help please! Question Below

Answer:

The Laplace transform of f(t) is (3/s^2) e^(-s) - (2/s) + (1/s^2).

Step-by-step explanation:

We use the definition of the Laplace transform:

L{f(t)} = ∫[0,∞) e^(-st) f(t) dt

For f(t) = t, 0 ≤ t < 1, we have:

L{t} = ∫[0,1] e^(-st) t dt

Integrating by parts with u = t and dv = e^(-st) dt, we get:

L{t} = [-t*e^(-st)/s] from 0 to 1 + (1/s) ∫[0,1] e^(-st) dt

L{t} = [-e^(-s)/s + 1/s] + (1/s^2) [-e^(-s) + 1]

L{t} = (1/s^2) - (e^(-s)/s) - (1/s) + (1/s^2) e^(-s)

For f(t) = 2-t, t ≥ 1, we have:

L{2-t} = ∫[1,∞) e^(-st) (2-t) dt

L{2-t} = (2/s) ∫[1,∞) e^(-st) dt - ∫[1,∞) e^(-st) t dt

L{2-t} = (2/s^2) e^(-s) - [e^(-st)/s^2] from 1 to ∞ - (1/s) ∫[1,∞) e^(-st) dt

L{2-t} = (2/s^2) e^(-s) - [(e^(-s))/s^2] + (1/s^3) e^(-s)

Combining the two Laplace transforms, we get:

L{f(t)} = L{t} + L{2-t}

L{f(t)} = (1/s^2) - (e^(-s)/s) - (1/s) + (1/s^2) e^(-s) + (2/s^2) e^(-s) - [(e^(-s))/s^2] + (1/s^3) e^(-s)

L{f(t)} = (3/s^2) e^(-s) - (2/s) + (1/s^2)

Therefore, the Laplace transform of f(t) is (3/s^2) e^(-s) - (2/s) + (1/s^2).

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Answer:

Step-by-step explanation:

Plugin x and y value in the equation. If both sides are equal, then the points lie on  the line,

1) (9 , 3)

y - 3 = 5(x -9) ;  x = 9 & y = 3

3 - 3 = 5 *(9 - 9)

0     = 5*0

   0   = 0

(9, 3) lies on the described line.

2) (3 , 9) ; x =3 & y = 9

9 - 3 = 5( 3 - 9)

  6   = 5*(-6)

  6 ≠ -30

(3 , 9) does not lies on the described line.

3) (-9, -3)  ; x = -9  & y = -3

-3 - 3 = 5(-9 - 9)

 - 6 = 5 * (-18)

  -6   ≠ -90

(-9 , -3) does not lies on the described line.

4) (-3, -9)

-9 - 3 = 5 (-3 - 9)

-12     = 5*(-12)

   -12 ≠ -60

(-3 , -9) does not lies on the described line.

The sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle. A right triangle is a triangle with two perpendicular sides and one angle that is a right angle.

The given figure has a large right triangle with sides g,h and j and a small right triangle with sides 12, j and 5.

Using the small triangle, we can find the value of j.

By Pythagoras theorem,

j² = 12² + 5² = 144 + 25 = 169

j = 13

Now using trigonometric relation we can find the angle ∅  between j and 5.

sin ∅ = 12/13 = 0.923

∅ =  sin ⁻¹ (0.923) = 67.37°

This angle is common for both triangles.

So for large triangle,

tan 67.37 = h/j = h/13

2.4 = h/13

h = 31.2

By Pythagoras theorem,

g² = h² + j²  = 31.2²  + 13² = 1142.44

g = 33.8

Therefore the sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13.

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The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

the variable.

Step-by-step explanation:

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

(The X intercept is 3) and (the Y intercept is -2)

Step-by-step explanation:

find x intercept by substituting y=0

2x-3×0=6

any expression multiplied by 0 equals 0

2x-0=6

when adding or subtracting 0, the quantity never changes

2x=6

divide both sides of the equation by 2

x=3

find Y intercept by substituting x = 0

2×0-3y=6

solve the equation for y

y=-2

( I hope this helps you! Have a wonderful day everyone!)

:)

Answer:

No, because the product of the slopes is not -1

Step-by-step explanation:

Slope of DE

m = (y2-y1)/(x2-x1)

m = (4 - -2)/(3 - 1) = 6/2 = 3

Slope of FG

m = (y2-y1)/(x2-x1)

m = (0 - 2)/(4 - -1) = -2/5

Product of the slopes of two perpendicular lines is −1

Product of DE and FG = 3(-2/5) = -6/5

Answer: hi

11,28 pound / usd

Step-by-step explanation:

Answer:

11/20

Step-by-step explanation:

5 cents is worth $0.05.

A quarter is worth $0.25.

A dime is worth $0.10

A nickel is worth $0.05

A penny is worth $0.01

In total there are 40 coins in the jar.

The coins that are worth more than $0.05 dollars are the dimes and quarters, so there are 22 coins worth more than $0.05.

Therefore, the probability of of picking a coin worth more than 5 cents is:

22 / 40 = 11/20

The expression (4x+8)² is equivalent to 16x²+64x+64 i.e.D.

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is (4x+8)²

=(4x)²+8²+2*4x*8         As ((a+b)²=a²+b²+2ab)

=16x²+64+64x

hence,

          (4x+8)² is equivalent to 16x²+64x+64.

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Based on the information provided, Jaya is twenty-eight years old.

We already know there are three siblings and their ages if added are 84. Based on this information, let's find the approximate age of these siblings:

This means their average age is twenty-eight.

However, they are not the same age and their ages are consecutive. Based on this let's create a sequence:

27+28+29 = 84

Based on this, Jaya is 28 years old and her siblings are 27 and 29.

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The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Answer:

The conditions for calculating a confident surgery were clearly not past.

Step-by-step explanation:

When you are testing a vaccine of a surgery, there needs to be a over 60% success rate at which the vaccine of the surgery is affective, otherwise, it is decided that that medical procedure of medicine isn't safe. There have been some exceptions in the past when a vaccine for example was used with a 40% success rate, only because the public required this vaccine in there time.

Answer:ur mom

Step-by-step explanation:

30/60=x

x*20

Step-by-step explanation:

What a question.. expect a huge number as the answer

What we need to do is convert days into seconds, and then multiply that number by 20.

30 days

24 hours in 1 day

60 minutes in 1 hour

60 seconds in 1 minute.

So what we do is multiple these 4 numbers

\(60 \times 60 \times 24 \times 30 = 2592000\)

There are 2,592,000 seconds in 30 days.

Now we take that number and multiply it by 20 coins

\(2592000 \times 20 = 51840000 \: coins\)

Answer:

-59049

Step-by-step explanation:

Find the common ratio

3 * r = -9

 r = -3

from first to 10th is 9 ratios

   3 * (-3)^9 = -59049

Answer:

see below

Step-by-step explanation:

My gas tank can hold 16 gallons.

I go to the station to fill it at 2 dollars a gallon.

The domain is how much gas I put in the car

The domain is the set of real number between 0 and 16 gallon

The range is the cost of my gas.  It is  the set of real numbers between 0 and 32 .00 dollars

Answer:

Create your own real-world example of a relation that is a function.

Domain: The set of: 0

Range: The set of: 16

The statement "The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained" is A) True.

The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained. This is a fundamental principle in statistics and is known as the central limit theorem.

The distribution of sample means is a probability distribution that shows the average values of a variable for all possible samples of a certain size taken from a population. The mean of this distribution is equal to the mean of the population.

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S = {1, -∞, ∞}: inf S = -∞, min S = d.n.e., max S = ∞, sup S = ∞

S = {x ∈ ℝ | x³ - 4x² + x + 6 > 0}: inf S = d.n.e., min S = d.n.e., max S = d.n.e., sup S = d.n.e.

For the set S = {1, -∞, ∞}, the infimum is -∞ as there is no lower bound, and the supremum is ∞ as there is no upper bound. However, there is no minimum or maximum element within the set.

The set S = {x ∈ ℝ | x³ - 4x² + x + 6 > 0} represents the solution set to the given inequality. In this case, the set has no infimum, minimum, maximum, or supremum since it does not have a lower bound or an upper bound.

The set S = {m, n ∈ ℕ | m ≥ 1, n ≥ 2} represents all pairs of natural numbers where m is greater than or equal to 1 and n is greater than or equal to 2. The infimum and minimum of the set are both 1 since the set includes 1 as the smallest element. However, there is no maximum or supremum as there is no upper bound to the set.

The set S = {x ∈ ℝ | x ≤ 2} represents all real numbers less than or equal to 2. In this case, the infimum is -∞ since there is no lower bound, and the supremum is 2 as it is the largest element in the set. However, there is no minimum element within the set.

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Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

The distance between (-4, 8) and (8, 8) is:

d₁ = √( (-4 - 8)² + (8- 8)²) = 12

The distance between (8, 8) and (-4, 3) is:

d₂ = √( (8 + 4)² + (8- 3)²) = 13

The distance between (-4, 8) and (-4, 3) is:

d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5

if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:

5² + 12² = 13²

Solving that we get:

25 + 144 = 169

169 = 169

This is true, so yes, the vertices are the vertices of a right triangle.

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Step-by-step explanation:

To solve the equation 4e^(2x) - 1 = 13 for x, we will follow these steps:

Step 1: Add 1 to both sides of the equation to isolate the term with the exponential:

4e^(2x) = 14

Step 2: Divide both sides of the equation by 4 to isolate the exponential term:

e^(2x) = 14/4

Simplifying the right side:

e^(2x) = 7/2

Step 3: Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential:

ln(e^(2x)) = ln(7/2)

By the properties of logarithms, the ln and e^(2x) cancel each other out:

2x = ln(7/2)

Step 4: Divide both sides of the equation by 2 to solve for x:

x = (1/2) ln(7/2)

Thus, the solution to the equation 4e^(2x) - 1 = 13 is x = (1/2) ln(7/2).

Answer:

b = 58°
c = 122°

Step-by-step explanation:

b = 180° - 122° = 58°

c = 122°

Hope this helps

Answer:

$3.78

Step-by-step explanation:

$1.79+$1.99=$3.78

Answer:

$3.78

Step-by-step explanation:

true

The planet that has the larger mass is the planet B and the measurements in standard forms are

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

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

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Statement:

Reason:

Answer:

statement:

4. sd = sd

im sorry if is a small answer

but hope its help

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The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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