Robert has a contrainer in the shape of a cube with an edge length of 6.1 cm

The polynomial expression that represents the volume of the box is V = w⁴ - 4w³ + 3w².

Given, the width of the box = w inches
Length of the box = ( w² - 3 ) inches
Height of the box = ( w - 1 ) inches
The polynomial expression that represents the volume of the box is given by:V = l × w × h
V = ( w² - 3 ) × w × ( w - 1 )
V = w × ( w² - 3 ) × ( w - 1 )
Multiplying the polynomial expressions,V = w⁴ - 4w³ + 3w²

The conclusion is, the volume of the box can be represented by the polynomial expression V = w⁴ - 4w³ + 3w², where w is the width of the box.

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The total balance on March 1, the next billing date is 2712$.

Given that The average daily balance of your credit card for the month of February was $2,350 and the unpaid balance at the end of the month is $2,665. If the monthly interest rate is 2.0% of the average daily balance.

The interest rate is applied to the average daily balance (ADB).ADB = 2350$

Interest rate= 2%

Monthly interest on the average daily balance = 2/100 * 2350= 47$

Balance at the end of the month = 2665$

Balance for the next billing date = Balance at the end of the month + Interest on the average daily balance = 2665+47 = 2712$

Therefore, the total balance on March 1, the next billing date is 2712$.

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La function f(x) = x^2 - 1 se puede evaluar para los valores de x desde -3 hasta 3 sustituyendo cada valor en la expresión y calculando el resultado. Aquí están los cálculos para cada valor:

Para x = -3: f(-3) = (-3)^2 - 1 = 9 - 1 = 8

Para x = -2: f(-2) = (-2)^2 - 1 = 4 - 1 = 3

Para x = -1: f(-1) = (-1)^2 - 1 = 1 - 1 = 0

Para x = 0: f(0) = (0)^2 - 1 = 0 - 1 = -1

Para x = 1: f(1) = (1)^2 - 1 = 1 - 1 = 0

Para x = 2: f(2) = (2)^2 - 1 = 4 - 1 = 3

Para x = 3: f(3) = (3)^2 - 1 = 9 - 1 = 8

Entonces, los valores de la function f(x) = x^2 - 1 para x En el rang de -3 a 3 son: 8, 3, 0, -1, 0, 3, 8 respectivamente.

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A ​4-ft vertical post casts a 10​-in shadow at the same time a nearby cell phone tower casts a 120​-ft shadow. The height of the cell phone tower is 576 ft.

To calculate the height of the cell phone tower, we will use proportions. We know that the height of the 4-ft post is proportional to the height of the cell phone tower. The ratio of the heights will be the same as the ratio of their shadows. This gives us the following proportion:

height of post / length of post shadow = height of cell phone tower / length of cell phone tower shadow

Let's plug in the given values and solve for the height of the cell phone tower:

4 ft / 10 in = height of cell phone tower / 120 ft

First, we need to convert the units to be consistent. Let's convert 4 ft to inches:4 ft = 48 in

Now, we can substitute the values and solve for the height of the cell phone tower:

48 in / 10 in = height of cell phone tower / 120 ft4.8

= height of cell phone tower / 120 ftheight of cell phone tower

= 4.8 * 120 ft

height of cell phone tower = 576 ft

Therefore, the height of the cell phone tower is 576 ft.

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To find the value of c such that the polynomial p(x) is divisible by (x - 4), we can use the remainder theorem. According to the theorem, if p(x) is divisible by (x - a), then p(a) = 0. Therefore, we need to find the value of c such that p(4) = 0.

Let's assume the polynomial p(x) is given by p(x) = ax^2 + bx + c.

To find the value of c, we substitute x = 4 into the polynomial and set it equal to 0:

p(4) = a(4)^2 + b(4) + c = 0

16a + 4b + c = 0

Since we want the polynomial to be divisible by (x - 4), we need p(4) to be equal to 0.

Therefore, we can set up the equation:

16a + 4b + c = 0

Solving this equation will give us the value of c.

Answer: The value of c can be found by solving the equation 16a + 4b + c = 0.

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The reaction of 2.00 mol of oxygen with gaseous ammonia produces a certain amount of nitrogen monoxide gas. The moles of nitrogen monoxide produced can be calculated using stoichiometry.

To determine the moles of nitrogen monoxide produced, we need to use the balanced chemical equation for the reaction between gaseous ammonia (NH₃) and oxygen (O₂):

4 NH₃ + 5 O₂ → 4 NO + 6 H₂O

From the balanced equation, we can see that 4 moles of NH₃ react with 5 moles of O₂ to produce 4 moles of NO. This means that the ratio between O₂ and NO is 5:4.

