Obtain the Inverse Laplace Transforms of: i. F(S) = (s+1)(s+5)

Answers

Answer 1

The inverse Laplace transform of F(S) = (s + 1)(s + 5) is δ''(t) + δ'(t) + 5δ(t), where δ(t) represents the Dirac delta function.

To obtain the inverse Laplace transform of F(S) = (s + 1)(s + 5), we can use the linearity property and the inverse Laplace transform table.

The table states that the inverse Laplace transform of s + a is equal to the Dirac delta function δ(t - a), and the inverse Laplace transform of a constant times F(S) is equal to the constant times the inverse Laplace transform of F(S).

Applying these properties, we can write:

F(S) = (s + 1)(s + 5)

= s^2 + 6s + 5

Using the linearity property, we can split this expression into three terms:

F(S) = s^2 + 6s + 5 = s^2 + s + 5s + 5

Taking the inverse Laplace transform of each term separately, we have:

L^(-1){s^2} + L^(-1){s} + 5L^(-1){s} + 5L^(-1){1}

Referring to the inverse Laplace transform table, we find that:

L^(-1){s^2} = δ''(t)

L^(-1){s} = δ'(t)

L^(-1){1} = δ(t)

Therefore, the inverse Laplace transform of F(S) = (s + 1)(s + 5) is:

L^(-1){F(S)} = δ''(t) + δ'(t) + 5δ(t)

In summary, the inverse Laplace transform of F(S) = (s + 1)(s + 5) is given by δ''(t) + δ'(t) + 5δ(t).

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Related Questions

The diameter of a circle is 20 centimeters. What is the circumference?

Answers

C ≈ 62.83cm is the answer!

Hope this helps!

What he said great! Wow

Cheryl's making trail mix for a friend she always uses three cups of almonds for every four cups of cashews if Cheryl wants to make a larger batch of trail mix which of the following has the same ratio of almonds cashews
A. 9 cups of almonds for every 20 cups of cashews
B. 6 cups of almonds for every 12 cups of cashews
C. 9 cup of almonds for every 12 cups of cashews
D. 12 cups of almonds for every 20 cups of cashews

Answers

Answer:

c

Step-by-step explanation:

3x3=9

4x3=12

Answer:

C

Step-by-step explanation:

3 cups of almonds / 4 cups of cashews

So to get 9 cups of almonds, we need to multiply almonds and cashews by 3

3*3 = 9 cups of almonds

4*3 = 12 cups of cashews

So the correct answer is C

How would I find the arc of WTV

Answers

To find the arc of circle WTV, you need the arc length or central angle. Use formulas: Arc Length = (Arc Angle / 360) × (2πr) or Arc Length = (Central Angle / 360) × (2πr).

To find the arc of a circle, WTV, you would need to know either the length of the arc or the measure of the central angle subtended by the arc. If you have the length of the arc, you can use the formula:

Arc Length = (Arc Angle / 360 degrees) × (2πr),

where r is the radius of the circle. Rearranging the formula, you can solve for the Arc Angle:

Arc Angle = (Arc Length / (2πr)) × 360 degrees.

If you know the measure of the central angle, you can calculate the arc length using a similar formula:

Arc Length = (Central Angle / 360 degrees) × (2πr).

To find the radius, you would need additional information such as the diameter or circumference of the circle. Once you have the radius, you can substitute the values into the appropriate formula to find either the arc length or the central angle of the circle.

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Find the value of x. I WILL MARK YOU BRAINLIEST!!!

Answers

Answer:

4x+3x+2x=180

9x=180

x=20

a 18 The number 21 has no composite factors. What is another number that has no composite factors? A. 27- B. 52- C. 77- D. 81-​

Answers

The number that has no composite factors is (c) 77

How to determine another number that has no composite factors

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

Number = 21

The factors of 21 are 3 and 7

These factors are composite numbers because they are prime numbers

using the above as a guide, we have the following:

The number 77 has no composite factors

This is so because

77 = 7 * 11

These factors are composite numbers because they are prime numbers

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There are 180 trees in gardner grove orchard, and 18 of them are pears. What percent of the trees are pear trees?

