A man is trapped in a room at the center of a maze. The room has three exits. Exit 1 leads outside the maze after 3 minutes, on average. Exit 2 will bring him back to the same room after 5 minutes. Exit 3 will bring him back to the same room after 7 minutes. Assume that every time he makes a choice, he is equally likely to choose any exit. What is the expected time taken by him to leave the maze?Hint: Let X = time taken by the man to leave the maze from this room. Let Y = exit he chooses first. So Y belongs in { 1,2,3} Calculate the conditional expectation of time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of time taken to leave the maze.

The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.

To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.

Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.

Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).

We can use the formula for conditional probability to verify our answer:

P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)

P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)

P(sum is 7) = 6/36 = 1/6

So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.

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The angle of x in the given circle is 51 degrees.

In the case when a tangent line and a secant line originate from the same external point, the mean of the exterior angle is equal to half the difference between the major arc and the minor arc that are created by the tangent and secant lines.

From the given figure we observe that the secant line and tangent line start from the same exterior angle.

Thus, according to the theorem of secant and tangent line of circle we have:

angle x = (DA - DB) /2

angle x = (178 - 76) / 2

angle x = 102 /2

angle x = 51 degrees.

Hence, the angle of x in the given circle is 51 degrees.

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In response to the stated question, we may state that therefore, the expressions value of vector will be n = 25.73.

An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

to find vector and magnitude we have

[tex]n^2 = (22.5)^2 + (12.5)^2\\n^2 = 506.25 + 156.25\\n^2 = 662.5\\n = \sqrt(662.5)\\n = 25.73[/tex]

therefore, the value of vector will be n = 25.73.

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Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.

Let's start by defining our variables. Let x be the number of cups of espresso sold and y be the number of cups of cappuccino sold. We know that the price of espresso is $2 per cup and the price of cappuccino is $2.50 per cup. We also know that Destiny sold 30 more cups of cappuccino than espresso and the total sales amount was $178.50.

Using this information, we can create a system of equations to solve for x and y. The first equation comes from the fact that Destiny sold 30 more cups of cappuccino than espresso:

y = x + 30

The second equation comes from the total sales amount:

2x + 2.5y = 178.5

Now we can substitute the first equation into the second equation and solve for x:

2x + 2.5(x + 30) = 178.5

2x + 2.5x + 75 = 178.5

4.5x = 103.5

x = 23        

So Destiny sold 23 cups of espresso. Using the first equation, we can find that she sold 53 cups of cappuccino:

y = x + 30

y = 23 + 30    

y = 53

Therefore, Destiny sold 23 cups of espresso and 53 cups of cappuccino on Friday, for a total sales amount of $178.50.

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The probability of drawing an ace and a queen from a pack of cards without replacement is 1/78. This can be explained as follows:

In a standard pack of 52 cards, there are 4 aces and 4 queens. When two cards are drawn without replacement, the probability of drawing an ace and then a queen is 4/52 x 3/51 = 12/2652. This can be simplified to 1/78.

Without replacement means that the card that is drawn is not replaced in the deck before the next card is drawn. In this case, when the first card is an ace, there are only 3 queens left in the deck so the probability of the second card being a queen is 3/51.

To put it another way, the chances of drawing an ace and a queen when the cards are drawn without replacement can be thought of as a ratio of the favorable outcomes to the total number of possible outcomes. There is only one favorable outcome (ace-queen) out of a total of 78 possible outcomes (4 aces and 4 queens combined with the remaining 44 cards). Thus, the probability of drawing an ace and a queen is 1/78.

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Answer: B

Step-by-step explanation: because

The pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay is represented in dollars per hour, and it ranges from $12 per hour for a new employee in a low-level position to $60 per hour for a senior developer with extensive experience.

For example, if we look at the table created in part a, we can see that a junior developer with less than a year of experience will earn $18 per hour, while a senior developer with more than 10 years of experience will earn $60 per hour. This means that the pay at the Digital Source is directly related to the employee's experience and job position.

Additionally, the table also shows that the pay rate increases as the employee gains more experience and moves up the career ladder. For instance, a junior developer with less than a year of experience will earn $18 per hour, but a mid-level developer with 3-5 years of experience will earn $35 per hour. This shows that employees are rewarded for their skills and experience, and they have the opportunity to advance their careers and earn higher pay rates.

