You are designing a rectangular poster to contain 75 in? or printing with a 6-in margin at the top and bottom and a 2-in margin at each side. What overall dimensions wil minimize the amount of paper used? What is the vertical height of the poster that will minimize the amount of paper used? What is tho horizontal width of the poster that wil minimize the amount of paper usod?

Answer:

28 in

Step-by-step explanation:

Use Pythagoras Theorem

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Where c is the hypotenuse of the right angle triangle ,and a and b the other sides. Just substitute the values and get your answer.

 Based on the given information, the ordered pairs formed to be plotted on graph are: (1,34) ; (2,68) ; (3,102) ; (4,136) ; (5,170) ; (6,204) and (7,238).

1.According to the values, k=34

2.Total revenue for 86 tickets=$2924

3.If venue has maximum of 200 people,total revenue earned=$6800

4.As the ratio of all the ordered pairs is same/equal to 1:34, it is proportional.

5.The pair (0,0) represents zero tickets sold & zero revenue earned.

6.The pair (6,204) indicates that for 6 tickets sold, $204 revenue earned.

What is graph?

Graph is a two or three dimensional axes or plane representing the location of any point from the reference point. This reference point is called origin which has coordinates (0,0) in 2-D plane and (0,0,0) in3-D plane.

Here, given that the cost of each ticket earns revenue of $34.

Similarly, revenue earned will be proportional to 34t, where t is the number of tickets.

2 tickets=2 x $34 =$68

3 tickets=3 x $34 =$102

4 tickets=4 x $34 =$136

5 tickets=5 x $34 =$170

6 tickets=6 x $34 =$204

7 tickets=7 x $34 =$238

The ordered pairs formed are:  (1,34) ; (2,68) ; (3,102) ; (4,136) ; (5,170) ; (6,204) and (7,238)

1.The value of constant K=$34

2.If tickets sold are 86:

86 tickets=86 x $34 =$2924

Total revenue for 86 tickets=$2924

3.If maximun capacity is 200 & all tickets are sold:

200 tickets=200 x $34 =$6800

If venue has maximum of 200 people,total revenue earned=$6800

4.As the ratio between number of tickets & total revenue at any point is 1:34, it is proportional.

5.The pair (0,0) represents zero tickets sold & zero revenue earned.

6.The pair (6,204) indicates that for 6 tickets sold, $204 revenue earned.

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Refer to the attachments for complete question,chart & graph.

Answer:

A

Step-by-step explanation:

Isolate M

Divide -5

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

Assuming c = x, you would substitute 2{(5)^(5)} - 6,

5^5 = 25,

2(25) = 50,

50 - 6 = 44

Answer would be 44, but only if c = x

Answer:

A

Step-by-step explanation:

because there's no charge for miles

Answer:

$400

..................

Answer:

Step-by-step explanation:

Their is no answer sorry

Answer:

B

Step-by-step explanation:

B is the right answer

Answer:

f is 14 And 8 is E

Step-by-step explanation:

so you have to solve the first step of 14 and 8 it is 90 dress angle

Answer:

Every angle of Square = 90°

diagonal bisects the angle in half.

=> angle FGI = 45°

=> 7x+3=45

=>7x=42

therefore, x=42/7=6

Answer:Decreasing the distance between the objects

Step-by-step explanation:

Answer:

I hope this helps you

Step-by-step explanation:

Area = Base × Height

= 1.8m × 2.5m

= 4.5m^2

In a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

It should be noted that a hypothesis is simply used to get information about a certain thing.

In this case, in a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

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Answer:

1

1

2

+

2

1

6

Convert

1

1

2

to an improper fraction.

Tap for more steps...

3

2

+

2

1

6

Convert

2

1

6

to an improper fraction.

Tap for more steps...

3

2

+

13

6

To write

3

2

as a fraction with a common denominator, multiply by

3

3

.

3

2

⋅

3

3

+

13

6

Write each expression with a common denominator of

6

, by multiplying each by an appropriate factor of

1

.

Tap for more steps...

3

⋅

3

6

+

13

6

Combine the numerators over the common denominator.

3

⋅

3

+

13

6

Simplify the numerator.

Tap for more steps...

