If $8000 is invested at 4. 25%, compounded continuously, how long will it take to double?


Round the nearest tenth of a


year

These roots are also complex conjugates, so the step response will be oscillatory with a decay factor. The response will look like a damped sinusoid. the value of s1 and s2 is 25i and -25j.

Here are the solutions for the given transfer functions and the corresponding step response plots:

G(s) =\(400 / (s^2 + 12s + 400)\)

First, let's find the roots of the denominator:

\(s^2 + 12s + 400 = 0\)

Using the quadratic formula, we get:

s1 = -6 + 14.96j

s2 = -6 - 14.96j

These roots are complex conjugates, so the step response will be oscillatory with a decay factor. The response will look like a damped sinusoid.

G(s) =\(900 / (s^2 + 90s + 900)\)

The denominator can be factored as \((s + 45)^2\). Therefore, the roots are:

s1 = s2 = -45

Since both roots are negative and equal, the response will be critically damped.

G(s) = \(225 / (s^2 + 30s + 225)\)

The denominator can be factored as\((s + 15)^2\). Therefore, the roots are:

s1 = s2 = -15

Again, since both roots are negative and equal, the response will be critically damped.

G(s) = \(625 / (s^2 + 625)\)

The denominator can be factored as (s + 25j)(s - 25j). Therefore, the roots are:

s1 = 25j

s2 = -25j

Note: The step response plots can be sketched by considering the damping ratio and natural frequency of each transfer function. For critically damped systems, the response reaches steady-state the fastest, but it also overshoots the most.

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Answer:

12.75

Step-by-step explanation:

Answer:

3,5

Step-by-step explanation:edg 2021

The reflexive closure of a relation R over a reflexive closure A is obtained by adding (a, a) to R for every a ∈ A. Symmetric Closure: The symmetric closure of R is for each ( a , b) ∈ R. The transitive closure of R is iteratively adding (a, c) to R for each (a, b) ∈ R and (b, c) ∈ R .

In mathematics, the recursive closure of a binary relation R on the set X is the smallest recursive relation on X that contains R', and the reflexive closure of R is the relation 'x is less than or equal to y'.

The reflexive closure S of a relation R on the set X is given by

         S = R ∪ {(x ,x): x ∈X}

The recursive closure of R is the union of R with the identity on X.

Example:

If X = {1,2,3,4}

  Y = {(1,1), (2,2),(3,3),(4,4)}

Then the relation R is already recursive by itself. That is, it is no different from its recursive closure.

However, if one of the R pairs is missing, it will be inserted for recursive closure. For example, the same set X, the recursive closure is

          R = {(1,1), (4,4),(2,2)}

then the reflexive closure is

S = R ∪ {(x ,x): x ∈X} = {(1,1), (2,2),(3,3),(4,4)}

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Answer:

144

Step-by-step explanation:

((9*6/2)*4)+(6*6)=144

Answer:

-2z-1

Step-by-step explanation:

For a binomial random variable with = 10 and = 0.4 P(X = 4) is ≈ 0.2508, P(X ≥ 4) is ≈ 0.6513, P(X > 4) ≈ 0.4756, P(X ≤ 4) ≈ 0.3487, E(X) = np = 10 * 0.4 = 4 and σ(X) is ≈ 1.55

Given,

X is a binomial random variable with n = 10 and p = 0.4.

a) P(X = 4) can be calculated using the probability mass function of the binomial distribution:

P(X = 4) = (10 choose 4) * 0.4^4 * 0.6^6 ≈ 0.2508

b) P(X ≥ 4) can be calculated using the cumulative distribution function of the binomial distribution:

P(X ≥ 4) = 1 - P(X < 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

Using the probability mass function, we get:

P(X ≥ 4) ≈ 0.6513

c) P(X > 4) can be calculated as:

P(X > 4) = P(X ≥ 5) = 1 - P(X < 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

Using the probability mass function, we get:

P(X > 4) ≈ 0.4756

d) P(X ≤ 4) can be calculated using the cumulative distribution function of the binomial distribution

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using the probability mass function, we get:

P(X ≤ 4) ≈ 0.3487

e) The expected value of a binomial random variable is given by np, so:

E(X) = np = 10 * 0.4 = 4

f) The standard deviation of a binomial random variable is given by √(np(1-p)), so:

σ(X) = √(np(1-p)) = √(10 * 0.4 * 0.6) ≈ 1.55

For a binomial random variable with = 10 and = 0.4 P(X = 4) is ≈ 0.2508, P(X ≥ 4) is ≈ 0.6513, P(X > 4) ≈ 0.4756, P(X ≤ 4) ≈ 0.3487, E(X) = np = 10 * 0.4 = 4 and σ(X) is ≈ 1.55

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Because the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse (the longest side), the ratio values will never be greater than one, because (some number) / (a larger number) is always less than one.

Sine & cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the side opposite that angle to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

The sine and cosine functions for an angle θ are simply denoted as sin θ and cos θ. In general, the definitions of sine and cosine can be extended to any real value expressed in terms of the lengths of specific line segments in a unit circle.

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If A backyard is 40. 5 feet long and 25 feet wide then, the area of the reduced yard is approximately 450.09 ft².

The area of the original backyard is:

40.5 ft x 25 ft = 1012.5 ft²

To reduce the yard by a scale of one-third, we need to multiply the length and width by 2/3:

40.5 ft x 2/3 = 27 ft

25 ft x 2/3 = 16.67 ft (rounded to two decimal places)

The area of the reduced yard is:

27 ft x 16.67 ft = 450.09 ft² (rounded to two decimal places)

Therefore, the area of the reduced yard is approximately 450.09 ft².

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Answer:

aₙ= -2n²

Step-by-step explanation:

The sequence:

The difference between the terms:

As per above, the nth term is: aₙ= -2n²

The sequence:

Answer: let x represent children's tickets and y represent adult's tickets. the equation could be written as 8x + 18y = 720

Step-by-step explanation:

When talking about a scale drawing or model, the scale factor is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object.

This can be written as a fraction, with the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if a drawing of a building has a scale factor of 1:100 and the length of a wall on the drawing is 5 cm, the corresponding length on the actual building would be 500 cm (5 cm x 100). Therefore, the scale factor can be written as 5/500 or simplified to 1/100.

When talking about a scale drawing or model, the term you're looking for is "scale factor." It is determined by the ratio of a given length on the drawing or model to its corresponding length on the actual object. To write this as a fraction, you would place the length on the drawing or model as the numerator and the corresponding length on the actual object as the denominator. For example, if the scale factor is 1:10, you would write it as 1/10.

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After four hours, the height of the candles will be the same.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.

Let x be the number of hours and y be the height.

y = -0.70x + 8           ...1

y = -0.20x + 6             ...2

From equations 1 and 2, then we have

- 0.20x + 6 = - 0.70x + 8

(0.70 - 0.20)x = 8 - 6

0.50x = 2

x = 4 hours

After four hours, the height of the candles will be the same.

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Answer:

X=-4, y=-7

Step-by-step explanation:

6x-5y=11.     1st equation

y=7x+21    2nd equation

6x-5(7x+21)=11. Sub value of y in 2nd equation (7x+22) into 1st equation

6x-35x-105=11. Solve by distributative property

-29x-105=11.   Add x values

-29x=116.         add 105 to both sides

x=-4.                Solve for x

solve for y:

y=7x+21

y=7(-4)+21

y=-28+21

y=-7

check answer by substituting x and y into either equation

6x-5y=11

6(-4)-5(-7)=11

-24+35=11

11=11

i got 64.98 i really hope this helps :)

The null hypothesis will be same as the claim value which is 75%.

What is null hypothesis?

The null hypothesis is a statistical claim that no statistical significance can be found in a set of given observations. To determine the validity of a theory, hypothesis testing is carried out using sample data. Its symbol is H₀, and it is occasionally referred to as simply "the null".

We are given that the claim is that the proportion is less than 75%.

So, the statement of the null hypothesis states that the population value is the same as the claim value.

So,

H₀ : p = 75% = 0.75

If this null hypothesis is correct, then 75% of all students at the researcher's school finished their homework assignments last night.

Hence, this will mean that the null hypothesis is true.

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Question: No homework? Refer to Exercise 1. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

Explain what it would mean for the null hypothesis to be true in this setting.

Hey there!

$10.00 + 0.25¢ + 0.25¢ + 0.25¢ + 0.25¢

= $10.25 + 0.25¢ + 0.25¢ + 0.25¢
= $10.50 + 0.25¢ + 0.25¢

= $10.75 + 0.25¢

= $11.00

OR YOU COULD READ THE EQUATION LIKE:

$10.00 + $1.00

= $11.00

Thus, your answer is: FALSE because $10 + 4 quarters gives you $11 NOT $15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

False

Step-by-step explanation:

$10+$1=$11 and .25+.25+.25+.25=$1

which would equal $12 so your answer would be falses if thats what your asking

Answer:

4/5 divided by 9/10

4/5 times 10/9

=8/9

Step-by-step explanation:

hope this help you good luck

The perimeter of the rectangle with the given vertices is 21.66 units.

Using Distance Formula, we have

\(AB = \sqrt{(1-1)^{2} +(6-1)^{2} } = \sqrt{25} = 5\)

And \(CD= \sqrt{(4-4)^{2} +(1-6)^{2} } = \sqrt{25} = 5\)

\(BD= \sqrt{(1-4)^{2} +(1-6)^{2} } = \sqrt{9+25} = \sqrt{34} = 5.8\)

\(AC = \sqrt{(4-1)^{2} +(1-6)^{2} } = \sqrt{9+25} = \sqrt{34} = 5.8\)

Hence, the length of the perimeter is 5 units and the breadth of the perimeter is 5.8 units.

Now, the perimeter of a rectangle with length l, and breadth b is given by

Perimeter = 2(l+b)

Perimeter= 2 ( 5 +5.8) = 2 * 10.8 = 21.66 units.

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After executing this code, the object "stats" will contain the vector of odd numbers: 21, 23, 25, 27, 29.

To assign a vector of odd numbers between 20 and 30 to an object called "stats" in a programming language like R, you can use the following code:

stats <- seq(21, 29, 2)

Here's how this code works:

seq() is a function in R used to generate a sequence of numbers.

We specify the starting point as 21 (the first odd number between 20 and 30).

The endpoint is set to 29 (the last odd number between 20 and 30).

The third argument, 2, indicates the step size. By setting it as 2, we ensure that only odd numbers are included in the sequence.

The resulting sequence of odd numbers between 20 and 30 is then assigned to the object called "stats" using the assignment operator <-.

After executing this code, the object "stats" will contain the vector of odd numbers: 21, 23, 25, 27, 29.

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The surface area of the generated surface by revolving the curve about (a) the x-axis is 15π square units, and (b) the y-axis is 144π square units.

Let's consider the parametric curve given by x = 4t, y = 3t + 1, where 0 ≤ t ≤ 1. This curve lies on the xy-plane. We can rotate this curve about the x-axis to generate a surface, and the formula for the surface area of the generated surface by revolution is given by S = ∫(a,b) 2πy * √(dx/dt)^2 + (dy/dt)^2 dt.

Substituting x = 4t and y = 3t + 1, we can find dx/dt = 4 and dy/dt = 3. Thus, the formula for the surface area becomes S = ∫(0,1) 2π(3t + 1) * √(16 + 9) dt. Simplifying further, we have S = 2π∫(0,1) (3t + 1) * 5 dt = 2π [5(t^2/2 + t)]_0^1 = 2π [5(1.5)] = 15π.

Therefore, the surface area of the generated surface when the curve is rotated about the x-axis is 15π square units.

Now, let's consider rotating the curve about the y-axis to generate the surface. The formula for the surface area is S = ∫(c,d) 2πx * √(dx/dt)^2 + (dy/dt)^2 dt. To determine the limits of integration, we need to find the points where the curve intersects the y-axis.

The curve intersects the y-axis at (0, 1). When the curve is rotated about the y-axis, we obtain a solid with a hole in the middle. The surface area of the generated surface is the area of the outer surface minus the area of the inner surface.

The inner surface is generated by rotating the point (0, 1) about the y-axis, resulting in a cylinder with a radius of 1 and a height of 3. Hence, its surface area is 2πrh = 2π(1)(3) = 6π square units.

