You invest $2500 in an account to save for college. account 1 pays 6%annual interest compounded quarterly. account 2 pays 4% annual interest compounded continuously. which account should you choose to obtain the greater amount in 10 years?



account 1


or


account 2

A. The distribution function F(x,y) is ¹¹/₁₈ + ¹/₁₂ x² - ¹/₁₈ y² + ¹/₁₂ xy

B. The marginal PDF of x is ¹/₂x + ¹/₆ + ¹/₁₂x² for 0≤x≤1 and for y is /₂y + ¹/₆ + ¹/₁₂y² for 0≤y≤2

C. P(0≤x≤1/2, 0≤y≤1/2) is ¹/₃₂ + ¹/₉₆ x² for 0≤x≤1/2

D. The joint PDF of u=2x-y and v=-x+y is f(u,v) = (1/27)(2u^2+2v^2-2uv)

a) To find the distribution function F(x,y), integrate the joint PDF over the appropriate limits.

F(x,y) = ∫∫f(u,v)dudv

The limits of integration are not specified, so, determine them from the limits of the variables x and y.

So,

F(x,y) = ∫∫f(u,v)dudv

= ∫∫f(x+y,x-y)dudv (substituting u = x+y and v = x-y)

= ∫∫(¹/₄(u²+v²)+¹/₆(u²-v²))dudv (substituting x and y back in terms of u and v)

The limits of integration for u and v can be found by solving for u and v in terms of x and y as follows:

u = x+y

v = x-y

x = (u+v)/2

y = (u-v)/2

0 ≤ x ≤ 1; 0 ≤ y ≤ 2

implies

0 ≤ (u+v)/2 ≤ 1; 0 ≤ (u-v)/2 ≤ 2

Solving the above inequalities gives the following limits:

0 ≤ u ≤ 2; -u ≤ v ≤ u;

Thus,

F(x,y) = ∫∫(¹/₄(u²+v²)+¹/₆(u²-v²))dudv

= ∫²₀ ∫ᵘ_(-u) (1/4(u²+v²)+¹/₆(u²-v²))dvdu

= ¹¹/₁₈ + ¹/₁₂ x² - ¹/₁₈ y² + ¹/₁₂ xy

b) To find the marginal PDF of x, integrate the joint PDF over all possible values of y:

f(x) = ∫f(x,y)dy

So,

f(x) = ∫²₀ (¹/₄x + ¹/₄y²/x + ¹/₆y) dy

= ¹/₂x + ¹/₆ + ¹/₁₂x² for 0≤x≤1

In the same way, find the marginal PDF of y, by integrating the joint PDF over all possible values of x:

f(y) = ∫f(x,y)dx

So,

f(y) = ∫¹₀ (¹/₄x²/y + ¹/₄y + ¹/₆xy) dx

= ¹/₂y + ¹/₆ + ¹/₁₂y² for 0≤y≤2

c) To find P(0≤x≤1/2, 0≤y≤1/2), integrate the joint PDF over the appropriate limits:

P(0≤x≤1/2, 0≤y≤1/2) = ∫∫f(x,y)dxdy

So,

P(0≤x≤1/2, 0≤y≤1/2) = ∫¹₀ ∫^(1/2)_0 (¹/₄x² + ¹/₄y²/x + ¹/₆xy) dydx

= ¹/₃₂ + ¹/₉₆ x² for 0≤x≤1/2

d) To find the joint PDF of u=2x-y and v=-x+y, express x and y in terms of u and v and then apply transformation formula.

From the given equations, solve for x and y in terms of u and v as follows:

x = (u+v)/3

y = (v-u)/3

Now, find the Jacobian of the transformation:

J = ∂(x,y)/∂(u,v) =

| ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

=

| 1/3 1/3 |

| -1/3 1/3 |

So, |J| = 2/9

Using the transformation formula for joint PDFs:

f(u,v) = f(x(u,v), y(u,v)) |J|

Substituting x and y in terms of u and v:

f(u,v) = f((u+v)/3, (v-u)/3) (2/9)

Substituting the given joint PDF for f(x,y), we get:

f(u,v) = (¼((u+v)/3)² + ¼((v-u)/3)² + ⅙((u+v)/3)((v-u)/3))(2/9)

Simplify:

f(u,v) = (1/27)(2u²+2v²-2uv)

So, the joint PDF of u=2x-y and v=-x+y is:

f(u,v) = (1/27)(2u²+2v²-2uv)

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Answer:

a) 18.84 cm

b) 28.26 cm²

Step-by-step explanation:

We Know

Each pancake is a circle with a diameter of 6 centimeters.

a)  Calculate the circumference of each pancake.