In summary, the pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay rate ranges from $12 per hour to $60 per hour, and it increases as the employee gains more experience and moves up the career ladder. The company values the skills and expertise of their employees and rewards them accordingly.

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Ashley's tower is 30 centimeters taller than Mason's tower. Ashley's tower is 10 x (1/10) = 1 meter tall. Mason's tower, on the other hand, is 7 x (1/10) = 0.7 meters tall.

Ashley's tower is 10 blocks high and each block has a height of 0.1 meters since 1 meter is divided into 10 equal parts. Therefore, the total height of Ashley's tower is 10 x 0.1 = 1 meter. Mason's tower, on the other hand, is 7 blocks high and has a total height of 7 x 0.1 = 0.7 meters. The difference between Ashley's tower and Mason's tower is the height of Ashley's tower minus the height of Mason's tower, which is 1 meter - 0.7 meters = 0.3 meters. To convert meters to centimeters, we need to multiply by 100, so Ashley's tower is 0.3 x 100 = 30 centimeters taller than Mason's tower.

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The prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.

The binοmial distributiοn is a prοbability distributiοn that describes the number οf successes in a fixed number οf independent trials, each with the same prοbability οf success. The distributiοn is characterized by twο parameters: the number οf trials (n) and the prοbability οf success (p) fοr each trial.

Tο sοlve this prοblem, we need tο use the binοmial distributiοn since we have a fixed number οf trials (25 animals brοught in) and each trial (animal) can either be a success (needs tο stay οvernight) οr a failure (dοesn't need tο stay οvernight).

Let X be the number οf animals that need tο stay οvernight. Then X fοllοws a binοmial distributiοn with n = 25 trials and p = 0.2 prοbability οf success (animal needing tο stay οvernight).

We want tο find the prοbability that mοre than 2 animals need tο stay οvernight, which can be expressed as:

nοw, P(X > 2) = 1 - P(X ≤ 2)

Tο calculate P(X ≤ 2), we can use the binοmial cumulative distributiοn functiοn (CDF) οr simply add up the prοbabilities οf X = 0, X = 1, and X = 2:

similarly, P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

[tex]= (0.8)^{25} + 25(0.2)(0.8)^{24} + (25\ \text{choose}\ 2)(0.2)^{2}(0.8)^{23}[/tex]

≈ 0.0876

Therefοre, P(X > 2) = 1 - P(X ≤ 2) ≈ 1 - 0.0876 = 0.9124

Sο the prοbability that mοre than 2 animals need tο stay οvernight is apprοximately 0.9124, οr 91.24%.

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Answer:

Step-by-step explanation:

3x^16

Answer:

3x^16

Step-by-step explanation:

the range of the function is at least $400 plus $50 for each month after the purchase. The average monthly cost of owning the cell phone can be represented as:

C(t) = 400 + 50t

Where t is the number of months after the purchase.

Since C(t) is a linear function, its range is all real numbers greater than or equal to 400, since the initial cost of the phone is 400 and the monthly cost is a positive constant. Therefore, the range of C(t) is:

Range of C(t) = {C(t) | C(t) ≥ 400} or [400, ∞)

In other words, the range of the function is all possible average monthly costs of owning the phone, which is at least $400 plus $50 for each month after the purchase.

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The sum of the matrices A and C from the list of options is the matrix B

Given the following matrices

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

To find the sum of matrices A and C, we add the corresponding elements in each matrix:

So, we have: A + C

| 0 - 2  6 + 5  2 + 3 |

| 1 - 1    5 - 7  -2 + 3|

Evaluate the sum

| -2  11  5 |

| 0   -2  1 |

This represents option B

Therefore, the sum of matrices A and C is (B)

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Complete question

What is the sum of A+C?

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

Answer: 63.8

Step-by-step explanation:

Yes, the given values constitute a possible bootstrap sample from the original sample.

Bootstrap samples are taken with replacement from the original data set. In other words, it means that each sample consists of a random sample of the same size as the original data set taken from the original data set.

Hence, a given set of values can be a bootstrap sample from the original sample as long as the values are randomly selected from the original sample and with replacement.