For the outer surface, we can take the limits of integration as c = 1 and d = 4. Substituting x = 4t and y = 3t + 1, we find dx/dt = 4 and dy/dt = 3. The formula for the surface area becomes S = ∫(1,4) 2π(4t) * √(16 + 9) dt. Simplifying further, we have S = 2π∫(1,4) (4t) * 5 dt = 2π [5(t^2)]_1^4 = 2π [5(15)] = 150π.

Therefore, the surface area of the generated surface when the curve is rotated about the y-axis is 150π - 6π = 144π square units.

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The solution to the system of equations is x = 11.5 and y = -27.5.

The solution to the system of equations is x = 2 and y = 1

The solution to the system of equations is x = -12 and y = 7.

The solution to the system of equations is x = 0.5 and y = -6.

A system of linear equations can be solved graphically, by substitution, by elimination, and by the use of matrices.

To solve the system of equations:

3x + y = 7

5x + 3y = -25

We can use the method of substitution or elimination to find the values of x and y.

Let's solve it using the method of substitution:

From the first equation, we can express y in terms of x:

y = 7 - 3x

Substitute this expression for y into the second equation:

5x + 3(7 - 3x) = -25

Simplify and solve for x:

5x + 21 - 9x = -25

-4x + 21 = -25

-4x = -25 - 21

-4x = -46

x = -46 / -4

x = 11.5

Substitute the value of x back into the first equation to find y:

3(11.5) + y = 7

34.5 + y = 7

y = 7 - 34.5

y = -27.5

Therefore, the solution to the system of equations is x = 11.5 and y = -27.5.

To solve the system of equations:

2x + y = 5

3x - 3y = 3

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to eliminate the y term:

6x + 3y = 15

6x - 6y = 6

Subtract the second equation from the first equation:

(6x + 3y) - (6x - 6y) = 15 - 6

6x + 3y - 6x + 6y = 9

9y = 9

y = 1

Substitute the value of y back into the first equation to find x:

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 2

Therefore, the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations:

2x + 3y = -3

x + 2y = 2

We can again use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express x in terms of y:

x = 2 - 2y

Substitute this expression for x into the first equation:

2(2 - 2y) + 3y = -3

Simplify and solve for y:

4 - 4y + 3y = -3

-y = -3 - 4

-y = -7

y = 7

Substitute the value of y back into the second equation to find x:

x + 2(7) = 2

x + 14 = 2

x = 2 - 14

x = -12

Therefore, the solution to the system of equations is x = -12 and y = 7.

To solve the system of equations:

2x - y = 7

6x - 3y = 14

Again, we can use the method of substitution or elimination.

Let's solve it using the method of elimination:

Multiply the first equation by 3 to eliminate the y term:

6x - 3y = 21

Subtract the second equation from the first equation:

(6x - 3y) - (6x - 3y) = 21 - 14

0 = 7

The resulting equation is 0 = 7, which is not possible.

Therefore, there is no solution to the system of equations. The two equations are inconsistent and do not intersect.

To solve the system of equations:

4x - y = 6

2x - y/2 = 4

We can use the method of substitution or elimination.

Let's solve it using the method of substitution:

From the second equation, we can express y in terms of x:

y = 8x - 8

Substitute this expression for y into the first equation:

4x - (8x - 8) = 6

Simplify and solve for x:

4x - 8x + 8 = 6

-4x + 8 = 6

-4x = 6 - 8

-4x = -2

x = -2 / -4

x = 0.5

Substitute the value of x back into the second equation to find y:

2(0.5) - y/2 = 4

1 - y/2 = 4

-y/2 = 4 - 1

-y/2 = 3

-y = 6

y = -6

Therefore, the solution to the system of equations is x = 0.5 and y = -6.

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The distance from each landing point to the boat pulled ashore at point C is given by:-d = sqrt(25^2 (y^2/x^2 + 1))

WHAT IS TRIGONOMETRY ?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving distances, heights, angles, and other geometric measurements. Trigonometric functions such as sine, cosine, and tangent are used to relate the angles of a triangle to its sides. Trigonometry has many practical applications in fields such as engineering, physics, and architecture, and is essential for understanding and solving problems involving waves, oscillations, and periodic phenomena. It is also used in navigation, surveying, and astronomy, among other areas.

