my cousin when in Vietnam was a personal banker for his Army buddies ... if they needed money mid-month he would give them $20 if you agreed to pay him $40 at month end on payday ... although he did not disclose his borrowing rate, what was the cost of money (APR) for his buddies who needed immediate gratification

The required answer is 350d ≤ 1400.

Given that the distance covered per day 350 miles and the target distance is 1400 miles.

To find the number of days d that they travel to reach a distance of at least 1400 miles by using the formula.

Number of days (d)= target distance/ distance covered per day.

By using given data and formula provides,

Number of days(d)  = 1400/350

Divide both numerator and denominator by 70 gives,

Number of days (d) = 20/5.

Divide both numerator and denominator by 5 gives,

Number of days (d) = 4.

Thus, d = 4.

That implies, 350 × 4 = 1400

Hence, the required answer is 350d ≤ 1400.

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The variance of the random quantity 8X - 48 is approximately 24.32.

To determine the variance of the random quantity 8X - 48, where X is the number of male kittens in the litter, we can use the properties of the binomial distribution.

The random variable X follows a binomial distribution with parameters n = 8 (number of trials) and p = 0.47 (probability of success).

First, let's calculate the mean of 8X - 48:

The mean of 8X - 48 is equal to 8 times the mean of X, minus 48 times the mean of X.

The mean of X follows a binomial distribution with parameters n and p, so the mean of X is given by μ = np.

Therefore, the mean of 8X - 48 is:

E(8X - 48) = 8E(X) - 48E(X) = 8(np) - 48(np) = (8 - 48)np = -40np

Now, let's calculate the variance of 8X - 48:

The variance of 8X - 48 is equal to 8^2 times the variance of X.

The variance of X follows a binomial distribution with parameters n and p, so the variance of X is given by σ^2 = np(1 - p).

Therefore, the variance of 8X - 48 is:

Var(8X - 48) = (8^2)Var(X) = 64np(1 - p)

Substituting n = 8 and p = 0.47 into the formula, we have:

Var(8X - 48) = 64 * 8 * 0.47 * (1 - 0.47)

Calculating the expression:

Var(8X - 48) = 24.32

Rounding the answer to 2 decimal places, the variance of the random quantity 8X - 48 is approximately 24.32.

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One disadvantage of a certificate of deposit (CD) is that you may have to pay a penalty if you withdraw your money before the agreed-upon maturity date. This penalty serves as a deterrent for early withdrawals and can reduce the overall return on your investment.

When you invest in a certificate of deposit, you commit to keeping your money in the account for a fixed period known as the maturity period. If you withdraw your funds before this maturity date, you are likely to incur a penalty fee. The penalty amount can vary depending on the terms and conditions set by the financial institution offering the CD.

This penalty is imposed to discourage premature withdrawals and compensate for the bank's loss of interest income.

The penalty for early withdrawal can have a negative impact on the overall return on your investment. It reduces the amount of interest you will earn and may even result in a partial loss of the principal amount.

Therefore, it is important to carefully consider the maturity period and your financial needs before investing in a certificate of deposit to avoid potential penalties and ensure the best possible return on your investment.

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The circumference of the circle is approximately 69.1 inches.

To find the circumference of a circle, you can use the formula:

Circumference = 2 * [tex]\pi[/tex] * radius

Given that the radius of the circle is 11 inches and π is approximated as 3.14, we can substitute these values into the formula to calculate the circumference:

Circumference = 2 * 3.14 * 11

Circumference = 69.08

Rounding to the nearest tenth, the circumference of the circle is approximately 69.1 inches.

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Paper Company will make the following entry:

Debit: Notes Receivable - Dame Company $4,700

Credit: Accounts Receivable $4,700

What is an entry?

An "entry" in accounting refers to the recording of a financial transaction or event in the company's books or accounting system. It is the process of documenting the impact of a transaction on the financial statements.