The sample is said to be a bootstrap sample from the original data set if it satisfies the following properties:

1. The bootstrap sample must be of the same size as the original data set.

2. Each observation from the original data set must have an equal chance of being selected in each bootstrap sample.3. The bootstrap samples must be independent of each other.

In the given problem, the sample consists of 5 values, namely 84, 71, 79, 96, and 87.

These values can be a bootstrap sample from the original sample as long as the values were randomly selected with replacement from the original sample.

Since the problem does not provide any information on how the sample was obtained, it cannot be determined whether or not it is a bootstrap sample.

Therefore, the answer is that the given values constitute a possible bootstrap sample from the original sample.

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Answer:

Step-by-step explanation:

(g * h)(24)

gh*24

24gh

Answer:

0.01 cm/min

Step-by-step explanation:

The volume of oil in the tank is given by the formula:

V = l × w × h

where l, w, and h are the length, width, and height of the tank respectively.

Substituting the given values, we get:

V = 60 cm × 100 cm × 100 cm = 600,000 cm³

The rate at which the oil is being lost is given as 3.6 litres per hour. Since 1 litre = 1000 cm³, we can convert this to cubic centimeters per hour as follows:

3.6 litres/hour × 1000 cm³/litre = 3600 cm³/hour

To find the rate at which the oil level is falling, we need to divide the rate of oil loss by the surface area of the oil in the tank. Since the tank is rectangular and has a flat bottom, the surface area of the oil is simply the area of the top of the tank, which is:

A = l × w = 60 cm × 100 cm = 6000 cm²

Now, we can calculate the rate at which the oil level is falling as follows:

rate of oil loss ÷ surface area of oil = (3600 cm³/hour) ÷ (6000 cm²)

= 0.6 cm/hour

To convert this to cm/min, we simply divide by 60:

0.6 cm/hour ÷ 60 min/hour = 0.01 cm/min

Therefore, the rate at which the oil level is falling is 0.01 cm/min

Answer:

1/20

Step-by-step explanation:

because you turn the denominators to 40, then subtract walk from run and you got your answer

The probability P(Xˉ−2<114<Xˉ+2) is approximately 0.95. (Option 3)

We know that the population mean is 114 and the standard deviation is 6. We also know that the sample size is 36, which is large enough to apply the central limit theorem. Thus, the distribution of sample means follows a normal distribution with a mean of 114 and a standard deviation of 6/√36=1.

Now, we need to calculate the z-score for the lower and upper bound of the inequality.

z1=(114-2-114)/1=-2

z2=(114+2-114)/1=2

Using a standard normal distribution table, we can find that the area to the left of -2 is 0.0228 and the area to the left of 2 is 0.9772. Thus, the area between -2 and 2 is approximately 0.9772-0.0228=0.9544, which is approximately 0.95.

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Complete Question:

In 2022, NBA teams score 114 points per game on average with a standard deviation of 6 points per game. Suppose that we randomly sample 36 NBA scores from this season and consider the sample mean (

Xˉ ); the average points per game scored in this sample.

Calculate P( Xˉ 2<114< Xˉ +2)

The probability of getting 3 black cards out of 4 drawn from a standard deck of 52 cards is approximately 0.253 or 25.3%.

To determine the probability of getting 3 black cards out of 4 cards drawn from a standard deck of 52 cards, we can use the hypergeometric distribution.

There are 26 black cards in the deck, and the total number of ways to choose 4 cards from 52 is given by the binomial coefficient C(52, 4). The number of ways to choose 3 black cards out of 26 is given by the binomial coefficient C(26, 3).

The number of ways to choose the fourth card from the remaining 26 non-black cards is given by the binomial coefficient C(26, 1).

Therefore, the probability of getting 3 black cards out of 4 is:

P(3 black cards) = C(26, 3) * C(26, 1) / C(52, 4)

P(3 black cards) = (2600 * 26) / 270725

P(3 black cards) ≈ 0.253

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Solution: x + 12

Step-by-step explanation:

first simplify then distribute!

Answer:x+12

Step-by-step explanation:

we have to multiply number outside of brackets to each of the numbers inside it:

2(2x+5)=4x+10

-(3x-2)=-1(3x-2)=-3x+2

4x+10-3x+2=x+12

Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.

The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.

Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.

Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.

