Consecutive numbers are whole numbers that follow in order such as 7, 8, 9 10, 11, 12. find three consecutive numbers such as the sum of the first and third is 118

The optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16.

Let's start by writing down the dual LP. The dual LP is obtained by interchanging the roles of variables and constraints in the primal LP. The dual variables corresponding to the constraints are y1 and y2, representing the multipliers for the first and second constraint, respectively. The objective function of the dual LP is given by minimizing 4y1 + 9y2, and the dual LP subject to the dual constraints is as follows:

min 4y1 + 9y2 subject to:

2y1 + y2 ≥ 4

3y1 + 3y2 ≥ 3

y1, y2 ≥ 0

To graphically solve the dual LP, we can plot the feasible region defined by the dual constraints and find the point that minimizes the objective function. By solving the dual LP, we obtain y1 = 1/3 and y2 = 2/3, with a minimum value of 10/3. Now, using the complementary slackness conditions, we can find the set of optimal solutions for the primal LP. The conditions state that for any optimal solution, the product of the primal constraint and the dual variable must be zero. Since the primal constraints are inequalities, we consider them as equalities to check the conditions. For the first constraint, 2x1 + 2x2 + x3 = 4, we have y1(2x1 + 2x2 + x3 - 4) = 0, which gives y1 = 0. Similarly, for the second constraint, x1 + 3x2 + x3 = 9, we have y2(x1 + 3x2 + x3 - 9) = 0, which gives y2 = 0. Hence, the optimal solution for the primal LP is x1 = 0, x2 = 2, x3 = 2, with a maximum value of z = 16, satisfying the complementary slackness conditions.

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Answer:

11 years 7 months 7 days(if 31 days a months) and change 7 days to 9 days if assuming 30 days a moths

Answer:

-7

Step-by-step explanation:

-10÷5= -2

-2+-5= -7

So Answer is (-7)

Slove the Parenthesis ( ) and then when you get the Answer slove it with what is on the outside and then you will have your Answer.

Hope this helps

Answer:

maybe you should use equation of a line first to solve the given equation

Let * be the binary operation on Z defined by a * b = a + 2b. To prove whether the set E of even integers is closed under the binary operation *, we need to show that for any two even integers a and b, their sum a + 2b is also an even integer.

Let a and b be two even integers, which means they can be written as a = 2m and b = 2n for some integers m and n. Then, the result of the binary operation * is:

a * b = a + 2b = 2m + 4n = 2(m + 2n)

Since m and 2n are both integers, their sum (m + 2n) is also an integer. Therefore, a * b can be written as 2 times an integer, which means it is an even integer.

Thus, we have shown that for any two even integers a and b, their binary operation * result a * b is also an even integer. Therefore, the set E of even integers is closed under the binary operation *.

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The sum of the measures of the angles of any triangle is 180 degrees. In triangle abc, angles a and b have the same measure, while the measure of angle c is 78 degrees larger than each of a and b.

x-intercepts: Locations where a particular plant or feature starts or ends horizontally.

Domain: The range of acceptable values for a specific gardening parameter, such as temperature, soil pH, or sunlight hours.

Range: Possible outcomes or results based on the input values, such as the range of possible plant heights or flower colors.

y-intercept: A specific feature or measurement that exists at the starting point of a vertical axis, such as the initial height of a plant or the starting point of a garden path.

Let's match the real-world descriptions with the features within the context of Melissa's garden.

x-intercepts: The points where a graph intersects the x-axis. In the context of Melissa's garden, this could represent the locations where a particular plant or feature starts or ends horizontally.

Domain: The set of all possible input values or the independent variable in a function. In Melissa's garden, the domain could represent the range of acceptable values for a specific gardening parameter, such as temperature, soil pH, or sunlight hours.

Range: The set of all possible output values or the dependent variable in a function. In Melissa's garden, the range could represent the possible outcomes or results based on the input values, such as the range of possible plant heights or flower colors.

y-intercept: The point where a graph intersects the y-axis. In the context of Melissa's garden, this could represent a specific feature or measurement that exists at the starting point of a vertical axis, such as the initial height of a plant or the starting point of a garden path.

Now, let's match the descriptions with the corresponding features:

x-intercepts: Locations where a particular plant or feature starts or ends horizontally.

Domain: The range of acceptable values for a specific gardening parameter, such as temperature, soil pH, or sunlight hours.