Answers

the answer is 32.4%

the quotient of 17 and z

Answers

Answer:

17÷z = quotient

Step-by-step explanation:

quotient = ÷

Renee is a sales associate at a store. She earns $80 a week plus a 15% commission on her sales. Last week, she sold $200 worth of items. What is the total amount Renee earned for the week? How much did she earn from commission?
Renee earned a total of $
for the week. The amount she earned from commission was $
.

Answers

Answer:

The amount earned for the week=$110

Amount earned from commission =$30

Step-by-step explanation:

commission earned on sales = $200×15%= $30

total amount for the week=$80 +$30= $110

Use the binomial series to find a Taylor polynomial of degree 3 for 1 91 +32 T3(0) X + c? + 23

Answers

The Taylor polynomial of degree 3 for the function 1/(1-2x) centered at x=0 is (1+2x+4x²+8x³).

Explanation: Given, 1/(1-2x) = ∑n=0 to infinity of 2^n * x^n The above series is the binomial series for (1+x)^n where n=-1Using the binomial series for n=-1, we have1/(1-2x) = ∑n=0 to infinity of 2^n * x^n= ∑n=1 to infinity of 2^(n-1) * x^(n-1)= 1 + ∑n=1 to infinity of 2^n * x^nTaking up to degree 3, we get1/(1-2x) = 1 + 2x + 4x² + 8x³ + ...Therefore, the Taylor polynomial of degree 3 for 1/(1-2x) is 1 + 2x + 4x² + 8x³.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. for Brook Taylor, who introduced the Taylor series in 1715, they are named for him. In honour of Colin Maclaurin, who made great use of this unique example of Taylor series in the middle of the 18th century, a Taylor series is sometimes known as a Maclaurin series where 0 is the point at which the derivatives are taken into account.

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Find the inverse Laplace transform of

a) F(s)= 10/s(s+2)(s+3)²

b) F(s)= s/s²+4s+5

c) F(s)=e^-3s s/(s-2)^2 +81

Answers

a) The solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

b) The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The solution to the given problem is L(F) = 1/9 [[tex]e^{2t}[/tex] sin 9t - 3[tex]e^{2t}[/tex]) cos 9t]

(a)The inverse Laplace transform of F(s) = 10/s(s + 2)(s + 3)² can be found as follows:

L(F) = L{10/[s(s + 2)(s + 3)²]}

= 10 ∫∞₀[tex]e^{-st}[/tex]) /[s(s + 2)(s + 3)²] dt

L{F} = L⁻¹{10/[s(s + 2)(s + 3)²]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily.

L(F) = 10 ∫∞₀ {1/s - 2/(s + 2) + 3/(s + 3) - 2/(s + 3)² + 1/(s + 2)(s + 3)} [tex]e^{-st}[/tex]dt

L{F} = L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

As the inverse Laplace transform of L{F} is given by L(F)

= L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}

Thus, the solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]

(b)

The inverse Laplace transform of F(s) = s/[s² + 4s + 5] can be found as follows:

L(F) = L{s/[s² + 4s + 5]}

= ∫∞₀ s e^(–st) / (s² + 4s + 5) dt

L{F} = L⁻¹{s/[s² + 4s + 5]}

By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily. L(F) = ∫∞₀ [s/(s² + 4s + 5)] [tex]e^{-st}[/tex]) dt

L{F} = L⁻¹{s/(s² + 4s + 5)}

The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)

c) The inverse Laplace transform of F(s) = ([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81] can be found as follows:

L(F) = L{([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81]}= ∫∞₀ ([tex]e^{-st}[/tex]) s/[(s - 2)² + 81] dt