1. Debit: Notes Receivable - Dame Company ($4,700) - This account represents the amount owed to Paper Company by Dame Company and is classified as a noncurrent asset since it will be settled in more than one year.

2. Credit: Accounts Receivable ($4,700) - This account represents the open accounts receivable from Dame Company, which is now being settled through the promissory note.

By making this entry, Paper Company acknowledges the receipt of the promissory note and removes the outstanding accounts receivable from their books, replacing it with a notes receivable asset.

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For every cake that Latonya produces, she is giving up the opportunity cost to make 4.5 pies.

Latonya's opportunity cost of producing 1 cake is 4.5 pies.

To find this, we need to look at the ratio of cakes to pies that each person can produce.

Latonya can make 4 cakes or 18 pies in one day, so her ratio is 4 cakes / 18 pies = 0.22 cakes/pie.

Tom can make 8 cakes or 33 pies in one day, so his ratio is 8 cakes / 33 pies = 0.24 cakes/pie.

Since Tom's ratio is higher, it means he is more efficient at making cakes. Therefore, Latonya's opportunity cost of producing 1 cake is giving up 0.22 pies. To find the reciprocal, we divide 1 by 0.22, which equals 4.545. Rounded to one decimal place, this is 4.5 pies.

So for every cake that Latonya produces, she is giving up the opportunity to make 4.5 pies.

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By 1850, the European population could not be accurately estimated using government statistics as such data was not systematically recorded.

In the mid-19th century, the collection of reliable population statistics was not yet standardized across European countries. Therefore, there was limited official data available to provide an accurate assessment of the European population during this period. However, based on estimates and historical records, it is believed that the population surpassed 58 million by 1850. This indicates an upward trend in population growth when compared to earlier figures from 1800.

The population growth was influenced by factors such as declining mortality rates, improvements in healthcare, and advancements in agriculture and industrialization, which contributed to increased food production and reduced famines and epidemics. Although the precise number cannot be determined, it is clear that the European population experienced significant growth during the first half of the 19th century.

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The equation that can be used to determine the number of hours, h, after which Fernando and Brenna will have saved the same amount of money is:  0.3(10 + 4h) = 0.25(6h).

This equation takes into account Fernando's initial $10 fee and his $4 per hour charge, as well as Brenna's $6 per hour charge and their respective savings percentages. Solving for h in this equation will give us the number of hours at which they will have saved the same amount of money.

To understand this better, let's follow these steps:

1. Fernando earns $10 for driving and $4 per hour. So, his total earnings are $10 + 4h.

2. Fernando saves 30% of his earnings, which is 0.3 times his total earnings: 0.3(10 + 4h).

3. Brenna earns $6 per hour, so her total earnings are 6h.

4. Brenna saves 25% of her earnings, which is 0.25 times her total earnings: 0.25(6h).

5. To find when they both save the same amount of money, set the expressions equal to each other: 0.3(10 + 4h) = 0.25(6h).

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Geordi's transition from working for the government to joining an engineering firm that advocates for increased government funding is an example of the "revolving door" phenomenon.

The "revolving door" refers to the movement of individuals between government positions and jobs in the private sector that are closely related to government affairs. In this case, Geordi's shift from a government job to an engineering firm involved in lobbying for government funding reflects this phenomenon.

The revolving door can raise concerns about potential conflicts of interest and the influence of special interest groups on government policies and decisions. While Geordi's move is not inherently unethical or illegal, it highlights the close relationship between government entities and private industries, and the potential for individuals to leverage their expertise and connections for personal or corporate gain.

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Answer:

Step-by-step explanation:

You want an inequality relating the number of 250 lb refrigerators (x) and the number of 425 lb pianos (y) a truck with a 5900 lb load limit can carry. And you want to know if 12 refrigerators and 8 pianos will overload the truck.

The weight of x refrigerators will be 250x. The weight of y pianos will be 425y. Then the restriction on the total weight is ...

  250x +425y ≤ 5900 . . . . . . the load limit of the truck

The weight of 12 refrigerators and 8 pianos will be ...

  250·12 +425·8 = 3000 +3400 = 6400 . . . . pounds

This weight will overload the truck.

__

Additional comment

The graph shows the point (12, 8) is not in the solution space of the inequality. Hence the truck will be overloaded with that load.

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To determine the weight of the stock fund in the minimum variance portfolio, we need to consider the standard deviations of both the stock fund and the bond fund, as well as the correlation between the two funds.

The minimum variance portfolio is a portfolio allocation that minimizes the overall portfolio's volatility or risk. The weight of each asset in the portfolio is determined based on the standard deviations of the assets and their correlation.

The formula to calculate the weight of an asset in the minimum variance portfolio is:

Weight of asset = (Standard deviation of other asset / Standard deviation of asset + Standard deviation of other asset) * (1 - Correlation)

In this case, the stock fund has a standard deviation of 16% and the bond fund has a standard deviation of 4%. The correlation between the two funds is 0.11.

To calculate the weight of the stock fund, we plug in the values into the formula:

Weight of stock fund = (4% / (16% + 4%)) * (1 - 0.11)

= (0.04 / 0.20) * (0.89)

≈ 0.178

Therefore, the weight of the stock fund in the minimum variance portfolio is approximately 17.8%.

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The fraction of girls in the class who have long brown hair, we need to calculate the fraction of brown-haired girls who have long hair.

- Fraction of girls with brown hair: 4/5

- Fraction of brown-haired girls with long hair: 1/4

To find the fraction of girls with long brown hair, we multiply the fractions:

(4/5) * (1/4) = 4/20 = 1/5

Therefore, 1/5 of the girls in the class have long brown hair.

Part 2:

The fraction of girls in the class who have long brown hair and green eyes, we need to calculate the fraction of girls with long brown hair who also have green eyes.

- Fraction of girls with long brown hair: 1/5

- Fraction of girls with long brown hair who have green eyes: 2/3

To find the fraction of girls with long brown hair and green eyes, we multiply the fractions:

(1/5) * (2/3) = 2/15

Therefore, 2/15 of the girls in the class have long brown hair and green eyes.

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The number of different ordered 3-tuples, where each item is an element of set A, can be determined by calculating the Cartesian product of set A with itself three times.

In general, the Cartesian product of two sets A and B is the set of all possible ordered pairs where the first element is from set A and the second element is from set B. Extending this concept to three sets, the Cartesian product will consist of ordered triples.

To find the number of different ordered 3-tuples, we need to consider the cardinality (number of elements) of set A. Let's denote the cardinality of A as n.

The number of different ordered 3-tuples can be calculated as n raised to the power of 3, since each position in the tuple can be filled with any element from set A. In other words, it is equivalent to finding the number of combinations with repetition.

Therefore, the number of different ordered 3-tuples is n^3.

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The described phenomenon is known as the "inflationary spiral" or "wage-price spiral," where there is a feedback loop between inflation expectations, wage negotiations, and actual inflation.

The inflationary spiral is a concept that describes a self-reinforcing cycle between inflation expectations, wage negotiations, and actual inflation.

It begins with the central bank, such as the Federal Reserve (Fed), announcing a target inflation rate for the future, such as 3 percent.

People, anticipating this inflation rate, factor it into their wage negotiations, demanding higher wages to maintain their purchasing power.

However, the central bank may have an incentive to increase inflation above the announced target rate.

By doing so, they aim to reduce real wages, which are wages adjusted for inflation, in order to stimulate economic growth. This occurs because higher inflation erodes the purchasing power of wages, effectively lowering real wages.

With lower real wages, employers can afford to hire more workers or invest in capital, leading to increased economic activity.

The cycle continues as workers, observing higher inflation rates than anticipated, demand further wage increases in response. This puts pressure on employers to raise prices to cover higher labor costs, leading to an increase in overall inflation.

As a result, the central bank may again respond by raising inflation rates to maintain control over the economy.