Range: Possible outcomes or results based on the input values, such as the range of possible plant heights or flower colors.

y-intercept: A specific feature or measurement that exists at the starting point of a vertical axis, such as the initial height of a plant or the starting point of a garden path.

Please note that not all tiles will be used in this matching exercise.

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Answer: (x^b)^a

Step-by-step explanation:

the inverse of a monomial with an exponent raised to another power will give the same product if you flip the exponents.

Here we have a general rule for exponents.

We will find that:

\((x^a)^b = x^{a*b}\)

To get this, we can first check it with some values for the exponents.

a = 2

b = 3

\((x^2)^3 = (x^2)*(x^2)*(x^2) = (x*x)*(x*x)*(x*x) = x^6 = x^{2*3}\)

Similarly, we can prove it for two general values of a and b:

\((x^a)^b = (x^a)*(x^a)*...*(x^a)\\b\ times\)

Now each one of these parentheses has a multiplying by itself a times.

So when we write all the x's, we will see that there are a total of b*a x's

Thus we will have:

\((x^a)^b = (x^a)*(x^a)*...*(x^a) = x^{a*b}\)

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The finance charge to make a down payment of 20% and to make 12 monthly payments is $464.72.

A finance charge is defined as the total amount of interest and loan charges we would pay over the entire life of the mortgage loan.

The finance charge formula is the following: Finance charge = Carried unpaid balance × Annual Percentage Rate (APR) / 365 × Number of Days in Billing Cycle

We have, Herb and marci jordan obtained an installment loan.

Annual Percentage Rate (APR) = 10%

Selling price of dishwasher= $699.5

The down payment is defined as the product of the principal and the down payment percentage.

down payment = $699.5× 20% = $139.99

Carried unpaid balance = $699.5 - $139.99 = $559.51

Monthly payment=pr(1.0 + r)ⁿ/ ((1 + r)ⁿ - 1.0)

Where p = $559.51, r = APR/n = rate per payment

= 10/12 = 0.83

n = number of payments = 12

So, Monthly payment = $559.51× 0.83(1.0 + 0.83)¹²/(1+0.83)¹² - 1.0)

= $559.51× 0.83(1.83)¹²/(1.83)¹² - 1.0)

= 655087.061917/1409.62987325

= 464.72274343

Hence, finance charge is $464.72 .

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Answer:

=

Step-by-step explanation:

Answer:

\(The\) \(answer\) \(is\) \(B\) = Both the mean and median will increase, but the mean will increase by more than the median

- written in \(2/5/2021\)

The Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated. The Publicity Test indicates that the decision has been well received and is aligned with public expectations.

- The Publicity Test is designed to assess whether the decision or action can withstand public scrutiny and be disclosed openly.

- I score this test an 8 because the decision or action in question has already been made public and received positive feedback from various stakeholders.

- The organization has been transparent in its communication, engaging with the public and addressing concerns promptly.

- The decision aligns with the organization's values and mission, which resonates positively with the public.

- The organization has effectively managed any potential negative publicity by proactively addressing criticisms and providing clear justifications for the decision.

- Overall, the Publicity Test indicates that the decision has been well received and is aligned with public expectations.

The Moral Mentor Test Score: 6

- The Moral Mentor Test evaluates the decision or action by considering whether it reflects the guidance of a wise and ethical mentor.

- I score this test a 6 because while the decision is generally ethical, there are some potential ethical dilemmas that need to be carefully addressed.

- The decision has considered the welfare of various stakeholders and adheres to legal and regulatory frameworks.

- However, there might be some moral complexities associated with certain aspects of the decision that need further evaluation.

- It is important for the organization to seek guidance from ethical experts and consider potential long-term consequences to ensure the decision aligns with the principles of a moral mentor.

- Overall, the Moral Mentor Test suggests that the decision is on the right track but requires careful ethical analysis and considerations.

The Admired Observer Test Score: 9

- The Admired Observer Test assesses whether the decision or action would be approved by an admired and objective observer.

- I score this test a 9 because the decision demonstrates a high level of integrity and is likely to be approved by an objective observer.

- The decision is aligned with industry best practices and follows ethical guidelines.

- It takes into account the interests of various stakeholders and aims to maximize positive outcomes for all parties involved.

- The decision is well-reasoned, considering both short-term and long-term implications.

