Find the Laplace transform of the following functions f(t)=e-21 sin 2t + e³42 a.

Answer:

8

Step-by-step explanation:

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The probability that the sum is a multiple of three is 0.2778

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If a pair of six-sided dice is rolled, and the sum is recorded, then the possible sum is the numbers from (1 + 1) = 2 to (6 + 6) = 12.

From 1 to 12, the multiples of 3 are 3, 6, 9, and 12. These can be resulted from having the following dice rolled.

3 : 1 & 2, 2 & 1

6 : 1 & 5, 2 & 4, 3 & 3, 4 & 2, 5 & 1

9 : 3 & 6, 6 & 3

12 : 6 & 6

Since there are 10 possible outcomes wherein the sum is a multiple of 3, and there are (6 x 6) total outcomes, then the probability is

p = 10 / 36 = 0.2778

Hence, the probability that this sum is a multiple of three is 0.2778.

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After 2.10 years, there will be 8 grams of radioactive substance left.

The rate of decay of a radioactive substance is proportional to the amount of substance present.

Thus, we can conclude that the quantity of the radioactive substance present decreases exponentially over time.

A radioactive decay constant is defined as the fraction of the substance that decays in a unit of time, t.

According to the given statement, the rate of decay of a radioactive substance is proportional to the amount of substance present.

Suppose that the quantity of radioactive substance present initially is A0.

Then, the decay constant is represented by λ.

As the substance continues to decay, the remaining amount of the substance present after time t can be given by the exponential decay equation:  A(t) = A0e-λt

where A(t) represents the amount of substance present after time t.

In this problem, we are given that 12 grams of the substance were initially present, and now there are 8 grams. Therefore, we need to find out the value of t using the given data.

For this, we can use the exponential decay equation:  A(t) = A0e-λt

Let's assume that the amount of the substance present after time t is A(t) = 8 g, A0 = 12 g

Thus, the equation becomes 8 = 12e-λt

To find the value of λ, we can rearrange the equation and take the natural logarithm on both sides:

ln (8/12) = ln (e-λt)ln (8/12)

= -λt ln (e)ln (8/12)

= -λt λ = -ln (8/12)/t λ = ln (12/8)/t λ = 0.2877/t

Since we now know the value of λ, we can substitute the values of A0 and λ in the exponential decay equation to find the value of t.

A(t) = A0e-λtA(t) = 12e-0.2877/t

A(t) = 8 (Given)

Therefore, 8 = 12e-0.2877/t 0.6667 = e-0.2877/t

Taking natural logarithm on both sides, we get:

ln (0.6667) = ln (e-0.2877/t)ln (0.6667)

= -0.2877/t ln (e)ln (0.6667)

= -0.2877/t t

= -0.2877/ln (0.6667) t

= 2.10 years.

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Given that a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level. For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the CI's width

Assuming all other factors remained constant, a larger sample would result in a narrower confidence range. Additionally, more sample variability results in a wider range of.

Hence,  a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.

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This means we can be 95% confident that the true population mean annual earnings of all students falls between $2908.29 and $3331.71.

To construct a confidence interval for the population mean, μ, we can use the formula:

CI = x ± z×(σ/√n)

where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), and CI is the confidence interval.

Plugging in the values given in the question, we get:

CI = 3120 ± 1.96×(677/√40)

Simplifying this expression, we get:

CI = 3120 ± 211.71

Therefore, the 95% confidence interval for the population mean, μ, is:

CI = (2908.29, 3331.71)

This means we can be 95% confident that the true population mean annual earnings of all students falls between $2908.29 and $3331.71.

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Answer:

58 tomatoes

37 squash

Step-by-step explanation:

let 's' = squash

let '2s - 16' = tomatoes

s + 2s + 16 = 95

3s + 16 = 95

3s = 111

s = 37 (squash)

2(37) - 16 = 58 (tomatoes)

Answer:

y= 6x -8

Step-by-step explanation:

Slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

\(\boxed{gradient = \frac{y1 - y2}{x1- x2} }\)

Gradient

\( = \frac{4 - ( - 2)}{2 - 1} \)

= 6

y= 6x +c

To find the value of c, substitute the equation with a pair of coordinates.

When x= 1, y= -2,

-2= 6(1) +c

c= -2 -6 (-6 on both sides)

c= -8

Thus, the equation of the line is y= 6x -8.

The statement “there exists a function f such that f(x) < 0, f’(x) > 0, and f”(x) < 0 for all x” is false.

To understand why this statement is false, we must first understand what the symbols mean. The symbol f(x) refers to a function of x, and the symbols f’(x) and f”(x) refer to the first and second derivatives of the function, respectively.

The statement is saying that for all x, the function f(x) will be less than 0, the first derivative f’(x) will be greater than 0, and the second derivative f”(x) will be less than 0.

To show that this statement is false, we need to find an example of a function where this is not the case. Let’s consider the function f(x) = x³. At x = 0, this function is equal to 0, and so f(x) < 0 is not true. Additionally, the first derivative at x = 0 is f’(0) = 0, which is not greater than 0. Thus, the statement is false.

We can also show that this statement is false by looking at the graph of the function f(x). A function with the properties given in the statement would have a graph that looks like a “U” shape, with a minimum point at the origin. However, this is not the case for the function f(x) = x³. The graph of this function is a parabola, which does not have the desired shape.

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Answer:

16 less than two times a number "x"

Answer:

190

Step-by-step explanation:

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Organizations that build strategic information systems create systems that are paramount to business success. The correct option is(D).

Strategic information systems are those that support the long-term goals and objectives of an organization, aligning the use of technology with the strategic direction of the business. These systems provide a competitive advantage by enabling the organization to achieve its strategic goals and objectives more efficiently and effectively.

They typically involve the integration of different types of information systems, such as transaction processing systems, decision support systems, and executive information systems, to support the decision-making process at all levels of the organization.

By building strategic information systems, organizations can improve their overall performance, enhance their operational efficiency, and gain a competitive advantage in the marketplace.

Such systems can help organizations to better understand their customers, identify new market opportunities, improve supply chain management, and optimize business processes.

In today's rapidly changing business environment, strategic information systems are essential for organizations to remain competitive and achieve long-term success.

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Answer:

50%

Step-by-step explanation:

Answer:

If three or more points do not lie on the same straight line, then they are said to be non-collinear points. If any point of all the points is not on the same line, then as a group they are non-collinear points.

Answer:

8% chance out of 19 marbles

Step-by-step explanation:

5 laps

400 meters each lap.

So, to answer this we have to multiply the number of laps by the length of each lap:

400 m x 5 = 2,000 meters

Then we have to convert into kilometers.

Since 1 km= 1000 meters

We have to divide the value in meters by 1000:

2,000 / 1,000 = 2 km

2 kilometers

Answer:

5 laps x 400m = 2000m = 2km

answer is 2 kilometres

Step-by-step explanation:

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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The equation is written as ; <SVT = 90/2

The measure of the angle SVT = 45 degrees

To determine the value of the angle, we need to take into considerations the properties of a right-angled triangle.

These properties are;

From the information given, we have that;

RVT is a right -angled triangle

Since the diagonal SV bisects the angle 90 degrees into two equal halves, then,

<SVT = 90/2

Divide the angle

<SVT = 45 degrees

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Answer:

nn

Step-by-step explanation:

nnnnnn

Answer:

6

Step-by-step explanation:

8 * (1.0 - .25) = 6

Answer: 6

Step-by-step explanation: 8 - 4 is equivalent to 8 - 50%, cut 4 in half which gives 2, 2 is 25% of 8, so 8 - 2 = 6

Answer:

Step-by-step explanation:

one kilogram is 100 times less than one gram

It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.

Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):

E = 10h

$1 = 10h

h = $1/10

Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

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Carys earns one dollar in one-tenth of an hour, or six minutes.

The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.

Set E (the amount earned) to $1 and solve for h (the number of hours):

E = 10h

$1 = 10h

h = $1/10

As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.

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Answer: 3344c^2m^2

Step-by-step explanation:

The solid in question is a triangular pyramid with a semicircular cross-section, the volume of the solid is 16/3 cubic units.

The volume of such a solid can be found using the formula:

V = (1/3)Bh

where B is the area of the base (a triangle) and h is the height of the pyramid.

The area of the triangle can be found using the formula for the area of a triangle:

B = (1/2)bh

where b is the base (4 units) and h is the height (4 units).

So, the area of the triangle is:

B = (1/2)(4)(4) = 8 square units

The height of the pyramid is equal to the radius of the semicircle (2 units), so:

V = (1/3)(8)(2) = 16/3 cubic units

Therefore, the volume of the solid is 16/3 cubic units.

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The objective of this question is to find the absolute maximum and minimum values of a function on a given set. The function is f(x, y) = x² + y² + x²y + 4 and the set is D = {(x, y): |x| ≤ 1, |y| ≤ 1}. We can solve this problem using the method of Lagrange multipliers.

Lagrange multiplier method Let g(x, y) = x² + y² - 1. The set D is the intersection of the region determined by g(x, y) = 0 and the rectangle -1 ≤ x ≤ 1, -1 ≤ y ≤ 1. We can write the Lagrange function as

L(x, y, λ)

= f(x, y) - λg(x, y) = x² + y² + x²y + 4 - λ(x² + y² - 1)

x + xy² = x(x² + y²/2)y + x²y = y(x² + y²/2)

Simplifying, we get:x(x² + y²/2 - y²) = 0y(x² + y²/2 - x²) = 0The solutions are:

x = 0,

y = ±1,

λ = 1/2x = ±1,

y = 0,

λ = 1/2x = ±1/√2,

y = ±1/√2, λ = 3/4

We evaluate f(x, y) at each of these points.

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Answer:

Hello,

Step-by-step explanation:

A very simple sudoku.

You just have to put the condidates.

SOLUTION:

Step 1:

In this question, we are given the following:

A pancake recipe asks for one and one-half times as much milk as flour.

If three and one-half cups of milk are used, what quantity of flour would then be needed, according to the recipe?

Step 2:

The details of the solution are as follows:

The pancakes require 1.5 cups of milk and 1 cup of flour or a ratio of 1.5:1 or a fraction of

(1.5) / (1)

If you have 3.5 cups of milk you need x cups of flour

Set up a ratio of 1.5 / 1 = 3.5 / x

(1.5 divided by 1 equals 3.5 divided by x)

Cross multiply one numerator by the other denominator, and then the other way.

1.5x = 3.5

divide both sides by 1.5

x = 35/15 = 2 1/3 cups

CONCLUSION:

The quantity of flour that would be needed, according to the recipe =