L{F} = L⁻¹{([tex]e^{-3s}[/tex])) s/[(s - 2)² + 81]}

So, The solution to the given problem is L(F) = 1/9 [([tex]e^{2t}[/tex]) sin 9t - 3([tex]e^{2t}[/tex]) cos 9t]

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Find the length of the third side if necessary write in simplest radical form

Answers

Answer:

hi

Step-by-step explanation:

Find the range of the function

Answers

Answer:

y€ R : y greater than or equal to 1

I'll give brainliest please help​

Answers

Answer:

∠R = 38°

Step-by-step explanation:

∠R = 1/2(arc PE - arc SQ)

∠R = 1/2(140 - 64) = 1/2(76) = 38°

The data set below represents a sample of scores on a 10-point quiz. 7, 4, 9, 6, 10, 9, 5, 4 Find the sum of the mean and the median

Answers

The sum of the mean and the median of the given dataset, which consists of the scores 7, 4, 9, 6, 10, 9, 5, and 4, is 13.25.

To find the sum of the mean and the median, we first need to calculate the mean and median of the given dataset.

The dataset is: 7, 4, 9, 6, 10, 9, 5, 4

To find the mean, we sum up all the numbers in the dataset and divide by the total number of data points:

Mean = (7 + 4 + 9 + 6 + 10 + 9 + 5 + 4) / 8 = 54 / 8 = 6.75

To find the median, we arrange the numbers in ascending order:

4, 4, 5, 6, 7, 9, 9, 10

Since we have 8 data points, the median will be the average of the two middle numbers:

Median = (6 + 7) / 2 = 6.5

Now we can find the sum of the mean and the median:

Sum of mean and median = 6.75 + 6.5 = 13.25

Therefore, the sum of the mean and the median of the given dataset is 13.25.

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The linear approximation at z = 0 to sin(42) is A + Bz where A is:

Answers

the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

The linear approximation of a function f(x) at a point x = a is given by the equation f(x) ≈ f(a) + f'(a)(x - a). In this case, we want to approximate sin(42) at z = 0.

The derivative of the sine function is cos(x), so the derivative of sin(42) with respect to z is cos(42). Evaluating the derivative at z = 0, we have cos(42).

To find A in the linear approximation A + Bz, we substitute z = 0 into the original function sin(42) and obtain A = sin(42).

Therefore, the linear approximation at z = 0 to sin(42) is A + Bz, where A = sin(42) and B is the coefficient of z, which is cos(42).

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Q1
The sum of the first 68 positive odd integers is ?

Q2
The degree of recurrence relation an = 2an-2 + 5an-49 is ??

Q3
In how many ways can an organization containing 19 members elect a president, treasurer and secretary (assuming no person is elected to more than one position)?

Q4
The Greatest Common Divisor (GCD) of 28 × 37 × 58 and 23 × 33 × 54 is ??

Answers

Q1: Sum of first 68 positive odd integers.

Let's represent the first 68 positive odd integers by: 1, 3, 5, 7, ..., 135, 137. The first term, a = 1. The last term, l = 137And, the number of terms, n = 68We need to find the sum of these terms. To find the sum of an arithmetic series, we use the following formula: Sn = n/2[2a + (n-1)d]. Here, d = common difference. Since the given sequence is of odd numbers, the difference between any two consecutive terms is 2. So, d = 2. Put these values in the formula to get: Sn = 68/2[2(1) + (68-1)2], Sn = 34[2 + 135], Sn = 68 × 67Sum of first 68 positive odd integers = 4546.

Q2: Degree of recurrence relation. To find the degree of a recurrence relation, we find the largest value of n in the relation. Here, an = 2an-2 + 5an-49The largest value of n in the relation is n = 49. So, the degree of the recurrence relation is 49.

Q3: Number of ways to elect office bearers in an organization. Let's assume that the 19 members of the organization are named M1, M2, M3, ..., M19. The president can be elected in 19 ways. After the president is elected, the treasurer can be elected in 18 ways. After the treasurer is elected, the secretary can be elected in 17 ways. Therefore, the total number of ways in which the president, treasurer, and secretary can be elected is:19 × 18 × 17 = 5,814.

Q4: Greatest Common Divisor (GCD)To find the GCD of two numbers, we need to find their prime factors.28 × 37 × 58 = 2² × 7 × 37 × 2 × 29 = 2³ × 7 × 29 × 37Similarly, 23 × 33 × 54 = 23 × 3² × 2 × 3 × 3 × 2 × 3 = 2³ × 3⁵ × 23.

The common prime factors are 2³ and 23. So, the GCD is: 2³ × 23 = 184. The GCD is 184.

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if a, b, and c are n n invertible matrices, does the equation c 1 .a c x /b 1 d i n have a solution, x? if so, find it.

Answers

The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.

Further information about the matrices and their properties is required to determine the specific solution.

To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.

Let's break down the equation:

c₁: The first column of matrix c.

a: Matrix a.

c: Matrix c.

x: The solution vector.

b₁: The first row of matrix b.

d: Matrix d.

iₙ: The identity matrix of size n.

For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.

Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.

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What is the probability of spinning a number greater than 4?

Answers

Answer:

Please upload the full question.....here the total number of outcomes is not mentioned and hence it can't be solved.

Answer:

Hence, the required probability of getting a number greater than 4, P(E) = 1/3.

Step-by-step explanation:

The width of a rectangular frame is 6 in. shorter than its length. The area of the frame is 216 in?
What is the frame's length?

Answers

Answer:

18 in

Step-by-step explanation:

len = y

width= y - 6

the area of rectangle is len x width

(Y) x (Y-6) = 216

Y^2 - 6Y = 216, Y^2 - 6y -216 = 0

y = (36 /2) or (-24 /2)

len couldn't be negative so 18

Joey made strawberry jam and raspberry jam. He made enough strawberry jam to fill 1/2 of a jar. If he made 2/5 as much raspberry jam as strawberry jam, how many jars will the raspberry jam fill?

Answers

Answer:  1/5 of a jar

Step-by-step explanation:

1/2 times 2/5= .2 = 1/5.

Answer:

1/5 of a jar

Step-by-step explanation:

A part manufactured at a factory is known to be 12.05 cm long on average, with a standard deviation of 0.350. One day you suspect that that the part is coming out a little longer than usual, but with the same deviation. You sample 14 at random and find an average length of 12.20. What is the z-score which would be used to test the hypothesis that the part is coming out longer than usual?

Answers

The z-score to test the hypothesis that the part is coming out longer than usual is approximately 1.61.

Sample mean = x = 12.20 cm

Population mean = μ = 12.05 cm

Standard deviation = σ = 0.350 cm

Sample size = n = 14

A hypothesis is an informed prediction regarding the solution to a scientific topic that is supported by sound reasoning. there is the expected result of the experimentation even if there is not proved in an experiment.

Calculating the z-score -

[tex]z = (x - u) / (\alpha / \sqrt n)[/tex]

Substituting the values -

[tex]z = (12.20 - 12.05) / (0.350 / \sqrt{14)[/tex]

= z = 0.15 / (0.350 / √14)

= 0.093

Substituting the value again into the formula:

z = 0.15 / 0.093

= 1.61

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Find the first three terms of x[n] using power series expansion if X(z) 2z3 + 13z2 + 7 73 + 722 + 2z + 1 =

Answers

The first three terms of x[n] using the power series expansion are x[0] = 73, x[1] = 2, and x[2] = 13.

We can select the first three terms of x[n] using the power series development by expressing the given articulation X(z) as a polynomial in z. We should modify the articulation as follows to obtain the power series development: By comparing the given expression to the power series form, the coefficients can be identified: X(z) equals 2z3, 13z2, 7z, 73, 722/z, 2/z, and 1: a0 rises to 73, a1 approaches 2, a2 approaches 13, and a3 approaches 7. X(z) = a0, a1z, a2z2, a3*z3, and... Consequently, the following are the first three terms of x[n]:

The initial three terms of x[n] are provided by the power series development: x[0] = a0; x[1] = a1; x[2] = a2; x[0] = a0; The values of x[0] and x[1] are 73, 2, and 13.

