In a certain class, 65% of the students have brown hair, 20% have blonde hair and 15% have red hair. in that same class 85% of students have brown eyes, 10% have blue eyes and 5% have green eyes. assuming that these physical traits are independent.

what is the probability a student picked at random has blonde hair and brown eyes? show all your work to receive full credit.

The synergy from the merger is $4,125,000.

To calculate the synergy from the merger, we need to compare the value of Fly-By-Night before and after the acquisition of Flash-in-the-Pan Restaurants. The synergy represents the additional value created through the combination of the two firms.

Given that the purchase of Flash-in-the-Pan Restaurants is expected to increase Fly-By-Night's annual after-tax cash flow by $330,000 indefinitely, we can calculate the present value of this incremental cash flow using the appropriate discount rate of 8 percent.

Present Value of Incremental Cash Flow = Incremental Cash Flow / Discount Rate

Present Value of Incremental Cash Flow = $330,000 / 0.08

Present Value of Incremental Cash Flow = $4,125,000

Now, we can determine the value of Fly-By-Night after the merger by adding the present value of the incremental cash flow to its current market value:

Value of Fly-By-Night after Merger = Current Market Value of Fly-By-Night + Present Value of Incremental Cash Flow

Value of Fly-By-Night after Merger = $23 million + $4,125,000

Value of Fly-By-Night after Merger = $27,125,000

The synergy from the merger can be calculated by subtracting the market value of Fly-By-Night before the merger ($23 million) from the value of Fly-By-Night after the merger ($27,125,000):

Synergy = Value of Fly-By-Night after Merger - Current Market Value of Fly-By-Night

Synergy = $27,125,000 - $23 million

Synergy = $4,125,000

Therefore, the synergy from the merger is $4,125,000. This represents the additional value that would be created through the acquisition of Flash-in-the-Pan Restaurants by Fly-By-Night.

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As a manager, it is important to make loan authorization decisions based on financial facts and objective analysis rather than personal biases or gut feelings.

As a responsible manager, it is essential to make loan authorization decisions based on objective criteria rather than personal biases or gut feelings. In the case where you disagree with your subordinate's recommendation to provide a loan to a customer intending to invest in a restaurant, it is important to evaluate the customer's financial facts such as their credit history, business plan, financial projections, and ability to generate sufficient revenue to repay the loan. Personal opinions about the viability of restaurants as investments should not be the sole basis for denial.

Similarly, if your subordinate recommends a loan for a medical operation, your decision should be based on the customer's financial stability, business plan, potential profitability, and risk management strategies.

When evaluating a loan application, it is crucial to focus on financial facts rather than personal opinions about family members. Assess the customer's creditworthiness, financial history, business plan, and repayment capacity to make an informed decision.

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The shrink-wrap required to cover the boxes is equaled to be divided in  1152 square inches long.

To determine the amount of shrink-wrap needed to cover the stack of boxes, we need to calculate the surface area of the boxes.

Each box has two rectangular faces with dimensions 18 inches by 9 inches, and two rectangular faces with dimensions 9 inches by 4 inches. The base of the top box and the top face of the bottom box are not included in the surface area calculation, as they will not be covered by shrink-wrap.

The surface area of each box can be calculated as follows:

Since all three boxes are identical, the total surface area of the stack of boxes is:

3 * (324 square inches + 72 square inches) = 1152 square inches

Therefore, 1152 square inches of shrink-wrap will be needed to cover the boxes.

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The value of measure of EF would be,

⇒ EF = 9/2 units

We have to given that;

Triangles ABC and DEF are similar and have measurements as shown

Since, WE know that;

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, In a similar triangles, ratio of there corresponding sides are equal.

Hence, We get;

AC / DF = CB / EF

Here, AC = 6

DF = 9

BC = 3

After substitute we get;

AC / DF = CB / EF

6 / 9 = 3 / EF

EF = 3 x 9 / 6

EF = 27 / 6

EF = 9/2

Thus, The value of measure of EF would be,

⇒ EF = 9/2 units

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Maria is exhibiting the compulsive symptoms of obsessive-compulsive disorder (OCD), characterized by repetitive behaviors or rituals performed to reduce anxiety or prevent a feared outcome.

Obsessive-compulsive disorder (OCD) is a mental health disorder characterized by intrusive, unwanted thoughts (obsessions) and repetitive behaviors or mental acts (compulsions). These obsessions and compulsions can cause significant distress and interfere with daily functioning.