Circumference of circle = d · π

d = 6 cm

We Take

6 · 3.14 = 18.84 cm

So, the circumference of each pancake is 18.84 cm.

b) Calculate the area of each pancake.

Area of circle = r² · π

r = 1/2 · d

r = 1/2 · 6 = 3 cm

We Take

3² · 3.14 = 28.26 cm²

So, the area of each pancake is 28.26 cm².

Answer:

let amount of games won and lost be x and y respectively

y+18=x

x+y=78

y+y+18=78

2y=78-18

2y=60

y=30

x=30+18

x=48

thus, games won is 48

We can conclude that Arnold's height of 4.75 feet by using tangent function is not accurate based on the calculations.

To determine whether Arnold's height is accurate, we can use trigonometry and the given information about the angle of elevation and distance to the building.

Let's start by drawing a diagram to represent the situation. We have a right triangle with the opposite side being Arnold's height (h), the adjacent side being the distance to the building (300 ft), and the angle of elevation being 22 degrees.

Using the tangent function, we can write:

tan(22) = h / 300

Solving for h, we get:

h = 300 * tan(22)

Using a calculator, we find that h is approximately 122.8 feet.

Therefore, we can conclude that Arnold's height of 4.75 feet is not accurate based on the calculations. The height we calculated is over 25 times greater than Arnold's claimed height, which is not possible.

It is important to note that this assumes that Arnold's line of sight is parallel to the ground. If Arnold is on uneven ground, this could affect the calculations. Additionally, it is possible that Arnold may have misspoken about his height or the angle of elevation. However, based on the given information and calculations, we can confidently say that Arnold's claimed height is not accurate.

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Equation of the circle: x^2 + (y - 2)^2 = 4

How to find the equation of the circle?

The circle centered at the origin and passing through the point (0, 4) can be represented by the equation of a circle. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.

Since the center is at the origin (0, 0), the equation simplifies to x^2 + y^2 = r^2. To determine the radius, we can use the point (0, 4) that lies on the circle. Substituting these coordinates into the equation, we get 0^2 + 4^2 = r^2. Simplifying, we find that 16 = r^2.

Therefore, the equation of the circle centered at the origin and passing through the point (0, 4) is x^2 + y^2 = 16.

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To comply with their general computer or Internet policy while allowing Bobby to access the internet for a specific task, the bank can implement several measures to monitor and restrict Bobby's Internet usage for personal and official use.

First, the bank can establish a separate, secured network for employees who need internet access for work purposes. This network should be isolated from the internal network to protect sensitive information.Second, the bank can implement strict access controls and authentication measures, such as providing a unique username and password for Bobby to access the internet. Third, the bank can install a firewall and web filtering system that blocks access to non-work-related websites and content. This will prevent personal use of the internet while still allowing access to the necessary websites for Bobby's work.

Fourth, the bank can regularly monitor and audit Bobby's internet usage, including the websites visited, the amount of time spent online, and any data transmitted or received. Finally, the bank should provide training and guidelines to Bobby regarding the acceptable use of the internet for work purposes, emphasizing the importance of confidentiality and adherence to the bank's security policies.

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Hence, [tex]\frac{-1-3}{4-(-2)}[/tex]  is the required fraction.

We know that the slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.

To set up the slope formula for the line that passes through the points (-2, 3) and (4, -1), we can use the formula of the slope

i.e. [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m is the slope of the line, and (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

So, x₁ = -2

y₁ = 3

x₂ = 4

y₂ = -1

Substituting the values in the formula

[tex]m = \frac{-1-3}{4-(-2)}[/tex]

Hence, [tex]\frac{-1-3}{4-(-2)}[/tex]  is the required fraction.

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Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.

Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.

In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.

Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.

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The derivative of y = x^(sin x) with respect to x is:

dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x)).

To find the derivative of y = x^(sin x) with respect to x using logarithmic differentiation, follow these steps:
1. Take the natural logarithm of both sides of the equation:

ln(y) = ln(x^(sin x))
2. Use the properties of logarithms to simplify:

ln(y) = sin x * ln(x)
3. Differentiate both sides with respect to x, using the chain rule and product rule:

(1/y) * dy/dx = cos x * ln(x) + sin x * (1/x)
4. Multiply both sides by y to solve for dy/dx:

dy/dx = y * (cos x * ln(x) + sin x * (1/x))
5. Substitute the original expression for y (y = x^(sin x)) back into the equation:

dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x))
So the derivative of y = x^(sin x) with respect to x is:

dy/dx = x^(sin x) * (cos x * ln(x) + sin x * (1/x)).

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To calculate the second derivative of a function, we need to take the derivative of the first derivative. The second derivative gives us information about the curvature of the function. A positive second derivative indicates that the function is concave up, while a negative second derivative indicates that the function is concave down. A second derivative of zero indicates that the function has no curvature at that point.

In the first example given, y = -5x^2 + x, we first find the first derivative by taking the derivative of the function with respect to x. This gives us dy/dx = -10x + 1. To find the second derivative, we take the derivative of dy/dx with respect to x. This gives us d²y/d²x = -10. This indicates that the function has a constant negative curvature, meaning it is concave down everywhere.

In the second example given, y = 7/x, we first find the first derivative by taking the derivative of the function with respect to x. This gives us dy/dx = -7/x^2. To find the second derivative, we take the derivative of dy/dx with respect to x. This gives us d²y/dx² = 14/x^3. This indicates that the function is concave up for positive values of x and concave down for negative values of x. The second derivative is undefined at x = 0, indicating a point of inflection.

Overall, the second derivative gives us important information about the behavior of a function and can help us identify points of inflection and concavity.
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The equation of the tangent plane to the surface z = ln(x - y) at the point (3, 2, 0) is x - y - z + 1 = 0.

To find the tangent plane to the surface z = ln(x - y) at the point (3, 2, 0), we can use the following steps

Find the partial derivatives of the surface with respect to x and y:

∂z/∂x = 1/(x - y)

∂z/∂y = -1/(x - y)

Evaluate these partial derivatives at the point (3, 2):

∂z/∂x (3, 2) = 1/(3 - 2) = 1

∂z/∂y (3, 2) = -1/(3 - 2) = -1

Use these values to find the equation of the tangent plane at the point (3, 2, 0):

z - f(3,2) = ∂z/∂x (3,2) (x - 3) + ∂z/∂y (3,2) (y - 2)

where f(x,y) = ln(x - y)

Plugging in the values we get:

z - 0 = 1(x - 3) - 1(y - 2)

Simplifying the equation, we get:

x - y - z + 1 = 0

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Answer:

i think the answer is 96

Step-by-step explanation:

The domain of the function f(x) = 1/x - 8 is (-∞, 0) U (0, +∞), and f = 1/x - 8.

The function f(x) is defined as 1/x - 8. The domain of the function is the set of all possible values of x for which the function is defined. Since the function involves division by x, x cannot be equal to zero. Therefore, the domain of f(x) is (-∞, 0) U (0, +∞), which means that x can take any value except 0.

To find f(x), we simply substitute the expression for f(x) in the definition of the function. Therefore, we have:

f(x) = 1/x - 8

This is the final answer. We cannot simplify it any further. The function f(x) represents a hyperbola with a vertical asymptote at x = 0 and a horizontal asymptote at y = -8.

As x approaches 0 from the left, f(x) goes to negative infinity, and as x approaches 0 from the right, f(x) goes to positive infinity. Similarly, as x approaches positive or negative infinity, f(x) approaches 0.

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Answer:

A. There is an asymptote at x = 0.

D. There is an asymptote at y = 23.

The distance traveled is 8ft and the displacement is 0ft.

The distance traveled is equal to the total distance that the ball travels, in this case it starts 4ft above the ground, then goes to the ground, and then returns to the initial position which is 4ft above the ground, then the total distance is 4ft + 4ft = 8ft

The displacement is equal to the difference between the final position and the inital one, here we know that both are the same, thus, the displacement is  0ft.

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The arc length (s) for a circle with radius 4.27 meters and central angle 2.16 radians is approximately 9.22 meters.

To find the arc length (s) for a circle with radius (r) and central angle (θ), you can use the formula:

s = r * θ

In this case, the radius (r) is 4.27 meters, and the central angle (θ) is 2.16 radians. Plug these values into the formula:

s = 4.27 * 2.16

Now, multiply the values:

s ≈ 9.2232

Round the answer to two decimal places:

s ≈ 9.22 meters

So, the arc length (s) for a circle with radius 4.27 meters and central angle 2.16 radians is approximately 9.22 meters.

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The probability that a randomly selected student got an A in Math, but not English, is 8%

Let A be the event that a student got an A in Math, and B be the event that a student got an A in English. Then, we want to find P(A and not B), or the probability that a student got an A in Math, but not English.

We know that P(A and B) = 0.16, or the probability that a student got an A in both Math and English. We also know that P(B) = 0.37, or the probability that a student got an A in English. Therefore, the probability of a student getting an A in Math, given that they got an A in English, can be calculated using the formula for conditional probability:

P(A | B) = P(A and B) / P(B)

P(A | B) = 0.16 / 0.37

P(A | B) = 0.43

This means that the probability of a student getting an A in Math, given that they got an A in English, is approximately 0.43.

To find the probability of a student getting an A in Math, but not English, we can subtract the probability of getting an A in both classes from the probability of getting an A in Math:

P(A and not B) = P(A) - P(A and B)

P(A and not B) = 0.24 - 0.16

P(A and not B) = 0.08

Therefore, the probability that a randomly selected student got an A in Math, but not English, is 0.08 or 8%.

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The circumference of the circle with a diameter of 10m is 31.4m, using 3.14 as the value of pi and including the correct unit in the answer.

The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Substituting the given value of the diameter, we get C = 3.14 x 10m = 31.4m as the circumference of the circle.

Since the value of pi is irrational, it cannot be expressed as a finite decimal or fraction, so we use an approximation, such as 3.14, to calculate the circumference. It is important to include the correct unit, which is meters in this case, in the answer to indicate the quantity being measured. Therefore, the circumference of the circle is 31.4m.

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Half way between 4/5 and 14/15 is 13/15.

To find the halfway point between 4/5 and 14/15, we need to calculate the average of the two fractions. Here's the process:

1. Make sure the fractions have a common denominator. In this case, the least common denominator (LCD) for 5 and 15 is 15.
2. Convert the fractions to equivalent fractions with the common denominator: 4/5 becomes 12/15 (multiply both numerator and denominator by 3), while 14/15 stays the same.
3. Add the two equivalent fractions together: 12/15 + 14/15 = 26/15.
4. Divide the sum by 2 to find the halfway point: (26/15) ÷ 2. To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number: 26/15 × 1/2 = 26/30.
5. Simplify the resulting fraction: 26/30 can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2 in this case. Thus, 26 ÷ 2 = 13, and 30 ÷ 2 = 15. The simplified fraction is 13/15.

So, the halfway point between 4/5 and 14/15 in its simplest form is 13/15.

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Answer is 15 meters

To solve this problem, we can use the formula for the perimeter of a rectangle, which is

P = 2l + 2w,

where P is the perimeter, l is the length, and w is the width.

We are given that Gabriella needs 120 meters of fence, which means that

P = 120.

We are also given that the length of the garden is three times its width, or

l = 3w.

Substituting these values into the formula, we get:

120 = 2(3w) + 2w

Simplifying this equation, we get:

120 = 8w

Dividing both sides by 8, we get:

w = 15

Therefore, the width of the garden is 15 meters.

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The measurement of the two shorter sides in Monica's wrapping paper is 17 inches.

We can use proportions to solve this problem. Since Francisco's piece of paper is similar to Monica's piece of paper, the ratios of the corresponding sides will be equal. Specifically, we have:

17 / x = 34 / y

where x is the length of one of Francisco's shorter sides, and y is the length of one of Monica's shorter sides.

To solve for y, we can cross-multiply and simplify:

17y = 34x

y = 2x

So the length of one of Monica's shorter sides is half the length of one of her longer sides, or:

y = 1/2 * 34 = 17

Therefore, the measurement of the two shorter sides in Monica's wrapping paper is 17 inches. Answer: a. inches.

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Answer:

x = 1/2, -4/3

Step-by-step explanation:

(2x - 1)(3x + 4) = 0

We know any number multiplied by 0 will be equal 0.

2x - 1 = 0

2x = 1

x = 1/2

3x + 4 = 0

3x = -4

x = -4/3

So, x = 1/2, -4/3

[tex]2x(3x + 4) - 1(3x + 4) = 0[/tex]

[tex]6 {x}^{2} + 8x - 3x - 4 = 0[/tex]

[tex]6 {x}^{2} + 5x - 4 = 0[/tex]

[tex]6 {x}^{2} + 5x = 4[/tex]

The volume of the box is 160 cubic inches. Using the volume of a rectangular prism formula the volume of the box is 160 cubic inches. Using another formula base area times height, the area is the same.