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How many zeros appear at the end of 115!? Do not compute 115!.
Your argument must come from prime factorizations to receive
credit.

Answers

there will be 27 zeros at the end of 115!.

To determine the number of zeros at the end of 115!, we need to consider the prime factorization of the number and examine how many factors of 5 are present.

A zero at the end of a factorial occurs when there is a factor of 10 present, which is equivalent to having both factors of 2 and 5. Since the number of factors of 2 is usually abundant, the crucial factor is the number of factors of 5.

In the prime factorization of 115!, the factors of 5 arise from the multiples of 5 (5, 10, 15, 20, ...) as well as higher powers of 5 (25, 50, 75, ...). We need to determine how many multiples of 5, multiples of 25, multiples of 125, and so on are present.

1. Multiples of 5: The number of multiples of 5 in 115! is given by ⌊115/5⌋ = 23.

2. Multiples of 25: The number of multiples of 25 in 115! is given by ⌊115/25⌋ = 4.

3. Multiples of 125: The number of multiples of 125 in 115! is given by ⌊115/125⌋ = 0 since there are no numbers in the range 1 to 115 that are multiples of 125.

Adding up these counts, we have 23 + 4 = 27 factors of 5.

Therefore, there will be 27 zeros at the end of 115!.

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A population of values has a normal distribution with u = 42.3 and o = 44.6. You intend to draw a random sample of size n = 20. Find the probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =
Previous question

Answers

(a) The probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = 0.6965.

(b) The probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =  0.9883.

To solve these probability questions, we can utilize the properties of the standard normal distribution since we know the mean and standard deviation of the population.

(a) Find the probability that a single randomly selected value is greater than 19.4.

To calculate this probability, we need to standardize the value 19.4 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (19.4 - 42.3) / 44.6 = -22.9 / 44.6 ≈ -0.51498

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -0.51498, which is approximately 0.6965.

Therefore, P(X > 19.4) ≈ 0.6965.

(b) Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4.

For this question, we need to consider the sampling distribution of the sample mean. The mean of the sampling distribution is equal to the population mean (μ = 42.3), and the standard deviation of the sampling distribution, also known as the standard error, is equal to σ / √n, where σ is the population standard deviation and n is the sample size.

Standard error = 44.6 / √20 ≈ 9.9766

To find the probability that the sample mean is greater than 19.4, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the value (19.4 in this case), μ is the mean, σ is the standard deviation, and n is the sample size.

z = (19.4 - 42.3) / (44.6 / √20) ≈ -22.9 / 9.9766 ≈ -2.2972

Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -2.2972, which is approximately 0.9883.

Therefore, P(M > 19.4) ≈ 0.9883.

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find vertex of this function ​

Answers

Answer:

Step-by-step explanation:

(-1,-9)

At the state fair, admission at the gate is $9. In addition, the cost of each ride is $2. Suppose that Reuben will go on x rides.
Reuben wants the total number of dollars he spends on admission and rides to be fewer than . Using the values and variables given, write an inequality describing this.

Answers

Answer:

i think you forgot to add how little he wants to spend

Step-by-step explanation:

Reuben wants the total number of dollars he spends on admission and rides to be fewer than ??? whats the number that he wants to spend

Write a survey question for which you would expect to collect numerical data.

Answers

Answer:

How many siblings do you have?

Clarence has $90 in a savings account that earns 10% annually. The interest is not
compounded. How much will he have in 5 years?

Answers

Answer:

132 dollars I think

Step-by-step explanation:

The domain of the function f(x) = 8 - 5x is restricted to the positive integers. Which values are elements of the
range?
-2
3
8
13
18
23

Answers

Answer:

23

Step-by-step explanation:

please mark me as brainliest

I need this answer as soon as possible

Answers

The perimeter is the distance all the way around. So it's the sum of the lengths of all 4 sides.

From the picture, you can clearly see the lengths of all 4 sides.

Writum down and adum up !

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The firm operates and experiences demand 365 days per year. Suppose that management mistakenly used the basic EOQ model to calculate the batch size instead of using the POQ model. How much money per year has that mistake cost the company? check sheets have been called which of the following? i. visual ii. complexiii. easy to use and interpret iv. easy to organize data v. a complete waste of timea. I,II,III,IV,Vb. I,III,IV,Vc. I,II,III,IVd. III,IV,V when was the element copper discovered? Who discovered the element copper? HELP!HELPPPPPPPPPPPPP!!!!!ASAPPPP NO LINKS!!!!!!!! ONLY GIVE ME REAL ANSWERS!!!!!!!!Memories of a MemoryHave you ever witnessed something amazing, shocking or surprising and found when describing the event that your story seems to change the more you tell it? Have you ever experienced a time when you couldn't really describe something you saw in a way that others could understand? If so, you may understand why some experts think eyewitness testimony is unreliable as evidence in scientific inquiries and trials. New insights into human memory suggest human memories are really a mixture of many non-factual things.First, memory is vague. Imagine your room at home or a classroom you see every day. Most likely, you could describe the room very generally. You could name the color of the walls, the floors, the decorations. But the image you describe will never be as specific or detailed as if you were looking at the actual room. Memory tends to save a blurry image of what we have seen rather than specific details. So when a witness tries to identify someone, her brain may recall that the person was tall, but not be able to say how tall when faced with several tall people. There are lots of different kinds of "tall."Second, memory uses general knowledge to fill in gaps. Our brains reconstruct events and scenes when we remember something. To do this, our brains use other memories and other stories when there are gaps. For example, one day at a library you go to quite frequently, you witness an argument between a library patron and one of the librarians. Later, when telling a friend about the event, your brain may remember a familiar librarian behind the desk rather than the actual participant simply because it is recreating a familiar scene. In effect, your brain is combining memories to help you tell the story.Third, your memory changes over time. It also changes the more you retell the story. Documented cases have shown eyewitnesses adding detail to testimony that could not have been known at the time of the event. Research has also shown that the more a witness's account is told, the less accurate it is. You may have noticed this yourself. The next time you are retelling a story, notice what you add, or what your brain wants to add, to the account. You may also notice that you drop certain details from previous tellings of the story.With individual memories all jumbled up with each other, it is hard to believe we ever know anything to be true. Did you really break your mother's favorite vase when you were three? Was that really your father throwing rocks into the river with you when you were seven? The human brain may be quite remarkable indeed. When it comes to memory, however, we may want to start carrying video cameras if we want to record the true picture.Which word from the text best describes memories of places? (5 points)VagueFamiliarIndividualRemarkable i need help with this questionn how to find what is the value of the correlation coefficient? What provision of the U.S. Constitution supported capitalism as an economic approach?(A) the article that prevents the government from interfering with contracts(B) the article that establishes the divided structure of the government(C) the section of the preamble devoted to the purpose of the document(D) the amendment that guarantees citizens the right to bear arms Please give me the correct answer.Only answer if you're very good at English.Please don't put a link to a website. How does the concern for nuclear possession and use fail to address human state itself as the ultimate issue? The primary purpose of the Black Codes was to __________.Options: A. make African-Americans inferior citizens in Southern statesB. establish the constitutionality of separate but equalC. segregate African-Americans from white neighbourhoods and schoolsD. integrate African-Americans into white society You catch, tag, and release 35 fish back into a pond. Then, you catch 70 more fish, 12 of which have tags on them,What is the best estimate of the number of fish in the pond?a 100b 150c 142 d 204