The answer in the box is wrongFind a general solution to the differential equation. 1 1 ay' + 4y = tan 4t 3t 3 1 The general solution is y(t) = C, cos 4t + C2 sin 4t - 15 3t 1 (cos 4t) In ( sec 4t + tan 4t) 4
Answers
The general solution to the differential equation is y(t) = y_h(t) + y_p(t) = C1 \(e^(-4t/a)\) + (1/(12a)) sin(4t)/(3t).
The given differential equation is ay' + 4y = tan(4t)/(3t).
To find the general solution, we first need to solve the homogeneous equation ay' + 4y = 0. This is a linear first-order differential equation with constant coefficients, so we can use the exponential function method.
Assuming y = \(e^(rt)\), we get are \(e^(rt)\) + \(4e^(rt)\) = 0, which simplifies to are + 4 = 0. Solving for r, we get r = -4/a.
Therefore, the general solution to the homogeneous equation is y_h(t) = C1 \(e^(-4t/a)\).
To find the particular solution, we can use the method of undetermined coefficients. Since the non-homogeneous term is tan(4t)/(3t), we can guess that the particular solution has the form y_p(t) = A cos(4t) + B sin(4t) + C ln(3t) + D.
Taking the first and second derivatives of y_p(t), we get y'_p(t) = -4A sin(4t) + 4B cos(4t) + C/t and y''_p(t) = -16A cos(4t) - 16B sin(4t) - C/t².
Substituting these into the original differential equation and equating coefficients of like terms, we get -4Aa sin(4t) + 4Ba cos(4t) + (C/t)(a² - 16) = tan(4t)/(3t).
Comparing the coefficients of sin(4t) and cos(4t), we get -4Aa = 0 and 4Ba = 1/3. Solving for A and B, we get A = 0 and B = 1/(12a).
Comparing the coefficients of ln(3t) and the constant term, we get (C/t)(a² - 16) = 0 and D = 0. Since a cannot be equal to 4 or -4, we have C = 0.
Therefore, the particular solution is y_p(t) = (1/(12a)) sin(4t)/(3t).
The general solution to the differential equation is y(t) = y_h(t) + y_p(t) = C1 \(e^(-4t/a) + (1/(12a)) sin(4t)/(3t).\)
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Related Questions
please help, why is -3x+2y=8 equal y=3/2x+4
Im going to fail lol
Answers
Steps:
1) Add 3x to both sides to get rid of it by the y.
2y=3x+8
2) Divide both sides by 2 to isolate the y.
y= 3/2x + 8/2
3) Simplify (divide 8 by 2)
y= 3/2x+4
Hope this helps!
a researcher finds a 0.31 pearson r correlation between amount of time it takes to complete a puzzle and iq scores for 97 adult participants. what is the correct decision about the null hypothesis test?
Answers
It can be concluded that there is a significant positive correlation between the time it takes to complete a puzzle and the IQ scores of these participants.
To determine the correct decision about the null hypothesis test, we need to compare the calculated Pearson's correlation coefficient (r) of 0.31 to a critical value based on the sample size and level of significance.
Assuming a significance level of 0.05 (or alpha = 0.05) and a two-tailed test, we can use a t-distribution with degrees of freedom (df) equal to n-2, where n is the sample size. For a sample size of 97, df = 95.
Using a table or calculator, we can find the critical t-value that corresponds to a significance level of 0.05 and 95 degrees of freedom. The critical t-value is approximately 1.984.
Next, we can calculate the t-value for the observed correlation coefficient using the formula:
\(t = r * sqrt(n-2) / sqrt(1-r^2)\)
where r is the observed correlation coefficient and n is the sample size.
Plugging in the values, we get:
t = 0.31 * sqrt(97-2) / sqrt(1-0.31^2) = 3.23
The absolute value of the calculated t-value (3.23) is greater than the critical t-value (1.984), indicating that the correlation coefficient is statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no correlation between the time it takes to complete a puzzle and the IQ scores of the adult participants.
Therefore, we can conclude that there is a significant positive correlation between the time it takes to complete a puzzle and the IQ scores of these participants. However, we cannot make any causal claims based on this correlation alone, as there may be other variables that could explain the relationship.
