Which mathematical concepts were the result of the work of René Descartes? Check all that apply. a. theory of an Earth-centered universe
b. formula for the slope of a line
c. Pythagorean theorem for a right triangle
d. problem solving by solving simpler parts first

The Laplace Transform of the function F(t) = 5sin(3t) can be found by using the definition of the Laplace Transform, which involves integrating the function with respect to time. The Laplace Transform of F(t) is not a number, but rather a function in the complex domain.

To find the Laplace Transform of F(t) = 5sin(3t) using the definition, we need to integrate the function with respect to time from 0 to infinity. The Laplace Transform is defined as L{F(t)} = ∫[0,∞] F(t)e^(-st) dt, where s is a complex number.

Integrating [tex]5sin(3t)e^(-st)[/tex]with respect to t results in a complex function that depends on s. The integration involves applying the integration rules and evaluating the integral limits. The resulting Laplace Transform is a function of s, denoted as L{F(t)}.

However, for the functions G(t) = [tex]t^5 - (1/4)e^(-9t) + 5(t - 1)^2 and F(t) = e^(-2t - 5)[/tex], the Laplace Transform can be computed using the Laplace Transform formulas. These formulas provide specific transformations for various types of functions, making the calculation more straightforward. By applying the Laplace Transform formulas to G(t) and F(t), we can obtain their respective Laplace Transform expressions, denoted as L{G(t)} and L{F(t)}. These expressions will involve algebraic manipulations and the use of the Laplace Transform tables to identify the corresponding transformations.

Overall, the Laplace Transform is a powerful tool in the field of mathematics and engineering that allows us to transform functions from the time domain to the complex frequency domain, facilitating the analysis and solution of differential equations and systems of equations.

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Answer:

About $9360

Step-by-step explanation:

There's about 52 weeks in one year, so if you multiply 52 by your weekly gain, your annual income will be approximately $9360.

I hope this is helpful ^^

Answer:

69

Step-by-step explanation:

Answer:

A. x² +10x +25

B. x² - 25

C. 5x² -5x + 25

D. x²- 10x + 25

Step-by-step explanation:

A. (x+5)(x+5)

x² + 5x + 5x + 25

x² +10x + 25

B. (x-5)(x+5)

x² + 5x - 5x - 25

x² -25

C. 5(x² -x +5)

5x² -5x + 25

D. (x-5)(x-5)

x² - 5x -5x + 25

x²- 10x + 25

Answer:

12y2

Step-by-step explanation:

Answer:

is it 160167

Step-by-step explanation:

hope i helped out

A. x and y are both within the same solar system.

7.2 light years= 455336 AU

The probability that the random variable described by the continuous probability distribution f(x) = 0.05x will take on a value greater than 2 is 0.6.

To calculate this probability, we need to find the area under the probability density function (PDF) curve for values greater than 2. Since the given PDF is in the form f(x) = 0.05x, we can integrate this function from 2 to infinity to find the desired probability.

∫[2, ∞] 0.05x dx

Integrating this function, we get:

[0.05 * (x^2)/2] evaluated from 2 to ∞

Simplifying further, we have:

(0.05/2) * (∞^2 - 2^2)

Since we are evaluating the integral from 2 to infinity, the upper limit (∞) will tend to infinity, making the difference (∞^2 - 2^2) also approach infinity.

As a result, the value (∞^2 - 2^2) is essentially infinity, which means the entire expression becomes:

(0.05/2) * ∞

Since infinity is not a well-defined value, we say that this probability is equal to 1, which corresponds to 100% probability. Therefore, the probability that the random variable will take on a value greater than 2 is 1 or 100%.

However, it seems there might be a typo in the given probability distribution function f(x) = 0.05x55. If it was intended to be f(x) = 0.05 * x^55 (raising x to the power of 55), then the probability would be different, and we would need to recalculate it based on the corrected function.

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Answer:

Infinitely many solutions

Step-by-step explanation:

ive learned thiss

Answer: Infinite amount of solutions since the two equations are equal

Basically x = x and y = y all numbers would work

Step-by-step explanation:

Answer:

The probability of selection of chocolate candy from bag A is ( 10%) bigger than from the bag B

Step-by-step explanation:

From bag A the probability (p₁ ) of selection  ( in a random sample) of one chocolate candy is

p₁ = 9/15       p₁  = 0,6

From bag B the probability ( p₂ ) of selection ( in a random sample) of one chocolate candy is:

p₂ = 5/10       p₂ = 0,5

Then the probability of selection of chocolate candy from bag A is bigger than from the bag B

p₁ > p₂      p₁ - p₂  = 0,6 - 0,5       p₁ - p₂ = 0,1    p₁ - p₂ = 10%

p

In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π/3 radians. The length of the arc is given by the formula L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the measure of the central angle in radians.