- Overall, the Admired Observer Test indicates that the decision is commendable and likely to be seen as fair and ethical by an objective observer.

The Transparency Test Score: 7

- The Transparency Test evaluates whether the decision-making process is transparent and accountable.

- I score this test a 7 because while the decision-making process has been relatively transparent, there is room for improvement.

- The organization has provided some level of information and rationale behind the decision, but there may be areas where more transparency is required.

- It is essential for the organization to proactively communicate the decision, its underlying factors, and potential impacts to ensure stakeholders have a clear understanding.

- Increasing transparency can help build trust and mitigate any potential misunderstandings or mistrust.

- The Person in the Mirror Test assesses whether the decision or action aligns with the individual's values and principles.

- I score this test an 8 because the decision demonstrates alignment with the individual's values and principles.

- The decision-maker has considered the ethical implications and personal integrity while making the decision.

- The decision reflects a commitment to fairness, honesty, and accountability.

I score this test a 9 because the decision demonstrates a high level of empathy and fairness towards others.

- The decision considers the interests and well-being of various stakeholders, treating them with respect and dignity.

- It reflects a commitment to fairness, equality, and reciprocity in relationships.

- The organization has taken steps to ensure that the decision does not cause harm or disproportionately benefit any specific group.

- Overall, the Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated.

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The calculated area bounded by the curves of the region is 0 square units

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

f(x) = sin(x) and g(x) = cos(x)

The intervals where curve intersect is

[0, π/2]

For the surface area between around the region bounded by the curves, we have

Area = ∫[a, b] [f(x) - g(x)] dx

This gives

\(Area = \int\limits^{\pi/2}_{0} {\sin(x) - \cos(x)} \, dx\)

Integrate

\(Area = (-\sin(x) - \cos(x))|\limits^{\pi/2}_{0}\)

Expand

\(Area = (-\sin(\pi/2) - \cos(\pi/2)) - (-\sin(0) - \cos(0))\)

Evaluate

Area = 0 - 0

Area = 0

Hence, the surface area is 0 square units

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Answer:

3 1/2 +7/15×11/4

7/2 +7/15×11/4

119/30×11/4

1309/120

Answer:

\({ \tt{(3 \frac{1}{2} + \frac{7}{15} ) \times 1\frac{1}{4} }} \\ \\ = { \tt{ \frac{119}{30} \times \frac{5}{4} }} \\ \\ = 4 \frac{23}{24} \)

The circumference of the circle with a radius of 9m is 56.5 m.

We know that,

The circumference of a circle can be calculated using the formula:

C = 2πr ----- (1)

where,

C ⇒ circumference of the circle

r ⇒ radius of the circle

Now, as per the question:

The radius of the circle, r = 9m

Substitute the value of the radius into equation (1):

C = 2 × π × 9

Find the value to one decimal place:

C ≈ 56.5

Therefore, the circumference of a circle with a radius of 9m is approximately 56.5 meters.

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The correct question is:-

Find the circumference of the circle with a radius of 9m.

The probability that neither roll is odd is 1/4.

When a pair of dice are rolled, each die can show an odd or even number, and there are a total of 36 possible outcomes (6 x 6) since each die has six possible outcomes.

There are 18 combinations of two dice that do not include an odd number (even-even), and so the probability of rolling an even number is 18/36  = 1/2.

Each die has the same probability of rolling an even or odd number, and so the probability of rolling an even number twice in a row (neither roll is odd) is

\((1/2)^2\) = 1/4.

Therefore, the probability of rolling a six-sided die twice in a row and not getting an odd number is 1/4 (25%).

Let E be the event of rolling an even number, and N be the event of rolling a number.

We need to find P(N'∩N')

i.e. the probability that the first roll is even and the second roll is even.

P(N') = 3/6P(N'∩N')

= P(N') * P(N')

= 3/6 x 3/6

= 9/36

= 1/4

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Answer:

I think it is 2 pounds correct me if I am wrong

Step-by-step explanation:

Answer:

2lb-

Step-by-step explanation:

The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.

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331.5 inches²  is the area of the octagon, rounded to the nearest square inch.

What is octagonal in shape?

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 × apothem × perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Put the values in the formula

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²  

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Answer: C). 332 in.2

Step-by-step explanation:

on edg

The expression that will be not equal to -{-20} are -20,{-20}. The correct options are B and D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is -(-20). The not equivalent expressions are written below,

-(-20) ≠ 20

-(-20) ≠ {-20}

Therefore, expressions like -20, and -20 will not be equal to —20. B and D are the appropriate choices.

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Answer: 0

Step-by-step explanation:

Since m is with x, you don't need to care about y

We would get 2x - 6x + 4x = mx

0x = mx

m is 0

Answer:

4). 0.00000302

corecct answer

Horizontal translation: 2 units right.

Vertical translation: 5 units up

Stretch/compression: stretched by a factor of 3.

Reflection: not reflected.

The values of a and b in the equations are 100 each

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equations are

a. 5x²/2 when x = 10

By substitution, a= 5(10)²/2

This implies that a=( 5 * 100)/2

a= 200/2 = 100

b = [2x²(x-5)]/10x

Substituting x=10 in the equation we have

b = 2*10²(10-5)]/[10(10)]

200(5)/100

b= 10000/100

Therefore b = 100

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3 x 80(4) = 960

80 multiply with 4 as the length of the sisi of the square is 80m and has four sisi.

3 multiply 80(4) as Kelly jog three times a week

Answer:

Slope = 1

Step-by-step explanation:

(5,7) (-4,-2) Answer:1

If an individual exercises 20 minutes daily, the predicted percentage of body fat would be approximately 21.63%.

To determine the predicted percentage of body fat for an individual who exercises 20 minutes daily, we can use linear regression to estimate the relationship between exercise duration and percentage of body fat.

First, let's calculate the slope and intercept of the regression line:

Mean of Exercise (min):

(10 + 18 + 26 + 33 + 44) / 5 = 22.2

Mean of % Fat:

(30 + 25 + 18 + 17 + 14) / 5 = 20.8

Calculate the deviations from the means for Exercise (min) and % Fat:

Exercise (min) deviations: 10 - 22.2, 18 - 22.2, 26 - 22.2, 33 - 22.2, 44 - 22.2

% Fat deviations: 30 - 20.8, 25 - 20.8, 18 - 20.8, 17 - 20.8, 14 - 20.8

Sum of the product of the deviations:

Σ(Exercise deviation × % Fat deviation) = (10 - 22.2) × (30 - 20.8) + (18 - 22.2) × (25 - 20.8) + (26 - 22.2) × (18 - 20.8) + (33 - 22.2) × (17 - 20.8) + (44 - 22.2) × (14 - 20.8)

Sum of Exercise (min) deviations squared:

Σ(Exercise deviation²) = (10 - 22.2)² + (18 - 22.2)² + (26 - 22.2)² + (33 - 22.2)² + (44 - 22.2)²

Calculate the slope (b):

b = Σ(Exercise deviation × % Fat deviation) / Σ(Exercise deviation²)

Calculate the intercept (a):

a = mean of % Fat - (slope × mean of Exercise)

Now we can substitute the given exercise duration of 20 minutes into the equation to find the predicted percentage of body fat:

Predicted % Fat = a + (b × 20)

Let's calculate these values:

Exercise deviations: -12.2, -4.2, 3.8, 10.8, 21.8

% Fat deviations: 9.2, 4.2, -2.8, -3.8, -6.8

Σ(Exercise deviation × % Fat deviation) = (-12.2 × 9.2) + (-4.2 × 4.2) + (3.8 × -2.8) + (10.8 × -3.8) + (21.8 × -6.8) = -305.24

Σ(Exercise deviation²) = (-12.2)² + (-4.2)² + (3.8)² + (10.8)² + (21.8)² = 1154.68

b = (-305.24) / 1154.68 ≈ -0.2648

Mean of Exercise (min) = 22.2

Mean of % Fat = 20.8

a = 20.8 - (-0.2648 × 22.2) ≈ 26.9496

Predicted % Fat = 26.9496 + (-0.2648 ² 20) ≈ 21.63

Therefore, if an individual exercises 20 minutes daily, the predicted percentage of body fat would be approximately 21.63%.

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Complete question =

A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded.

Individual: 1, 2, 3, 4, 5

Excercise (min): 10, 18, 26, 33, 44

% Fat: 30, 25, 18, 17, 14

Based on the above data, if an individual exercises 20 minutes daily, his predicted % body fat would be ?

21.63

27.74

27.88

23.75

True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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Answer:

Yes

Step-by-step explanation:

In \(a^2+bx+c\), b is the middle term.