Solve AEFG. Round all measurements to the nearest tenth.
E
5.8 cm
F
4.9 cm

Answer:

49950

Step-by-step explanation:

111% of 45000 is 49950

Answer:

The amount Craig financed at the beginning(P) = 45000

Number of years he took to repay(T) = 5

Rate of interest(R) = 11%

Total interest he paid = PTR/100

= 45000(5) (11) / 100

= 450 × 55 = 24,750

Therefore Craig will have paid $24,750

Step-by-step explanation:

The polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

What is factoring a polynomial?

Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a given field or in integers.

Consider, the given polynomial

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

We can use a factoring "trick" here....write this as

x^4 +  9x^3 + 14x^2  + x^2  + 9x  + 14 = 0    factor by grouping

x^2 ( x^2 + 9x + 14)  +  1 ( x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

⇒ (x^2 + 1) = 0,  (x^2 + 9x + 14) = 0

x^2 = -1,          x^2 + 7x + 2x + 14 = 0

x = ±i ,              x(x + 7) + 2(x + 7) = 0

x = ±i ,              (x + 7)(x + 2) = 0

⇒ (x + i)(x - i)(x + 7)(x - 7) = 0

(x + 1i) ( x - 1i) (x+ 7) ( x + 2) = 0

Hence, the polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

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Answer:

g(x) = (x + 5)(x + 1)(x - 7)

Step-by-step explanation:

i know for a fact im right

The complete equation of function whose zeros are given;

                               f(x) = (x+5)(x+1)(x-7)

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.

Here, given zeros are;

   -5, -1, 7

then we can write;

x = -5,  x = -1; x = 7

x +5 = 0 ; x + 1 = 0 ; x - 7 = 0

On multiplying all the terms we get;

(x+5)(x+1)(x-7) = 0

Thus, The complete equation of function whose zeros are given;

                               f(x) = (x+5)(x+1)(x-7)

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The number of boxes required to ship n units of the product can be expressed using the floor notation as \($\left\lfloor\frac{n}{36}\right\rfloor$\) and using the ceiling notation as \($\left\lceil\frac{n}{36}\right\rceil$\).

The floor notation gives the largest integer less than or equal to the quotient of n divided by 36. It is appropriate to use the floor notation when we want to round down to the nearest integer value. For example, if we have 100 units of the product, we would need \($\left\lfloor\frac{100}{36}\right\rfloor=2$\) boxes, meaning we would need to ship the product in two boxes.

The ceiling notation gives the smallest integer greater than or equal to the quotient of n divided by 36. It is appropriate to use the ceiling notation when we want to round up to the nearest integer value. For example, if we have 38 units of the product, we would need \($\left\lceil\frac{38}{36}\right\rceil=2$\) boxes, meaning we would need to ship the product in two boxes.

In most cases, it is appropriate to use the ceiling notation since it ensures that we always have enough boxes to ship the product. However, in some cases, such as when we want to minimize shipping costs, it may be more appropriate to use the floor notation to reduce the number of boxes needed.

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(a) The vectors [8, 10] and [x, 9] in R^2 are linearly independent for x ≠ 7.2.

(b) The vectors [1, 10, 1] and [2, x, 11] are linearly dependent for x = 20.

(a) To determine the values of x for which the vectors [8, 10] and [x, 9] in R^2 are linearly independent, we can set up the linear independence equation:

c1 * [8, 10] + c2 * [x, 9] = [0, 0]

where c1 and c2 are scalars.

Expanding the equation, we get:

[8c1 + xc2, 10c1 + 9c2] = [0, 0]

This gives us the following system of equations:

8c1 + xc2 = 0

10c1 + 9c2 = 0

To determine the values of x for linear independence, we need to find non-zero solutions for c1 and c2. Let's solve the system of equations:

From the first equation, we can solve for c1 in terms of c2:

c1 = -xc2/8

Substituting this into the second equation:

10(-xc2/8) + 9c2 = 0

-10xc2 + 72c2 = 0

(72 - 10x)c2 = 0

For the equation to hold true, either (72 - 10x) = 0 or c2 = 0.

If (72 - 10x) = 0, then x = 7.2.

If c2 = 0, it implies that c1 = 0 as well, which means the vectors are linearly dependent.

Therefore, the vectors [8, 10] and [x, 9] in R^2 are linearly independent for x ≠ 7.2.

(b) To determine whether the vectors [1, 10, 1] and [2, x, 11] are linearly dependent or independent in R^3, we can set up the linear independence equation:

c1 * [1, 10, 1] + c2 * [2, x, 11] = [0, 0, 0]

Expanding the equation, we get:

[c1 + 2c2, 10c1 + xc2, c1 + 11c2] = [0, 0, 0]

This gives us the following system of equations:

c1 + 2c2 = 0

10c1 + xc2 = 0

c1 + 11c2 = 0

To determine the linear independence, we need to find non-zero solutions for c1 and c2. Let's solve the system of equations:

From the first equation, we can solve for c1 in terms of c2:

c1 = -2c2

Substituting this into the second equation:

10(-2c2) + xc2 = 0

-20c2 + xc2 = 0

(-20 + x)c2 = 0

For the equation to hold true, either (-20 + x) = 0 or c2 = 0.

If (-20 + x) = 0, then x = 20.

If c2 = 0, it implies that c1 = 0 as well, which means the vectors are linearly dependent.

Therefore, the vectors [1, 10, 1] and [2, x, 11] are linearly dependent for x = 20.

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Answer:

C) 60 ft

Step-by-step explanation:

From any dot in the graph you can figure out the speed.

Let's take the one at 2 minutes, because it is on a grid point.

That one tells us that in 2 minutes, the animal travels 40 feet.

That means in 1 minute, it travels half that, i.e., 20 feet.

So in 3 minutes it will travel 20*3=60 feet.

The height of the cylinder is 4 feet.

The volume of a cylinder can be found as follows;

volume of a cylinder = base area × height

Therefore,

base area = πr²

volume of the cylinder = 48π ft³

base area = 12π ft²

Therefore, let's find the height of the cylinder as follows:

48π = 12π × h

divide both sides of the equation by 12π

h = 48π / 12π

h = 4 ft

Therefore,

height of the cylinder  = 4 feet

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Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14

Step-by-step explanation:

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

  (x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

  if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

  magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

  by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

 and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The composition of transformations that maps BCD to B"C"D" is described by the following rule:

Composition translation of 6 units x, negative 5 units y across the y-axis last response

Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.

1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)

2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)

3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)

∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.

The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)

The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)

The x-coordinates of the triangle B'C'D' vertices are added by 6.

The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.

The y-coordinates of triangle B'C'D' vertices are subtracted by 5.

∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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Answer:

c.6x-8 d.-x-12 e.-40x f.9x-13 g.6x-18 h.15x-30 i.-15a+35 j.-12

Answer:

68

Step-by-step explanation:

just put the value of a and b in the expression and you will get the answer

20/a+7.b is

20/4+7×9

5+63

68

Answer:

C. 68

Step-by-step explanation:

Fill in your values.

20/ 4 + 7 x 9

Solve using PEMDAS.

5 + 7 x 9

5 + 63

68

The points that are collinear are points E,H and K

Two or more points are said to be collinear, if the points are on the same line

From the figure, we have the following points

J, E, H, K, L and I

Of the 6 points, the points E, H and K are on the same line

i.e. line EK

Hence, the points that are collinear are points E,H and K

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Answer:E,H and K

Step-by-step explanation:

Approximately 47.72% of the students scored between 167 and 253 on the exam. To find the percentage of students who scored between 167 and 253 on the exam, we can use the properties of the normal distribution.

Given that the scores are normally distributed with a mean of 253 and a standard deviation of 43, we can calculate the z-scores for the two given scores and then use the z-table to find the corresponding probabilities. First, let's calculate the z-score for the lower score of 167:

z1 = (167 - 253) / 43

z1 ≈ -2

Next, let's calculate the z-score for the upper score of 253:

z2 = (253 - 253) / 43

z2 = 0

Using the z-table, we can find the area under the normal curve between z1 and z2, which represents the percentage of students who scored between 167 and 253 on the exam.

Since the z-score of z1 is -2, we look up the area to the left of -2 in the z-table, which is approximately 0.0228. This represents the percentage of students who scored below 167.

Since the z-score of z2 is 0, we look up the area to the left of 0 in the z-table, which is 0.5000. This represents the percentage of students who scored below 253.

To find the percentage of students who scored between 167 and 253, we subtract the percentage below 167 from the percentage below 253:

Percentage = 0.5000 - 0.0228 ≈ 0.4772

Therefore, approximately 47.72% of the students scored between 167 and 253 on the exam.

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Therefore, on average, a customer arriving during the morning rush would wait approximately 2.17 hours to be served.

To determine the average waiting time for a customer arriving during the morning rush at the coffee shop, we need to consider the arrival rate and the capacity of the shop.

Given that 100 customers per hour arrive at the coffee shop during the two-hour morning rush, and the shop has a capacity of 80 customers per hour, we can conclude that there will be more customers arriving than the shop can accommodate.

To calculate the average waiting time, we need to account for the time spent by customers who have to wait due to the shop being at full capacity. For simplicity, let's assume that customers arrive uniformly throughout the two-hour period.

During the first hour (8 a.m. to 9 a.m.), there will be 100 customers arriving, but the shop can only serve 80 customers. Therefore, 20 customers will have to wait for their turn to be served.

During the second hour (9 a.m. to 10 a.m.), again, 100 customers will arrive, but since the shop is already at full capacity, all 100 customers will have to wait for their turn.

In total, during the two-hour morning rush, there will be 20 customers who wait for one hour and 100 customers who wait for the entire two hours.

To calculate the average waiting time, we can sum up the waiting times and divide by the total number of customers:

Average waiting time = (20 * 1 hour + 100 * 2 hours) / (20 + 100) = (20 + 200) / 120 = 2.17 hours

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Answer:

180.

Step-by-step explanation:

Trust me.

The probability that there are no counts in a 30 second interval is 0.284

What is probability ?

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.

Given that,

Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.

0.284

P(X < 10 Seconds)  = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284

Therefore, the  probability that there will be no counts in a 30-second period is 0.284.

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There are 210 sequences for 7 church bells to rung with the given conditions. Using permutations, the required number of sequences is calculated.

A sequence or arrangement that can be framed by taking some or all of a finite set of things (or objects) is called a permutation.

The formula for finding the number of such arrangements is,

ⁿPₓ = n!/(n - x)!

It is given that, a church's bell tower has 7 bells. 3 of them will ring in a sequence before each service and no bell is rung more than once.

So, the number of sequences that the bells will form is calculated by using the permutations formula. I.e., ⁿPₓ = n!/(n - x)!

Here, n = 7; x = 3

Then,

ⁿPₓ = n!/(n - x)! ⇒ ⁷P₃ = 7!/(7 - 3)! = 7!/4!

⇒ ⁷P₃ = (7 × 6 × 5 × 4!)/4! = 7 × 6 × 5 = 210

Therefore, there are 210 sequences for ringing the bells.

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The expected activity time for the given statement is = 5.33

The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.

A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.

optimistic = 2

most likely = 5

pessimistic = 10.

We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:

Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6

Putting the values into formula:

= (2 + (4 x 5) + 10)/ 6

= (2 + 20 + 10) / 6

= 5.33

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Answer:

126

Step-by-step explanation:

180-54=126

Answer:

m=-11/14

Step-by-step explanation:

Answer: 75 Grapes

Step-by-step explanation:

14 grapes left + 39 grapes Ana ate + 22 grapes Xan ate = Original 75 grapes in the bag

Answer:

There were 75 grapes in the bag before the trip

Step-by-step explanation:

First, you will need to add up all the grapes that they ate.