To solve this problem, we need to use the concept of right triangle trigonometry.

Let's assume that point C is directly opposite the midpoint of AB, and that the distance from point C to the midpoint of AB is x. Then we can draw a right triangle with legs of length x and 25 (half of 50) and a hypotenuse of length d (the distance from point C to each landing point).

Using the Pythagorean theorem, we can write:

d^2 = x^2 + 25^2

We also know that the angles opposite the legs of the right triangle are complementary, so we can use the tangent function to write:

tan(theta) = x/25

where theta is the angle between the hypotenuse and the side of length 25.

We can rearrange this equation to solve for x:

x = 25 tan(theta)

Now we can substitute this expression for x into the equation for d^2:

d^2 = (25 tan(theta))^2 + 25^2

Simplifying this equation, we get:

d^2 = 25^2 (tan^2(theta) + 1)

Finally, we can use the fact that tan(theta) is equal to the height of the opposite bank divided by the distance from point C to the midpoint of AB. Let's call this distance y. Then we have:

tan(theta) = y/x

Substituting this expression for tan(theta) into the equation for d^2, we get:

d^2 = 25^2 (y^2/x^2 + 1)

So the distance from each landing point to the boat pulled ashore at point C is given by:

d = sqrt(25^2 (y^2/x^2 + 1))

where x and y are the distances from point C to the midpoint of AB and the opposite bank, respectively.

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Answer:

StartRoot 58 EndRoot

Step-by-step explanation:

Given the coordinates (-4, -3) and (-1, 4)

To get the distance between the two points, we will use the formula:

D =√(y2-y1)²+(x2-x1)²

From the coordinates, x1 = -4, y1 = -3, x2 = -1 and y2 = 4

Substitute

D =√(4-(-3))²+(-1-(-4))²

D = √(4+3)²+(-1+4)²

D = √7²+3²

D = √49+9

D = √58

Hence the correct option is D

StartRoot 58 EndRoot

Answer:

D. 58

Step-by-step explanation:

Answer:

In Fourier series, To show that cos(mx) and cos(nx) for m ≠ n are orthogonal in [-π, π], we need to prove that∫-ππ cos(mx)cos(nx)dx = 0 if m ≠ n

Firstly, let's use the identity cos(A)cos(B) = (1/2) [cos(A + B) + cos(A - B)]So the above equation can be written as∫-ππ (1/2) [cos(m + n)x + cos(m - n)x] dx = 0Now, the integral of cos(m + n)x and cos(m - n)x over [-π, π] is 0 because they are odd functions. So we are left with∫-ππ cos(mx)cos(nx) dx = 0 which is what we needed to prove.

So, the functions cos(mx) and cos(nx) for m ≠ n are orthogonal in [-π,π].2. To expand the function f(x) = { 0 π < x < 0 π- x 0 < x < π into Fourier series, we need to compute the Fourier coefficients which are given by the formula an = (2/π) ∫f(x)sin(nx)dx and bn = (2/π) ∫f(x)cos(nx)dx Note that a0 = (1/π) ∫f(x)dx= (1/π) [∫0π (π - x) dx] = π/2

Computing an, we have an = (2/π) ∫π0 (π - x) sin(nx) dx= 2 ∫π0 π sin(nx) dx - 2 ∫π0 x sin(nx) dx= 2 [(1/n) cos(nπ) - (1/n) cos(0)] - 2 [(1/n²) sin(nπ) - (1/n²) sin(0)]= 2 (-1)^n / n²So the Fourier series becomes f(x) = π/2 + ∑n=1∞ 2 (-1)^n / n² sin(nx)

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Answer:

1st one is proportional

2nd is not proportional

Step-by-step explanation:

30/5=6 24/4=6

Yes, 1 is proportional.

12/6=2 16/4=4

No, 2 is not proportional.

---

hope it helps

Answer:

the first one is a square and the second is a parallelogram and the third is rectangle,fouth is rhombuse and last one is trapizoid

Step-by-step explanation: