What is the answer please?

Answer:

a)    1/11

b)    25/66

c)     41/66

Step-by-step explanation:

The following is the number of each type of can
Cola (C) = 6

Soda (S) =  5

Fizz  (F) = 1

Total number of cans = 12

Since the sampling is done without replacement, the probability will be different for different draws

Let P(C₁) = Probability of drawing a cola on first draw
P(C₁) = 6/12

P(C₂|C₁) = Probability of cola on second draw given that the first draw was a cola = 5/11  (11 total cans left for second draw and only 5 cans of cola)

The probabilities for the other two types of cans can be calculated in the same way
P(S₁) = 5/12
P(S₂|S₁) = 4/11

P(F₁) = 1/12
P(F₂|F₁) = 0/11 = 0  (since there is only one can of Fizz the probability of drawing a second can of Fizz is 0

a)

In two draws what is the probability that one can is C and other is F

There are two ways in which this can occur - C₁ F₂ and F₁C₂

So the combined probability = sum of these probabilities for both possibilities

P(one C and one F) = P(C₁F₂) + P(F₁ C₂)
P(C₁F₂) = P(C₁) · P(F₂|C₁) = 6/12 · 1/11 = 1/2  ·  1/11 = 1/22  

P(F₁C₂) = P(F₁) · P(C₂|F₁) = 1/12 · 6/11 = 1/12 · 6/11 = 1/22

So P(C₁F₂ or F₁C₂) = 1/22 + 1/22 = 2/22 = 1/11

b)
P(both cans having same contents).
This can be represented as

P(C₁C₂ or S₁S₂ or F₁F₂)
= P(C₁C₂) + P(S₁S₂) + P(F₁F₂)
= P(C₁) x P(C₂|C₁) + P(S₁) x P(S₂|S₁) + P(F₁) x P(F₂|F1)

= 6/12 x 5/11 + 5/12 x 4/11 + 1/12 x 0

= 50/132

= 25/66

c)

Probability that the two cans will differ is the complement of the event the the two cans have the same contents

P(complement of event E) = 1 - P(event E)

P(can contents differ) = 1 - P(can contents are the same)

= 1 - 25/66

= 41/66

I hope I got it right, please let me know .Thanks

Thus, the average value of f' over [1, 6] is -2 found using the integration by substitution.

To find f'(6), we first need to evaluate the integral of f(x). Using integration by substitution, we have:

f(x) = x∫1(1-t)dt = x[t - (1/2)t^2] from t=1 to t=x
f(x) = x(x/2 - 1/2) - x(1/2 - 1/2)
f(x) = (x^2 - x)/2

Now, to find f'(6), we simply take the derivative of f(x) and evaluate it at x=6:

f'(x) = (2x - 1)/2
f'(6) = (2(6) - 1)/2
f'(6) = 5/2

Finally, to find the average value of f' over [1, 6], we need to calculate the definite integral of f'(x) over that interval and divide by the length of the interval:

Avg. value of f' = (1/6 - 1/2)∫1-6 (2x - 1)dx
Avg. value of f' = (-1/3) [x^2 - x] from x=1 to x=6
Avg. value of f' = (-1/3)[36-6-1+1]/5
Avg. value of f' = (-1/3)[30/5]
Avg. value of f' = -2

Therefore, the average value of f' over [1, 6] is -2.

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Answer:

The diagram is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

[tex] \tan( \alpha ) = \frac{110}{450} [/tex]

[tex] \alpha = {tan}^{ - 1} \frac{11}{45} = 13.74 \: degrees[/tex]

The angle of elevation is 13.74°.

y-1=3/2(x+3) is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-3, 1)

We have to find the slope of the line in the given graph

(2, 2) and (-2, -4) are the points

Slope = -4-2/-2-2

=-6/-4

=3/2

We know that the slope is same in parallel lines

Let us find the equation of the line passing through the point (-3, 1) in point slope form

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

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The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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Answer:

2,075 = 5 × 5 × 83

√2,075 = 5√83 = about 45.55

The coordinates of the vertices of polygon L'M'N'P'Q'R' after dilation are (0, 0), (1.693, 2.257), (3.77, 2.257), (5.385, 0), (9.231, 0), and (21, 7).

To find the coordinates of the vertices of polygon LMNPQR after dilation, we need to know the scale factor of dilation. The scale factor is the ratio of the corresponding side lengths of the dilated and original polygons. Since we know the location of vertex Q', we can use the distance formula to find the length of Q'Q and then find the scale factor using the fact that LMNPQR and L'M'N'P'Q'R' are similar.

Let's call the center of dilation O. Since O is the origin, we can use the distance formula to find the length of Q'Q:

Q'Q = sqrt((21-12)^2 + (7-4)^2) = sqrt(109)

We know that LMNPQR and L'M'N'P'Q'R' are similar, so the scale factor is equal to the ratio of corresponding side lengths. Let the scale factor be k, then:

k = Q'Q/QP = sqrt(109)/10

Now we can use the scale factor to find the coordinates of the other vertices:

L' = (0, 0)

M' = (k(3), k(4))

N' = (k(7), k(4))

P' = (k(10), k(0))

R' = (k(15), k(0))

So the coordinates of the vertices of polygon L'M'N'P'Q'R' after dilation are (0, 0), (1.693, 2.257), (3.77, 2.257), (5.385, 0), (9.231, 0), and (21, 7).

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The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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Answer: The index of refraction for the unknown wavelength is approximately 1.355.

Step-by-step explanation:

We can use Snell's law to relate the incident angle and refracted angle to the indices of refraction:

n1 sinθ1 = n2 sinθ2

where n1 and θ1 are the index of refraction and incident angle of the light in air, and n2 and θ2 are the index of refraction and refracted angle of the light in glass. Since the incident angle is 45.00 degrees, we have:

sinθ1 = sin(45.00) = √2/2

Since we know the index of refraction for the 450.0 nm light is 1.482, we can solve for the refracted angle θ2:

1.000 * √2/2 = 1.482 * sinθ2

sinθ2 = 1.000 * √2/2 / 1.482 = 0.4951

θ2 = sin^(-1)(0.4951) = 29.07 degrees

Now, we can use Snell's law again to relate the index of refraction to the refracted angle for the unknown wavelength:

n1 sinθ1 = n3 sinθ3

where n3 is the index of refraction for the unknown wavelength, and θ3 is the refracted angle for the unknown wavelength. We know that θ3 is 0.8000 degrees greater than θ2:

θ3 = θ2 + 0.8000 = 29.87 degrees

Substituting all the known values into Snell's law, we get:

1.000 * √2/2 = n3 * sin(29.87)

n3 = 1.000 * √2/2 / sin(29.87) = 1.355

Therefore, the index of refraction for the unknown wavelength is approximately 1.355.

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The area and the circumference are explained below.

Given that are objects having shape of a circle we need to find area and the circumference of these objects,

So,

Circumference = π × diameter

Area = π × radius²

So,

1) The circumference of the dime =

= π × 2×8.95

= 3.14 × 17.9

= 56.21 mm

2) Area of the circle =

3.14 × 8 × 8 = 200.96 cm²

3) Area of the circle =

3.14 × 32 × 32 = 3215.36 mm²

4) The area of a semicircle is half of the area of the circle,

So, area of the desktop = 3.14 × 14 × 14 / 2 = 307.72 in²

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A stationary probability distribution is a probability distribution that remains unchanged over time, even as the system it describes undergoes stochastic processes. It is also called a steady-state distribution.

To find the stationary probability distribution π for the given continuous-time Markov chain, we need to solve the detailed balance equations. These equations state that for any two states i and j,
π(i) q(i,j) = π(j) q(j,i)
Substituting the given values of q, we get:
π(0) β = π(1) α
π(1) β = π(2) α
Also, we know that the probabilities must add up to 1:
π(0) + π(1) + π(2) = 1
Solving these equations, we get:
π(0) = αβ/(αβ + β² + α²)
π(1) = βα/(αβ + β² + α²)
π(2) = β²/(αβ + β² + α²)
Therefore, the stationary probability distribution π is (αβ/(αβ + β² + α²), βα/(αβ + β² + α²), β²/(αβ + β² + α²)).

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No function f(r,θ) is given, we cannot evaluate the integral further.

To write ∬rfda as an iterated integral in polar coordinates for the given region rr, we need to determine the limits of integration for r and θ.

Let's first look at the region rr. From the given graph, we can see that the region is bounded by the circle with radius 3 centered at the origin. Therefore, we can express the region as:

r ≤ 3

To determine the limits for θ, we need to examine the region rr more closely. We can see that the region is symmetric about the x-axis, which means that the limits for θ are:

0 ≤ θ ≤ π

Now, we can write the iterated integral as:

∬rfda = ∫₀³ ∫₀ᴨ f(r,θ) r dθ dr

where f(r,θ) is the integrand function and r and θ are the limits of integration. Note that r is integrated first, followed by θ.

In this case, since no function f(r,θ) is given, we cannot evaluate the integral further.

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Answer:

BF = √(12^2 - 8^2) = √(144 - 64) = √80

= 4√5 = about 8.9 cm

The maximum amount the money supply can increase is $66.7 million.

To calculate the maximum amount the money supply can increase, we need to consider the concept of the money multiplier. The money multiplier represents the factor by which an initial change in reserves can increase the money supply through the lending and deposit creation process.

In this case, the required reserve ratio is 5%, meaning that banks are required to hold 5% of their deposits as reserves. The remaining portion, which is 95%, can be used for lending and creating new deposits.

Additionally, banks hold excess reserves of 10%, which means that they choose to hold an additional 10% of their deposits as reserves beyond the required amount.

To calculate the money multiplier, we can use the formula:

Money Multiplier = 1 / (Required Reserve Ratio + Excess Reserves Ratio)

In this case, the required reserve ratio is 5% (0.05) and the excess reserves ratio is 10% (0.10).

Money Multiplier = 1 / (0.05 + 0.10) = 1 / 0.15 = 6.67

The money multiplier tells us that for every dollar of reserves, the money supply can potentially increase by $6.67.

Since the Federal Reserve buys $10.00 million in Treasury securities, we can multiply this amount by the money multiplier to determine the maximum potential increase in the money supply:

Maximum Increase in Money Supply = $10.00 million * 6.67 = $66.7 million

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Statistical time division multiplexing is sometimes called asynchronous time division multiplexing. The correct answer is "c. asynchronous."

Statistical time division multiplexing is sometimes called asynchronous time division multiplexing. However, it should be noted that statistical time division multiplexing is different from synchronous time division multiplexing, which divides the time slots in a fixed, predetermined manner. In statistical time division multiplexing, the time slots are allocated dynamically based on the data traffic, hence the term "statistical".

More specifically, asynchrony describes the relationship between two or more events/objects that interact in the same system but do not occur in a predetermined manner and are not necessarily dependent on each other's existence for escape. They do not cooperate with each other, which means they may or may not occur simultaneously as they have their own separate processes.

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Therefore, according tot the given information:(a) sin(26°), (b) cos(70°), (c) cos(16θ).

(a) Using the Double-Angle Formula for sine, we get sin(26°)/2. Using the Double-Angle Formula for cosine, we get cos(26°)/2. Multiplying these together gives the simplified expression of cos(26°)sin(26°)/4.
(b) Using the Double-Angle Formula for cosine, we get cos(70°). Using the Double-Angle Formula for sine, we get sin(70°). Subtracting the squares of these gives the simplified expression of cos(140°).
(c) Using the Half-Angle Formula for cosine, we get cos(4°). Using the Half-Angle Formula for sine, we get sin(4°)/2. Subtracting the squares of these gives the simplified expression of cos(8°)/2.
(a) cos(26°)sin(26°)/4, (b) cos(140°), (c) cos(8°)/2.
(a) 2 sin(13°) cos(13°)
Using the Double-Angle Formula for sine: sin(2θ) = 2sin(θ)cos(θ), where θ = 13°.
So, sin(2 × 13°) = sin(26°).
(b) cos²(35°) - sin²(35°)
Using the Double-Angle Formula for cosine: cos(2θ) = cos²(θ) - sin²(θ), where θ = 35°.
So, cos(2 × 35°) = cos(70°).
(c) cos²(8?) - sin²(8?)
Assuming you meant to type "cos²(8θ) - sin²(8θ)", where θ represents an angle.
Using the Double-Angle Formula for cosine: cos(2θ) = cos²(θ) - sin²(θ).
So, cos(16θ) = cos²(8θ) - sin²(8θ)

Therefore, according tot the given information:(a) sin(26°), (b) cos(70°), (c) cos(16θ).

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No, the ordered pair (9, 5) is not a solution of the equation 3x - 5y = -1.

The given equation is 3x - 5y = -1. An ordered pair is said to be a solution of an equation if the values of the variables in the ordered pair make the equation true. In other words, when we substitute the values of the variables in the equation, the equation becomes a true statement.

Let's substitute the values of x and y in the given ordered pair (9, 5) in the equation 3x - 5y = -1:

3(9) - 5(5) = 27 - 25 = 2

As we can see, the equation is not true for the ordered pair (9, 5) since the left-hand side of the equation is not equal to the right-hand side of the equation. Therefore, the ordered pair (9, 5) is not a solution of the equation 3x - 5y = -1.

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The center of mass (x¯,y¯,z¯) of the homogeneous solid block is located at the geometric center of the block, which is (L/2, W/2, H/2).

To determine the center of mass (x¯,y¯,z¯) of a homogeneous solid block, we need to use the formula:

x¯ = (1/M) ∫∫∫ xρ(x,y,z) dV
y¯ = (1/M) ∫∫∫ yρ(x,y,z) dV
z¯ = (1/M) ∫∫∫ zρ(x,y,z) dV

where M is the mass of the block, ρ(x,y,z) is the density of the block at point (x,y,z), and dV is the volume element at point (x,y,z).

Since the solid block is homogeneous, the density is constant throughout the block, and we can simplify the above formula as:

x¯ = (1/M) ∫∫∫ x dV
y¯ = (1/M) ∫∫∫ y dV
z¯ = (1/M) ∫∫∫ z dV

We can further simplify this formula by using the fact that the solid block is a rectangular parallelepiped, and its volume is given by:

V = L x W x H

where L is the length, W is the width, and H is the height of the block.

Therefore, the mass of the block is given by:

M = ρ V = ρ LWH

Using these values, we can calculate the center of mass as:

x¯ = (1/M) ∫∫∫ x dV = (1/ρLWH) ∫∫∫ x dV = L/2
y¯ = (1/M) ∫∫∫ y dV = (1/ρLWH) ∫∫∫ y dV = W/2
z¯ = (1/M) ∫∫∫ z dV = (1/ρLWH) ∫∫∫ z dV = H/2

Therefore, the center of mass (x¯,y¯,z¯) of the homogeneous solid block is located at the geometric center of the block, which is (L/2, W/2, H/2).

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The expressions that represent the derivative of the function y = f(x) are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

So, the correct options are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

Option (C) and option (D) are the same expressions, just with a different notation.

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The critical value of t for a 90% confidence interval with "df" degrees of freedom is:

1.81 (approximately).

To find the critical value of t for a 90% confidence interval with degrees of freedom (df), follow these steps:

Identify the degrees of freedom (df). In this case, you mentioned "df."

Determine the desired confidence level. Here, it's a 90% confidence interval.

Calculate the tail probabilities. Since it's a two-tailed test, you'll need to find the probability for each tail. A 90% confidence interval leaves 10% in the tails, so each tail has 5% or 0.05.

Use a t-distribution table or calculator to find the critical value corresponding to the given degrees of freedom (df) and tail probability (0.05).

For example, if the degrees of freedom (df) is 10, you would find the critical value of t by looking up the value in a t-distribution table or using a calculator. The critical value for a 90% confidence interval with 10 degrees of freedom is approximately 1.81.

So, the critical value of t for a 90% confidence interval with df degrees of freedom is approximately 1.81 (rounded to two decimal places).

The correct question should be :

Find the critical value of t for a 90% confidence interval with degrees of freedom (df).

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The equation of the variable y in terms of x is y = -2x + 16

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

(2, 12) and (6, 4)

A linear equation is represented as

y = mx + c

Substitute the given points in the above equation, so, we have the following representation

2m + c = 12

6m + c = 4

When the equations are subtracted, we have

-4m = 8

So, we have

m = -2

Next, we have

2(-2) + c = 12

Evaluate

c = 16

Recall that

y = mx + c

So, we have

y = -2x + 16

Hence, the variable y in terms of x is y = -2x + 16

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[tex]ANSWER[/tex]

9 to the second power means :)

[tex]9 {}^{2} \\ = 9 \times 9 \\ = 81[/tex]

~hope it helps~

The correct answer is Option D, 72 Square inches.

To find the area of the label needed to cover the face of the box, we need to first determine the dimensions of the face.

The given vertices form a rectangle, with the length being the distance between (-8,4) and (4,4), which is 12 inches, and the width being the distance between (-8,4) and (-8,-2), which is 6 inches.

Therefore, the area of the rectangular face is 12 x 6 = 72 square inches.

This means that the label needed to cover the face of the box must also have an area of 72 square inches. Therefore, the correct answer is option (d), 72 Square inches.

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There are 25 possible outcomes where we either get a blue die 3 or an even sum or both.

To solve this problem, we need to use the concept of probability. Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. In this case, we want to find the probability of rolling either a blue die 3 or an even sum or both.

First, let's count the number of outcomes where the blue die is 3. There is only one way to get a 3 on the blue die, and the red die can be any number from 1 to 6. Therefore, there are 6 possible outcomes where the blue die is 3.

Next, let's count the number of outcomes where we get an even sum. There are three ways to get an even sum: (1,1), (2,2), and (3,3). For each of these outcomes, the blue die can be any number from 1 to 6. Therefore, there are 18 possible outcomes where we get an even sum.

Finally, let's count the number of outcomes where we get both a blue die 3 and an even sum. There is only one way to get a blue die 3 and an even sum: (3,3). Therefore, there is only one possible outcome where we get both a blue die 3 and an even sum.

To find the total number of outcomes that have either a blue die 3 or an even sum or both, we need to add the number of outcomes where the blue die is 3, the number of outcomes where we get an even sum, and the number of outcomes where we get both. This gives us:

6 + 18 + 1 = 25

Therefore, there are 25 possible outcomes where we either get a blue die 3 or an even sum or both.

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When two normal distributions have the same mean, but different standard deviations, the distribution with the larger standard deviation will have a wider spread, while the distribution with the smaller standard deviation will have a narrower spread.

We have,

Let's consider two normal distributions with a mean of 50.

One distribution has a standard deviation of 5, while the other has a standard deviation of 15.

The distribution with the smaller standard deviation of 5 will have the majority of the data points clustered closely around the mean of 50.

This means that there will be less variation in the data and the curve will be taller and narrower.

On the other hand,

The distribution with the larger standard deviation of 15 will have more variation in the data, resulting in a flatter and wider curve.