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your box of cereal may be a contest winner! it's rattling, which 100% of winning boxes do. of course 1% of all boxes rattle and only one box in a million is a winner. what is the probability that your box is a winner? note on answer formatting: please specify your answer as a decimal probability (i.e. .05 rather than 5%). do not include zeros before the decimal. to receive credit, your answer must match ours exactly.
Answers
The probability that the box is a winner is 0.0001.
Probability of Winning BoxThe steps to calculate the probability that your box is a winner are as follows:
The probability that a box rattles is 1%. Therefore, the probability that a box does not rattle is 99%.The probability that a box is a winner given that it rattles is 100%.The probability that a box is a winner given that it does not rattle is 0%.Using Bayes' theorem, we can calculate the probability that a box is a winner by taking into account both the probability that it rattles and the probability that it is a winner given that it rattles.P(winner | rattles) = P(rattles | winner) * P(winner) / P(rattles)
P(winner | rattles) = (1/1000000) * (1) / (1/100)
P(winner | rattles) = 0.0001
So the probability that the box is a winner is 0.0001.
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Your brother works for a company that cleans and paints the outside of houses at a rate of $35 per hour. The company charges a flat rate of $500 for their supplies.
f (x) =500+35x represents this scenario. Determine the total bill of 8 hours of work.
pls help
Answers
Answer:
780$
Step-by-step explanation:
f(8) = 500 + 35x8
500 + 280
WILL MARK BRANLIEST TO ACCURATE ANSWER. URGENT ANSWER REQUIRED. ANSWER NOW.
Answers
Answer:
It’s D. 4
Step-by-step explanation:
GOOD LUCK HOMIE AND USE A CALCULATO ;)
Construct a 97 percent confidence interval around a sample mean of 31. 3 taken from a population that is not normally distributed with a standard deviation of 7. 6 using a sample of size 40?
Also for an error calculation of 5, what sample size should we consider?
Answers
The sample size is 12 with an error calculation of 5 if 97% of the confidence interval is around a sample mean of 31. 3.
Percent confidence = 97
Sample mean = 31. 3
Standard deviation = 7. 6
Sample size = 40
Error calculation = 5
The formula for a confidence interval using the t-distribution is:
CI = x ± tα/2 * (s/√n)
CI = 31.3 ± 2.423 * (7.6/√40)
CI = 31.3 ± 3.940
CI = (27.36, 35.24)
The population mean with an error of 5,
n = (Zα/2 * σ / E)^2
Assuming a 95% confidence level, the sample size is,
n = (1.96 * 7.6 / 5)^2
n = 11.69
Therefore we can conclude that the sample size is 12 with an error calculation of 5.
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An automatic machine in a manufacturing process is operating groperly if the iengths of an important subcomponent are normally distributed with a mean of izal cri and a otandard deviation of 5.6 cm. A. Find the probability that one selected subcomponent is longer than 122 cm, Probability = B3. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 122 cm. Probability win C. Find the probabilify that if 3 are randomly selected, ail 3 have lengths that exceed 122 cm. Probability =
Answers
A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.
z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)
Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.
B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.
The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.
Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm
Now we can calculate the z-score for a mean length of 122 cm:
z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)
Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.
C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.
Probability = (0.9999)^3 ≈ 0.9997
Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.
Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.
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Use #1-9 to identify each property below.
A. ab?.0=0
B. (7 + 5) + 1 = 7 + (5 + 1)
C. 6 = 6
D. 7(x – 3) = 7x - 21
E. x + (-x) = 0
F. if y = 3, then 3 = y
G. (a + b) + 0 = 0 + (a + b)
H. if x = -1, and -1 = z, then x = 2
I, 4x.1=4r
Answers
Here we need to see which axioms or properties are used in each case.
A: ab²×0 = 0
Here we have a given number (ab²) times zero, and the outcome is zero. This comes from the existence of zero, which states that there must exist a value that represents nothingness, the zero, such that the product between any number and this one is zero.
B: (7 + 5) + 1 = 7 + (5 + 1)
This is the associative property of addition, which says that we can perform the addition in any order we want.
C: 6 = 6
This is the reflexive property of equality, which says that every number is equal to itself.
D: 7(x – 3) = 7x - 21
This is the distributive property, which says that:
C*(A + B) = C*A + C*B
We can see that if we apply it to the left side we get:
7(x - 3) = 7x - 7*3 = 7x - 21
E: x + (-x) = 0
This is the existence of the opposite number. This property says that for any real number N there exists a real number A such that:
N + A = 0
Particularly, in the real set, we can see that A = -N
G: (a + b) + 0 = 0 + (a + b)
Here we can see that the order changes in the addition, this is the commutative property of the addition, which says that:
A + B = B + A
So the elements in the sum can commute.
H: if x = -1, and -1 = z, then x = z
This is the transitive property, we can apply it in the next way:
x = -1 = z
then x = z
So if both variables are equal to the same number, then the variables are equal.
I: 4x×1 = 4x
This is the existence of the identity with respect to multiplication. It says that there exist a number A such that for any number X, the product between A and X is equal to X:
X*A =X
Particularly, A = 1.
X*1 = X.
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Answer:
Step-by-step explanation: I also need help
Which equation represents the line that passes through the point (10, 1) and is perpendicular to the graph of 2x – y = 7?
Answers
If x=a sinø and y=b cos ø, show that b²x² + a²y² =a²b²
Answers
Hope you could understand.
If you have any query, feel free to ask.
What integer values satisfy both inequalities?
-2 2
Thanks.
Answers
Answer:
I think + 2 plz make me brainliest
Step-by-step explanation:
In this polygon, all angles are right angles.
What is the area of the polygon? Show your work.
Answers
The area of the polygon is solved to be 1044 squared cm
How to find the are of the c]polygonThe area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas
Section 1 has dimensions:
length * width = 46 * 14 = 644
section 2 has dimensions:
length = 46 - 21 = 25
width = 30 - 14 = 16
Area = 25 * 16 = 400
Area of the composite figure
section 1 + section 2
= 644 + 400
= 1044 squared cm
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Joyce’s teacher asks her to write the sequence formed by the number of red squares in each picture for the first five pictures. What sequence should Joyce write?
Answers
Answer:
Joyce should write \(1,8,64,512,4096\)
Step-by-step explanation:
Let's analyze the procedure of how the pictures are formed.
Her teacher said the images were created by taking a red square, dividing it into 9 smaller squares, and removing the center square.
For the first two images we can see and count that there is 1 red square in the first picture and 8 red squares in the second picture.
For the third image, there are 8 squares formed by 8 red squares each one.
The number of red squares is 8 x 8 = 64
We can write the sequence as
1 , 8 , 64 ⇒ 1 , 8 , \(8^{2}\)
For the fourth picture we can do the same reasoning and figure out that there are 8 x 8 x 8 = 512 red squares in the fourth image.
The sequence so far is
1 , 8 , 64 , 512 ⇒ 1 , 8 , \(8^{2}\) , \(8^{3}\)
We can generalize the sequence and write that the sequence is :
\(8^{n}\) with \(n\) ∈ IN ⇒ The first five numbers will be
\(8^{0},8^{1},8^{2},8^{3},8^{4}\) = \(1,8,64,512,4096\)
let the matrix operator t : r2 → r2 be defined by t (x1, x2) = (3x1 −x2, −7x1 3x2). find a formula for t −1(w1, w2).
Answers
The formula for T^(-1)(w1, w2) is ((1/16)(w1 - w2), (1/16)(3w1 + 7w2)).
To find a formula for the inverse of the matrix operator T, denoted as T^(-1), we need to solve the equation T(x) = (w1, w2) for the variables x1 and x2.
Given that T(x1, x2) = (3x1 - x2, -7x1 + 3x2), we want to find x1 and x2 in terms of w1 and w2 such that T(x1, x2) = (w1, w2).
Setting up the equations, we have:
3x1 - x2 = w1,
-7x1 + 3x2 = w2.
To solve this system of equations, we can use matrix notation:
|3 -1| |x1| = |w1|,
|-7 3| |x2| |w2|.
Calculating the inverse of the coefficient matrix on the left-hand side:
|3 -1|^(-1) = 1/(3*3 - (-1)(-7)) * |3 1| = 1/16 * |3 1|,
|7 3| |7 3|.
Multiplying both sides by the inverse of the coefficient matrix, we have:
|3 1| |x1| = 1/16 * |w1|,
|7 3| |x2| |w2|.
Simplifying, we get:
3x1 + x2 = (1/16)w1,
7x1 + 3x2 = (1/16)w2.
Therefore, a formula for T^(-1)(w1, w2) is given by:
x1 = (1/16)(w1 - w2),
x2 = (1/16)(3w1 + 7w2).
Hence, T^(-1)(w1, w2) = ((1/16)(w1 - w2), (1/16)(3w1 + 7w2)).
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A triangle has sides with lengths of 6 meters, 12 meters, and 16 meters. Is it a right triangle?
Formula(a^2 +b^2=c^2)
Answers
Answer:
i'd say so
Step-by-step explanation: none of the sides are the same length as another
In a survey, 10% of the people said they live in a city. If 70 people
said they live in a city, how many people were surveyed?
Answers
SOLUTION
70/10%
=700
Or
7 x 10^2
=700
HOPE THIS HELPS!! :))
Melissa had $20 to purchase candy for a party. She purchased 3.6 pounds of candy that cost $2.50 per pound. How much money does Melissa have remaining after this purchase?
Answers
Answer:
1738
Step-by-step explanation:
Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Melissa had $20 to purchase candy for a party.
She purchased 3.6 pounds of candy that cost $2.50 per pound
Melissa spent 3.6 x $2.50
= 9 on candy.
Subtracting this amount from her initial $20, we get:
$20 - $9 = $11
Therefore, Melissa has $11 remaining after purchasing 3.6 pounds of candy that cost $2.50 per pound.
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If there are 1,400 costumers in a given week, how many would you expect to prefer chocolate strawberry or vert berry mix?
Answers
Answer:
770 customers
Step-by-step explanation:
Oooh I love these types of questions!
First we should add all of the numbers to find the total number of people so we can set up a proportion later.
70+36+46+40+8=200
Now that we've found the total, we need to find chocolate strawberry and vert berry, because the wording "or" would mean either. If the wording said "and" we would not have enough information to solve that.
Chocolate Strawberry is 70, and Very Berry is 40. Add that to get 110.
Now we have our needed numbers to make a proportion! This is because for each 200 people, we know that they'd want 110 Chocolate Strawberry or Very Berry.
So we would need to make a proportion for 1400.
110/200=x/1400
Cross multiply (or do that trick where you divide 1400 by 200 and then multiply 110 by that number, but cross-multiplying is a good habit)
110(1400)=200x
Simplify
154000=200x
Isolate the variable
154000=200x
/200 /200
770=x
And that would be your answer! If I made any errors, please tell me!
h 10 yd.
L 14 yd.
W 3 yd.
Volume=
Answers
Answer:
10yd x 14 yd x 3yd = 420yd ^3
Step-by-step explanation:
When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.
Put decimals numbers in order
Ok, ok I need help with this and it’s due tomorrow and if I don’t complete it until 11:45 PM I’m gonna fail immediately
Answers
Answer:
Least to greatest:
0.03
0.2
0.36
0.38
0.9
Step-by-step explanation:
Yvonne ran 3/8 of the race stopping for water. She wants to stop for water one more time before finishing the race. List two ways Yvonne can do this
Answers
Yvonne stops for water after 6/8 on the race for one more time.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Yvonne ran 3/8 of the race stopping for water.
This means,
After every 3/8 Yvonne stopped for water.
Now,
Total distance = 1
Distance remaining after one stop.
= 1 - 3/8
= 5/8
And,
Another stop will be after 3/8.
This means,
Distance remains after the second stop.
= 5/8 - 3/8
= 2/8
Now,
1 - 2/8
= 6/8
The second stop is after 6/8 of the race.
Thus,
Yvonne stops for water after 6/8 on the race for one more time.
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Hiro has 5 kilog of potatos a 2 kg of onions he plans to use 3.25 kg of potatoes and 550 grams of onions for recipe. how many total kilograms of the produce will not be used?
Answers
Please help me thanks
Answers
Answer:
1,2,4,5,10
1,2,3,5,6
60
Step-by-step explanation:
Which equation represents a proportional relationship that has a constant of proportionality equal to –10?
Answers
9514 1404 393
Answer:
y = –10x
Step-by-step explanation:
A proportional relationship has the equation ...
y = kx
where k is the constant of proportionality.
Here, you are told that "[the] constant of proportionality [is] equal to –10," so you expect the equation to be ...
y = –10x
Answer:
A
Step-by-step explanation:
took the test on edge 2021
Please help with this question!
Answers
Answer:
G is the answer
Step-by-step explanation: 8*((40-16)/2)= 8*12 = 96, 6*((40-12)/2) = 6*14 = 84, and 96-84 = 12
In regression analysis, if the dependent variable is measured in dollars, the independent variable _____.
Answers
In regression analysis, if the dependent variable is measured in dollars, the independent variable can be units.
What are dependent and independent variables in regression analysis?The outcome variable is also called the response or dependent variable, and the risk factors and confounders are called the predictors, or explanatory or independent variables. In regression analysis, the dependent variable is denoted "Y" and the independent variables are denoted by "X".The variable that is used to explain or predict the response variable is called the explanatory variable. It is also sometimes called the independent variable because it is independent of the other variable.To learn more about Dependent and Independent Variable, refer to:
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Determine the approximate ordered pair for f(x) =g(x).
=
○ (26,4)
O (18,4)
O (4.26)
○ (4,18)
-50
40
-30
-20
8
10
10
f(x)
g(x)
20
농
50
Answers
The approximate solution of the system of equations is given as follows:
(4, 26).
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
For the point of intersection in this problem, we obtain the coordinates as follows:
x-coordinate of approximately 4, as it is less than the half way between 0 and 10.y-coordinate of 26, as it is a value between 20 and 30.This means that the correct option is given by the third option.
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write the expanded expression for [2×3]^5didn't you write each term of the expanded expression as a product of two single powers
Answers
[2×3]^5 = ( 2^5 ) * (3^5) = 32 * 243 =7,776
we have used the rule
![write the expanded expression for [23]^5didn't you write each term of the expanded expression as a product](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/kspsJ5Z7d9yHnWxlNlGmmgPdhiuFTdk5.png)
Why are 3/4 and 8/12 NOT equivalent? Thanks!
Answers
Answer:Does this help?
Step-by-step explanation:
3/4 needs to have the same denominator as 8/12 so you can do this by multiplying the denominator by 3 and the top by 3 you get 9/12 When you convert them to percents you get , 3/4= 75% and 8/12= 66.666%
USA Todoy reports that the average expenditure on Valentine's Day was expected to be \$100.89. Do male and female consumers ditfer in the amounts they spend? The average expenditure in a sample survey of 58 male consumers was $139.54, and the average expenditure in a sample survey of 39 female consumers was \$60.48. Based on past surveys, the standard deviation for male consumers is assumed to be \$33, and the standard deviation for female consumers is assumed to be 314 . The x value is 2.576. round your answers to 2 decimal places. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expend ture for females? b. At 99% confidence, what is the margin of error? 2
c. Deveop a 99% confidence interval for the difference between the two popuiaton means.
Answers
a. The point estimate of the difference between the population mean expenditure for males and females is $79.06.
b. At a 99% confidence level, the margin of error is approximately $240.61.
c. The 99% confidence interval for the difference between the two population means is approximately (-$161.55, $319.67).
a. The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females can be calculated as the difference between the sample means:
Point estimate = Sample mean for males - Sample mean for females
= $139.54 - $60.48
= $79.06
b. To calculate the margin of error at a 99% confidence level, we need to use the formula:
Margin of Error = Z * (sqrt((s1^2/n1) + (s2^2/n2)))
Where:
Z is the critical value corresponding to the desired confidence level. For a 99% confidence level, Z = 2.576.
s1 and s2 are the standard deviations of the male and female samples, respectively.
n1 and n2 are the sample sizes of the male and female samples, respectively.
Given:
Standard deviation for males (s1) = $33
Standard deviation for females (s2) = $314
Sample size for males (n1) = 58
Sample size for females (n2) = 39
Z = 2.576
Plugging in the values into the formula, we have:
Margin of Error = 2.576 * (sqrt((33^2/58) + (314^2/39)))
≈ 2.576 * (sqrt(607.48 + 8106.87))
≈ 2.576 * (sqrt(8714.35))
≈ 2.576 * 93.37
≈ 240.61
Therefore, the margin of error at a 99% confidence level is approximately $240.61.
c. To develop a 99% confidence interval for the difference between the two population means, we can use the formula:
Confidence Interval = (Point estimate - Margin of Error, Point estimate + Margin of Error)
Substituting the values we calculated earlier:
Point estimate = $79.06
Margin of Error = $240.61
Confidence Interval = ($79.06 - $240.61, $79.06 + $240.61)
= (-$161.55, $319.67)
Therefore, the 99% confidence interval for the difference between the two population means is approximately (-$161.55, $319.67).
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