The inflationary spiral highlights the complex relationship between inflation expectations, wage negotiations, and actual inflation.

It demonstrates how the actions and reactions of both individuals and central banks can influence and perpetuate inflationary trends.

Managing inflation expectations and striking a balance between inflation and economic growth are key challenges for central banks in maintaining stability in the economy.

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2,3-DPG is produced in anaerobic respiration in red blood cells and plays a key role in regulating oxygen transport to tissues with high oxygen demands. Option b is the correct answer.

2,3-DPG, also known as 2,3-diphosphoglycerate, is a small molecule that plays an important role in regulating the oxygen-carrying capacity of red blood cells.

It is produced in red blood cells through the process of anaerobic respiration, which occurs in the absence of oxygen. During anaerobic respiration, glucose is broken down into pyruvate, which is then converted into lactate and ATP. As a byproduct of this process, 2,3-DPG is produced in red blood cells.

The production of 2,3-DPG is a crucial adaptation that allows red blood cells to efficiently transport oxygen to tissues with high oxygen demands, such as the brain and heart.

2,3-DPG binds to hemoglobin, the protein in red blood cells that carries oxygen, and decreases its affinity for oxygen. This allows hemoglobin to release oxygen more easily in tissues with low oxygen levels.

Therefore, the correct option is b.

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Juliet spends 7 hours coaching lacrosse each day and 17 hours coaching field hockey each day.

(a) Let's define the variables:

Let x be the number of hours Juliet coaches lacrosse.

Let y be the number of hours Juliet coaches field hockey.

According to the given information, we can set up the following system of equations:

Equation 1:

x + y = 24 (total coaching hours)

Equation 2:

y = 2x + 3 (field hockey practice lasts 3 hours more than twice the time she coaches lacrosse)

(b) To solve the system of equations, we can use the substitution or elimination method. Let's use substitution in this case:

From Equation 2, we have:

y = 2x + 3

Substitute this value of y into Equation 1:

x + (2x + 3) = 24

3x + 3 = 24

3x = 24 - 3

3x = 21

x = 21/3

x = 7

Now, substitute the value of x back into Equation 2 to find y:

y = 2(7) + 3

y = 14 + 3

y = 17

Therefore, Juliet spends 7 hours a day coaching lacrosse and 17 hours a day coaching hockey.

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The correct hypotheses for this test are:

H0: There is no association between grade level and whether the student makes their bed in the morning.

Ha: There is an association between grade level and whether the student makes their bed in the morning.

In statistical hypothesis testing, we set up two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis represents the default assumption of no effect or no relationship, while the alternative hypothesis represents the opposite or what we are trying to prove.

These hypotheses state that there is no relationship or association between grade level and whether the student makes their bed in the morning (null hypothesis), while the alternative hypothesis suggests that there is an association between these two variables.

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A(n) example is a specific case that is utilized to illustrate a broader concept, and it can take the form of factual occurrences, hypothetical scenarios, or personal experiences.

Examples operate as concrete proof that makes it easier to understand and put into practice abstract ideas. They offer concrete or fictitious examples that exemplify a broad topic, making it more straightforward for others to understand and relate to the underlying notion.

Examples make complex theories or concepts more understandable and relatable, promoting effective communication and improved comprehension across various subjects and disciplines.

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The form of supervision that requires frequent meetings between the client and probation officer is regular-supervision probation.

Regular-supervision probation typically involves a moderate level of supervision for individuals who have been placed on probation. It requires frequent meetings between the client (the probationer) and their probation officer. These meetings serve as a means of monitoring the client's progress, addressing any issues or concerns, and providing guidance and support.

The frequency of these meetings may vary depending on the specific terms of probation and the individual's circumstances. In some cases, it could involve weekly or biweekly meetings, while in others, monthly meetings may be sufficient.

Regular-supervision probation strikes a balance between providing support and accountability to ensure that the individual adheres to the terms of their probation while also allowing them the opportunity for rehabilitation and reintegration into society.

