The graph of y = f(x) is shown below. Find the value of f(3).
10
-10-9-8-7-6-5-4-3-2-1
9
8
7
6
10 + 120
5
4
3
2
1
5
-1
-2
-3
-4
-5
-6
-8
-9
-10
ο
11
2 3
4
5 6 7 8 9 10
pls help!!

22! / 20! × 2!

[tex]21 \times 11 = 231 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

The library is 8 kilometres away from Bree's residence.

1. The equation represents the total travel time of 2 hours.

2. Bree's speed on her way to the library is 6 mph, so the time taken for this part is x/6 hours.

3. Bree's speed on her way home is 12 mph, so the time taken for this part is x/12 hours.

4. Adding the time taken for both parts, we get the equation: x/6 + x/12 = 2.

5. This equation can be solved to find the value of x, which represents the distance from Bree's house to the library.

6. Simplifying the equation further, we have (2x + x)/12 = 2.

7. Combining like terms, we get 3x/12 = 2.

8. Multiplying both sides by 12, we have 3x = 24.

9. Dividing both sides by 3, we find that x = 8.

10. Therefore, the distance from Bree's house to the library is 8 miles.

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Job sharing is the name for this type of arrangement as Annette and Nathan share their work at Wood Grove Elementary.

A job share arrangement is a full-time of work of  job  and it is split between two individuals, each with responsibility for the success of the total job. Work sharing, sometimes known as work sharing, is a work arrangement in which two persons, or occasionally more, are kept on a part-time or reduced-time basis to carry out tasks that are typically completed by one person working full-time of job.

As a result, there is a net decrease in per-employee income. The individuals who share the job are jointly accountable for the workload of the shared job and work together to fulfill the task.

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a) The pressure at the exit of the turbine can be determined using the isentropic expansion process and the ideal gas model.

b) The work out of the turbine per kilogram of oxygen flowing can be calculated using the ideal gas equation and the temperature and pressure changes during the expansion process.

a) To determine the pressure at the exit, we can use the isentropic expansion process, which assumes no heat transfer and reversible adiabatic conditions. Using the ideal gas model, we can apply the relationship between temperature and pressure for an isentropic process:

P1 / [tex]T2^(γ)[/tex] = P2 / [tex]T2^(γ)[/tex]

where P1 and T1 are the initial pressure and temperature, P2 is the pressure at the exit, T2 is the temperature at the exit, and γ is the specific heat ratio of the gas.

b) The work out of the turbine per kilogram of oxygen flowing can be calculated using the ideal gas equation for a steady-state process:

Work = ∫(Cp × dT)

where Cp is the specific heat at constant pressure. By integrating the equation with respect to temperature from the initial to final states, and assuming constant Cp, we can calculate the work.

The specific values of γ and Cp will depend on the gas being used (oxygen in this case). Using the given initial and final conditions, the specific values of γ and Cp for oxygen, and the equations mentioned above, we can calculate the pressure at the exit and the work out of the turbine per kilogram of oxygen flowing.

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On a demand curve for most goods, as the price of the product decreases, the number of units the customer is willing to buy increases.

The relationship between price and quantity demanded is a fundamental concept in economics and is typically represented by a demand curve. According to the law of demand, as the price of a product decreases, the quantity demanded by customers tends to increase, and vice versa. This inverse relationship between price and quantity demanded can be attributed to various factors.

When the price of a product decreases, it becomes more affordable for consumers, leading to an increase in their willingness to purchase it. Lower prices may also create a perception of greater value or incentivize customers to buy more of the product. Conversely, as the price of a product increases, consumers may find it less affordable or less attractive, resulting in a decrease in their willingness to buy.

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The correct option is A. Although births are less likely on the weekends, births are more than twice as likely during the week.

The doctor's null hypothesis was that babies are equally likely to be born any day of the week. The alternative hypothesis was that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday).

The chi-square test statistic for goodness of fit is χ2 = 12.95 and the P-value is between 0.025 and 0.05. Because the P-value is less than 0.05, the doctor rejects the null hypothesis.

The follow-up analysis shows that the observed counts are significantly different from the expected counts. The observed counts are more than twice as large as the expected counts for weekdays and less than half as large as the expected counts for weekends. This suggests that the doctor's alternative hypothesis is correct.