Given that we have 2.00 mol of O₂, we can set up a proportion to calculate the moles of NO produced:

(2.00 mol O₂) / (5 mol O₂) = (x mol NO) / (4 mol NO)

Cross-multiplying the equation, we get:

5x = 8

Solving for x, we find that x = 8/5 = 1.6 mol NO.

Therefore, the moles of nitrogen monoxide produced by the reaction of 2.00 mol of oxygen is 1.6 mol NO.

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b = -15.

Thus, for any value of a = 6 and b = -15, any value of x would be a solution of the equation 3(2x-5) = ax + b.

To find the values of a and b for which any value of x would be a solution of the equation 3(2x-5) = ax + b, we need to consider the properties of the equation.

In the equation 3(2x-5) = ax + b, the left side represents a linear expression that simplifies to 6x - 15. We can equate this to the right side, ax + b.

So, we have the equation 6x - 15 = ax + b.

For any value of x to be a solution, the left side and the right side of the equation should always be equal, regardless of the value of x.

To achieve this, we need the coefficients of x to be equal on both sides of the equation. This means that the coefficient of x on the left side (which is 6) should be equal to the coefficient of x on the right side (which is a).

Therefore, a = 6.

Additionally, the constant term on the left side (-15) should be equal to the constant term on the right side (which is b).

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27 heartbeats in 15 seconds is equivalent to 108 heartbeats in 60 seconds or 81 heartbeats in 45 seconds.

Yes, 27 heartbeats in 15 seconds are equivalent to 81 heartbeats in 60 seconds.

This is because the heart rate per minute is calculated by multiplying the heart rate per second by 60, which is the number of seconds in a minute.

Let's look at the calculations below:

Heart rate in 15 seconds = 27

Heart rate in 1 second = 27 / 15

Heart rate in 60 seconds (1 minute) = ( 27 / 15 ) x 60 = 1620 / 15

Heart rate in 60 seconds (1 minute) = 108

Therefore, 27 heartbeats in 15 seconds is equivalent to 108 heartbeats in 60 seconds or 81 heartbeats in 45 seconds.

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The function that represents the amount of money the student saves after x months is y = 12x + 15.

In the given scenario, the student initially has $15. Every month, the student saves an additional $12. This means that the amount of money saved after x months can be calculated by multiplying the number of months (x) by the monthly savings of $12 and adding the initial amount of $15. Therefore, the function y = 12x + 15 represents the amount of money (y) the student saves after x months. For example, after 3 months, the student would have saved $12 * 3 + $15 = $51. The function allows for easy calculation of the savings based on the number of months elapsed.

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The mean height of the players on the girls' basketball team, rounded to the nearest whole number, is 68 inches.

The mean height of the players on the girls' basketball team, rounded to the nearest whole number, is X inches.

To find the mean height, we sum up the heights of all the players and divide it by the total number of players.

Given the heights of the players: 66, 68, 69, and 70 inches, we can calculate the mean height.

66 + 68 + 69 + 70 = 273

Next, we divide the sum of the heights by the total number of players, which is 4 in this case.

273 / 4 = 68.25

Rounding the mean height to the nearest whole number, we get X = 68 inches.

Therefore, the mean height of the players on the girls' basketball team, rounded to the nearest whole number, is 68 inches.

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The required potters purchased 33 cans of Pepsi.

The potters purchased a total of 50 cans of soda.

34% of the purchased soda was Coke.

To find the number of cans of Pepsi purchased, we need to subtract the number of Coke cans from the total number of cans.

Number of Coke cans = 34% of 50 cans = 0.34 * 50 = 17 cans

Number of Pepsi cans = Total number of cans - Number of Coke cans

Number of Pepsi cans = 50 cans - 17 cans

Number of Pepsi cans = 33 cans

Therefore, the potters purchased 33 cans of Pepsi.

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In a quadrilateral inscribed in a circle, the angles formed by the intersection of opposite sides are supplementary because they are subtended by the same arc. This property holds true for any inscribed quadrilateral, including ABCD in circle O.

To prove that in a quadrilateral inscribed in a circle, its opposite angles are supplementary, we can use the properties of angles in a circle.

Given: Quadrilateral ABCD is inscribed in circle O.

To prove: ∠ABC and ∠ADC are supplementary (add up to 180 degrees).

        ∠DAB and ∠DCB are supplementary (add up to 180 degrees).