22

6

Cancel the common factor of

22

and

6

.

Tap for more steps...

11

3

The result can be shown in multiple forms.

Exact Form:

11

3

Decimal Form:

3.

¯

6

Mixed Number Form:

3

2

3

Step-by-step explanation:

Answer:

3.25 or 3 1/4

Step-by-step explanation:

Convert both fractions into improper fractions: 3/2 * 13/6

Multiply 3/2 and 13/6 together: 39/12

Divide the fraction by 3/3: (39/3) / (12/3)

New fraction: 13/4

The mixed number form: 3 1/4

Decimal form: 3.25

A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.

Explanation:

A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Additionally, if animals were used while conducting experiments, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. If a survey was used to collect data, the researcher should have ensured the survey was properly designed and administered to avoid any biases or errors. Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.

The scientific method requires researchers to conduct experiments in a transparent and objective manner. This means that the researcher should design experiments to test hypotheses, collect data systematically, and analyze data objectively. Any manipulation of data to support a hypothesis undermines the scientific method and is considered unethical. Researchers who intentionally manipulate data can be considered fraudulent and may face disciplinary action.

If animals were used in the experiment, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. Ethical guidelines ensure that animals are treated humanely, minimize their pain and discomfort, and maximize their welfare. Researchers who violate these guidelines can be considered fraudulent and may face disciplinary action.

If a survey was used to collect data, the researcher should have ensured that the survey was properly designed and administered to avoid any biases or errors. Surveys can be susceptible to various sources of error, including sampling errors, measurement errors, and non-response bias. Researchers who fail to address these sources of error can produce biased or invalid results, which can be considered fraudulent.

Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Debriefing allows participants to understand the purpose of the study, ask questions, and voice any concerns they may have. Participants who are not debriefed may feel deceived or harmed by the study, which can damage their trust in research and researchers.

In summary, researchers must adhere to ethical standards and maintain the integrity of their research. This includes avoiding data manipulation, following ethical guidelines for animal welfare, ensuring that surveys are properly designed and administered, and debriefing participants after completion of the study. Failure to do so can result in fraudulent research and harm to participants, animals, and the scientific community as a whole.

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The height of the wall where the ladder reaches will be 23.6 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.

The height of the wall where the ladder reaches is given as,

\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)

\(\sf h = 24 \times \text{sin 80}^\circ\)

\(\sf = 24 \times \text{0.9848}\)

\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)

The height of the wall where the ladder reaches will be 23.6 feet.

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Solution

We want to find the area of the triangle given te sides

b = 20

a = 29

c = 21

Note: Hero formula for calculating the Area of a Triangle

We will first find S

To find the Area

Therefore, the area is

Answer:

Therefore, each person should pay $9.21 for dinner and the tip.

Step-by-step explanation:

To calculate the amount to leave for the tip, you can first determine the total cost of the tip by multiplying the cost of the dinner by the tip percentage: $31.85 * 0.15 = $4.78Then, you can divide the total cost of the tip by the number of people in the group to determine the amount that each person should contribute to the tip: $4.78 / 4 people = $1.19So, each person should contribute $1.19 towards the tip. If you want to split the bill evenly, you can add this amount to the cost of the dinner and divide by the number of people to determine the total amount that each person should pay: ($31.85 + $1.19) / 4 people = $9.21

The percent increase in the volume of the prism is 33.1%.

We have,

To calculate the percent increase in the volume of a rectangular prism when all dimensions are increased by 10%, we can use the formula:

Percent Increase

= (New Volume - Original Volume) / Original Volume x 100

Let's denote the original width, length, and height as W, L, and H, respectively.

The original volume (V1) can be calculated as:

V1 = W x L x H

After increasing each dimension by 10%, the new width, length, and height become 1.1W, 1.1L, and 1.1H, respectively.

The new volume (V2) can be calculated as:

V2 = (1.1W) x (1.1L) x (1.1H) = 1.331W x L x H

Now, we can substitute the values into the percent increase formula:

Percent Increase = (V2 - V1) / V1 x 100

= (1.331W x L x H - W x L x H) / (W x L x H) x 100

= 0.331 x 100

= 33.1%

Therefore,

The percent increase in the volume of the prism is 33.1%.

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The percent increase in the volume of the prism is 33.1%.

Given:

To the percent increase in the volume of a rectangular prism when all dimensions are increased by 10%.

The formula for percent increase is as:

Percent Increase = (New Volume - Original Volume)/Original Volume × 100

The original width, length, and height as W, L, and H, respectively.

The original volume (V₁) can be calculated as:

V₁ = W x L x H

After increasing each dimension by 10%, the new width, length, and height become 1.1 W, 1.1 L, and 1.1 H, respectively.

The new volume (V₂) can be calculated as:

V₂ = (1.1 W) x (1.1 L) x (1.1 H) = 1.331 (W x L x H)

Now, we can substitute the values into the percent increase formula:

Percent Increase = (V₂ - V₁) / V₁ x 100

                             = (1.331 W x L x H - W x L x H) / (W x L x H) x 100

                             = 0.331 x 100

                             = 33.1%

Therefore, the percent increase in the volume of the prism is 33.1%.

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Answer:

See Below

Step-by-step explanation:

A)

There are two runners that run at different average speeds, let these be Ra (runner a) and Rb (runner b). We also have two differnt distances that can be ran, let Leg A La and Leg b Lb. We get the equation bellow:

\(Total time = L_a/R_1 + L_b/R_2\)

B)

Mickey = 35km/h

Minnie = 25km/h

Leg A = 30

Leg B = 20

Since Mickey is the fastes, he should run the section with the longest distance:

\(Total time = L_a/R_1 + L_b/R_2\\Total time = 30_k_m/35_k_m_/_h + 20_k_m/25_k_m_/_h\\Total time = (30/35)_h + (28/35)_h\\Total time = (58/35)_h\)

Answer:

Step-by-step explanation:

\(4)a) Time =\dfrac{Distance}{Speed}\)

Micky:

Distance covered = 30 Km   {Leg A}

Speed = x Kmph

Minnie:

Distance covered = 20 Km  {Leg B}

Speed = y Kmph

\(Total \ time = \dfrac{30}{x}+\dfrac{20}{y}\)

b) x = 35 Km/h

y = 25 Km/h

\(Total \ time = \dfrac{30}{35}+\dfrac{20}{25}\\\\ = \dfrac{6}{7}+\dfrac{4}{5}\\\\=\dfrac{6*5}{7*5}+\dfrac{4*7}{5*7}\\\\=\dfrac{30+28}{35}\\\\=\dfrac{58}{35}\\\\=1\dfrac{23}{35} \ hours\)

(a) The cost function is C(x) = 200 + 15x

(b) The revenue function is R(x) = 25x

(c) The profit function is P(x) = 10x - 200

(d) The break-even point is x = 20. Since the restriction is that no more than 19 units can be sold, the product should not be produced.

We shall determine the functions in the following way:

Given:

Fixed cost = $200

Variable cost = $15

Price of item = $25

(a) The cost function

C(x) = Fixed Cost + Variable Cost per unit * Number of units produced

C(x) = 200 + 15x

(b) The revenue function:

R(x) = Price per unit * Number of units sold

R(x) = 25x

(c) The profit function:

P(x) = R(x) - C(x)

P(x) = 25x - (200 + 15x)

P(x) = 10x - 200

(d) To find the break-even point, we shall set the profit function = 0 and solve for x:

P(x) = 0

10x - 200 = 0

10x = 200

x = 20

Therefore, the break-even point is 20 units. The restriction is that no more than 19 units can be sold, so, it is not profitable to produce this product.

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Answer:

a i think not for sure though

Step-by-step explanation:

Answer:

2,040 cm²

Step-by-step explanation:

Given:

Volume of quarter sphere = 1,944π cm³

Required:

Surface area

Solution:

✔️First, find the radius (r).

Volume of the quarter sphere = ¼(⁴/3πr³)

Thus:

1944π = ¼(⁴/3×π×r³)

1944π = ⅓×π×r³

Multiply both sides by 3

1944π×3 = 1×π×r³

5,832π = πr³

Divide both sides by π

5,832π/π = r³

5,832 = r³

Find the cube root of both sides

r = 18

Radius = 18 cm

✔️Find the surface area of the quarter sphere

Surface area of quarter sphere = ¼ of 4πr² + 2(½ of πr²)

Radius (r) = 18 cm

Plug in the values

Surface area of quarter sphere = ¼×4×π×18² + 2(½×π×18²)

= π×18² + π×18²

= 2,035.75204 ≈ 2,040 cm² (to 3 SF)

ω = 26π radians per minute

The definition of angular speed is the rate of change of angular displacement, which is the angle a body travels along a circular route. The ratio of the number of rotations or revolutions made by a body to the time taken is used to compute angular speed. The Greek letter "," or Omega, stands for angular speed. Rad/s is the angular speed unit in the SI.

The angular speed (ω) of a wind turbine with blades turning at a rate of 13 revolutions per minute can be calculated using the following formula:

ω = 2π * revolutions per minute

For the given wind turbine:

ω = 2π * 13

ω = 26π radians per minute

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Answer

=6a3+7a2+a−1

Step-by-step explanation:

Let's simplify step-by-step.

−3a2+4a−5+6a3−3a+4+10a2

=−3a2+4a+−5+6a3+−3a+4+10a2

Combine Like Terms:

=−3a2+4a+−5+6a3+−3a+4+10a2

=(6a3)+(−3a2+10a2)+(4a+−3a)+(−5+4)

=6a3+7a2+a+−1

The geometric series to give a series for 1 1+x Then differentiate your series to give a formula for + ((1+x)-4)= ... (1 +x)2 1 dx is (1+x)^(-4) = -4/(1+x) + 4/(1+x)^3.

To obtain a series representation for 1/(1+x), we can use the geometric series formula:

1/(1+x) = 1 - x + x^2 - x^3 + ...

This series converges when |x| < 1, so we can use it to find a series for 1/(1+x)^2 by differentiating the terms of the series:

d/dx (1/(1+x)) = d/dx (1 - x + x^2 - x^3 + ...) = -1 + 2x - 3x^2 + ...

Multiplying both sides by 1/(1+x)^2, we get:

d/dx (1/(1+x)^2) = -1/(1+x)^2 + 2/(1+x)^3 - 3/(1+x)^4 + ...

To obtain a formula for (1+x)^(-4), we can use the power rule for differentiation:

d/dx (1+x)^(-4) = -4(1+x)^(-5)

Multiplying both sides by (1+x)^4, we get:

d/dx [(1+x)^(-4) * (1+x)^4] = d/dx (1+x)^0 = 0

Using the product rule and the chain rule, we can expand the left-hand side of the equation:

-4(1+x)^(-5) * (1+x)^4 + (1+x)^(-4) * 4(1+x)^3 = 0

Simplifying the expression, we get:

-4/(1+x) + 4/(1+x)^3 = (1+x)^(-4)

Therefore, (1+x)^(-4) = -4/(1+x) + 4/(1+x)^3.

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Answer:

4) c

6) a, b

7) a

8) b, c

10) I'm not sure but I believe it is C.

Step-by-step explanation:

A metric is a single, quantifiable type of data that can be utilized for various tasks in different domains. Metrics serve as essential tools for measuring progress, assessing performance, and making informed decisions.

By converting complex information into manageable and comparable units, metrics enable individuals and organizations to monitor their objectives and drive improvement.
In business, metrics are often employed to evaluate the success of marketing campaigns, employee performance, or financial growth. They assist in identifying trends, pinpointing areas that need attention, and guiding strategic planning. Key performance indicators (KPIs) are a common type of metric used to measure the effectiveness of business processes and track progress toward organizational goals.
In scientific research, metrics provide valuable insight into the progress and impact of studies. For example, citation metrics measure the influence of a published work within a given field. Metrics also facilitate the assessment of experimental results and the development of new theories, ultimately advancing scientific knowledge.
In education, metrics serve as essential tools for gauging student performance and the quality of educational programs. They provide data on student learning outcomes, helping educators refine their teaching methods and tailor instruction to the needs of individual learners.
Overall, a metric is a versatile, quantifiable data type that plays a vital role in assessing and improving various aspects of performance across multiple domains. By offering concrete, measurable information, metrics empower decision-makers to make informed choices and drive progress.

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