In Maria's case, her repetitive checking behavior, specifically ensuring that her kitchen stove is turned off, is a compulsive symptom of OCD. She feels compelled to perform this interest repeatedly to alleviate her fear and anxiety of her house burning down. The belief that not checking the stove will lead to a catastrophic outcome is a common feature of OCD, where individuals assign excessive significance to certain thoughts or actions.

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The height of the broken part of the tree is approximately 9 meters

We can make use of the angle of elevation notion and trigonometry.

In this case, we have an angle of elevation of 60 degrees and a horizontal distance of 3√3 meters. We want to find the height of the broken part of the tree.

Let's denote the height of the broken part as "h." The tangent function can be used to relate the angle of elevation and the vertical and horizontal distances:

tan(angle of elevation) = vertical distance / horizontal distance

tan(60°) = h / (3√3)

To isolate h, we can rearrange the equation:

h = tan(60°) * (3√3)

Using a calculator, we can find the value of tan(60°):

tan(60°) ≈ √3

Now, we can calculate the height of the broken part of the tree:

h ≈ √3 * (3√3)

h ≈ 3 * 3

h ≈ 9

Therefore, the height of the broken part of the tree is approximately 9 meters

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The probability to form a triangle using the endpoints of the sticks is 3/35 or approximately 0.0857 (rounded to four decimal places).

Length of the seven sticks in inches = 2, 3, 5, 7, 11, 13, and 17.

Number of sticks selected randomly = 3

To determine the probability of forming a triangle by randomly selecting three sticks from the given set,

Consider the triangle inequality theorem.

According to the theorem, for a triangle to be formed,

The sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

Let us analyze the possibilities,

Selecting sticks with lengths 2, 3, and 5,

In this case, we can form a triangle because 2 + 3 > 5, 3 + 5 > 2, and 5 + 2 > 3.

Selecting sticks with lengths 2, 3, and any other stick greater than 5,

As the longest stick is greater than the sum of the two smaller sticks (2 + 3), we can form a triangle.

Selecting sticks with lengths 2, 3, and the longest stick (17),

In this case, we cannot form a triangle because 2 + 3 is not greater than 17.

In total, there are 3 possible combinations that can form a triangle out of the total 7C3 = 35 combinations selecting 3 sticks out of 7.

Probability

= favourable outcomes / total number of outcomes

= 3/ 35

Therefore, the probability of forming a triangle is 3/35.

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According to ISM (Institute for Supply Management), a framework of measurable corporate policies and procedures and resulting behavior designed to benefit the workplace and, by extension, the individual, the organization, and the community is referred to as "social responsibility."

Social responsibility encompasses the idea that businesses have a responsibility to operate ethically, sustainably, and in a manner that contributes positively to society. It involves adopting policies and practices that prioritize the well-being of employees, stakeholders, and the environment. By implementing social responsibility measures, organizations aim to create a positive impact on society while also enhancing their own reputation, long-term success, and overall value. This framework encourages businesses to integrate social, environmental, and ethical considerations into their decision-making processes and day-to-day operations.

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When the government deliberately alters its level of spending and/or taxes to achieve specific national economic goals, it is exercising discretionary fiscal policy.

Discretionary fiscal policy refers to the deliberate actions taken by the government to influence the economy through changes in government spending and taxation. It involves the use of fiscal measures, such as changes in tax rates, government expenditures on goods and services, and transfer payments, to stabilize or stimulate the economy.

These policy actions are determined and implemented through legislative decisions and government intervention. Unlike automatic government budgetary policy, which refers to the automatic adjustments in government spending and taxation based on predetermined rules and formulas, discretionary fiscal policy involves intentional decisions made by policymakers to actively manage the price.

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The number of leaves in a stem of 5 is 2

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

12,15,34,34.25,98,65,57,76,50,85

Write out the numbers that begin with 5

So, we have

57 and 50

This means that the leaves of the stem of 5 are 7 and 0 i.e 2 leaves

And as such the number of leaves in a stem of 5 is 2

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The type of Balance Sheet Report showing information for today and a year ago is typically a C. Comparison.

A comparison balance sheet report compares the financial position of a company at two different points in time.

In this case, the current day and a year ago.

It presents the assets, liabilities, and equity of the company side by side, allowing for a comparison and analysis of the changes.

That have occurred over the specified period.

The other options mentioned are,

Balance Sheet A,

This is not a recognized classification for balance sheet reports.

Summary,

A summary balance sheet report provides a condensed overview of the financial position.

Usually presenting summarized categories of assets, liabilities, and equity.

It may not include specific details or comparisons with previous periods.

Detailed,

A detailed balance sheet report provides a comprehensive breakdown of all individual accounts.

Assets, liabilities, and equity, offering a more granular view of the financial position.

It may not necessarily include a comparison with a previous period.

Therefore, in the context of comparing the financial position for today and a year ago, the most suitable type of balance sheet report would be a C. Comparison.

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One of the primary factors determining your card's A.P.R. is your credit score is "True". The correct answer is B.

Credit card issuers evaluate applicants' creditworthiness based on their credit scores, among other factors, and use this information to determine the interest rate they will be charged. Higher credit scores generally result in lower A.P.R.s, reflecting a lower risk profile.

However, it is important to note that the specific A.P.R. offered to an individual may also depend on other factors, such as the card's terms and conditions, the applicant's income, and the card issuer's policies. It is incorrect to assume that most cardholders pay the lowest rate listed when given a range of A.P.R.s, as individual circumstances and creditworthiness vary.

Additionally, higher A.P.R.s do not benefit cardholders, as they result in increased interest charges. The notion that A.P.R.s on credit cards are usually fixed and not adjusted is also incorrect, as A.P.R.s can be variable and subject to change based on various factors.

Therefore, the correct answer is B) One of the primary factors determining your card's A.P.R. is your credit score.

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Note: The question would be as

Reading through a credit card disclosure (aka the Schumer Box), you see the A.P.R. for a specific card is set at 9.99% -23.99%. Which of the following statements is probably TRUE?

a. When given a range of A.PR.s like this, you can assume most cardholders pay the lowest rate listed

b. One of the primary factors determining your card's A.P.R. is your credit score

c. With credit card A.PR.s, cardholders like higher A.P.R.s because they earn more

d. The A.PR. on credit cards is usually fixed so they won't be adjusted as long as you are a cardholder

The movement of voluntary skeletal muscles involved in doing calisthenics is under the control of the somatic nervous system.

The somatic nervous system is responsible for the voluntary control of skeletal muscles. It is a division of the peripheral nervous system that transmits signals from the central nervous system (brain and spinal cord) to the muscles, allowing conscious control over their movements. During calisthenics or any other form of voluntary muscle movement, such as walking, running, or weightlifting, the somatic nervous system plays a key role.

It receives signals from the brain that initiate and coordinate the desired muscle contractions and movements. In contrast, the autonomic nervous system controls involuntary actions and regulates functions such as heart rate, digestion, and breathing. It is further divided into the sympathetic and parasympathetic nervous systems, which have opposing effects on various bodily functions.

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All of the factors listed in options a, b, c, and d are important in determining whether an individual is required to file an income tax return, except for option e, which states that none of the choices are correct.

When determining whether an individual is required to file an income tax return, several factors come into play. The first factor, option a, is the taxpayer's gross income. The Internal Revenue Service (IRS) sets specific income thresholds, and if an individual's gross income exceeds those thresholds, they are generally required to file a tax return.

The second factor, option b, is the taxpayer's filing status. Different filing statuses, such as single, married filing jointly, or head of household, have different income thresholds for filing requirements. Therefore, a taxpayer's filing status is an important consideration in determining whether they need to file a tax return.

The third factor, option c, is the taxpayer's total itemized deductions. Itemized deductions can reduce a taxpayer's taxable income, and if these deductions are substantial, it may affect the requirement to file a tax return.

The fourth factor, option d, is the availability of the additional standard deduction for taxpayers

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Answer:

[tex]\frac{33}{8}[/tex]

Step-by-step explanation:

4.125 = [tex]\frac{4125}{1000}[/tex] because if you take 4125 divided by 1000, you will get 4.125.

Now we simplify the fraction by 125

[tex]\frac{4125}{1000}[/tex]  = [tex]\frac{33}{8}[/tex]

So, the answer is  [tex]\frac{33}{8}[/tex]

The longest item that the student can wrap if the item is positioned diagonally is 15 inches.

Assuming the length, breadth and height of the gift box be 10, 10 and 5 inches respectively. Thus, the diagonal on the base will be calculated using Pythagoras theorem.

Diagonal = ✓(10² + 10²)

Diagonal = ✓200

Diagonal = 14.14 inches

Now, the height is 5 inches and diagonal base is 14.14 inches. Thus, the diagonal equal to longest item will be -

Longest item = ✓(5² + 14.14²)

Longest item = ✓(25 + 200)

Longest item = ✓225

Longest item = 15 inch

Hence, 15 inch item can be positioned diagonally.

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The complete question is -

A student has a gift box that measures 5in by 10in by 10in. The student knows that large items will have to be placed diagonally inside the box. What is the longest item that the student can wrap if the item is positioned diagonally.

A major characteristic of a pure market economy is the absence of government intervention in economic activities. In such an economy, the forces of supply and demand determine the allocation of resources, prices, and production decisions.

In a pure market economy, the government plays a minimal role and does not actively regulate or control economic transactions. The market forces of supply and demand, along with competition among buyers and sellers, shape the economic landscape. Prices are determined by the interactions between consumers and producers, reflecting the relative scarcity of goods and services. Producers have the freedom to set prices based on their costs and profit objectives, while consumers have the autonomy to choose which goods and services to purchase based on their preferences and budget constraints.

Additionally, a pure market economy is characterized by private ownership of resources and means of production. Individuals and private businesses own property, land, capital, and other productive assets. This ownership allows individuals and businesses to make decisions regarding the allocation and use of these resources. The profit motive serves as a driving force, incentivizing individuals and businesses to produce goods and services that are in demand by consumers. Competition among market participants encourages efficiency and innovation, as producers strive to offer better products or services at competitive prices.

However, it is worth noting that in reality, most economies exhibit some level of government intervention, even if they are predominantly market-oriented. Governments often implement regulations to safeguard consumer rights, protect the environment, promote fair competition, and address market failures such as externalities or monopolies. These interventions aim to maintain a balance between the benefits of market forces and the need for social welfare and public interest.

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The kind of meeting described, where LaShonda meets with a family friend to ask questions and gain knowledge about working in the marketing industry, is called an informational interview.

An informational interview is a meeting between a job seeker and a professional in a particular field or industry. It is a way for individuals to gather information, insights, and advice about a specific career path or industry from someone who has first-hand experience. The purpose of an informational interview is to learn more about the industry, gain insights into job roles and responsibilities, and gather information that can help in career planning and decision-making.

In this case, LaShonda is interested in marketing and has arranged to meet with a family friend who works in a marketing firm. During the meeting, LaShonda will have the opportunity to ask price, seek advice, and learn more about the industry from her family friend's perspective.

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The mean number of steps for the particle to return to its starting position is infinite.

To find the mean number of steps for the particle to return to its starting position, we can analyze the probabilities of different outcomes and use the concept of expected value.

Let's consider the situation where the particle is currently at a point on the circle. The probability of moving one step clockwise is 1/2, and the probability of moving one step counterclockwise is also 1/2.

Now, let's define a random variable X as the number of steps it takes for the particle to return to its starting position. We want to find the expected value or mean value of X.

Let's consider the possible outcomes for the first step:

If the particle returns to its starting position in one step, then X = 1.

If the particle moves to an adjacent point (clockwise or counterclockwise), then the problem reduces to a similar but smaller subproblem with one less point on the circle.

In this case, the expected number of additional steps required to return to the starting position is E[X] (the mean value we are trying to find).

Based on the probabilities of moving clockwise or counterclockwise, we can express the expected value of X as:

E[X] = 1 + (1/2) * E[X] + (1/2) * E[X]

The first term "1" represents the case where the particle returns to the starting position in one step. The second term "(1/2) * E[X]" represents the case where the particle moves to an adjacent point and needs additional expected steps to return.

The third term "(1/2) * E[X]" represents the case where the particle moves to the other adjacent point and needs additional expected steps to return.

Simplifying the equation, we get:

E[X] = 1 + (1/2) * E[X] + (1/2) * E[X]

E[X] = 1 + E[X]

Now, solving for E[X], we find:

E[X] - E[X] = 1

0 = 1

This equation is not possible. It implies that the expected value of X is equal to 1, which contradicts the fact that it takes more than one step on average for the particle to return to its starting position.

However, this result suggests that the particle will never return to its starting position with a finite number of steps. This is because the probabilities of moving clockwise and counterclockwise are equal at each step, leading to a symmetrical distribution of positions.

The particle will keep oscillating between different points on the circle, never settling on the starting position.

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The given function, after applying the series of transformations, results in the following equation:

y = -3 * f(3(x + 1)) - 2 * f(2(x - 2)) - 2 - 3 * f(x + 1) + 3 - 3 * |f(x + 2)| - 1 * |f(x)| / 2 - 3

The series of transformations can be summarized as follows:

(1) Compress horizontally by a factor of 3 and translate left 1 unit: f(3(x + 1)).

(2) Compress horizontally by a factor of 2 and translate right 2 units: f(2(x - 2)).

(3) Translate left 2 units and translate down 2 units: f(x + 1) - 2.

(4) Translate right 1 unit and translate up 3 units: -3 * f(x + 2) + 3.

(5) Expand vertically by a factor of 3 and reflect across the x-axis: -3 * |f(x + 2)|.

(6) Translate left 2 units and translate down 3 units: -3 * |f(x + 2)| - 1.

(7) Reflect across the x-axis and translate left 1 unit: -1 * |f(x)| / 2.

(8) Compress vertically by a factor of 2 and translate down 3 units: -1 * |f(x)| / 2 - 3.

The resulting equation combines all these transformations to describe the final function.

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Answer: This can be done in 9C5 ways (9 choose 5), which is calculated as 9!/(5! 4!) = 126 ways.

Scout says the class is suspicious of their first-grade teacher, Miss Caroline Fisher, because she comes from a county in North Alabama that supported the secession of the Confederate States from the Union during the Civil War.

The secession of the Confederate States from the Union during the Civil War refers to the act of Southern states, including Alabama, separating from the United States in order to form their own independent nation. Scout's statement suggests that Miss Caroline Fisher comes from a county in North Alabama that actively supported this secession.

During the Civil War, Alabama was a Confederate state, meaning it sided with the Southern states that seceded from the Union. Many counties within Alabama showed support for the Confederate cause and were known for their allegiance to the Confederacy.

Scout's statement implies that the class views Miss Caroline Fisher's background from a county in North Alabama as a reason for suspicion. The historical context of the Civil War and the divide between the Union and Confederate states likely contribute to the class's skepticism or concern regarding their teacher's origins and potential biases.

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The parks in a large county are classified as either urban or rural depending on their location. The probability it is an urban park is 0.5833.

To find the probabilities, we need to use the total number of parks in each category.

Given:

Number of urban parks = 50

Number of rural parks = 40

Number of urban parks updated with new picnic tables = 35

Number of rural parks updated with new picnic tables = 25

a. Probability of selecting an urban park:

Probability = Number of urban parks updated with new picnic tables / Total number of parks updated with new picnic tables

Probability = 35 / (35 + 25) = 35 / 60 = 7/12 ≈ 0.5833

b. Probability of selecting a rural park:

Probability = Number of rural parks updated with new picnic tables / Total number of parks updated with new picnic tables

Probability = 25 / (35 + 25) = 25 / 60 = 5/12 ≈ 0.4167

Therefore, the probability of selecting an urban park is approximately 0.5833, and the probability of selecting a rural park is approximately 0.4167.

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The expression -25 - 3(10) would give us -55, but it does not take into account the sea lion's greater depth.

To find the expression that represents the sea lion's position in relation to sea level, we need to use the given information that the seal went 25 feet below sea level and the sea lion dove 10 feet less than three times as deep as the seal.
We can start by finding out how deep the sea lion dove. Three times as deep as the seal would be 3 x 25 = 75 feet. Subtracting 10 feet less from that gives us 75 - 10 = 65 feet. This means that the sea lion dove 65 feet below sea level to catch a larger fish.
Therefore, the expression that represents the sea lion's position in relation to sea level is:
-65 feet
We don't need to use any of the other options given as they do not give us the correct answer. The expression 3(25) - 10 would give us 65, but it does not have the negative sign indicating the sea lion's position below sea level. The expression 3(-25) - (-10) would give us -65, but it has the opposite sign indicating the sea lion's position above sea level. The expression -25 - 3(10) would give us -55, but it does not take into account the sea lion's greater depth.

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Answer:

yo

Step-by-step explanation:

its D on edge or 3(–25) – (–10)

i know i helped

ur welcome

Electrical devices can start operating almost immediately after you throw a switch, despite individual electrons taking hours to reach the device, due to the rapid propagation of electric fields in the wire.

When a switch is thrown, completing an electrical circuit, the electric field generated by the voltage source travels through the wire at nearly the speed of light. Although electrons move relatively slowly, the electric field causes the outermost electrons to push the adjacent ones, creating a chain reaction. This flow of charge enables the signal or energy required for device operation to be transmitted rapidly, allowing the device to turn on almost instantly. While individual electrons may take hours to traverse the wire, the swift propagation of electric fields ensures electrical devices begin operating promptly after the switch is thrown.

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The similar triangles formed by the boy and the lamp, indicates that ratio of the length of the shadow of the boy cast by the lamp to the boy's height, indicates;

The length of the shadow cast by the lamp is; 2.4 meters

The angle of elevation  of the lamp from the boy is about 27°

Similar triangles are triangles that have the same shape but may have different sizes.

Part of the question obtained from a similar question on the internet includes;

i) Calculate the length of the shadow of the boy cast by the lamp

ii) The angle of elevation of the lamp from the boy correct to the nearest degree

The length of the shadow can be found using the equivalent ratio of the corresponding lengths of similar triangles as follows;

i) According to the equivalent ratios of the corresponding sides on similar triangles, we get;

The ratio of the length of the shadow of the boy cast by the lamp to the height of the boy is equivalent to the distance from the tip of the shadow to the base of the lamp to the height of the lamp

Let s represent the height of the shadow, we get;

l/1.2 = (6 + l)/4.2

4.2·l = 7.2 + 1.2·l

4.2·l - 1.2·l = 7.2

l·(4.2 - 1.2) = 7.2

l = 7.2/(4.2 - 1.2) = 2.4

The angle of elevation of the lamp from the boy, θ, can be calculated as follows;

tan(θ) = (4.2 - 1.2)/6 = 0.5

θ = arctan(0.5) ≈ 27°

The first part of the question includes the length of the shadow of the boy cast by the lamp

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Answer:

Step-by-step explanation:

Factor to solve.

12a2 + a – 35 = 0

>Multiply the first and the last, 12 and -35

     (12)(-35) = -420

>  Find 2 numbers that multiply to -420 but add to middle term, 1

       -20 and +21 multiply to -420 but adds to 1

>Replace the middle term with -20 and 21

      12a² + a – 35 = 0

       12a² + 20a -  21a – 35 = 0

>Group the first 2 and last 2 terms

      ( 12a² + 20a) (-  21a – 35) = 0

>Take out GCF from each of the groupings

      4a ( 3a + 5) -7(3a + 5) = 0

>Take out GCF (3a + 5)

      ( 4a - 7) ( 3a + 5) = 0

>Set each =0 and solve for a

       ( 4a - 7) = 0                      ( 3a + 5) = 0

          a=7/4                                  a = -5/3

Answer:

£13.35

Step-by-step explanation:

We Know

18 identical phone cases for £240.30

Estimate the cost of one phone case.

We Take

240.30 ÷ 18  = £13.35

So, the cost of one phone case is £13.35

A systemic approach to policy analysis focuses on understanding the underlying conditions causing a public problem, while a symptomatic approach focuses on alleviating shorter term symptoms of the problem.

The systemic approach to policy analysis involves examining the root causes and underlying conditions that contribute to a public problem. It seeks to understand the complex interactions and interdependencies among various factors that give rise to the problem. This approach looks beyond the immediate symptoms and aims to identify long-term solutions by addressing the underlying systemic issues.

On the other hand, the symptomatic approach to policy analysis focuses more on addressing the immediate symptoms or manifestations of a public problem. It aims to provide relief or mitigation for the short-term effects without necessarily delving into the deeper causes. This approach often involves implementing measures or interventions that directly target the visible symptoms of the problem, seeking to alleviate them or minimize their impact.

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Answer:

125.66 cm²

Step-by-step explanation:

area of larger circle = π r²

= π (7)²

= 49π

area of smaller circle = π r²

= π (3)²

= 9π

area of shaded region = 49π  - 9π  

= 40π

= 125.66 cm² to nearest one hundredth

Answer:

125.76 cm²

Step-by-step explanation:

A quick way to do this is to take the radius of the larger circle, R, and then take the radius of the smaller circle, r, and find the difference between the two areas:

[tex]\pi(R^2-r^2)=\pi(7^2-3^2)=\pi(49-9)=40\pi[/tex]

Therefore, the area of the shaded region is 40π cm², or about 125.76 cm².