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Locks and conditionals enable agents to proceed independently based on their conditions, creating a realistic simulation of ticket-selling scenarios.

a) When all agents try to sell the 40 tickets simultaneously without any synchronization mechanism like semaphores, the threads of each agent to sell the tickets will exhibit randomness. This randomness arises due to the nature of concurrent execution where the order of execution and access to shared resources (tickets in this case) is non-deterministic.

Since the threads are running concurrently, the order in which they access and sell the tickets can vary on each execution. It is possible that some agents may sell their tickets quickly, while others may take more time. This randomness can be attributed to factors such as thread scheduling, resource contention, and the timing of each agent's operations.

b) Using lock and unlocking of threads with synchronization mechanisms ensures that each agent starts and finishes selling its allocated 40 tickets before the next agent starts selling. This eliminates the randomness observed in the previous scenario.

By utilizing locks, an agent acquires the lock before starting to sell tickets and releases it after completing the sale of its allocated tickets. This ensures exclusive access to the shared resource (tickets) for each agent, preventing multiple agents from accessing and selling tickets simultaneously. As a result, the execution order becomes deterministic, and each agent sells its tickets sequentially.

c) To simulate real conditions where one agent may be occupied (e.g., stuck on the phone) while others continue selling tickets, a lock and unlocking mechanism can be used along with conditional statements or signaling.

Agents acquire the lock and check if it is their turn to sell tickets. If an agent is stuck or unable to sell, it releases the lock, allowing other agents to proceed. This way, the other agents can continue selling tickets while the stuck agent waits for an opportunity to sell. Once the agent is ready, it acquires the lock again and resumes ticket sales.

Therefore, this approach simulates a scenario where agents can proceed independently as long as they acquire the lock and meet the conditions to sell tickets, providing a more realistic representation of real-world situations.

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The area of the quilt is 1127/20 square feet. This can also be written as a mixed number, which would be 56 7/20 square feet.

To find the area of the quilt, we need to multiply the width by the length. Let's calculate it step by step:

Width: 9 4/5 ft. We can convert the mixed number to an improper fraction by multiplying the whole number (9) by the denominator (5) and adding the numerator (4). Then we divide the result by the denominator.

9 * 5 = 45. 45 + 4 = 49.

So, the width is 49/5 ft.

Length: 5 3/4 ft. We can convert the mixed number to an improper fraction using the same method.

5 * 4 = 20. 20 + 3 = 23.

So, the length is 23/4 ft.

Now, we can calculate the area:

Area = Width * Length.

Area = (49/5 ft) * (23/4 ft).

To multiply fractions, we multiply the numerators together and the denominators together:

Area = (49 * 23) / (5 * 4) ft².

Area = 1127/20 ft².

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The missing lengths are:

AB= 7.211 unit

CD = 5.83 unit

EF = 10.77 unit

GH = 6.088 unit

Using Pythagoras Theorem we get

AB² = 6² + 4²

AB² = 36 + 16

AB² = 52

AB= 7.211

Again, CD²= 5² + 3²

CD² = 25 + 9

CD = 5.83

Again, EF² = 10² + 4²

EF² = 100 + 16

EF² = 116

EF = 10.77

and, GH² = 6² + 1²

GH² = 36 + 1

GH² = 37

GH = √37

GH= 6.088

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The term that best describes this scenario is "self-fulfilling prophecy."

This is because a self-fulfilling prophecy occurs when an individual believes something to be true, and as a result, they act in ways that cause that belief to become reality. In this case, the individual's father had always told them that they had mechanical abilities, which led the individual to believe that they were good at fixing things.

However, when they tried to fix their bike for the first time and failed miserably, this experience could reinforce the belief that they are not good at mechanical tasks. This could lead to the individual avoiding mechanical tasks in the future, further reinforcing the belief that they are not good at them. Therefore, it is important to recognize self-fulfilling prophecies and try to break the cycle by challenging negative beliefs and trying new things to build confidence and competence.

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Answer:

Step-by-step explanation:

Answer is in the pic...

Using the formula for gravitational force on Mars, determine the weight of the astronaut on the surface of Mars, which is approximately 358.6 N.

To calculate the weight of the astronaut on the surface of Mars, we can use the formula for gravitational force:

[tex]F = (G * m_1 * m_2) / r^2[/tex]

Where:

F is the gravitational force,

G is the gravitational constant (approximately [tex]6.67430 * 10^{-11} N m^2/kg^2[/tex]),

[tex]m_1[/tex] is the mass of the astronaut,

[tex]m_2[/tex] is the mass of Mars,

and r is the radius of Mars.

Mass of Mars ([tex]m_2[/tex]) = [tex]6.39 * 10^{23} kg[/tex]

Radius of Mars (r) = 3376.2 km = 3,376,200 meters

Weight on Earth = 950 N

950 N = (G * mass of the astronaut * mass of Earth) / radius of Earth^2

mass of the astronaut = (950 N * radius of Mars^2 * mass of Mars) / (radius of Earth^2 * mass of Earth)

[tex]F = (G * m_1 * m_2) / r^2[/tex]

First, let's convert the radius of Mars from kilometers to meters:

r = 3,376,200 meters

Next, we can rearrange the formula to solve for m1:

[tex]m_1 = (F * r^2) / (G * m_{2})[/tex]

[tex]m_1 = (950 N * (3,376,200 m)^2) / ((6.67430 * 10^{-11} N m^2/kg^2) * (6.39 * 10^{23 }kg))\\m_1 = 78.656 kg[/tex]

Weight on Mars =[tex](G * m_1 * m_2) / r^2[/tex]

Weight on Mars = [tex](6.67430 * 10^{-11}N m^2/kg^2) * 78.656 kg * \frac{ (6.39 * 10^{23} kg)}{(3,376,200 m)^2}[/tex]

Weight on Mars ≈ 358.6 N

Therefore, the weight of the astronaut on the surface of Mars would be approximately 358.6 N.

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Cognitive and behavioral approaches to treatment view psychopathology as the result of faulty thought patterns and faulty learning and environmental experiences.

Cognitive and behavioral approaches to treatment in psychology emphasize the role of cognition, thought patterns, and learned behaviors in the development and maintenance of psychopathology. These approaches posit that faulty or distorted thinking, as well as maladaptive behaviors learned through environmental experiences, contribute to psychological disorders.

Cognitive approaches, such as cognitive therapy, focus on identifying and challenging irrational or negative thoughts and beliefs that contribute to emotional distress. By helping individuals recognize and restructure their cognitive patterns, these approaches aim to improve emotional well-being and reduce symptoms of psychopathology.

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The surface area of the triangular prism is 684 cm²

Now,

Using the formulas

A=2[tex]A_{b}[/tex] + (a+b+c)h

[tex]A_{b}[/tex] = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

s=a+b+c/2

s= Semi-perimeter

a, b, c = Base sides of the triangle.

Solving for A,

A=( ah + bh + ch )+1/2[tex]\sqrt{-a^{4} +2(ab)^2+2(ac)^2-b^4+2(bc)^2 - c^4}[/tex]

Substitute the values,

A = ( 12 × 16 + 9 × 16 + 15 × 16  ) + 1/2[tex]\sqrt{- 12^4 + 2 (12 * 9 )^2 + 2(12 * 15)^2 - 9^4 + 2(9*15)^2 - 15^4}[/tex]

A = 684 cm².

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CosA in simplest radical form will be 4/√97

Given,

Right angled triangle with right angle at C.

Perpendicular = 9

Base = 4

Hypotenuse = √97

Now trigonometric functions are formulated as,

SinA = P / H

CosA = B / H

TanA = P / B

To find CosA,

CosA = Base / Hypotenuse

CosA = 4 / √97

Thus all the trigonometric functions can be found out.

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The type of data collected by the postal worker counting the number of complaint letters received by the United States Postal Service in a given day is quantitative discrete data.

Quantitative data refers to numerical data that can be measured or counted. In this case, the postal worker is counting the number of complaint letters, which is a numerical value.

Discrete data refers to values that can only take on specific whole numbers, in this case, the count of complaint letters. Since the number of complaint letters is a countable value and does not take on fractional or continuous values, it falls under the category of discrete data.