Proof:

1. Inscribe quadrilateral ABCD in circle O.

2. The opposite sides of a quadrilateral inscribed in a circle are subtended by supplementary angles.

3. Therefore, ∠ABC and ∠ADC are supplementary.

4. Similarly, ∠DAB and ∠DCB are supplementary.

5. Thus, the theorem is proven.

In a quadrilateral inscribed in a circle, the angles formed by the intersection of opposite sides are supplementary because they are subtended by the same arc. This property holds true for any inscribed quadrilateral, including ABCD in circle O.

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C(76.1) represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

The function C(F) = (5/9)(F - 32) is used to convert temperatures from degrees Fahrenheit to degrees Celsius. In this case, the input of the function is 76.1, which represents the temperature in degrees Fahrenheit. By substituting this value into the function, we can calculate the corresponding temperature in degrees Celsius.

To convert 76.1 degrees Fahrenheit to degrees Celsius, we plug it into the function: C(76.1) = (5/9)(76.1 - 32). By performing the necessary calculations, we can find the value of C(76.1), which represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. Therefore, the correct answer is the first option: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.


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The question asks about the recovery time for a randomly selected patient from a surgical procedure. This recovery time follows a normal distribution with a mean of 4 days and a standard deviation of 1.9 days.

To answer questions about probabilities or specific values of the recovery time, we can use the properties of the normal distribution.

Standardize the variable: Convert the recovery time value (X) into a standard score or z-score using the formula: z = (X - μ) / σ, where μ is the mean and σ is the standard deviation.

Use the standard normal distribution table or a calculator to find the corresponding probability or value associated with the standardized z-score.

For example, if you want to find the probability that a randomly selected patient has a recovery time less than a certain number of days (X), you would calculate the z-score, look up the corresponding probability in the standard normal distribution table, and round the answer to four decimal places.

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The article about endangered species occupies approximately 1/2 of the cover page.

To determine the portion of the cover page occupied by the article about endangered species, we need to calculate the product of the fractions representing the text and photographs.

First, we find the portion of the cover page occupied by text: 3/8.

Next, we find the portion of the text occupied by photographs: 2/3.

To find the portion of the cover page occupied by the article about endangered species, we multiply these two fractions: (3/8) * (2/3) = 6/24 = 1/4.

Therefore, the article about endangered species occupies 1/4 of the cover page, which is equivalent to 1/2 when simplified.

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The transformation used for this problem is given as follows:

90° clockwise rotation.

The five more known rotation rules are given as follows:

Comparing A with A', B with B', C with C' and D with D', the rule used in this problem is given as follows:

(x, y) -> (y, -x).

Hence the rotation is given as follows:

90° clockwise rotation.

The image is missing, however we can look at the coordinates to obtain the rule.

The equivalent vertices are:

(-5,5) and (5,5).

Hence we just identify the transformation rule from these two vertices.

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[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-13\\ d=4\\ n=27 \end{cases} \\\\\\ a_{27}=-13+(27-1)4\implies a_{27}=-13+104\implies a_{27}=91[/tex]

It is not sensible to measure a football pitch in nanometres because they  are extremely small units of length which are typically used to measure particles or atomic structures.

Nanometres are a billion times smaller than a meter making them unsuitable for measuring macroscopic objects like a football pitch. Football pitches are typically measured in meters or yards which provide a more appropriate scale for their size.

Nanometres are better suited for measuring things on a molecular or atomic level such as the size of nanoparticles or the spacing between atoms. Attempting to measure a football pitch in nanometres would not only be impractical but also misleading as it would not accurately reflect the dimensions of the pitch in a meaningful way.

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When a store advertises sales on different combinations of goods, they are engaging in price discrimination. In this case, the holiday store is practicing second-degree price discrimination because it has different prices for different quantities of bows and wrapping paper.

According to the signs in the store, there are two different deals on bows and rolls of wrapping paper. One sign says that one bow and one roll of wrapping paper can be purchased for $6.00. This means that the store is offering a bundle deal that gives a discount if you purchase both items together. The second sign offers five bows and one roll of wrapping paper for $10.00.

This means that the store is offering an even larger discount for customers who purchase a larger quantity of bows.The fact that the store is offering different prices based on the quantity of goods purchased is an example of price discrimination. Specifically, the store is practicing second-degree price discrimination because it is offering different prices for different quantities of goods.

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SO, 3 is the value of x and y for triangle RSTU.Given, RSTU and MNOP are similar triangles. We are to find the scale factor of RSTU to MNOP and then find the values of x and y.

In similar triangles, the ratio of the corresponding sides are equal.

Let us find the scale factor of RSTU to MNOP by comparing the corresponding sides.

Scale factor RSTU to MNOP = RT/MN

We have RT = 4x - 10, and

MN = 2x + 5.

So,RT/MN = (4x - 10) / (2x + 5)

= 2(2x - 5) / (2x + 5)

The scale factor of RSTU to MNOP is 2(2x - 5) / (2x + 5).

For x and y, we need to find the value of x and y for triangle RSTU.

Let us write the corresponding sides and their ratios.

RT/PN

= 4x - 10 / 2y + 3RS/MP

= 6x - 7 / 4y - 5RU/PO

= 5x - 7 / 4y + 2

Since RSTU and MNOP are similar, the ratio of corresponding sides should be equal.

Hence,

4x - 10 / 2y + 3

= 6x - 7 / 4y - 54x - 10 * 4y - 5

= 2y + 3 * 6x - 7 * 4y - 54x - 10 * 4y - 5 + 2y + 3 * 4y - 5

= 6x - 7 * 2y + 3-8y - 15

= 6x - 14y - 4y - 8y - 15 - 3

= 6x - 14y - y-8y - 18

= 6x - 15y

Simplifying further,

6x - 15y + 8y

= 18 + 8y - 15y6x - 7y

= 3

This is the value of x and y for triangle RSTU.

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For a distribution that is skewed right, the median is typically less than the mean and is located to the left of the distribution's peak.

It represents the middle value when the data is arranged in ascending order and is less affected by extreme outliers compared to the mean. The median provides a measure of central tendency that is more representative of the "typical" value in a positively skewed distribution.

In a skewed right distribution, the tail of the distribution extends towards the higher values. This indicates that there are relatively more lower values and fewer higher values in the dataset. As a result, the mean is pulled towards the higher values, making it larger than the median.

The median, on the other hand, represents the middle value in the dataset when arranged in ascending order. It is less sensitive to extreme outliers compared to the mean because it focuses on the middle value rather than the overall distribution. Therefore, in a skewed right distribution, the median tends to be smaller than the mean and is located to the left of the peak of the distribution.

The use of median in a skewed right distribution helps provide a more robust measure of central tendency, as it is less influenced by extreme values and better represents the typical value in the data.

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Matilda paid to have the bike checked out for 9 hours. Answer: 9 hours.

Let x be the number of hours Matilda rented the bike.Therefore, the equation which expresses the given problem is:12 + 6x = 66

Rent is the sum of money that a tenant or lessee pays a landlord or lessor in return for the right to use and occupy a building or other asset. It is often a recurrent payment made on a regular period, as defined in a rental agreement or lease contract, such as monthly, quarterly, or annually.

Although it also applies to businesses, offices, and other assets, rent is most frequently linked with residential buildings like apartments or homes. Typically, criteria including location, size, condition, amenities, and market demand decide the rent amount. Rent gives tenants the right to use and enjoy the rented space while generating cash for property owners.

We need to solve for x, so isolate x on one side of the equation.12 + 6x = 66 → subtract 12 from both sides.6x = 54 → divide both sides by 6.x = 9

Therefore, Matilda paid to have the bike checked out for 9 hours. Answer: 9 hours.

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Histograms and summary statistics are tools used to summarize and analyze data. They provide a visual representation and numerical summary of the distribution of a variable or set of data.

In the context of baseball players and their number of hits in a season, histograms and summary statistics can help identify patterns, measure central tendency, and assess the variability of the data. To summarize the data using histograms and summary statistics for the number of hits in the season by baseball players in two leagues, follow these steps:

Collect the data on the number of hits for each player in each league.

Create separate histograms for each league, with the number of hits on the x-axis and the frequency or count of players on the y-axis. The histograms will visually represent the distribution of hits in each league.

Calculate summary statistics for each league, including measures of central tendency (such as mean or median) and measures of variability (such as standard deviation or range). These statistics will provide numerical summaries of the data for each league.

Compare the histograms and summary statistics between the two leagues to identify any differences or similarities in the number of hits by baseball players.

Use the histograms and summary statistics to gain insights into the performance and distribution of hits in each league, potentially identifying league-specific trends or patterns.

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Given, Completing one house always takes 200 days of labor. To find, Let the time taken by one person to complete one house be 't' days. We know that; Work = Time × Rate of Work

The work required to complete one house is 1 (as they need to construct only one house).The rate of work is the number of houses constructed by all the people in one day. Therefore, if 'n' people are working, then their combined rate of work is 1/200.

We have only one person working here, so his rate of work is 1/t.

Therefore, we get;1/200 = 1/t

⇒ t = 200

Therefore, it will take one person 200 days to complete one house.

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In order to determine the number of cars that were residents with a Green Key and the number of cars parked without the Green Key, we will use the following formula:

Let x be the number of residents with a Green Key who parked. Let y be the number of cars that parked without a Green Key.

We can set up two equations based on the information given in the problem:

x + y = 10,867 (the total number of cars parked in the lot)  

9x + 20y = 169,820 (the total amount of money collected)

Solve for x using the first equation:

x + y = 10,867

x = 10,867 - y

substitute this value for x in the second equation

and solve for y:

9x + 20y = 169,8209(10,867 - y) + 20y

= 169,82097,803 - 9y + 20y

= 169,82011y

= 72,017y

= 6557.909

We can round this number to 6558 since you cannot park a fraction of a car.

So, approximately 6558 cars are parked without a Green Key.

To find the number of residents with a Green Key who parked, we can substitute y = 6558 into the equation:

x + 6558 = 10,867x

= 10,867 - 6558x

= 4309

So, approximately 4309 cars parked that were residents with a Green Key, while approximately 6558 cars parked without the Green Key.

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Answer:

the answer is D

Step-by-step explanation:

A. since 2 is greater than -4, this is not correct

B. since -1/3  is greater than -1/6, this is also not correct

C. Here, 3/10 = 0.3 and 1/4 = 0.25 so since 0.3 is greater than 0.25, this is not correct

D.Here, the order is correct since -11/2<-0.75<-0.25<11/2

E.Here, -3/4 is greater than -3, so this order is also not correct

It will take Julia and Natalie 9 hours to be 162 miles apart.

The two women left the coffee shop at the same time, but went in opposite directions.

One of the easiest ways to solve this problem is to figure out how far apart they move in one hour, and then calculate how long it will take them to move 162 miles apart.

The distance that they move apart in one hour is simply the sum of the distances that they each travel,

or: Distance apart after 1 hour = (6 mph + 12 mph) x 1 hour = 18 miles/hour

This tells us that they move 18 miles further apart for each hour that passes.

To find out how many hours it will take for them to be 162 miles apart, we need to divide the total distance they need to move apart (162 miles) by the distance they move apart each hour (18 miles/hour):

Time until 162 miles apart = 162 miles ÷ 18 miles/hour

= 9 hours

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Rounded to the nearest tenth of a gram, the amount of the original sample that is still radioactive after half an hour is approximately 17.7 grams.

To model the decay of carbon-11 over time, we can use the exponential decay formula A = A₀ * (1/2)^(t/h), where A is the amount remaining, A₀ is the initial amount, t is the time elapsed, and h is the half-life. In this case, the initial amount is 50 grams and the half-life is 20 minutes. Using this model, we can determine the amount of carbon-11 remaining after a half-hour (30 minutes). Using the exponential decay model A = A₀ * (1/2)^(t/h), we can calculate the amount of carbon-11 remaining after a certain time. For a half-life of 20 minutes, the equation becomes A = 50 * (1/2)^(t/20). To find the amount remaining after half an hour (30 minutes), we substitute t = 30 into the equation:

A = 50 * (1/2)^(30/20)

A = 50 * (1/2)^(3/2)

A = 50 * (√1/2)^3

A = 50 * (√1/8)

A = 50 * (1/2√2)

A = 25/√2

To determine the decimal value of the amount remaining, we can approximate √2 as 1.414. Therefore:

A ≈ 25/1.414 ≈ 17.68 grams

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To make each pair of radicals similar by reducing the radicand, we need to simplify the radicands to their lowest terms. Simplifying radicals involves finding the largest perfect square factor of the number under the radical sign and rewriting it. Let's take an example:

Pair 1: √50 and √32

To make these radicals similar, we simplify the radicands:

√50 = √(25 × 2) = 5√2

√32 = √(16 × 2) = 4√2

Now, both radicals have the same simplified radicand, which is √2. The pair becomes 5√2 and 4√2, making them similar.

Similarly, you can apply the same process to any other pairs of radicals, simplifying the radicands to their lowest terms and making the pairs similar by having matching simplified radicands.

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The upthrust on the object would be 5N.

Given data:

One quarter of the object is submerged under water, the volume of water displaced is one quarter of the object's total volume.

According to Archimedes' principle, the upthrust is equal to the weight of the water displaced.

Weight of the fluid displaced = (1/4) * Weight of the object

= (1/4) * 20N

= 5N.

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