An arc is a portion of the circumference of a circle. Substituting the given values, we have L = 3 * (2π/3) = 2π ft. Therefore, the length of the arc is 2π ft. The length of an arc can be calculated using the formula L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the measure of the central angle in radians. In this case, the radius of the circle is 3 ft and the central angle is 2π/3 radians, so the length of the arc is 2π ft.

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Answer:

I cant see the full question enough to help you. Its showing like part of the question.

Answer:

4x+y=-7

Step-by-step explanation:

The mode of the distribution is 11, the median is 7, the mean is 8, and the range is 6. The measure of central tendency that would change the most if an additional test score of 2 were included is the median.

Mode: The mode is the value(s) that appear(s) most frequently in a distribution. In this case, the mode is 11, as it appears twice, while the other scores appear only once.

Median: To find the median, we arrange the scores in ascending order: 5, 6, 7, 11, 11. Since there are an odd number of scores, the median is the middle value, which is 7.

Mean: The mean is calculated by summing all the scores and dividing by the total number of scores. Adding the given scores, we get 7 + 11 + 5 + 6 + 11 = 40. Dividing by the total number of scores (5), the mean is 40/5 = 8.

Range: The range is the difference between the highest and lowest values in a distribution. In this case, the lowest score is 5 and the highest score is 11, so the range is 11 - 5 = 6.

If an additional test score of 2 were included in the distribution, the measure of central tendency that would change the most is the mean. Adding the score of 2 would decrease the overall average because 2 is significantly lower than the other scores. Since the mean is affected by the magnitude of each score, the addition of a low value like 2 would have a larger impact on the mean compared to the mode or median, which are based on the frequency or position of the scores rather than their actual values.

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Diagonals congruent: rectangle, square, isosceles trapezoid

Perpendicular bisectors: Rhombus, Square

Step-by-step explanation:

[tex]x + 22 + 3x = 90[/tex]

[tex]4x = 9 0- 22 \\ 4x = 68 \\ x = 17[/tex]

M1

[tex]17 + 22 = 39[/tex]

M2

[tex]3 \times 17 = \\ = 51[/tex]

Answer:

80 %

Step-by-step explanation:

I hope this helps!!

The adjacency matrix for the graph K4,5 will consist of two distinct sets of vertices with edges connecting every vertex from one set to every vertex in the other set.

The graph K4,5 is a complete bipartite graph with two sets of vertices, let's call them A and B. Set A contains four vertices (A1, A2, A3, A4), and set B contains five vertices (B1, B2, B3, B4, B5). In the adjacency matrix representation, the rows correspond to the vertices of set A, and the columns correspond to the vertices of set B. Therefore, the adjacency matrix will have dimensions 4x5.

To construct the adjacency matrix, we assign a value of 1 to the element at row i and column j if there is an edge between vertex Ai and vertex Bj. Since K4,5 is a complete bipartite graph, every vertex in set A is connected to every vertex in set B. Thus, all elements in the matrix will be 1.

The graph representation of K4,5 will consist of two distinct sets of vertices, A and B, with edges connecting every vertex from set A to every vertex in set B. This means that there will be a total of 20 edges in the graph. The graph can be visualized as two distinct groups of vertices, with no edges connecting vertices within the same set but with edges connecting every vertex from one set to every vertex in the other set.

In summary, the adjacency matrix for K4,5 will be a 4x5 matrix with all elements equal to 1. The graph representation will consist of two sets of vertices, A and B, with 20 edges connecting every vertex from one set to every vertex in the other set.

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Step-by-step explanation:

Hi,

"To begin, I need to figure out how triangle ABC eventually got to triangle DEF. The first thing I noticed was orientation, the point was not facing the same direction, and right away I knew that there had to be some sort of flip. The triangle ABC was flipped across the y-axis. After that, I also noticed that the triangle was not in the same quadrant. Triangle ABC was in quadrant 2 while triangle DEF was in quadrant 1. So I knew that triangle ABC was translated 2 units down. Even though it looked like the triangle was somehow moved to the right, IT WAS NOT. Since it was flipped, all we had to do was move it 2 units down. That is how I knew that in order for triangle ABC to get to triangle DEF it was flipped and translated 2 units down."

I hope this helps :)

Linear programming can be used to identify the critical path for a PERT network.

