Zoe keeps track of the miles per gallon her car gets per week. she has accumulated the following data: (1,24), (2,24,38), (3,24,76) (4,25,14) what is the common difference or ratio?

(A) The optimal solution to this problem = 2.125

(B) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution is, = 10.625

(C) Instead of an increase in the profit coefficient X to $ 8, suppose that profit was overestimated and should only have been $ 3 is, = 10.625

Given that,

The following LP problem:

Maximize profit = 5X + 6Y

Subject to 2X+Y= 120

2X+ 3Y = 240

X,Y= 0

Maximize C = 5X + 6Y

2X+Y= 120

2X+ 3Y = 240

and x = 0, y = 0

Plot the lines on graph,

2X+Y= 120

2X+ 3Y = 240

x = 0, y = 0

So, boundary points of feasible region are (0,1.7) , (2.125,0) and (0,0)

Substitute the points in  Maximize C

At  (0,1.7)

Maximize C = 5X + 6Y

C = 5(0) + 6(1.7)

C = 0 + 10.2

Maximize C = 10.2

At  (2.125,0)

Maximize C = 5(2.125) + 6(0)

Maximize C = 10.625

At   (0,0)

Maximize C = 5(0) + 6(0)

Maximize C = 0

So, Maximum value is attained at   (2.125,0)

So, the optimal value of x is 2.125

The optimal value of y is 0

The maximum value of the objective function is 10.625

There are several ways to calculate optimal solution; one of them, is by using graphs.

The optimal value of x is 2.125

The optimal value of y is: 0

The maximum value of the objective function is: 10.625

Therefore,

(A) The optimal solution to this problem = 2.125

(B) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution is, = 10.625

(C) Instead of an increase in the profit coefficient X to $ 8, suppose that profit was overestimated and should only have been $ 3 is, = 10.625

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n to the power of 6, also written as n⁶, is a mathematical operation that raises the number n to the sixth power. This means that n is multiplied by itself six times.

For example, if n = 2, then n⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64.

Exponentiation is a mathematical operation that is used to represent repeated multiplication. The number that is being multiplied is called the base, and the number that represents how many times the base is being multiplied is called the exponent. In the case of n⁶, the base is n and the exponent is 6.

In general, when raising a number to a power, the result is the product of that number multiplied by itself the number of times represented by the exponent. For example, n³ = n × n × n and n⁴ = n × n × n × n.

In addition to being a mathematical operation, exponentiation also has practical applications in fields such as computer science, engineering, and physics.

For example, in computer science, exponentiation is used to perform fast computations, such as in the process of encryption and decryption. In engineering and physics, exponentiation is used to calculate rates of growth, such as in the case of compound interest and radioactive decay.

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The angle at the vertex of an isosceles triangle has a measure of 80 degrees.

According to the information provided:

A right triangle, also known as an isosceles triangle, is characterized by having two sides that are equal in length and an angle sum of 180 degrees.

8:5 is the ratio of the angle at the vertex to the angle at the base.

Let's say the angles come out to be 5x, 5x, and 8x.

To calculate the angle formed by the vertex, we can apply the formula as follows:

5x + 5x + 8x = 180°

18x = 180°

X = 10°

Thus, the vertex angle would be 8 x 10° = 80°

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The division of 16 - 8x - 7x² + 2x³ by x - 4 will have a quotient of 2x² + x - 4 and a remainder of 0 using synthetic division.

The procedure for synthetic division involves the following steps:

Divide.

Multiply.

Subtract.

Bring down the next term, and

Repeat the process to get zero or arrive at a remainder.

We shall rearrange 16 - 8x - 7x² + 2x³ to become 2x³ - 7x² - 8x + 16 and then divide by x - 4 as follows;

2x³ divided by x equals 2x²

x - 4 multiplied by 2x² equals 2x³ - 8x²

subtract 2x³ - 8x² from 2x³ - 7x² - 8x + 16 will give x² - 8x

x² divided by x equals x

x - 4 multiplied by x equals x² - 4x

subtract x² - 4x from x² - 8x will give us -4x + 16

-4x divided by x equals -4

x - 4 multiplied by -4 equals -4x + 16

subtract -4x + 16 from -4x + 16 will result to a remainder of 0

Therefore by synthetic division, 16 - 8x - 7x² + 2x³ divided by x - 4 is equal to the quotient of 2x² + x - 4 with a remainder of 0.

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A. Without computing, the sum of 2, 3, and -2 is 3.

B. The explanation that supports the answer in Part A is (A) 2 and -2 are additive inverses and the sum of any number and its additive inverse is zero. The integer 3 is positive, so the sum with be positive.

An additive inverse of a number is the value that results in zero when added to the original number. It is the value that we add to a number in order to get zero. If an is the original number, then its additive inverse is minus a, i.e., -a, such that;

a+(-a) = a – a = 0

By changing the sign of a number, we can find its additive inverse. A positive number's additive inverse is negative, while a negative number's additive inverse is positive. Except for the sign, the numerical value will not change. The additive inverse of 8 is -8, for example, while the additive inverse of -6 is 6.

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Answer:

8 in each bag 32 total hoped this helped :)

Step-by-step explanation:

The formula for a triangle is the area of a triangle = ½ × base × height. The formula for a square is the area of a square = side2.

This formula is used to calculate the area of any triangle when the base and height are known. For example, if the base of a triangle is 10 cm and the height is 5 cm, the area of the triangle is 25 cm2.

The formula for a square is the area of a square = side2. This formula is used to calculate the area of any square when the side length is known. For example, if the side of a square is 10 cm, the area of the square is 100 cm2. To calculate this, we can use the formula by squaring 10 (102 = 100).

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Answer:

-3x^2 +3x +18

Step-by-step explanation:

Y= -3(x+2)(x-3)

= - 3 (x^2 - x - 16)

= - 3x^2 - 3(-x) - 3(-6)

= - 3x^2 +3x +18

On solving the provided question, we can say that Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

here,

we have a cuboid

Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

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Based on the information, it can be inferred that Gustave gives 2,100 steps for every mile he walks.

To calculate the number of steps Gustave takes in a mile, we must take into account the information available about the ratio of steps to the distance he covers. In this case, we know that for every 3 miles, Gustave takes 6,300 steps.

To find how many steps he takes in a mile we must divide the number of steps into the number of miles he walked as shown below:

According to the above, Gustave takes 2,100 steps for every mile he walks.

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Answer:

The break even point is 380.

Step-by-step explanation:

36x + 200 = 76x

200 = 76x - 36x

200 = 40x

200/40 = x

5 = x

C = 36(5) + 200            R = 76(5)

C = 180 + 200              R = 380

C = 380

Answer:

The breakeven point is 5 units

Step-by-step explanation:

C is the cost ($) and R is the revenue ($).

We are told that :

R=76x

C=36x+200

Profit would be the Revenue minus the Cost:

Profit = R - C

The "breakeven point" is the situation in which there is neither a profit nor a loss.  That means that the total profit equals the total cost for x units. We want to find the value of x that would result in no profit or loss: Profit = 0.

0 = R-C

====

Profit = 76x - (36x+200)

Profit = 40x - 200

0 = 40x - 200         [The Breakeven Point]

-40x = -200

x = 5 units

5 units results in 76*5 or $380 in revenue.

5 units results in a cost of 36*(5)+200 or $380 in costs.

The result is breakeven (Profit = $390 - $380) of $0.00

Answer:

Step-by-step explanation:

Find angle U

180 - 42 - 62 = 76°

Find interior angle s

62° because it's an opposite angle

Find angle R

180 - 78 - 76 = 40°

no, the triangles are not similar, angles are different, so answer n° 4

Answer:

Step-by-step explanation:it is 38

Answer:

No solution.

Step-by-step explanation:

2y-8=6x

y=3x+2

-----------

2(3x+2)-8=6x

6x+4-8=6x

6x-4=6x

6x-6x=4

0=4

Answer:

c.

Step-by-step explanation:

Answer:

9 hours.

Step-by-step explanation:

Ella earned $54 in total.

We know she makes $6 an hour, so we just divide 54/6 to find the amount of hours she babysat last week.

54/6 = 9 hours

Side note: You are obviously competent enough to make this question, so I am sure you can do the basic math too.

Answer: 9 hours.

Step-by-step explanation:

Divide 54 by 6. 54/6 = 9.

The exponential equation that matches the number of bacteria after 3 hours is given as follows:

y = 50(4)^3.

An exponential function is used to model this situation as the output is multiplied for each unit of the input.

The general format of an exponential function is given as follows:

y = a(b)^x.

In which:

In a lab experiment, a population of 50 bacteria is able to quadruple every hour, hence the parameters a and b are given as follows:

a = 50, b = 4.

Thus the exponential function that gives the population after x hours is of:

y = 50(4)^x.

After three hours, we have that x = 3, hence the population is given as follows:

y = 50(4)^3.

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Answer:

(6, 0)

Step-by-step explanation:

Any combination of rotations, reflections, and translations that maintain the size and shape of the original figure would be considered a series of transformations that would result in a congruent shape.

A congruent square would be produced, for instance, by rotating a square by 90 degrees and then reflecting it over a line of symmetry. A congruent triangle would also result from shifting a triangle to a different place on the plane while maintaining its orientation.

Transformation vital.

It is necessary to realign an institution's structures, cultures, and business models in order to establish a learning environment that significantly and fairly improves student results and educational value. This process can be described as transformation.

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The expressions that could represent the amount Bo would pay for the game: 0.82B and  B - 0.18B

The correct options are: option (a) and option (e)

Given that the board game costs B dollars.

And the price is reduced by 18%.  

So, the discount percentage is 18%

i.e., the price is reduced by 0.18

To find out discount amount on  the board game, we multiply cost of the board game by discount percentage.

So, we get an expression for the discount amount = 0.18B

Now we calculate total price of the board game.

Subtract the discount amount from original price B

So, we get an expression for the total price of the board game.

B - 0.18B

As the  discount percentage is 18%, then the original percentage of pay is about 100 - 18 = 82%

i.e., total price of the board game would be 0.82B

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The complete question is:

Bo is buying a board game that usually costs BBB dollars. The game is on sale, and the price has been reduced by 18\%18%18, percent.Which of the following expressions could represent how much Bo pays for the game?

a) 0.82B

b) 1.18 B

c) B - 0.18

d) B - 18

e)  B - 0.18B

The solution of (15 feet, 51.5 feet) represents the perimeter of a shape with a longest side of 15 feet.

Equation is a mathematical statement that express the equality of two expression use in equal sign.

The equation for this perimeter can be written as y = 2.5x + 14, where y is the perimeter of the shape and x is the longest side of the shape.

Thus, when x is 15 feet, the perimeter of the shape is 51.5 feet, as represented by the solution (15 feet, 51.5 feet).

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The ratio of people who prefer streaming to the people surveyed is 25:50, or 1:2.

Ratio is a comparison of two or more numbers or quantities that indicates the relative size of the quantities. Ratios are expressed in the form of a fraction or decimal, and they are used in mathematics, statistics, and other sciences. Ratios can be used to compare the sizes of different objects or values, or to compare the relationships between different numbers. Ratios are often used to measure the efficiency of a process or the relationship between different variables.

This ratio indicates that half of the people surveyed prefer to stream movies, while the other half prefer to rent DVDs.

Of the 50 people surveyed, 5 had no preference, meaning that 45 out of the 50 people had a preference for either streaming or renting DVDs.

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It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 10.2 and 5.8

10.2 + 5.8 > 4.5

16 > 4.5

Now we add 10.2 and 4.5

10.2 + 4.5 > 5.8

14.7 > 5.8

Now we add 5.8 and 4.5

5.8 + 4.5 > 10.2

10.3 > 10.2

It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are smaller than third sides.

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Both triangles ABC and DEF are similar to each other based on angle angle similarity

Two triangles are said to be similar if the ratio of the corresponding sides of both triangles are proportional to each other. Also, all the three angles of one triangle are equal to that of the other triangle.

The angle angle (AA) similarity theorem states that two triangles are similar if two angles of one triangle is equal to that of the other triangle.

Both triangles ABC and DEF are similar to each other

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Therefore , the solution to the given problem of slope intercept comes out to be y = 3/4x + 2 * 1/5.

The place where the the line slope intersects the y-axis is known as the intersection point. where, on a line or a curve, the una crosses that location. This is demonstrated by using y = changes in different as the formula for the single direction, where m denotes the slope while c denotes the y-intercept. In the intercepting form of the equation, the line's slope (m) the y-intercept (b) are indicated. Slope and y-intercept are, respectively, m and b for equations with the intercept form (y=mx+b). Additionally, certain equations might be modified to look like slope intercepts. When y=x is written as y=1x+0, for example, the slope and una become 1 and 0, respectively.

Here,

In this case, you must first set up your equation in the "Slope intercept" form.

6x=8y+10

Because your y should be alone, add 8y to each of your sides.

8y + 6x = 10

Since subtraction is the exact reverse of addition, multiply 6 times on both sides.

8y = 6x + 10

You will now divide both sides by 8. You will be alone yourself while completing this.

y= 6/8x + 10/8

Though you might leave it as is, you should probably simplify.

either y = 3/4x + 2 1/5 or y = 3/4x + 5/2

Therefore , the solution to the given problem of slope comes out to be

y = 3/4x + 2 * 1/5.

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The statement that best compares the theoretical and experimental probability for a spin to land on blue is A. The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.

Theoretical probability is calculated by analyzing the total number of possible outcomes of an event and the number of favorable outcomes. Experimental probability, on the other hand, is calculated by conducting an experiment and observing the results.

This means that the theoretical probability of landing on blue is:

= Number of sections of blue / Number of total sections

= 1 / 4

The experimental probability of landing of blue is :

= Number of times blue is spun / Number of spins

= 7 / 20

= 35 %

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Answer: A 35%

Step-by-step explanation:

We must factor the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial. The zeros of the three-degree polynomial are then easily ascertainable.

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Answer:

Step-by-step explanation:

so basically Use the Triangle Sum Theorem to find the measure of each angle. Drag and drop the angle measures into the correct boxes to show the measure of each angle.

your welcome lol. -_-

Answer:

-6 7 2.62 20 54

Step-by-step explanation: