Graph the line that represents this equation:

Y=-5x+2



Drawing Tools.

Copyright protection for works of authorship available through the Internet is expressly provided by the WIPO Copyright Treaty (b).

The WIPO Copyright Treaty (WCT) specifically addresses copyright protection in the digital environment, including works of authorship available through the Internet. The treaty was adopted in 1996 by member states of the World Intellectual Property Organization (WIPO). It aims to address the challenges posed by digital technologies and the Internet to the protection of copyright. The WCT provides a framework for protecting digital works, ensuring that authors' rights are respected and their works are protected from unauthorized copying, distribution, and other forms of infringement. Therefore, the WIPO Copyright Treaty is the international agreement that expressly provides copyright protection for works of authorship available through the Internet.

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(a) The rate at which the tip of his shadow is moving is 0 feet per second.

(b) The rate at which the length of his shadow is changing is 0 feet per second, indicating that the length of the shadow remains constant.

(a) To find the rate at which the tip of the man's shadow is moving, we need to determine the rate of change of the length of the shadow. Let's denote the length of the shadow as 'L' and the distance between the man and the light source as 'x'.

From the similar triangles, we can establish the following relationship:

Height of the man / Length of the shadow = Height of the light / Distance between the man and the light source

Since the height of the man is 6 feet, the height of the light is 15 feet, and the distance between the man and the light source is 10 feet, we can substitute these values into the equation:

6 / L = 15 / 10

Simplifying the equation, we have:

6L = 15 * 10

6L = 150

L = 150 / 6

L = 25 feet

So, when the man is 10 feet from the base of the light, the length of his shadow is 25 feet.

Now, we know that the man is moving away from the light at a rate of 5 feet per second. To find the rate at which the tip of his shadow is moving, we differentiate the length of the shadow 'L' with respect to time 't':

dL/dt = dL/dx * dx/dt

Since dx/dt is given as 5 feet per second, we need to find dL/dx, the rate of change of the length of the shadow with respect to the distance between the man and the light source.

Differentiating the equation 6L = 150 with respect to x, we get:

6 * dL/dx = 0

dL/dx = 0

Therefore, the rate at which the tip of the man's shadow is moving when he is 10 feet from the base of the light is 0 feet per second. This means that the tip of the shadow is not moving horizontally.

(b) To find the rate at which the length of the man's shadow is changing, we differentiate the equation 6L = 150 with respect to time 't':

6 * dL/dt = 0

Since we already know that dL/dt is 0 (as found in part (a)), we can substitute this value into the equation:

6 * 0 = 0

Therefore, the rate at which the length of the man's shadow is changing when he is 10 feet from the base of the light is also 0 feet per second. This means that the length of the shadow remains constant.

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Complete Question:

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. (a) When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving? (b) When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?

The desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

What is the sample proportion of respondents who prefer to live somewhere other than where they currently live?

The sample proportion of respondents who prefer to live somewhere else can be calculated by dividing the number of respondents who indicated a preference for a different location by the total number of respondents.

To make confidence intervals and perform hypothesis testing in this scenario, the researcher can use formulas based on proportions. Since the question asks respondents about their preference (either yes or no), it involves a binomial distribution.

1.Confidence Interval Formula (Proportions): To construct a confidence interval for the proportion of people who prefer to live somewhere other than their current location, the researcher can use the following formula:

Confidence Interval=p​±Z×[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

where:

2.Hypothesis Testing Formula (Proportions): To perform a hypothesis test to determine if the proportion of people who prefer to live elsewhere is significantly different from a particular value (null hypothesis), the researcher can use the following formula:

[tex]Z=\frac{p-p_{0} }{\sqrt{\frac{p_{0}(p_{0} -1)}{n} } }[/tex]

​​where:

By comparing the calculated Z-value with the critical value(s) for the desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.

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The consideration of intermediaries in reaching the target markets relates to the 'Place' element of the marketing mix.

The distribution channel or 'Place' refers to how a company gets its products or services to the target market.

In this scenario, Scott Paper is using many intermediaries to reach its target markets.

Indicating that it relies on various distribution channels or middlemen to distribute its products.

On the other hand, Citibank is stated to use none.

Implying that it adopts a direct distribution approach or a channel that does not involve intermediaries.

Therefore, the marketing mix variable being considered here is Place.

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The above question is incomplete the complete question is:

Scott Paper uses many intermediaries to reach its target markets; Citibank uses none. Which of the marketing mix variables is being considered here?

Group of answer choices

Place

Price

Promotion

Product

Penetration

Answer:

2198.9 cm³

Step-by-step explanation:

Volume of flower vase = volume of cuboid - voume of cone

Volume of cuboid = lbh (length×breath×height) = 12 × 10 × 20 = 2400 cm³

Volume of cone = ⅓ × base area × height

Base area = area of circle = pi radius² = pi 4² = 16 pi

(the diameter of the circle is 8 so to find the radius you just divide it by 2 and you'll get 4)

So,

vol of cone = ⅓ × 16 pi × 12 = 64 pi = 201.06192

Volume of flower vase = 2400 - 201.06192 = 2198.93808 = 2198.9

If a=4, b=6, and sina=3/5 in triangle abc, then sin b equals: 9/10

To find sin(b) in triangle ABC, we can use the sine function in a right angle and the given information.

Given:

a = 4

b = 6

sin(a) = 3/5

We know that the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, let's label the side opposite angle a as side c and the hypotenuse as side h.

sin(a) = c / h

Substituting the given values:

3/5 = 4 / h

To solve for h, we can cross-multiply:

3h = 5 * 4

3h = 20

h = 20 / 3

Now, we can use the sine function to find sin(b):

sin(b) = side opposite angle b / hypotenuse

sin(b) = 6 / (20 / 3)

sin(b) = 6 * (3 / 20)

sin(b) = 18 / 20

sin(b) = 9 / 10

Therefore, sin(b) equals 9/10.

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Instead, the law governing the Federal Reserve

requires it to take a dual mandate into account.

The Federal Reserve's dual mandate, as stated in the Federal Reserve Act, is twofold:

1. Price Stability: The Federal Reserve aims to maintain stable prices and control inflation. While not exclusively focused on inflation targets, the Federal Reserve considers price stability as a crucial objective for promoting a healthy and sustainable economy.

2. Maximum Employment: The Federal Reserve also has a mandate to promote maximum employment. This means that it seeks to foster conditions that support robust job growth, reduce unemployment rates, and facilitate a strong labor market.

The dual mandate recognizes the importance of both price stability and employment in achieving overall economic stability and well-being. It reflects the broader responsibilities assigned to the Federal Reserve in managing monetary policy and guiding the nation's economic performance.

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The probability of having two years with high sales in a row for Apple Inc. is 0.16 or 16%.

To find the probability of two independent events happening in succession, you multiply their individual probabilities together. In this case, the probability of high sales in a given year is 40%, or 0.4.

Step 1: Convert percentages to decimal form.
High sales: 40% = 0.4

Step 2: Multiply the probabilities of high sales for two consecutive years.
Probability of two high sales years in a row = 0.4 * 0.4

Step 3: Calculate the result.
Probability = 0.4 * 0.4 = 0.16

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Experiment Name: Dough Rising. The purpose of this experiment is to investigate the variables that can affect the rising process of dough.

The rising of dough is an essential step in baking as it allows the dough to increase in volume and develop a light and fluffy texture. By understanding the factors that influence dough rising, we can optimize the baking process and ensure consistent results.

In this experiment, we will explore several variables that may impact the dough rising process. These variables include the temperature of the environment, the types and amounts of leavening agents used (such as yeast or baking powder), the hydration level of the dough (ratio of water to flour), and the duration of the rising period. By manipulating these variables and observing the resulting changes in dough volume and texture, we can gain insights into the optimal conditions for achieving optimal dough rising.

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Area of circle is 78.5 square units and Perimeter of circle is 31.4 units.

The radius of the circle is 5 units.

We have to find the area and circumference of the circle.

The area of circle is πr²:

Where r is the radius and π is 3.14.

Area of circle =3.14×5²

=3.14×25

=78.5 square units.

Perimeter of circle is 2πr:

Perimeter =2×3.14×5

=31.4 units.

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The Cost of One Tomato Plant is $1.4 and the cost of one pepper plant is $1.25 .

Here are a pair of two linear equations in two variables.

Let assume ,

One tomato plant is x

one pepper plant is y

Pair of two linear equations in two variables :

         4x + 3y = 9.35     →  (i)

        2x + 11y = 16.55    →  (ii)

Multiplying equation (ii) by 2 , we have :

      4x + 3y = 9.35    (iii)

    4x + 22y = 33.10   (iv)

Subtracting equation (iv) from (iii)

     19y = 23.75

 ⇒    y = 1.25

substituting the value of y in any of the equation (i) & (ii), we have:

      4x +3(1.25) = 9.35

 ⇒    x = 1.4

therefore , x = 1.4 & y = 1.25 is the point where the given equations intersect.

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Answer:

3.2.1. 15 cm is equal to 150 mm (since 1 cm = 10 mm)

3.2.2. To determine the number of boxes that can be tied together to form a bundle, we need to divide the thickness of the bundle by the thickness of each box. Thus, 15 cm (or 150 mm) divided by 8 mm is approximately 18.75. Since you cannot have a fraction of a box, the answer is 18 boxes.

3.2.3. To determine the number of bundles used to make one block of cardboard, we need to divide the height of the block (1.2 m or 1200 mm) by the height of each bundle (150 mm). Thus, 1200 mm divided by 150 mm is equal to 8. Therefore, 8 bundles are used to make one block of cardboard.

The result is assigned tο variable x, sο the value stοred in x is 3.

The value stοred in x can be determined by evaluating the expressiοn οn the right-hand side οf the assignment statement.

Given the statement int x; x = 3 /static_cast<int>(1.5 + 2.4), the expressiοn inside the static_cast is evaluated first:

1.5 + 2.4 = 3.9

Then, the result οf the expressiοn is cast tο an int using static_cast<int>. This perfοrms a static cast, cοnverting the flοating-pοint value tο an integer by truncating the decimal pοrtiοn:

static_cast<int>(3.9) = 3

Finally, the result is assigned tο x, sο the value stοred in x is 3.

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Step-by-step explanation:

Using the given formula, we can substitute x = 1 and solve for y:

y = 5 x 2^x

y = 5 x 2^1 (substitute x = 1)

y = 5 x 2

y = 10

Therefore, when x = 1, y = 10.

Answer:

y = 10

Step-by-step explanation:

Chlorine has two stable isotopes , Cl-35 and Cl-37 with atomic masses 34.968 u and 36.956 u respectively. If the average atomic mass is 35.453 u.

Using the constant rate of melting of a glacier to calculate its past position is an example of applying the principle of uniformitarianism.

The principle of uniformitarianism states that the same natural laws and processes that operate in the present have also operated in the past, allowing us to understand and interpret geological events and phenomena. By assuming that a glacier is melting at a constant rate per year, a researcher can extrapolate this information to estimate the past position of the glacier. This assumption is based on the idea that the melting process has been consistent over time, allowing the researcher to calculate the probability of the glacier's past position. This application of uniformitarianism enables scientists to make inferences about past events and understand Earth's geological history.

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The difference in premiums between the put options is the initial cost or potential profit of the strategy. The specific choice of strike prices and the investor's outlook on the stock will determine the risk and potential return of the spread strategy.

(a) To create a bull spread using the put options, an investor can buy the put option with the lower strike price ($30) and simultaneously sell the put option with the higher strike price ($35). This strategy is called a bull put spread. By buying the lower strike put option and selling the higher strike put option, the investor aims to profit from a bullish or neutral outlook on the stock.

(b) To create a bear spread using the put options, an investor can sell the put option with the lower strike price ($30) and simultaneously buy the put option with the higher strike price ($35). This strategy is called a bear put spread. By selling the lower strike put option and buying the higher strike put option, the investor aims to profit from a bearish or neutral outlook on the stock.

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The answers are =

a) 1, b) 1, c) 1, d) (√2 + 2)/2.

Let's evaluate the given expressions:

a) (sec 30) (cos 30)

To evaluate this expression, we need to substitute the values of sec 30 and cos 30:

sec 30 = 1/cos 30 = 1/(√3/2) = 2/√3

cos 30 = √3/2

Substituting the values:

(sec 30) (cos 30) = (2/√3) * (√3/2) = (2√3)/(2√3) = 1

Therefore, (sec 30) (cos 30) evaluates to 1.

b) (tan 60) (cot 60)

To evaluate this expression, we need to substitute the values of tan 60 and cot 60:

tan 60 = √3

cot 60 = 1/tan 60 = 1/√3 = √3/3

Substituting the values:

(tan 60) (cot 60) = (√3) * (√3/3) = (3/3) = 1

Therefore, (tan 60) (cot 60) evaluates to 1.

c) 5(sin^5 30) + cos^2 45)

To evaluate this expression, we need to substitute the values of sin 30 and cos 45:

sin 30 = 1/2

cos 45 = 1/√2

Substituting the values:

5(sin^5 30) + cos^2 45) = 5((1/2)^5) + (1/√2)^2 = 5(1/32) + 1/2 = 5/32 + 1/2 = 5/32 + 16/32 = 21/32

Therefore, 5(sin^5 30) + cos^2 45) evaluates to 21/32.

d) 2(sin 30) (cos 45) + tan 45

To evaluate this expression, we need to substitute the values of sin 30, cos 45, and tan 45:

sin 30 = 1/2

cos 45 = 1/√2

tan 45 = 1

Substituting the values:

2(sin 30) (cos 45) + tan 45 = 2(1/2)(1/√2) + 1 = 1/√2 + 1 = (√2/2) + 1 = (√2 + 2)/2

Therefore, 2(sin 30) (cos 45) + tan 45 evaluates to (√2 + 2)/2.

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The physical layout of Alcoa Corporation's headquarters, with minimal traditional offices, open-air escalators, and low-walled cubicles, encourages an open and collaborative culture.

The physical layout of Alcoa Corporation's headquarters, characterized by the minimal number of traditional offices, open-air escalators, and low-walled cubicles, fosters an open and collaborative culture within the organization. The absence of traditional offices with four walls and a door eliminates physical barriers and promotes accessibility and visibility among employees. This layout encourages communication, interest, and collaboration, as employees are more likely to engage with one another in an open workspace.

The placement of elevators in out-of-the-way alcoves and the presence of an open-air escalator in the center of the building encourage employees to move around, interact with colleagues from different departments, and engage in impromptu conversations, fostering a sense of community and teamwork.

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Public policies created by the government can attempt to build a ladder of opportunities so people are not just determined by their socioeconomic background by which they grew up.

Socioeconomic background refers to the social and economic status of an individual, often influenced by factors such as family income, education level, and occupation. It can significantly impact a person's access to resources, opportunities, and social mobility. However, public policies can play a crucial role in mitigating the influence of socioeconomic background and providing equal opportunities for individuals to succeed.

By implementing policies that address issues such as education, healthcare, employment, housing, and social welfare, governments can create an environment where individuals are not solely limited by the circumstances of their upbringing. For example, investing in quality education and providing equal educational opportunities can help level the playing field and ensure that children from disadvantaged backgrounds have access to the same resources and opportunities as their more privileged counterparts. This can break the cycle of intergenerational poverty and enable individuals to reach their full potential.

Furthermore, policies that promote inclusive economic growth, job creation, and skills development can offer individuals from all backgrounds the chance to improve their socioeconomic status. Implementing social welfare programs and safety nets can provide a safety net for those facing financial hardships and help reduce socioeconomic disparities.

In addition to addressing immediate needs, public policies can also focus on long-term strategies such as promoting equitable economic policies, reducing income inequality, and fostering social cohesion. By creating an environment that fosters equal opportunities and social mobility, governments can enable individuals to transcend the limitations imposed by their socioeconomic background.

In conclusion, public policies can be designed to build a ladder of opportunities that aim to reduce the influence of socioeconomic background on an individual's prospects. By implementing measures that enhance access to education, employment, healthcare, housing, and social welfare, governments can work towards creating a more equitable society where individuals are not solely determined by the circumstances in which they grew up.

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The binding energy of the F-19 nucleus is approximately 143.15 MeV.. The binding energy of an F-19 nucleus is determined by calculating the mass defect.

The mass defectwhich is the difference between the mass of the nucleus and the sum of the masses of its individual protons and neutrons. The F-19 nucleus has a mass of 18.99840325 amu. Each proton has a mass of 1.00728 amu, and each neutron has a mass of 1.008665 amu. To convert amu to energy, we use the conversion factor of 1 amu = 931 MeV. The first step is to calculate the total mass of the protons and neutrons in the F-19 nucleus. There are 9 protons and 10 neutrons in F-19, so the total mass of the protons is 9 * 1.00728 amu = 9.06552 amu, and the total mass of the neutrons is 10 * 1.008665 amu = 10.08665 amu.

Next, we calculate the mass defect by subtracting the total mass of the protons and neutrons from the mass of the F-19 nucleus: 18.99840325 amu - (9.06552 amu + 10.08665 amu) = -0.15376625 amu.

Finally, we convert the mass defect to energy using the conversion factor: -0.15376625 amu * 931 MeV/amu = -143.15071575 MeV.

Therefore, the binding energy of the F-19 nucleus is approximately 143.15 MeV.

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The total number of sodium atoms in 92 grams of sodium can be calculated by using Avogadro's number and the molar mass of sodium.

To find the total number of sodium atoms, we need to first calculate the number of moles of sodium in 92 grams. The molar mass of sodium (Na) is approximately 22.99 grams/mol. By dividing the given mass (92 grams) by the molar mass, we can determine the number of moles of sodium.

92 grams of sodium / 22.99 grams/mol = 4 moles of sodium

Next, we can use Avogadro's number, which is approximately 6.022 x 10²³ atoms/mol, to convert the number of moles of sodium into the total number of sodium atoms.

4 moles of sodium x (6.022 x 10^²³ atoms/mol) = 2.409 x 10²⁴ sodium atoms .Therefore, there are approximately 2.409 x 10²⁴ sodium atoms in 92 grams of sodium.

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In the equation y = X - 6, the values of A, B, and C may be calculated as follows:

A = 1 (X coefficient)

B = 0 (X's coefficient is 0)

(constant term) C = -6

1. The provided equation is y = X – 6, where y is the dependent variable and X is the independent variable.

2. We may discover the values of A, B, and C by comparing the equation to the usual form y = AXE + B.

3. Because the coefficient of X in this case is 1, A = 1.

4. Because there is no X phrase, the coefficient of X is 0, resulting in B = 0.

5. Because the equation's constant term is -6, C = -6.

6. Therefore, the values of A, B, and C are A = 1, B = 0, and C = -6, respectively.

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The organizational chart highlights subdivisions of the company, shows lines of authority, provides information about different management levels, and identifies the different types of work performed.

It serves as a visual representation of the company's structure and hierarchy. The main purpose of an organizational chart is to provide a clear understanding of how the company is organized and how different departments and positions relate to one another.

It illustrates the various divisions, departments, and teams within the organization, showcasing the reporting relationships and lines of authority from top-level executives to front-line employees.

By displaying the management levels, the organizational chart helps employees and stakeholders understand the chain of command and who they report to. It helps clarify roles and responsibilities, facilitating efficient decision-making and coordination within the company.

The organizational chart identifies different types of work performed by showcasing different departments or units. This allows for a better understanding of the company's functional areas and the specific responsibilities and expertise of each department.

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When an I/O output module controls an AC voltage, Interposing relay is used to actually control the load.

An I/O (Input/Output) οutput mοdule is a device used in autοmatiοn and cοntrοl systems tο interface with external devices and cοntrοl οutputs. It is typically part οf a larger system, such as a prοgrammable lοgic cοntrοller (PLC) οr a distributed cοntrοl system (DCS).

The I/O οutput mοdule serves as a bridge between the cοntrοl system and the external devices οr equipment that need tο be cοntrοlled. It receives signals οr cοmmands frοm the cοntrοl system and cοnverts them intο apprοpriate οutput signals that can cοntrοl actuatοrs, mοtοrs, valves, sοlenοids, οr οther devices.

The I/O οutput mοdule may include multiple οutput channels οr pοints, allοwing fοr the cοntrοl οf multiple devices simultaneοusly. It is respοnsible fοr prοviding the necessary vοltage, current, οr οther signals required tο οperate the cοnnected devices.

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b is the correct answer. Q is 3 units away from the origin along the y-axis.

Given point Q(2,3) is 2 units away from the origin along the x-axis and 3 units away from the origin along the y-axis.

a is incorrect as Q is not 2 units away from the origin along the y-axis.

b is correct as Q is 3 units away from the origin along the y-axis.

c is incorrect as Q is not 5 units away from the origin along the x-axis.

d is incorrect as Q is not 1 unit away from the origin along the x-axis.

Therefore, the correct answer is b.

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The limit of 1/f(x) as x approaches c exists and is equal to L.

To show that the limit of 1/f(x) exists as x approaches c, we can use the definition of the limit. We need to prove that for any ε > 0, there exists a δ > 0 such that if 0 < |x - c| < δ, then |1/f(x) - L| < ε, where L is the limit of f(x) as x approaches c.

Since f(x) ≠ 0 for 0 ≤ |x - c| < α, we can assume without loss of generality that f(x) > 0 for 0 ≤ |x - c| < α (otherwise, consider -f(x) instead). This implies that 1/f(x) is well-defined for 0 ≤ |x - c| < α.

Let's consider the limit of f(x) as x approaches c: lim x→c f(x) = L. By the definition of a limit, for any ε' > 0, there exists a δ' > 0 such that if 0 < |x - c| < δ', then |f(x) - L| < ε'.

Now, let's choose ε> 0. We want to find a δ> 0 similar that if 0<| x- c|< δ, also| 1/ f( x)- L|< ε. Since f( x) ≠ 0 for 0 ≤| x- c|< α, we can choose α as the upper bound for δ( i.e., δ ≤ α).

Consider the inequality| 1/ f( x)- L| = | 1/ f( x)- L| *| f( x)/ f( x)| = | f( x)- L|/| f( x)|. Since f( x)> 0 for 0 ≤| x- c|< α, we have

| 1/ f( x)- L| = | f( x)- L|/| f( x)|< ε'/ f( x).

Now, let's choose δ = min( α, δ'). For 0<| x- c|< δ, we've| x- c|< δ ≤ δ', which implies| f( x)- L|< ε'. also, since f( x)> 0 for 0 ≤| x- c|< α, we can conclude that 1/ f( x) is well- defined.

thus, for 0<| x- c|< δ, we have

| 1/ f( x)- L|< ε'/ f( x) ≤ ε'/a.

Since ε'/ a> 0, we can set ε = ε'/ a to gain| 1/ f( x)- L|< ε.

therefore, we've shown that for any ε> 0, there exists a δ> 0 similar that if 0<| x- c|< δ, also| 1/ f( x)- L|< ε. This satisfies the description of the limit, and thus, the limit of 1/ f( x) as x approaches c exists and is equal to L.

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Answer:

20/3

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Let's denote the length of the two legs of the triangle as 'a' and 'b', and the length of the hypotenuse as 'c'. We are given that the triangle has interior angles of 30, 60, and 90 degrees.

In a triangle, the sum of the interior angles is always 180 degrees. So, we can set up the equation:

30 + 60 + 90 = 180

Simplifying, we have:

180 = 180

This equation is true, which confirms that we have a valid triangle with the given angle measurements.

Now, we can use the trigonometric ratios to find the lengths of the sides. In a 30-60-90 right triangle, the ratios are as follows:

sin(30) = opposite/hypotenuse = a/c

sin(60) = opposite/hypotenuse = b/c

From these ratios, we can express 'a' and 'b' in terms of 'c':

a = c * sin(30)

b = c * sin(60)

We are given that the wire is 20 cm long, so the perimeter of the triangle is the sum of the three sides:

20 = a + b + c

Substituting the expressions for 'a' and 'b':

20 = c * sin(30) + c * sin(60) + c

20 = c * (sin(30) + sin(60) + 1)

To simplify further, we substitute the values of sin(30) and sin(60):

20 = c * (0.5 + √3/2 + 1)

20 = c * (1.5 + √3/2)

Now, we can solve for 'c':

c = 20 / (1.5 + √3/2)

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator:

c = 20 * (2 / (3 + √3)) * (2 / (3 - √3))

c = 40 / (9 - 3)

c = 40 / 6

Simplifying, we have:

c = 20/3

Therefore, the length of the hypotenuse of the triangle is 20/3 cm, expressed in surd form with a rational denominator.

Answer:

(60 - 20√3) / 3

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ²

call the length of the opposite x and the adjacent x√3.

A 30, 60, 90 triangle takes the form x² + (x√3 )²

= x² + 3x²

= 4x² = hypotenuse²

hypotenuse = 2x.

so 2x + x + x√3 = 20

3x  + x√3 = 20

x (3 +  √3) = 20

x = 20 ÷ (3 +  √3)

hypotenuse = 2x.

2x = 2 X [20 ÷ (3 +  √3) ]

= 40 ÷ (3 +  √3)

= [ 40 ÷ (3 +  √3)] X [(3 -  √3) ÷ (3 - √3)]

= (120 - 40√3) ÷ (9 - 3)

= (120 - 40√3) ÷ 6

= (60/3) ÷ [(20√3) / 3]

= (60 - 20√3) / 3

The values of all sub-parts have been obtained.

What is binomial distribution?

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure. It is used in probability theory and statistics.

As given,

Sample size, n = 9

P (doing a one-time fling), p = 0.05

q = 1 - p

q = 1- 0.05

q = 0.95

Binomial distribution:

P(X) = nCx*px*q^(n-x)

A) Evaluate the probability when no one has done a one-time fling.

P (no one has done a one-time fling) = P(0)

= 0.959

= 0.6302.

B) Evaluate the probability when at least one person has done a one-time fling.

P (at least one person has done a one-time fling) = 1 - P(no one has done a one time fling)

= 1 - 0.6302

= 0.3698.

C) Evaluate the probability when no more than two people have done a one-time fling.

P(no more than two people have done a one-time fling) = P(0) + P(1) + P(2)

= 0.6302 + 9x0.05x0.958 + 9C2 x 0.052x0.957

= 0.6302 + 0.2985 + 0.0629

= 0.9916.

Hence, the values of all sub-parts have been obtained.

To learn more about Binomial distribution from the given link.

https://brainly.com/question/9325204

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The Answer is 5%              

step by step explanation: