Can someone please help me with this ?

Can Someone Please Help Me With This ?

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Answer 1

Answer:

Dealership 2 has the higher loan cost.

Step-by-step explanation:

see attached answer.

Can Someone Please Help Me With This ?

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cant use thisqwdwiwied

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Answer:

ooffffffffffff have a good day/night lol

Answer:

What?? lol

Step-by-step explanation:

(-5,4) and (1,6)
y-6 =? plz help me

Answers

Answer:

(-5,4) and (1,6) are cordanites on a graph 1st square is ++ 2nd is +- 3rd is -- and 4th is -+

Step-by-step explanation:

Write the simplest polynomial function for each set of zeros

Zeros = -2, 5, -1

Answers

Answer:

the answer should be y = x^3 - 2x^2  - 13x - 10

Step-by-step explanation:

x = -2 5 -1

x + 2 = 0

x - 5 = 0

x + 1 = 0

f(x) = (x + 2) (x + 1)

x(x) + 2(x) + x(1) + 2(1)

x^2 + 2x + x + 2

x^2 + 3x + 2

f(x) = (x^2 + 3x + 2) ( x - 5)

x^2(x) + 3x(x) + 2(x) + x^2(- 5) + 3x(- 5) + 2(- 5)

x^3 + 3x^2 + 2x - 5x^2 - 15x - 10

x^3 - 2x^2 - 13x - 10

f(x) = x^3 - 2x^2 - 13x - 10

Step-by-step explanation:

this is your answered give me point

Write the simplest polynomial function for each set of zerosZeros = -2, 5, -1

A rancher genotypes all of her 150 head of cattle. In her herd, 25 are A1A1, 75 are A1A2, and 50 are A2A2. Assuming there is random mating, no selection, no mutation, and no cattle are introduced into or removed from the population, what is the probability that the A1 allele will be fixed

Answers

The probability that the A1 allele will be fixed is 0.4167, or about 42%.

We are given that;

Number of head= 150

Now,

Substitute all known values into the equation from step 4, then solve for the unknown quantity. We know that N = 150, (A1A1) = 25, (A1A2) = 75, and (A2A2) = 50. Substituting these values into the equations for p and q, we get:

\($$p = \frac{2(25) + (75)}{2(150)}$$$$p = \frac{125}{300}$$$$p = 0.4167$$$$q = \frac{2(50) + (75)}{2(150)}$$$$q = \frac{175}{300}$$$$q = 0.5833$$\)

Substituting these values into the equation for Pfix, we get:

\($$Pfix = \frac{p}{p + q}$$$$Pfix = \frac{0.4167}{0.4167 + 0.5833}$$$$Pfix \approx \frac{0.4167}{1}$$$$Pfix \approx 0.4167$$\)

Therefore, by probability the answer will be 0.4167 or about 42%.

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help. i’ll mark brainliest or whatever

help. ill mark brainliest or whatever

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Answer:

angle 1 is 140 degrees and angle 2 is 70 degrees

Step-by-step explanation:

it is two parallel lines with an intersecting line. This means that the two angles will be the same. Your welcome btw ur mom is hot

Answer:

Angle 1 is 140 degrees and Angle 2 is 70 degrees.

help please l......................................

help please l......................................

Answers

Answer:

yo mom

Step-by-step explanation:

https://smart.newrow.com/room/nr2/?room_id=ihe-281&firstRun
come fastttttttttttttttttttt
pleaassssssssssssssssss
ll

Answers

Answer:

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤-❤-❤-

Answer:

i'll be there and if anyone cares to join please do

Step-by-step explanation:

Let X be an exponential random variable with a given parameter λ. Show (mathematically) that for any nonnegative t1, t2 the following expression is true: P(Xt1) = P(X (Hint: use the standard formulas for exponential distribution and conditional probability.) This fact is often referred to as the "lack of memory" property of the exponential distribution. Give an
example of a practical interpretation of this fact.

Answers

we have shown mathematically that for any nonnegative values t1 and t2, P(X > t1 + t2 | X > t1) = P(X > t2), which demonstrates the "lack of memory" property of the exponential distribution.

To prove the "lack of memory" property of the exponential distribution, we need to show that for any nonnegative values t1 and t2, the following expression is true:

P(X > t1 + t2 | X > t1) = P(X > t2)

Let's start by using the definition of conditional probability:

P(A | B) = P(A ∩ B) / P(B)

In this case, we have A: X > t1 + t2 and B: X > t1. We want to find P(A | B), which is the probability that X is greater than t1 + t2 given that it is greater than t1.

We can rewrite the conditional probability as:

P(X > t1 + t2 | X > t1) = P(X > t1 + t2 and X > t1) / P(X > t1)

Since X is a continuous random variable, we can express these probabilities using the cumulative distribution function (CDF) of the exponential distribution.

P(X > t1 + t2 | X > t1) = [1 - F(t1 + t2)] / [1 - F(t1)]

where F(t) is the CDF of the exponential distribution with parameter λ.

The CDF of the exponential distribution is given by:

F(t) = 1 - e^(-λt)

Substituting this into the equation, we have:

P(X > t1 + t2 | X > t1) = [1 - (1 - e^(-λ(t1 + t2)))] / [1 - (1 - e^(-λt1))]

Simplifying, we get:

P(X > t1 + t2 | X > t1) = e^(-λ(t1 + t2)) / e^(-λt1)

Using the properties of exponents, we can rewrite this as:

P(X > t1 + t2 | X > t1) = e^(-λt2)

which is equivalent to:

P(X > t2)

Practical interpretation:

The "lack of memory" property of the exponential distribution means that the distribution does not remember its past. In practical terms, it implies that the probability of an event occurring after a certain amount of time does not depend on how much time has already passed. For example, if X represents the time until a light bulb fails, and X follows an exponential distribution, then the probability that the light bulb will fail in the next hour is the same regardless of how long the light bulb has already been in use.

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help pls i don’t understand can someone explain this

help pls i dont understand can someone explain this

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Answer: The answer is between C and D. There is no real solution for D because the discriminant is negative.

what is the answer for this y=__x+__

what is the answer for this y=__x+__

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the answer is y=mx+b

whats the answer for that qustion

Answers

Answer to Whats the answer for that question?:

A correct response to a question asked to test one's knowledge.

Step-by-step explanation:

The way you answer a question depends on how you view it. This could entail thought process, method, and calculations. So overall it depends on perspective.

The population of a town has grown at an annual rate of approximately 2.7%. How long will it take for its population of 14,450 people to double at this growth rate?

Answers

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{28900}\\ P=\textit{initial amount}\dotfill &14450\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ t=years \end{cases} \\\\\\ 28900 = 14450(1 + 0.027)^{t} \implies \cfrac{28900}{14450}=(1.027)^t\implies 2=1.027^t \\\\\\ \log(2)=\log(1.027^t)\implies \log(2)=t\log(1.027) \\\\\\ \cfrac{\log(2)}{\log(1.027)}=t\implies 26.02\approx t\)

6ab + 2ac + 3db+ dc needs to be factorized

Answers

Answer:

Step-by-step explanation:

6ab+2ac+3db+dc

Taking 2a common in the first 2 terms and d common in the next 2 terms, we get---

=>2a(3b+c)+d(3b+c)

=>(3b+c)(2a+d)------Answer!

i need help to find the square units of this triangle

i need help to find the square units of this triangle

Answers

Answer:

24square unit

Step-by-step explanation:

triangle area=1/2.b.h

=1/2.8.6=24

Which function decreases faster please help

Which function decreases faster please help

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Answer:

Step-by-step explanation:

Which function decreases faster please help

The following information should be taken into consideration to answer this item: If the scores of 400 subjects in a psychological scale have been distributed normally with the mean score of 100 and standard deviation of 15: The Z score that equivalent to the raw score 92.5 is.... A.+ 0.5 B. -1.25 C.-0.5 D.-0.25

Answers

The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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The average amount of time, in minutes, for students to complete a standardized test is normally distributed. A data analyst takes a sample of n=36 student times and finds a 90% confidence interval to be [108.6,143.4].

What is the population parameter?

What is the interpretation of the confidence interval?

Answers

The population parameter is the average amount of time for all students to complete the standardized test. The 90% confidence interval [108.6, 143.4] means that we are 90% assured that the true population means lies within this range.

The population parameter in this case is the average amount of time, in minutes, for all students to complete the standardized test.

The interpretation of the 90% confidence interval [108.6, 143.4] is that we are 90% confident that the true population means that it falls within this interval. It means that if we were to repeat the sampling process multiple times and construct 90% confidence intervals, approximately 90% of these intervals would capture the true population mean. In this specific case, we can be 90% assured that the average time for all students taken to complete the standardized test must be between 108.6 and 143.4 minutes.

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Consider the initial value problem: y′=3x(ln(y)+3) where y(1)=51​ Use Euler's method: yn+1​=yn​+hyn′​ with step-size h=0.1 to obtain an approximate solution to the initial value problem at x=1.2. Your answer must be accurate to 4 decimal digits (i.e., |your answer - correct answer ∣≤0.00005 ). Note: this is different to rounding to 4 decimal places You should maintain at least eight decimal digits of precision throughout all calculations. When x=1.2 the approximation to the solution of the initial value problem is: y(1.2)≈

Answers

The approximation to the solution of the initial value problem at x = 1.2 is y(1.2) ≈ 53.8774. Using Euler's method, we can approximate the solution to the initial value problem.

Using Euler's method, we can approximate the solution to the initial value problem by iteratively calculating the values of y at each step. Given the initial condition y(1) = 51 and the step size h = 0.1, we can find an approximate solution at x = 1.2.

Let's perform the calculations step by step:

Step 1: Calculate the derivative at the initial point:

y'(1) = 3(1)(ln(51) + 3) = 3(ln(51) + 3) ≈ 13.4167.

Step 2: Use Euler's method to calculate the next approximation:

y(1.1) ≈ y(1) + h * y'(1) = 51 + 0.1 * 13.4167 = 52.3417.

Step 3: Repeat the process for subsequent steps:

y(1.2) ≈ y(1.1) + h * y'(1.1)

≈ 52.3417 + 0.1 * (3(1.1)(ln(52.3417) + 3))

≈ 53.8774.

Therefore, the approximation to the solution of the initial value problem at x = 1.2 is y(1.2) ≈ 53.8774.

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what is the median of the following numbers? 8, 10, 10, 10, 6, 7, 88,10,10,10,6,7,88, comma, 10, comma, 10, comma, 10, comma, 6, comma, 7, comma, 8

Answers

The median is 10 as the value 10 is at 10th position.

What is Median?

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data collection.

Solution:

Firstly we need to arrange the data in ascending order

6,6,6,7,7,7,8,8,10,10,10,10,10,10,10,10,10,88,88

the total number of digits are

n = 19

So, the middle value that divide the data in two halves will be at n = 10

The median is 10 as the value 10 is at 10th position.

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the water in a pool is evaporating at a rate of 2% per day. if the pool has 16,000 gallons in it today, how many gallons will it have in 12 days? round your answer to the nearest whole number, if necessary.

Answers

The pool will have approximately 12,555 gallons of water left in it after 12 days.

To find out how many gallons of water will be left in the pool after 12 days, given that it evaporates at a rate of 2% per day and has 16,000 gallons today, follow these steps:

1. Determine the rate of water remaining in the pool each day:

Since the pool loses 2% of water daily, the remaining percentage is 100% - 2% = 98%.

In decimal form, this is 0.98.

2. Calculate the amount of water after 12 days:

To do this, raise the daily remaining water rate (0.98) to the power of the number of days (12):

0.98¹² ≈ 0.7847.

This represents the percentage of water remaining in the pool after 12 days.

3. Multiply the initial water amount (16,000 gallons) by the percentage of water remaining after 12 days (0.7847):

16,000 * 0.7847 ≈ 12,555 gallons.

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A class conduct an experiment in biology. They place a number of 1 m by 1 m square grids on the playing field and count the number of plants in each grid. The results obtained are given below.

6 3 2 1 3 2 1 3 0 1
0 3 2 1 1 4 0 1 2 0
1 1 2 2 2 4 3 1 1 1
2 3 3 1 2 2 2 1 7 1
(a)
Calculate the mean number of plants.

Answers

Step-by-step explanation:

their mean is....

6+3+2+1+3+2+1+3+0+1/10=2.1

3+2+1+1+4+0+1+2+0/10=1.4

1+1+2+2+2+4+3+1+1+1/10=1.8

2+3+3+1+2+2+2+1+7+1/10=2.4

the means are 2.1,1.4,1.8,2.4

the average mean is

21+14+18+24/40

32+45/40

77/40=1.925

the average mean is 1.925

Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer

Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer

Answers

The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively

What is a kite?

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

The given figure is a kite with two intersecting lines that are perpendicular to each other.

Since the lines are perpendicular to each other, hence;

m<1 = 90 degrees

For the measure of m<2

m<2 + 90 + 27 =180

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63degrees

Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees

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Four types of flower​

Answers

Answer: Daisies, Lilies, Roses & Gardenias

Step-by-step explanation:

f (x) =-3x^2-2 and g (x) = 4x-3. find f (3) and g (-5). simplify your answere much as possible

Answers

To find f(3), we simply substitute x=3 in the expression for f(x) and simplify: f(3) = -3(3)^2 - 2 = -27 - 2 = -29. Therefore, f(3) = -29 and g(-5) = -23. Both answers are already simplify as much as possible.

What mathematical functions are there?

A mathematical function is a rule that determines the value of a dependent variable in relation to one or more independent variables whose values are given. There are several ways to depict a function, including a table, a formula, or a graph.

What five mathematical operations are there?

Some of the most popular functions are listed below, along with their graphs:

The linear formula is f(x) = mx + b.Function Square: f(x) = x2Function of a Cube: f(x) = x3Square f(x) = x is the root function.F(x) = |x| Reciprocal Function is an absolute value function. f(x) = 1/x.

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two customers took out home equity loans.
Cathy took out a 10-year loan for $20,000 and paid %5.20 annual simple interest
Steven took out a 15-year loan for 20,000 and paid %4.80 annual simple interest

what is the difference that Cathy and Steven paid for their loans?

Answers

The difference in the amount paid by Cathy and Steven is $4000.

What is the difference in the amounts?

Simple interest is when the interest that is paid on the loan of a customer is a linear function of the loan amount, interest rate and the duration of the loan.

Simple interest = amount borrowed x interest rate x time

Simple interest of Cathy = $20,000 x 0.052 x 10 = $10,400

Simple interest of Steven = $20,000 x 0.048 x 15 = $14,400

Difference in interest = $14,400 - $10,400 = $4000

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{x - 2y + 4z = 4 -5x + 9y - 22z = -16 -2x + 3y - 10z = k In order for the system of equations above to be a consistent system, k must be equal to

Answers

In order for the system of equations to be a consistent system, the value of k must be equal to -4.

To determine the value of k that makes the system of equations consistent, we can use the method of elimination or substitution. Let's use the method of elimination.

First, we can multiply the first equation by 5, the second equation by -1, and the third equation by 2 to make the coefficients of x in the three equations cancel each other out when added together.

The modified system of equations becomes:

5x - 10y + 20z = 20

5x - 9y + 22z = 16

-4x + 6y - 20z = 2k

Now, let's subtract the first equation from the second equation:

(5x - 9y + 22z) - (5x - 10y + 20z) = 16 - 20

y + 2z = -4

Next, let's add this equation to the third equation:

(-4x + 6y - 20z) + (y + 2z) = 2k - 4

-4x + 7y - 18z = 2k - 4

For the system of equations to be consistent, there must be no contradictions or inconsistencies. This means that the equations must be linearly dependent, and the last equation must be a multiple of the second equation.

Comparing the last equation (-4x + 7y - 18z = 2k - 4) with the second equation (y + 2z = -4), we can see that the two equations will be dependent and consistent if 2k - 4 is equal to 0.

2k - 4 = 0

2k = 4

k = 2

Therefore, in order for the system of equations to be a consistent system, the value of k must be equal to -4.

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what is the first error holden made in his proof? choose 1 answer: choose 1 answer: (choice a) holden used an invalid reason to justify the congruence of a pair of sides or angles. a holden used an invalid reason to justify the congruence of a pair of sides or angles. (choice b) holden only established some of the necessary conditions for a congruence criterion. b holden only established some of the necessary conditions for a congruence criterion. (choice c) holden established all necessary conditions, but then used an inappropriate congruence criterion. c holden established all necessary conditions, but then used an inappropriate congruence criterion. (choice d) holden used a criterion that does not guarantee congruence. d holden used a criterion that does not guarantee congruence.

Answers

The first error that Holden made in his proof is option (B) Holden only established some of the necessary conditions for a congruence criterion.

Congruence of triangles is a relationship between two triangles where they have exactly the same shape and size. When two triangles are congruent, all their corresponding sides and angles are equal in measure.

Holden's proof contains an error because he only established the congruence of one pair of corresponding sides in the two triangles. However, to prove the congruence of two triangles, all corresponding sides and angles must be shown to be congruent using a congruence criterion such as SSS or SAS. Therefore, Holden's proof is incomplete and does not provide sufficient evidence to conclude that the two triangles are congruent.

Therefore, the correct option is (B) Holden only established some of the necessary conditions for a congruence criterion.

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The given question is incomplete, the complete question is:

Holden tried to prove that △FGH≅△FIH

1 IH≅GH

Given

2 FH≅FH

Line segments are congruent to themselves.

3 △FGH≅△FIH

Side-side congruence

What is the first error Holden made in his proof?

(A) Holden used an invalid reason to justify the congruence of a pair of sides or angles.

(B) Holden only established some of the necessary conditions for a congruence criterion.

(C) Holden established all necessary conditions, but then used an inappropriate congruence criterion.

(D) Holden used a criterion that does not guarantee congruence.

what is the first error holden made in his proof? choose 1 answer: choose 1 answer: (choice a) holden

subject = Control System
Determine RHP roots in the following polynomial p(S)=S5 +S4 +25³ +35² +S+4
Determine RHP roots in the following polynomial p(S)=S5 +S4 +6S³ +6S² +255 +25

Answers

The solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

The following are the solutions to determine RHP roots in the given polynomials in Control System:

Polynomial: \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)

To identify the number of RHP (Right Half Plane) roots of the given polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\), the number of sign changes in the coefficients of the polynomial's terms can be counted.

Using the Descartes rule of sign, the number of sign changes in the polynomial's coefficients will indicate the number of positive or RHP roots present in the polynomial.

Therefore, there is no change in the sign of coefficients in the polynomial p(S).Thus, the number of RHP roots of the polynomial \(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\)is zero.

Polynomial: \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\)

The given polynomial is \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\).

The coefficients of the polynomial are as follows:

a5 = 1, a4 = 1, a3 = 6, a2 = 6, a1 = 1, and a0 = 25.

According to the Routh-Hurwitz criterion, the RHP roots of the polynomial p(S) are given by the following conditions:

For the polynomial \(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\), the Routh array can be written as:

1    6    25 0
1    6    25 0
6    155 0
5    25    0
25 0

Thus, the polynomial p(S) has no RHP roots since the Routh array contains no changes of sign.

Therefore, the given polynomial has no RHP roots.

Hence, the solutions for the given problem are as follows:

\(p(S) = S5 + S4 + 25^3 + 35^2 + S + 4\) has no RHP roots.

\(p(S) = S5 + S4 + 6S^3 + 6S^2 + 255 + 25\) has no RHP roots.

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Gil charges $5 per bracelet plus $2 for each string colour. If Gil makes 3 bracelets
with x colours, write an expression that represents how much money Gil makes.

Answers

Answer: 15 + 2x

Step-by-step explanation:

5b + 2x

5 (3) + 2x

15 + 2x

I think I'm right so I hope it helped!!

Expression for this word problem: $5x + 2.
Now, if Gil makes three bracelets, then we will apply and substitute this into our equation:
$5(3) + 2 = $17.00

Consider the PDE au(x, t) = 4 d²u(x, t) 2 Ət əx² For each of BCs and ICs, solve the initial value problem. du(π,t) a) BCs: u(0,t)=0 = = 0 and əx IC: u(x,0) = x ANSWER: f(x)= n=1 u(2,t) = 0 and u(0,t)=0 u(x,0)=sin x ANSWER: f(x)=¹1_sin(2 + nx) na n=1 1+ 2 X b) BCs: IC: 8 (2n-1) T n+1 (-1)041 -4(2n-1)²t sin(2-nπ) nπ 1- 2 e sin (2n-1) 2 na sin X 2 -(nn)²t x -X

Answers

the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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