True.Linear programming can be used to identify the critical path for a PERT network. This statement is true.Linear programming is a mathematical technique that is used for optimizing an objective function, subject to a set of constraints. It can be used to solve problems that involve finding the best outcome among a set of linear constraints. Linear programming has applications in various fields such as economics, engineering, management science, and others. PERT is a project management technique that is used to schedule, organize, and coordinate tasks within a project. It helps in identifying the critical path, which is the sequence of tasks that determines the total duration of the project. Linear programming can be used to identify the critical path for a PERT network by formulating the problem as an optimization problem. By minimizing the duration of the critical path, we can find the optimal solution for the project.

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Step-by-step explanation:

put them in least to greatest, so that would be: 0,0,1,1,1,1,2,3,3,6,8,7,8, then do the greatest minus the lowest: 8-0=8

Answer:

A

Step-by-step explanation:

Answer:

a = 4

b = -3

Step-by-step explanation:

Let a and b be the two numbers.

According to question,

4a - b = 19........(i)

And,

a + 4b = -8........(ii)

From (i),

4a - b = 19

or, b = 4a - 19

Replacing b in (ii),

a + 4(4a - 19) = -8

a + 16a - 76 = -8

17a = -8 + 76

17a = 68

a = 68/17

a = 4

And,

b = 4a - 19

= 4 x 4 - 19

= 16 - 19

= -3

The values 93, 87 and 4 are cardinal , ordinal and nominal numbers respectively

The value 93 is a cardinal number as it represents a specific number, in this case the student's test score.

The value 87 is an ordinal number as It represents the student's identification number, which indicates their place in a sequence.

The value 4 is a nominal number as It represents the test number, which is a label or name for something.

In general, cardinal numbers are used to count things, ordinal numbers are used to rank things, and nominal numbers are used to identify things.

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Answer:

-6

Step-by-step explanation:

it is going through the y axis

Answer:

20%

Of Australia's total percent were gold!

Answer:

A

Step-by-step explanation:

Remarks

Solution

The power of matrix A can be calculated by repeatedly multiplying the matrix by itself. For the given matrix A = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1], we have A^16 = [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1].

To find A^16, we need to multiply the matrix A by itself 16 times. However, we can observe a pattern in the matrix: the entries in the matrix alternate between 1 and -1, with zeros everywhere else.

Since the entries in the matrix A alternate with a period of 4, we can see that A^4 will yield the same pattern. Therefore, we can rewrite A^16 as (A^4)^4.

Calculating A^4:

A^4 = [1 0 0 0] * [1 0 0 0] * [1 0 0 0] * [1 0 0 0]

    = [1 0 0 0] = [1 0 0 0]

      [0 0 1 0]   [0 0 1 0]

      [0 1 0 0]   [0 1 0 0]

      [0 0 0 -1]  [0 0 0 -1]

Now, calculating (A^4)^4:

(A^4)^4 = [1 0 0 0] * [1 0 0 0] * [1 0 0 0] * [1 0 0 0]

          [0 0 1 0]   [0 0 1 0]   [0 0 1 0]   [0 0 1 0]

          [0 1 0 0]   [0 1 0 0]   [0 1 0 0]   [0 1 0 0]

          [0 0 0 -1]  [0 0 0 -1]  [0 0 0 -1]  [0 0 0 -1]

Simplifying the calculations, we get:

(A^4)^4 = [1 0 0 0]

          [0 0 1 0]

          [0 1 0 0]

          [0 0 0 -1]

Therefore, A^16 is equal to [1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 -1].

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The integral ſ sin(x - 2) dx is transformed into L 9(t)dt an appropriate change of variable g(t) = -cos(t) + C.

To transform the integral of ſ sin(x - 2) dx into L 9(t)dt by applying an appropriate change of variable,

t = x - 2

To find the limits of integration, to determine the new values of x when t takes its limits.

When t = a (lower limit),

t = x - 2

a = x - 2

x = a + 2

When t = b (upper limit),

t = x - 2

b = x - 2

x = b + 2

express the integral in terms of t:

∫ ſ sin(x - 2) dx = ∫ ſ sin(t) dt

The integral has been transformed into L 9(t)dt.

To determine the function g(t), integrate sin(t) with respect to t:

∫ sin(t) dt = -cos(t) + C

where C is the constant of integration.

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Complete question:

The integral ſ sin(x - 2) dx is transformed into L 9(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = sin )= g(t) = cos .This option This option g(t) = cos (3) g(t) = sin. This option

A)g(t)= -cos(t)+C

B)g(t)=cos(t)+C

C)g(t)=cos(t)-C

D)g(t)=cos(t-2)-C