The data points will be more spread out, with some data points falling far away from the mean of 50.

Thus,

When two normal distributions have the same mean, but different standard deviations, the distribution with the larger standard deviation will have a wider spread, while the distribution with the smaller standard deviation will have a narrower spread.

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FALSE, Bank runs are usually associated with financial crises or economic instability, which can undermine the public's confidence in banks.

each statement about bank runs as true or false.

"Institutions like the Federal Deposit Insurance Corporation (FDIC) decrease the frequency of bank runs." - This statement is TRUE. The FDIC insures deposits, which helps to maintain confidence among customers and prevent bank runs.

"A bank run is when too many of a bank's customers withdraw too much at the same time." - This statement is TRUE. A bank run occurs when a large number of customers withdraw their deposits simultaneously due to concerns about the bank's solvency.

"A bank run is when many of a bank's customers make large deposits at once." - This statement is FALSE. A bank run is related to withdrawals, not deposits.

"A bank run only occurs when the economy is doing well." - This statement is FALSE. Bank runs are usually associated with financial crises or economic instability, which can undermine the public's confidence in banks.

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Each cube has a volume of 1 cubic unit. The area of the base is 12 square units.

The rectangular prism is made up of 4 layers of 3 by 2 cubes stacked on top of each other. Each layer has 3 by 2 = 6 cubes. So the total number of cubes in the rectangular prism is 4 × 6 = 24 cubes.

Therefore, the volume of the rectangular prism is 24 cubic units.

The base of the rectangular prism is a rectangle with a length of 4 units and a width of 3 units. So, the area of the base is:

Area of base = length × width = 4 × 3 = 12 square units.

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The particular solution to the system of differential equations X’ = [ 2 3 ][ 2 1 ] which satisfies the initial conditions : Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

To obtain the particular solution using the eigenvalue method, we first need to get the eigenvalues and eigenvectors of the coefficient matrix [2 3; 2 1].The characteristic equation is given by:

det([2 3; 2 1] - λ[I]) = 0

where λ is the eigenvalue and I is the identity matrix.Solving for λ, we get:

(2-λ)(1-λ) - 6 = 0

λ^2 - 3λ - 4 = 0

(λ-4)(λ+1) = 0

So, the eigenvalues are λ1 = 4 and λ2 = -1. To get the eigenvector corresponding to λ1, we need to solve the equation:

([2 3; 2 1] - 4[I])v1 = 0

where v1 is the eigenvector.Substituting the values, we get:

[-2 3; 2 -3][x1; x2] = [0; 0]

Solving the system of equations, we get:

-2x1 + 3x2 = 0

2x1 - 3x2 = 0

x1 = 3x2/2

So, the eigenvector corresponding to λ1 = 4 is [3/2; 1]. Similarly, to get the eigenvector corresponding to λ2, we need to solve the equation:

([2 3; 2 1] + 1[I])v2 = 0

where v2 is the eigenvector.Substituting the values, we get:

[3 3; 2 2][x1; x2] = [0; 0]

Solving the system of equations, we get:

3x1 + 3x2 = 0

2x1 + 2x2 = 0

x1 = -x2

So, the eigenvector corresponding to λ2 = -1 is [1; -1]. Now, we can write the general solution to the differential equation as:

X(t) = c1e^(4t)[3/2; 1] + c2e^(-t)[1; -1]

To get the particular solution that satisfies the initial conditions x(0) = [1; 2], we can substitute the values of t = 0 and x(0) into the general solution and solve for the constants c1 and c2.x(0) = c1*[3/2; 1] + c2*[1; -1]

[1; 2] = [3c1/2 + c2; c1 - c2]

Solving the system of equations, we get:

c1 = 2

c2 = -1/2

So, the particular solution is:

Xp = 2e^(4t)[3/2; 1] - (1/2)e^(-t)[1; -1]

Therefore, Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

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