after x week  is 700 - 40x

b. Olivia can withdraw can withdraw money from her account money for  approx. 13 weeks.

Let x represent the number of weeks. Then the amount of withdrawal in this time is 40x

So, the amount remaining in the account after x weeks is 700 - 40x

Since he needs 150$ in the account for safety net, we must have

700 – 40x ≥ 150

So,

700 - 150 ≥ 40x

550 ≥ 40x

550/40 ≥ x

x ≤ 13.75

Hence, he can withdraw money for  approx. 13 weeks.

Withdrawal involves removing money from a bank account, savings plan, pension or trust. In some cases, conditions must be met for funds to be withdrawn without penalty, and an early withdrawal penalty usually occurs when a condition of the investment agreement is violated. Withdraw money from account: With this account you can withdraw a maximum of $500 per day. withdraw money/money/savings With the financial crisis, people had to withdraw their savings.

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Here is a flowchart solution for the given scenario:

START

  |

  |__ Enter the quantity of products purchased

  |        |

  |        |__ If quantity <= 20, discount = 0%

  |        |

  |        |__ If quantity > 20 and quantity <= 30, discount = 10%

  |        |

  |        |__ If quantity > 30 and quantity <= 40, discount = 15%

  |        |

  |        |__ If quantity > 40 and quantity <= 50, discount = 20%

  |        |

  |        |__ If quantity > 50, discount = 30%

  |

  |__ Calculate the total amount due

           |

           |__ Total amount due = Quantity * (1 - Discount) * Price per item

  |

  |__ Display the total amount due

END

And here is a C++ program that implements this solution using Visual Studio:

#include <iostream>

using namespace std;

int main()

{

   int quantity;

   double discount = 0.0, price_per_item = 1.0, total_amount_due;

   cout << "Enter the quantity of products purchased: ";

   cin >> quantity;

   if (quantity > 20 && quantity <= 30)

   {

       discount = 0.1;

   }

   else if (quantity > 30 && quantity <= 40)

   {

       discount = 0.15;

   }

   else if (quantity > 40 && quantity <= 50)

   {

       discount = 0.2;

   }

   else if (quantity > 50)

   {

       discount = 0.3;

   }

   total_amount_due = quantity * (1 - discount) * price_per_item;

   cout << "Total amount due: $" << total_amount_due << endl;

   return 0;

}

Note that in this program, we have assumed that the price per item is $1. You can change this value to match the actual price of the products sold by Shoprite.

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Answer:

Step-by-step explanation:

Answer:

For the 2 first exponents you multiply for the last 2 you add the powers

Step-by-step explanation:

-2x4=-8=4^-8

2x-1=-2 4^-2

2+6= 4^8

5-3=2 4^2

The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm

The density of an object is the ratio of the mass of the object to its volume. Mathematically;

Density = mass/volume

Given the following

Mass of block = 82.8grams

Density = 0.69g/cm^3

volume = lwh
Volume = 20h

Substitute

0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120

h = 6cm

Hence the height of the block of sugar maple is 6cm

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6cm

Step-by-step explanation i can confirm that the answer is 6 ;}

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer:

See attached graph

Step-by-step explanation:

The equation is y-3=(x + 6)

Write the equation in a slope intercept form, then graph the equation on a graph tool to see the points that line on the line.

Alternatively , using the coordinates in the answer choices given, input them in the equation of the graph and select the answer choice that has all its coordinates true to the equation.

y-3 = x+6  -----can be written as : y= x+9

Graph  y= x+9 to see the graph and the points that are on the line as attached.

The line passes through points (-5, 4) and (-4, 5).

Hence, option E is correct.

Use the concept of drawing a graph defined as:

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The given equation of a line:

y – 3 = (x + 6)

To plot the graph:

Put x = 0  we get y = 9

put x = 1 we get y = 10

put x = 2 we get y = 11

put x = 2 we get y = 12

proceed similarly.

Now plot the curve by addressing these points.

Hence,

The line passes through points (-5, 4) and (-4, 5) which is option E.

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The complete question is:

Which is the graph of y – 3 = (x + 6)?

A. A coordinate grid with a line passing through the points at (negative 3, 1), (0, negative 1), and (3, negative 3).

B. A coordinate grid with a line passing through the points at (negative 2, 1), (0, 0), and (4, negative 3).

C. A coordinate grid with a line passing through the points at (negative 3, 0), (0, negative 2), and (3, negative 4).

D. A coordinate grid with a line passing through the points at (negative 3, 3), (0, 1), and (3, negative 1).

E. A coordinate grid with a line passing through the points at (negative4, 5)and (negative 5, 4).

we know that

the points in this graph are the points that lies on the linear equation

To find out the equation of the line

we need at least two points

the graph is unclear

Answer:

quadrant III

Step-by-step explanation:

Answer:

44.1

Step-by-step explanation:

Cosine = Adjacent over Hypotenuse

Adjacent of ∠T = 28 and hypotenuse = 39

Which means that  \(cos(x)=\frac{28}{39}\)

Now we solve for x

To get rid of the "cos" we take the inverse of cos ( which is \(cos^-^1\) ) and apply it to each side

\(cos^-^1((cos)x) = x\\cos^-^1(\frac{28}{39} )=44.11461855\)

We're left with x = 44.11461855

Our last step is to round to the nearest tenth and we get that the answer is 44.1

Answer:

Step-by-step explanation:

Tan 70 = 16/x

x = 16/tan70

x = 5.824 to the nearest thousandth

tan 41 = 16 / (x + y)

tan 41 = 16 /(5.8235 + y)

tan41(5.8235 + y) = 16

5.8235 + y = 16/ tan41

y = (16/ tan41) - 5.8235

y = 12.582 to the nearest thousandth

"The analysts at the casino try to choose the spread so that there is a 50% chance that the outcome will be below that amount, and a 50% chance that the outcome will be above that amount" is TRUE.

The analysts at the casino do not try to choose the spread so that there is a 50% chance of the outcome being below or above that amount. The spread is chosen based on factors such as the teams playing, their past performances, and other relevant statistics.

The goal of the casino is to balance the amount of money bet on each side, not to ensure a 50/50 chance of winning for either side. The spread is simply a tool used to even out the betting and ensure a profit for the casino.
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the lateral area of the figure to the right is 160 m². Option C

From the information given, the shape is a triangular prism.

Thus, the formula for calculating the lateral area of a triangular prism is expressed as;

A = (a + b + c)h

Such that the parameters of the formula are;

Substitute the values, we have;

Lateral area = 16(10)

Multiply the values

Lateral area = 180 m²

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So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).

Here,

In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.

Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.

The slope can be represented as:

slope = Δcost/Δtime = $28/hour

So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.

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