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Answer:

1. I don't know

2. 10

Step-by-step explanation:

[tex]c=\sqrt{a^{2}+b^{2} } = \sqrt{6^{2}+8^{2} } = \sqrt{36+64} = \sqrt{100} = 10[/tex]

The decrease in the time spent exercising is 0.74.

A scatter plot is a type of data visualization that is used to display the relationship between two continuous variables. It consists of a set of data points, each representing an observation, plotted as a point on a two-dimensional graph with one variable on the x-axis and the other variable on the y-axis.

Scatter plots are often used to identify patterns or relationships between two variables, such as correlation or causation. If the points on the plot tend to form a pattern, such as a straight line, then there may be a relationship between the two variables. If the points do not form a pattern, then there may be no relationship between the two variables.

The answers are quite straightforward.

(a) Here, we substitute x=4

(b) Again, we substitute x= 0

(c) Here, if y1=y2-y1= (-0.74x- 0.74+8.54)-(-0.74x + 8.54)= y2-y1= -0.74x- 0.74+8.54 + 0.74x + 8.54= y2- y1= 0.74.

Thus, the decrease in the time spent exercising is 0.74.

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The complete question is

Answer: 28x+8y+2

Step-by-step explanation:

Remove parentheses: -2(14x-4y-1)

Solution: 28x+8y+2

Answer:

28x+8y+2

Step-by-step explanation:

Equations are used in many fields, including physics, engineering, economics, and finance, to model and analyse relationships between variables.

The expressions on either side of the equal sign are referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Solving an equation involves finding the values of the variables that make the equation true.

Two amounts or values are equal when they are stated as so in a mathematical equation, such as 6 x 4 = 12 x 2. two. Noun with a count.

A situation that requires the consideration of two or more elements in order to perceive or comprehend the total situation is referred to as an equation.

[tex]2+2+2+2+2+3-3-3-3-21-456--42 =[/tex]

[tex]2+2+2+2+2+3 = 13[/tex]

[tex]-3-3-3 = -9[/tex]

[tex]-456--42 = -456+42 = -414[/tex]

Therefore,

[tex]2+2+2+2+2+3-3-3-3-21-456--42 = 13 - 9 - 414 = -410[/tex]

Therefore, the value of the expression is  [tex]2+2+2+2+2+3-3-3-3-21-456--42[/tex]  [tex]= 13 - 9 - 414 = -410[/tex]     . As per the given equation.

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In order to solve for x in this equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3 as the answer. So, x = 8.3.

An equation is a mathematical statement that expresses the equality of two expressions, usually containing one or more variables. It is used to describe the relationships between different variables, such as the area of a circle or the slope of a line. Equations can be used to describe the behavior of physical systems, calculate the solutions to problems, and make predictions about future events.

This is happening because when we divide 75 by 9, we are essentially asking "how many 9s go into 75?". 75 divided by 9 is equal to 8.3, meaning 8 and 3/9ths of 9 go into 75. Therefore, x = 8.3.

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In order to solve for x the given equation, we must divide 75 by 9. Dividing 75 by 9 gives us 8.3. So, x = 8.3.

An equation is a mathematical statement that expresses the equality of two expressions, usually involving one or more variables. Used to describe relationships between different variables. Area of ​​circle or slope of line. Equations can be used to describe the behavior of physical systems, calculate solutions to problems, and predict future events.

That's because when you divide 75 by 9, you're essentially asking, "How many 9s are there in 75?" 75 divided by 9 is 8.3. So 3/9 of 8 and 9 is 75. So x = 8.3.  

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The complete question is as follows:

Solve for x. Round to the nearest tenth, if necessary.

75 = 9x

Answer:

The 99% confidence interval will be wider than the 95% confidence interval because it encompasses a greater range of possible values, meaning that there is a lower chance of the true population parameter falling outside the interval. The 95% confidence interval means that if the study was repeated many times, 95% of the intervals constructed would contain the true population parameter, whereas the 99% confidence interval means that 99% of the intervals constructed would contain the true population parameter.

Step-by-step explanation:

The final equation of motion for the system is: x(t) = [(8v0 - 2x0)/6]*[tex]e^{(-2t)} + [(2x0 - 8v0)/6]*e^{(-8t).[/tex]

To determine the initial conditions and equations of motion, we can use the following steps:

Write down the equation of motion for the system. The equation of motion for a mass-spring-damper system is given by:

m * [tex]d^2x/dt^2[/tex] + c * dx/dt + k * x = 0

where m is the mass, c is the damping coefficient, k is the spring constant, x is the displacement from the equilibrium position, and t is time.

In this case, the mass is 1 kg, the spring constant is 16 N/m, and the damping coefficient is 10 times the instantaneous velocity, or 10 * dx/dt.

Substituting these values into the equation of motion, we get:

1 * [tex]d^2x/dt^2[/tex] + 10 * dx/dt + 16 * x = 0

Determine the initial conditions. The initial conditions refer to the position and velocity of the mass at time t = 0.

Let x(0) be the initial displacement of the mass from the equilibrium position, and let v(0) be the initial velocity of the mass. Then the initial conditions are:

x(0) = ?

v(0) = ?

These values are typically given in the problem statement.

Solve the differential equation. To solve the differential equation, we can use the characteristic equation method. First, we assume that the displacement of the mass is of the form:

x(t) = A[tex]e^{(rt)[/tex]

where A and r are constants to be determined.

Taking the first and second derivatives of x(t), we get:

dx/dt = Are^(rt)

d^2x/dt^2 = Ar^2*e^(rt)

Substituting these expressions into the equation of motion, we get:

A * ([tex]r^2[/tex] + 10r + 16) * [tex]e^{(rt)[/tex]= 0

Since [tex]e^{(rt)[/tex]is never zero, we can divide both sides by it and simplify to obtain the characteristic equation:

[tex]r^2 + 10r + 16 = 0[/tex]

Solving for r using the quadratic formula, we get:

r1 = -2

r2 = -8

Therefore, the general solution for the displacement of the mass is:

[tex]x(t) = Ae^{(-2t)} + Be^{(-8t)[/tex]

where A and B are constants determined by the initial conditions.

To find A and B, we use the initial conditions x(0) = x0 and v(0) = v0. Taking the derivative of x(t) and setting t = 0, we get:

v(0) = -2A - 8B

Using the second initial condition, we get:

x(0) = A + B = x0

Solving for A and B, we get:

A = (8v0 - 2x0)/6

B = (2x0 - 8v0)/6

Therefore, the final equation of motion for the system is:

[tex]x(t) = [(8v0 - 2x0)/6]*e^{(-2t)} + [(2x0 - 8v0)/6]*e^{(-8t)[/tex]

Complete question: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine the equations of motion if (a) the mass is initially released from rest from a point 1 meter below the equilibrium position, and then (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s.

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The pοssible dimensiοns (length and width) οf the rectangular plοt are:

Length = 21 meters, width = 8.05 meters

Length = 8.05 meters, width = 21 meters

Let the length οf the rectangular plοt be L and the width be W. Then we knοw that the perimeter οf the rectangular plοt, which is equal tο the length οf fencing Baο has, is given by:

2L + W = 39

Alsο, the area οf the rectangular plοt is given by:

L × W = 169

We can use these twο equatiοns tο sοlve fοr L and W. First, we can sοlve the equatiοn 2L + W = 39 fοr W:

W = 39 - 2L

Substituting this into the equation for the area, we get:

L × (39 - 2L) = 169

Expanding and rearranging this equation, we get a quadratic equation in terms of L:

[tex]-2L^2 + 39L - 169 = 0[/tex]

We can solve for L using the quadratic formula:

[tex]L = [ -39 \± sqrt(39^2 - 4(-2)(-169)) ] / (2(-2))\\L = [ -39 \± sqrt(1681) ] / 4\\L = [ -39 \± 41 ] / 4[/tex]

L = 1/2 or L = 21

If L = 1/2, then W = 38, which gives a negative area and is therefore not possible.

If L = 21, then W = 169/21, which simplifies to W = 8.05 (rounded to two decimal places).

Therefore, the possible dimensions (length and width) of the rectangular plot are:

Length = 21 meters, width = 8.05 meters

Length = 8.05 meters, width = 21 meters

Note that these are the only possible dimensions, as the sum of the length and width must be less than or equal to 19.5 meters (half of the available fencing).

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