The data collected by the postal worker represents the quantity of complaint letters received and can be used for further analysis and statistical interpretation.

Therefore, the data collected by the postal worker, which counts the number of complaint letters received by the United States Postal Service in a day, is categorized as discrete quantitative data.

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Hello !

Answer:

[tex]\Large \boxed{\sf r=\frac{3}{2} }[/tex]

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

[tex]\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2[/tex]

Let's solve this equation for r.

First, substract [tex]\sf 2\pi r^2[/tex]  from both sides :

[tex]\sf \frac{4}{3} \pi r^3-2\pi r^2=0[/tex]

We can now factorize by taking out the highest common factor: 2r²

[tex]\sf 2r^2(\frac{2}{3} \pi r-\pi )=0[/tex]

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

Given 2000 unique customers and 500,000 fielded units, the total number of warranty claims can be calculated based on the assumption of a constant failure rate.

To calculate the total number of warranty claims, we need to determine the average number of claims per unit. Given that there are 2000 unique customers and each customer owns one unit, the average number of claims per unit can be calculated as the total number of claims divided by the number of units.

If we assume a constant failure rate, we can use the concept of failure rate (λ) to calculate the average number of claims per unit.

Average number of claims per unit = Number of claims / Number of fielded units = 2000 / 500,000

Once the average number of claims per unit is calculated, the total number of claims can be obtained by multiplying it by the total number of units:

Total number of claims = Average number of claims per unit × Number of fielded units

By performing the calculation, you will find the total number of warranty claims based on the given information.

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Answer: $9095.44

Step-by-step explanation:

Given:

P=7380

r=1.9% = .019

t= 11

V = P[tex]e^{rt}[/tex]                               >substitute

V = 7380 [tex]e^{(.019)(11)}[/tex]              >Plug into calculator

V= $9095.44

Suburban living encourages walking, riding bicycles, and other kinds of physical activity. The design of suburban neighborhoods often includes sidewalks, bike lanes, and recreational spaces.

Suburban living tends to promote walking, riding bicycles, and engaging in various forms of physical activity. The design of suburban neighborhoods often includes sidewalks, providing residents with opportunities to engage in active transportation and outdoor activities. The lower population density and typically quieter streets in suburban areas can create a safer and more pleasant environment for walking and biking.

Additionally, suburban neighborhoods may feature parks, trails, and green spaces that encourage residents to engage in physical activities such as jogging, hiking, or playing sports. These factors contribute to a lifestyle that encourages physical movement and promotes a healthier and more active way of living in the suburbs.

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The character invented by Lorde to narrate the poem can be referred to as a persona.

In the context of the given question, Lorde, the poet, invents a character or voice to narrate the poem. This character serves as a representation of the speaker or the point of view from which the poem is presented. By creating a persona, Lorde can express emotions, thoughts, or experiences that may or may not align with her own.

The use of a persona allows poets to experiment with different voices and engage the reader in a more immersive and expressive manner. It adds depth and complexity to the poem by introducing a distinct character that brings the words to life. Through this technique, poets can explore various themes, perspectives, and narratives, providing a richer and more engaging experience for the reader.

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Martin has read 40% of the book, he had 12 more pages to finish then the book had 20 pages.

The number of pages read by Martin = 40% of the total pages in the book

⇒ Number of pages left to be read by Martin = (100-40) % of the total                                pages

                                                                              = 60% of the total pages

Let the total number of pages in the book = x

Hence, we need to find the value of 'x'

We are given that 12 pages are left to be read

∴ 60% of x = 12

⇒ [tex]\frac{60x}{100}[/tex]=12

⇒ x=[tex]\frac{1200}{60}[/tex]

⇒ x = 20 pages

∴ The total number of pages in the book is 20.

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It will take Paris two hours to catch up with Helen.

Suppose Paris catches up with Helen after x hours, and in that time Paris travels d kilometers. Then, since Helen has a 4-km head start, Helen travels d + 4 kilometers in x hours. We can write a distance formula for each person as follows:

Distance covered by Helen = 6x + 4 (since Helen is traveling at 6 kph)

Distance covered by Paris = 8x (since Paris is traveling at 8 kph)

Since they will be at the same distance when Paris catches Helen, we can set both these equations equal. Solving for x, we get:

6x + 4 = 8x

2x = 4

x = 2

We can also verify our answer by finding the distance they each travel over the two hours. Since Paris is traveling at 8 kph for two hours, he will travel a distance of 16 km. Since Helen has a 4-km head start and is traveling at 6 kph for two hours, she will travel a distance of (6 x 2) + 4 = 16 km. This confirms that Paris has caught up with Helen after two hours.