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The coterminal angles within the range 0° ≤ θ < 360° are -423°, -23° and 337°.

Since -783° is negative, it lies in the clockwise direction means it falls in the fourth quadrant.

The reference angle is 423°.

The coterminal angle, quadrant and reference angle for the rotation of -783°, we can use the following calculations:

Coterminal Angle:

To find a coterminal angle, we need to add or subtract multiples of 360° to the given angle until we obtain an angle within the range of 0° to 360°.

-783° + 360° = -423°

-783° + 2 × 360° = -23°

-783° + 3 × 360° = 337°

The coterminal angles within the range 0° ≤ θ < 360° are -423°, -23° and 337°.

Quadrant:

To determine the quadrant in which the angle lies, we can observe the sign of the angle:

Reference Angle:

The reference angle is the acute angle between the terminal side of the angle and the x-axis.

To find the reference angle, we can calculate the positive equivalent of the angle within one revolution (360°).

The positive equivalent of -783° can be found by adding 360° repeatedly until we obtain a positive angle:

-783° + 360° = -423° (already found as a coterminal angle)

The positive equivalent of -783° is -423°.

The reference angle is the absolute value of the positive equivalent:

Reference angle = |-423°| = 423°

The coterminal angles are -423°, -23°, and 337°.

The angle -783° falls in the fourth quadrant.

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The probability of getting a sum of 9 or higher when rolling two dice is 10/36, which can be simplified to 5/18 or approximately 0.2778.

For the probability that the sum of two fair six-sided dice is 9 or higher, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes when rolling two dice is given by 6 * 6 = 36, as each die has 6 possible outcomes.

Now, let's determine the number of favorable outcomes. We need to find the combinations of numbers on the two dice that result in a sum of 9 or higher.

The possible combinations for a sum of 9 are (3, 6), (4, 5), (5, 4), and (6, 3), which gives us 4 favorable outcomes.

The possible combinations for a sum of 10 are (4, 6), (5, 5), and (6, 4), which gives us 3 favorable outcomes.

The possible combinations for a sum of 11 are (5, 6) and (6, 5), which gives us 2 favorable outcomes.

Finally, the possible combination for a sum of 12 is (6, 6), which gives us 1 favorable outcome.

Adding up the favorable outcomes, we have 4 + 3 + 2 + 1 = 10.

Therefore, the probability of getting a sum of 9 or higher when rolling two dice is 10/36, which can be simplified to 5/18 or approximately 0.2778.

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In the context of companies navigating an uncertain future, those who take the existing total industry structure and its future trajectory as given and decide where to compete are known as "strategic planners."

Strategic planners are entities that assess the prevailing industry structure and dynamics, acknowledging the uncertainty of the future but assuming that the industry will largely follow its expected trajectory. They carefully analyze the competitive landscape, including market conditions, customer preferences, technological advancements, and regulatory factors. By doing so, they identify areas where they can leverage their strengths and capabilities to outperform rivals.

Strategic planners understand that the industry structure may evolve over time due to various factors, such as technological disruptions, changing consumer behavior, or new market entrants. However, rather than attempting to reshape the industry or disrupt the status quo, they focus on identifying specific market segments or niches where they can excel within the existing industry framework.

These companies or individuals strategically position themselves by capitalizing on their unique strengths, whether it's cost leadership, differentiation through product innovation, superior customer service, or efficient supply chain management. They align their resources, capabilities, and competitive strategies to effectively compete in the chosen segments, while recognizing the need to adapt and evolve as the industry landscape changes.

By accepting the industry's structure and future trajectory as given, strategic planners mitigate risks associated with attempting to reshape the market or betting on uncertain outcomes. Instead, they concentrate their efforts on optimizing their performance within the existing industry context, thereby maximizing their chances of success in an uncertain future.

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In a joint venture, the parties typically combine their labor or property for a single undertaking and share profits and losses equally. They assume no personal liability beyond the risk of losing their initial investment.