The volume of James' rectangular prism box can be calculated using both unit cubes and a formula. Part (a) involves counting the unit cubes in the model and multiplying the number of cubes by their volume, which is 1 cubic inch. In this case, there are 160 unit cubes, so the volume of the box is 160 cubic inches.

Part (b) involves using the formula for volume of a rectangular prism, which is length times width times height. Plugging in the given dimensions, we get 8 x 4 x 5 = 160 cubic inches, which is the same as the answer in part (a) using unit cubes.

Part (c) involves using a different formula for volume, which is base area times height. In this case, the base of the rectangular prism is a rectangle with length 8 inches and width 4 inches, so the base area is 8 x 4 = 32 square inches. Multiplying by the height of 5 inches, we get 160 cubic inches, which is again the same as the answers in parts (a) and (b).

Using the volume formulas is much quicker and more efficient than counting unit cubes, especially for larger boxes. However, counting unit cubes can provide a more concrete visual representation of the volume and can be helpful for students who are just learning about volume. In this case, the answers obtained using the formulas were the same as the answer obtained by counting unit cubes, which reinforces the accuracy of the formulas.

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The total number of bikes that can be painted in an hour would be 60 bikes.

With three identical machines,

the number of bikes machine can paint per hour = 20,

the number of machines bought again = 2,

so the total number of machines will be = 3,

when there are two same machines the productivity will be = 20 * 3 = 60 bikes.

This is because each machine works independently and can paint bikes simultaneously.

By adding two additional machines to the existing one,

the productivity of the painting process can be significantly increased. The new machines will not only increase the overall capacity but also reduce the turnaround time required for painting a large number of bikes.

By investing in additional machines,

the business can increase its output and generate more revenue,

which can be used to expand the operations further.

It's important to note that the investment in additional machines needs to be justified by the demand for painted bikes and the expected return on investment.

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The value of angle 5 and angle 8 will be 118° and 62° respectively.

Parallel lines are lines that are always the same distance apart and never intersect. In other words, they have the same slope and will never meet or cross each other. The symbol for parallel is ||.

For example, in the Cartesian coordinate system, the equation of a straight line is represented as y = mx + b, where m is the slope of the line and b is the y-intercept. If two lines have the same slope, they are parallel.

The value of angle 5 will be 118. Angle 8 will be:

= 180 - 118

= 62°

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The present ages of Raj and his daughter are respectively: 42 years and 12 years.

Present Age of Raj =y years

Present Age of daughter =x years

According to Question :

7 Years ago,

y − 7 = 7(x − 7)

⇒ 7x − y − 42 = 0.............(1)

And 3 Years from now

y + 3 = 3(x + 3)

⇒ 3x − y + 6 = 0............(2)

From eq (1) and eq (2)

Subtract eq 2 from eq 1 to get:

7x − 3x − y + y − 42 − 6 = 0

⇒ 4x = 48

⇒ x = 12

Putting x = 12 in Equation (2). we get,

(3 × 12) − y + 6 = 0

⇒ y = 42

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The probability that she will select the two pink bean bags from the box on her first two attempts is approximately 2.2%.

To calculate the probability that she will select the two pink bean bags from the box on her first two attempts, we need to;
1. Determine the total number of bean bags in the box. There is one yellow, four blue, three red, and two pink bean bags, which makes a total of 1 + 4 + 3 + 2 = 10 bean bags.
2. Calculate the probability of selecting a pink bean bag on the first attempt. There are two pink bean bags out of 10, so the probability is 2/10 or 1/5.

3. After selecting one pink bean bag, there are now nine bean bags left in the box. Calculate the probability of selecting the second pink bean bag on the second attempt. Since there is only one pink bean bag left, the probability is 1/9.
4. To find the overall probability of selecting two pink bean bags in the first two attempts, multiply the probabilities from steps 2 and 3. So, the probability is (1/5) * (1/9) = 1/45.
5. Convert the fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. (1/45) * 100 = 2.22% (rounded to the nearest tenth of a percent).

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If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.

I apologize, but it seems that the circuit diagram you mentioned is not displayed here. Without the circuit diagram, it is not possible for me to provide a specific answer to your question.

However, in general, the probability of current flowing from s to t in an electrical circuit depends on several factors such as the voltage level, the resistance of the circuit components, and the state of the switches. If the switches are all closed, then the probability of current flowing from s to t will depend on the overall resistance of the circuit.

If you provide me with a specific circuit diagram and the relevant details, I would be happy to help you determine the probability of current flowing from s to t when the switch is thrown.

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