39+22=61

Then, you need to add the left over grapes and the grapes that both of them ate all together.

61+14=75

So, they had 75 grapes in the bag before the trip.

In this simulation experiment, the population distribution represents the lifetimes of a certain type of electronic control and the density curve in the figure represents the population distribution.

The distribution is skewed and follows a lognormal distribution with an expected value of ln(X) equal to 3 and a variance of ln(X) equal to 0.16. The experiment consisted of 500 replications and examined different sample sizes: n = 5, n = 10, n = 20, and n = 30.

The density curve in the figure represents the population distribution, with an expected value of E(A) equal to 21.7584 and a variance of V(X) equal to 82.1449. The histograms shown illustrate the distribution of sample means for the different sample sizes. Additionally, a normal probability plot from MINITAB is included for the x-values based on a sample size of n = 30, allowing for an assessment of the normality assumption for the sample means.

These visual representations provide valuable insights into the characteristics of the simulated experiment's population distribution, as well as the behavior of the sample means for different sample sizes.

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The complete question is:

Consider a simulation experiment in which the population distribution is quite skewed. The figure below shows the density curve for lifetimes of_a certain type of electronic control [this is actually a lognormal distribution with E(ln(X)) = 3 and V(ln(X)) = 0.16]. The statistic of interest is the sample mean X. The experiment utilized 500 replications and considered these sample sizes: n = 5, n = 10, n = 20, and n = 30. The resulting histograms along with a normal probability plot from MINITAB for the x values based on n = 30 are shown in the figures below. Density curve for the simulation experiment (E(A) = 21.7584, V(X) = 82.1449].

Answer:

SA: 456

V: 408

Step-by-step explanation:

To find the volume of this prism, you first need to find the area of the triangular base. The base has dimensions 6 by 8, and since it's a triangle, the area of the base is 6*8/2=24. Multiplying this by the length of the prism, you get a volume of 24*17=408. For the surface area, you need to find and add together the areas of all of the surfaces. We have already determined that the area of the two triangular bases are 24. The rectangle formed by the leg with length 6 has area 6*17=102, the one with length 8 has area 136, and the hypotenuse has area 170. Adding all of this together, you get a surface area of 24+24+102+136+170=456 square centimeters. Hope this helps!

Answer:

y=3

Step-by-step explanation:

y=mx+b where m = slope and b=y-intercept
slope: 0, y-intercept: 3

y=(0)x + 3

y=3

A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.

Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.

Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.

Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.

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Recovered memory in CSA refers to the new development of abusive memories. Repressed memory is when the patient believes the CSA occurred, even though they have no specific memory of the event.

Recovered memory:

The term "recovered memory" implies that at some point the memory must become inaccessible to conscious awareness (as opposed to "continuous memory"). Although the term is not ideal, it is clear that people often fail to report important events, such as known hospitalizations (Loftus, 1993). In 1995, the debate over reclaiming memory was near its most violent climax. Hundreds of people have recovered memories of child sexual abuse (CSA), and sometimes in therapy it is thought that repressed or dissociative memories need to be recovered for a person to 'heal'.

Repressed Memory:

Repressed memory is a purported psychiatric phenomenon involving the inability to recall autobiographical information, usually traumatic or stressful. The concept has its origins in psychoanalytic theory, where repression is understood as a defense mechanism that keeps painful experiences and unacceptable impulses out of awareness. Repressed memory is a controversial concept, especially in a legal context, where it is used to unjustly and inaccurately accuse individuals, causing significant harm. Meanwhile, a working group from the American Psychological Association has stated that while "most people who were sexually abused in childhood remember some or all of what happened to them, it is possible to remember long-forgotten abuses.

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