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The one-year forward rate is the exchange rate at which two currencies are expected to be traded in the future, specifically after one year.

In this case, we need to calculate the one-year forward rate between the British pound and the US dollar, given the spot exchange rate and the expected interest rates.

To calculate the one-year forward rate, we can use the interest rate parity (IRP) formula, which states that the forward exchange rate should equal the spot exchange rate multiplied by the ratio of the interest rates between the two countries.

Mathematically, it can be represented as:

Forward rate = Spot rate x (1 + Foreign Interest Rate) / (1 + Domestic Interest Rate)

In this scenario, the spot exchange rate is 1.82 dollars per sterling pound. The British interest rate is expected to be 2%, while the US interest rate is expected to be 3%.

Plugging these values into the formula, we can calculate the one-year forward rate:

Forward rate = 1.82 x (1 + 0.02) / (1 + 0.03) = 1.82 x 1.02 / 1.03 = 1.80 dollars per sterling pound.

Therefore, the one-year forward rate between the British pound and the US dollar is expected to be 1.80 dollars per sterling pound.

This implies that the market expects the British pound to depreciate slightly against the US dollar over the next year.

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The Israeli-Palestinian conflict is a complex and long-standing dispute between Israelis and Palestinians over land and political rights. It originated from conflicting nationalist aspirations and the establishment of the State of Israel in 1948.

The conflict has resulted in numerous wars, violence, and ongoing tensions in the region. Resolving the conflict requires addressing key issues such as the status of Jerusalem, borders, the right of return for Palestinian refugees, and the establishment of a viable Palestinian state. International efforts, including peace negotiations and diplomatic initiatives, have been made to find a peaceful solution to the conflict.

The Israeli-Palestinian conflict stems from the clash between Jewish and Palestinian nationalist aspirations and the establishment of the State of Israel in 1948. Both Israelis and Palestinians lay claim to the same land, which has led to territorial disputes and competing narratives. The conflict has been characterized by periods of violence, including wars and terrorist attacks, resulting in loss of life and widespread suffering for both sides. The status of Jerusalem, a city considered holy by multiple religions, has been a major point of contention, with both Israelis and Palestinians asserting their rights to control it.

To reach a resolution, key issues need to be addressed. One of the major points of contention is the establishment of borders that are acceptable to both parties. The borders established after the 1948 war, commonly referred to as the Green Line, have been a subject of dispute. Additionally, the issue of the right of return for Palestinian refugees, who were displaced during the establishment of Israel, is crucial for Palestinians seeking justice and recognition. Another critical aspect is the creation of a viable Palestinian state, which would provide self-governance and sovereignty to the Palestinian people.

International efforts to resolve the conflict have been ongoing for decades. These efforts include peace negotiations mediated by third parties, such as the United States, and initiatives by regional and international organizations. The Oslo Accords in the 1990s aimed to establish a framework for peace and the creation of a Palestinian state but encountered challenges and setbacks. The conflict remains a highly complex and deeply rooted issue, requiring continued diplomatic efforts and political will from all parties involved to achieve a lasting resolution and a just and peaceful coexistence between Israelis and Palestinians.

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In the rescorla-wagner model, the symbol "λ" (lambda) refers to the limit of the amount of associative strength or learning that may occur.

What is Rescorla Wagner model?

Rescorla-Wagner model is a classical conditioning model which tries to establish a the relationship or association between the CONDITIONED STIMULI (CS) AND THE UNCONDITIONED STIMULI.

According to the Rescorla-Wagner model, proves that for learning to occur the subject must be surprised which means the subject must not expect it(AN UNEXPECTED US FOLLOWS A CS).

In the Rescorla-Wagner model, the symbol "V" (or sometimes referred to as "V_max") indicates the limit or maximum value of associative strength or learning that can occur between a conditioned stimulus (CS) and an unconditioned stimulus (US). This symbol represents the maximum strength or magnitude of association that can be formed during classical conditioning.

According to the Rescorla-Wagner model, learning occurs when there is a discrepancy or prediction error between expected and actual outcomes. As learning progresses, associative strength increases but eventually reaches a point of saturation or maximum value (V). This maximum value represents the point at which the association has reached its peak and further learning becomes unlikely or minimal.

Briefly, the “V” in the Rescorla-Wagner model represents an upper limit or ceiling on the amount of associative strength or learning that can be achieved between the CS and the US.

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i. After 6 years, the amount in the bank account with annual compounding will be $4,238.51.

ii. After 6 years, the amount in the bank account with quarterly compounding will be $4,243.06.

iii. After 6 years, the amount in the bank account with monthly compounding will be $4,245.97.

iv. After 6 years, the amount in the bank account with continuous compounding will be $4,246.93.

To calculate the future amount in the bank account after 6 years with different compounding frequencies, we can use the formula for compound interest: A =[tex]P(1 + r/n)^(nt)[/tex], where A is the future amount, P is the principal amount, r is the interest rate, n is the compounding frequency per year, and t is the number of years.

i. With annual compounding: A = [tex]3000(1 + 0.06/1)^(16)[/tex] = $4,238.51.

ii. With quarterly compounding: A = [tex]3000(1 + 0.06/4)^(46)[/tex]= $4,243.06.

iii. With monthly compounding: A = [tex]3000(1 + 0.06/12)^(126)[/tex] = $4,245.97.

iv. With continuous compounding: A = [tex]3000e^(0.066)[/tex] = $4,246.93 (using the formula A = Pe^(rt) where e is the base of the natural logarithm).

These calculations demonstrate how the compounding frequency affects the growth of the investment over time, with more frequent compounding resulting in slightly higher future amounts.

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I would not agree with an article that claimed a “majority” of people think that critical thinking should be taught in schools based solely on an online poll of 810 adults.

The poll may suffer from sampling bias, have a margin of error, and fail to capture the full range of perspectives on the topic.

While the poll indicates that 53% of the respondents think critical thinking should be taught, it does not necessarily represent the entire population or provide a comprehensive view of public opinion.

The online poll was conducted among 810 adults, but the sample may not be representative of the broader population.

It's important to consider factors such as the demographic composition, geographic distribution, and methodology used to select participants.

The margin of error associated with the poll should also be considered.

A sample size of 810 is relatively small, and depending on the methodology used, there may be a margin of error that affects the precision of the results.

The article should ideally mention the margin of error to provide a clearer understanding of the data's reliability.

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Recent observations, such as the cosmic microwave background radiation and large-scale galaxy surveys, have confirmed the isotropy of the universe on a large scale.

One of the key assumptions in Einstein's equations of general relativity was the isotropy of the universe, meaning that it appears the same in all directions. In recent years, observational evidence has supported this assumption.

The cosmic microwave background radiation (CMB) is one of the crucial pieces of evidence supporting the isotropy of the universe. The CMB is a faint radiation that permeates the entire universe and is considered the remnant of the Big Bang. Observations of the CMB have revealed that it is remarkably isotropic, exhibiting almost uniform temperature in all directions with very slight fluctuations. This uniformity suggests that the early universe was also isotropic.

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The total develop a product  amount capitalized for the patent through March 31, 2020, is $557,000.

To the total amount capitalized for the patent through March 31, 2020,  the research and development costs, the costs associated with obtaining the patent, and the legal fees for defending the patent.

The research and development costs incurred by Chan Resources to develop the product amount to $280,000. These costs are eligible for capitalization.

The costs associated with obtaining the patent total $97,000. These costs are also eligible for capitalization.

The legal fees paid for the successful Defense of the patent amount to $180,000. These fees are considered direct costs of maintaining and defending the patent and are also eligible for capitalization.

To calculate the total amount capitalized for the patent through March 31, 2020,

Research and development costs: $280,000

Costs associated with obtaining the patent: $97,000

Legal fees for defense: $180,000

Total amount capitalized for the patent through March 31, 2020:

$280,000 + $97,000 + $180,000 = $557,000

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