A joint venture is a business arrangement where two or more parties come together to pursue a specific business project or goal. The nature of the joint venture and the rights and responsibilities of the parties involved can vary based on the terms outlined in the joint venture agreement.

In the context of the provided options, the correct answer is option b: "combine their labor or property for a single undertaking and share profits and losses equally." This means that the parties involved in the joint venture pool their resources, such as labor, expertise, or capital, for a specific project or venture. They share both the profits and losses resulting from the undertaking in an equal manner.

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The balance on the Jacksons' mortgage when they retire, one year from today, will depend on several factors such as the loan amount, interest rate, repayment term, and their monthly mortgage payments.

To determine the balance on their mortgage when they retire, we need more specific information about the Jacksons' mortgage terms. The loan amount, interest rate, and repayment term will all play a crucial role in calculating the remaining balance.

Assuming the Jacksons take out a fixed-rate mortgage with a specific loan amount, interest rate, and repayment term, we can estimate the monthly mortgage payments using an amortization schedule. The monthly payments will consist of both principal and interest portions. Over time, the principal portion will gradually increase, while the interest portion will decrease.

If the Jacksons make regular monthly payments for one year, a portion of each payment will go towards reducing the principal balance. However, without knowing the specific mortgage terms, it is difficult to provide an exact balance at retirement. The Jacksons' mortgage balance will depend on their monthly payments and the remaining term on the loan at the time of their retirement.

It is important for the Jacksons to consult with their mortgage lender or use a mortgage calculator to determine their remaining balance at retirement. By considering their current mortgage details and projecting the payments made until retirement, they can obtain a more accurate estimate of the balance on their mortgage when they retire.

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Organizational politics can be triggered by various factors, including scarce resources in the workplace and clear and specific resource allocation decisions. The correct option is (C):Organizational politics is triggered  by scarce resources in the workplace.

However, it is not necessarily limited to these factors alone. Organizational politics can also arise in organizations that support altruism, where individuals may compete for recognition and resources to further their own goals or agendas. Even in the presence of formal rules and regulations, organizational politics can still occur as individuals seek to advance their own interests within the organization. Therefore, it is important for leaders to be aware of the potential for organizational politics and take steps to mitigate its negative effects.

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To calculate the amount of plywood Trenton will need to buy, we need to find the total surface area of the ramp.

The triangular prism consists of two triangular sides and three rectangular sides.

Triangular sides:

The base of each triangular side is 2 feet, and the height is 1.5 feet.

The area of one triangular side is given by:

Area of triangle = (1/2) * base * height

Area of one triangular side = (1/2) * 2 feet * 1.5 feet = 1.5 square feet

Since there are two triangular sides, the total area of the triangular sides is:

Total area of triangular sides = 2 * 1.5 square feet = 3 square feet

Rectangular sides:

The dimensions of the rectangular sides are as follows:

1) 3 feet by 2 feet

2) 3 feet by 2.5 feet

3) 3 feet by 1.5 feet

The area of each rectangular side is given by:

Area of rectangle = length * width

Calculating the areas of the rectangular sides:

Area of rectangular side 1 = 3 feet * 2 feet = 6 square feet

Area of rectangular side 2 = 3 feet * 2.5 feet = 7.5 square feet

Area of rectangular side 3 = 3 feet * 1.5 feet = 4.5 square feet

Adding up the areas of the rectangular sides:

Total area of rectangular sides = 6 square feet + 7.5 square feet + 4.5 square feet = 18 square feet

Total surface area of the ramp:

To find the total surface area, we add the area of the triangular sides to the area of the rectangular sides:

Total surface area = Total area of triangular sides + Total area of rectangular sides

                 = 3 square feet + 18 square feet

                 = 21 square feet

Therefore, Trenton will need to buy 21 square feet of plywood to cover all the faces of the ramp.

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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

Answer:

Step-by-step explanation: