a researcher took a random sample of 100 students from a large university. she computed a 95% confidence interval to estimate the average weight of the students at this university. the confidence interval was too wide to provide a precise estimate. true or false? the researcher could produce a narrower confidence interval by increasing the sample size to 150.

The measure of ML is 8.69

Pythagoras theorem states that ;the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore, a²+b²= c²

Line JL is a diameter and it passes in through the center of the circle meeting a tangent JK. The angle formed between this lines is 90°. Therefore ∆JKL is a right angled triangle and Pythagoras theorem can be applied.

JL = √ 10.3²+ 14²

JL = √ 302.09

JL = 17.38

ML = JL/2

ML = 17.38/2

ML = 8.69

therefore the measure of ML is 8.69

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The dimensions of the page that will minimize the amount of paper used are 11 inches wide (9 + 2) and 22 inches tall (18 + 4).

To minimize the amount of paper used for a rectangular page with 162 square inches of print, we need to find the dimensions that will result in the smallest possible area, considering the given margin sizes.

Let the width of the printed area be x inches and the height be y inches. The area of the printed area is given as x * y = 162 square inches.

Taking into account the margins, the overall width of the page will be (x + 2 * 1) inches, and the height will be (y + 2 * 2) inches since there is a 1-inch margin on each side and a 2-inch margin at the top and bottom.

The area of the entire page, including margins, can be represented as A = (x + 2)(y + 4). To minimize this area, we need to find the dimensions x and y that satisfy the equation x * y = 162 while minimizing the function A = (x + 2)(y + 4).

To do this, we can use calculus to find the critical points of the function and then test them to find the minimum value. By using the first derivative test and analyzing the dimensions, we find that the dimensions that minimize the paper used are x = 9 inches for the width of the printed area and y = 18 inches for the height of the printed area.

So, the dimensions of the page that will minimize the amount of paper used are 11 inches wide (9 + 2) and 22 inches tall (18 + 4).

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We need to find the bank discount and proceeds. First, we'll find the discount rate (r). The ordinary interest method uses a 360-day year.

Step 1: Calculate the discount rate fraction for 180 days
r = (180 days) / (360 days) = 0.5

Step 2: Find the bank discount
Bank discount = Amount due at maturity * r
Bank discount = $20,000 * 0.5 = $10,000

Step 3: Calculate the proceeds
Proceeds = Amount due at maturity - Bank discount
Proceeds = $20,000 - $10,000 = $10,000

So, the completed table looks like this:

Amount due at maturity: $20,000
Discount rate: 0.5 (50%)
Time: 180 days
Bank discount: $10,000
Proceeds: $10,000

Please note that the provided scenario seems unusual, as a 50% discount rate for 180 days is quite high. However, the calculation method demonstrated above is still accurate.

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Answer:

16 circumference ohh area and circumference is same man\women

Answer:

   First, we multiply:

   9/100 multiplied by 70

   We get 6.3 as the answer.

   Now we add 70+6.3

Step-by-step explanation:

The answer would be 76.3 hoped this helped pl s give me brainliest

have a good day :)

Answer:76.3

Step-by-step explanation:

9% of 70 is 6.3.

Since it is increased, add 6.3 to 70.

You get 76.3

The amount of money that Gina will earn after working 40 hours is given as follows:

C. $250.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table, the constant is given as follows:

k = 93.75/15 = 125/20 = 6.25.

Hence the equation is:

y = 6.25x.

Then the amount earned working 40 hours is given as follows:

y = 6.25 x 40

y = $250.

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The solution to the system of equations is: x = 10/3 and y = -5/3

To solve the system of equations by elimination, we want to eliminate one of the variables (x or y) by adding or subtracting the two equations.

In this case, we can eliminate y by multiplying the first equation by -5 and the second equation by 3, then adding them together:

-5(y = -3x+5) → -5y = 15x - 25

3(y = -8x+25) → 3y = -24x + 75

Adding the two equations gives:

-2y = -9x + 50

Now we can solve for y:

y = (9/2)x - 25

To find x, we substitute this expression for y into one of the original equations. Let's use the first equation:

y = -3x+5

(9/2)x - 25 = -3x + 5

Solving for x gives:

x = 10/3

Therefore, the solution to the system of equations is: x = 10/3 and y = -5/3

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The number of pastries baked by Katie is 40, and each pastry is shared by 5 people, making a total of 200 people served.

Let's define two variables to represent the number of pastries and the number of people per pastry:

p = number of pastries

pp = number of people per pastry

Then, the total number of pastries and the total number of people can be expressed as:

total pastries = p = 40

total people = p * pp = 200

We can solve for pp by dividing both sides by p:

pp = total people / p = 200 / 40 = 5

So, the algebraic expression to represent this situation is:

p = 40, pp = 5, total people = p * pp = 200

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Yes, using the 0.10 level of significance, we can conclude that the assembly time using the new method is faster.

To support this claim, we can conduct a hypothesis test:
1. Set up hypotheses:
Null hypothesis (H0): The mean assembly time using the new method is not faster (μ_new >= 64 minutes).

Alternative hypothesis (H1): The mean assembly time using the new method is faster (μ_new < 64 minutes).

2. Choose the level of significance (alpha): α = 0.10.

4. Determine the critical value: Since it's a one-tailed test, we look up the z-table for 0.10 level of significance. The critical value is -1.28.
5. Compare the test statistic to the critical value: Since -6.23 < -1.28, we reject the null hypothesis.
Thus, we can conclude that the assembly time using the new method is faster at the 0.10 level of significance.

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Answer: 1

Step-by-step explanation:

the two points given tell us the following information:

the difference in y coordinates, (4), will be the width of the rectangle

the difference in x coordinates, (3), will be the length of the rectangle.

haha! actually the width is the length and the length is the width lol.

anyways, the length is 1 longer than the width, since 4 -3 = 1.

To find the number of ways to choose 4 red marbles from the urn, we need to use the combination formula. The number of combinations of r objects chosen from a set of n objects is given by nCr = n!/r!(n-r)!.

In this case, we want to choose 4 red marbles from a total of 19, so n=19 and r=4. Plugging these values into the formula, we get 19C4 = 19!/4!(19-4)! = 3876. Therefore, there are 3876 ways to choose 4 red marbles from the urn containing 19 red marbles and 14 blue marbles when 16 marbles are chosen in total.

To determine the number of ways to choose 4 red marbles from the 19 available, we will use the concept of combinations. Combinations allow us to calculate the number of possible arrangements without considering the order. The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where n represents the total number of items and r is the number of items to choose.

In this case, n = 19 (total red marbles) and r = 4 (red marbles to be chosen). Applying the formula, we have C(19, 4) = 19! / (4! * (19-4)!). After calculating, we get 3876 ways to choose 4 red marbles from the urn.

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The value of k ends up being 1 after the differential equation, but this depends on the specific function and the value of k. In general, we cannot assume that k will always be 1 after differentiation.

You are asking about the use of a constant "k" when applying L'Hôpital's Rule in differentiation and if it would just become 1.

In the line f'(x), we multiply by k because we are differentiating with respect to x, not k. The derivative of a function with a constant multiplier is the derivative of the function multiplied by the constant. So, if we have f(x) = k*cos(k(x-1)), then f'(x) = k*(-sin(k(x-1))*k). The k outside of the parentheses is still a constant multiplier, so it remains in the expression.

L'Hôpital's Rule is used to find the limit of a function in indeterminate forms like 0/0 or ∞/∞. Here's a step-by-step explanation:

1. Identify an indeterminate form in the limit, like 0/0 or ∞/∞.
2. Differentiate both the numerator and the denominator of the function.
3. Multiply any constants that come from the differential equation process.
4. Evaluate the limit of the newly derived function.

Regarding the constant "k" and differentiation, it's important to note that when you differentiate a function multiplied by a constant, the constant remains the same. It does not become 1. For example, let's say we have a function g(x) = k * h(x), where h(x) is another function. The derivative of g(x) with respect to x would be:

g'(x) = k * h'(x)
Here, the constant "k" remains unchanged when you differentiate the function.

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Answer:

6.97

Since we have 9 on the tenth place, and an eight on the hundredth place, it's rounded to 7.0

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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The estimated number of sugar cubes that remain on Max's pyramid is C. 550 cubes.

To estimate the number of sugar cubes remaining on Max's pyramid, we need to subtract the number of cubes that fell off on the way to school and the number of cubes that Max's friends ate from the original 587 sugar cubes.

Subtracting 34 cubes that fell off on the way to school from 587 gives us 553 sugar cubes. Subtracting another 18 cubes that Max's friends ate from 553, we get 535 sugar cubes remaining on Max's pyramid.

Therefore, the closest answer choice to this estimate is C. 550 cubes.

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For a measurement of 7.84 cm, 8 digit is the estimated digit

In the decimal system, each digit in a number represents a place value based on its position relative to the decimal point.

The digit to the left of the decimal point represents the units place, and each subsequent digit to the right represents a smaller unit, such as tenths, hundredths, and so on.

The digit to the right of the decimal point that is not zero is known as the estimated digit.

In the given measurement of 7.84 cm, the digit to the left of the decimal point is 7, which represents the units place.

The digit to the right of the decimal point is 8, which represents the tenths place. Since the digit in the hundredths place is 4 and not zero, the digit in the tenths place (i.e., 8) is the estimated digit.

This means that the measurement of 7.84 cm is accurate to the nearest tenth of a centimeter, and the digit 8 is the estimated digit.

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A regression model is a statistical approach to determine the relationship between a dependent variable and one or more independent variables.

If a regression model involves only one independent variable, it is called a simple regression model. In simple regression, the dependent variable is modeled as a linear function of the independent variable. The model estimates the slope and intercept of the line that best fits the data, and uses them to predict the dependent variable for a given value of the independent variable. Simple regression is useful when there is a clear and strong relationship between the independent and dependent variables, and when there are no confounding variables or interactions with other independent variables.

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75 employees were absent for six or more days.

To determine how many employees were absent for six or more days, we need to refer to the given frequency distribution of days absent:

- 0 up to 3 days: 2 employees

- 3 up to 6 days: 25 employees

- 6 up to 9 days: 14 employees

- 9 up to 12 days: 19 employees

- 12 up to 15 days: 42 employees

To find the number of employees absent for six or more days, we need to add the number of employees in the last three categories:

14 (6 up to 9 days) + 19 (9 up to 12 days) + 42 (12 up to 15 days) = 75 employees

Therefore, 75 employees were absent for six or more days.

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For  triangle EFD, the value of x is 24 units.

We know that the side-splitting theorem states that, 'if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.'

For  triangle EFD we can obaserve that GH is parallel to side ED.

By applying the side-splitter theorem to triangle EFD,

⇒ FG/GE = FH/HD

Here, FG = 18 units, GE = 6 units, HD = 8 units

substituting values,

⇒ 18/6 = x/8

⇒ 3 = x/8

⇒ x = 3 × 8

⇒ x = 24 units

Therefore, the value of x is 24 units.

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a. The probability that it will take more than 420 minutes to process all these books  is 0.4452.

b. The probability that at least 25 books will be processed in the first 240 minutes is  0.0002.

Let X be the time it takes to process one book, then X has a normal distribution with mean μ = 10 and standard deviation σ = 3.

(a) The total time it takes to process 40 books is Y = 40X. The mean of Y is E(Y) = E(40X) = 40E(X) = 40(10) = 400 minutes. The variance of Y is Var(Y) = Var(40X) = 40^2 Var(X) = 40^2 (3^2) = 14400. Therefore, the standard deviation of Y is σ(Y) = sqrt(Var(Y)) = 120.

To find the probability that it will take more than 420 minutes to process all these books, we standardize Y as follows:

Z = (Y - E(Y)) / σ(Y) = (420 - 400) / 120 = 1/6

Using a standard normal distribution table or calculator, we can find that P(Z > 1/6) ≈ 0.4452. Therefore, the approximate probability that it will take more than 420 minutes to process all these books is 0.4452.

(b) To find the probability that at least 25 books will be processed in the first 240 minutes, we standardize X as follows:

Z = (240 - μ) / σ = (240 - 10) / 3 = 230/3

Using a standard normal distribution table or calculator, we can find that P(Z > 230/3) ≈ 0.0002. Therefore, the approximate probability that at least 25 books will be processed in the first 240 minutes is 0.0002.

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Naveen gets $2.00 in change.

We have,

Naveen buys 1 ½ yards of ribbon, which is equivalent to 1.5 yards.

The cost of 1 yard of ribbon is $2, so the cost of 1.5 yards.

= 1.5 x $2

= $3

Naveen gives the clerk a $5.00 bill, so the amount she paid is $5.00.

To find the change Naveen gets back, we need to subtract the amount she paid from the cost of the ribbon:

Change = Amount paid - Cost of ribbon

Change = $5.00 - $3.00

Change = $2.00

Therefore,

Naveen gets $2.00 in change.

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If the perimeter of square based pyramid is 18.5 ft and height is 7.6 ft, then the volume of pyramid will be  54.4 cubic foot.

The "Volume" of a square pyramid is defined as the amount of space occupied by the pyramid, and it is given by the formula: V = (1/3) × B × h, where V is = volume, B is = area of base, and h = height of pyramid,

The base of pyramid is a square, we find the "base-area" by dividing the perimeter by 4 and squaring the result:

⇒ Perimeter of  base = 18.5 ft,

⇒ Length of one side of base = 18.5/4 = 4.625 ft,

⇒ Base area = (4.625 ft)² = 21.390625 sq ft,

Now, we use the formula to find the volume of the pyramid:

⇒ Volume = (1/3) × 21.390625 × 7.6 ,

⇒ Volume = 54.384375 cubic feet,

Rounding volume to nearest tenth of a cubic foot, we get:

⇒  Volume ≈ 54.4 cubic feet.

Therefore, the volume of the pyramid is approximately 54.4 cubic feet.

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The given question is incomplete, the complete question is

Find the volume of a pyramid with a square base, where the perimeter of the base is 18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest tenth of a cubic foot.

The value of the car after two years is £8400.

Given that a car has an original value of £14000 after two years its cost has reduced by 40%,

We need to find the cost of the car in current year.

So, 100-40 = 60

Therefore, the value of the car after two years =

60% of 14000 = 0.60 × 14000

= 8400

Hence, the value of the car after two years is £8400.

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Answer:

D. 50%

Step-by-step explanation:

The total amount of hours in the circle graph is equal to 24.

We just need to subtract the number of hours spent on sleeping and eating.

Sleeping = 9 hours

Eating = 3 hours

24 - 9 - 3 = 12 hours.

12 hours is half of 24 hours.

So, 50% is the answer. (D)

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2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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The probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96%.

To find the probability that a randomly selected toaster will have a total resistance of 345 to 355 ohms, we need to know the distribution of total resistance and parameters such as mean and standard deviation.

Expecting that the dispersion of add up to resistance takes after a typical conveyance with cruel μ and standard deviation σ, ready to utilize the standard ordinary dispersion to calculate the likelihood that the entire resistance will be between 345 and 355 ohms.

 First, we need to normalize the 345 and 355 values ​​with the following formula:

z = (x - μ) / σ

where x=desired value, μ = mean, σ = standard deviation, and z =corresponding z-score.

For x = 345 ohms:

z1 = (345 - μ) / σ

For x = 355 ohms:

z2 = (355 - μ) / σ

Next, we need to find the area under the standard normal distribution curve between z-scores z1 and z2. This represents the probability that the total resistance will be between 345 and 355 ohms.

You can find this range using a standard regular table or calculator. For example, using the standard normal table, we can find the region between z1 and z2 like this:

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(z2) - Φ(z1)

where Φ(z) is the standard cumulative normal distribution function (CDF), the probability that a standard normal random variable is less than or equal to z.

For example, if z1 = -1.5 and z2 = 1.5, then

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(1.5) - Φ(-1.5) = 0.8664 - 0.0668 ≈ 0.7996

Therefore, the probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96% (assuming the distribution of total resistance follows a normal distribution with a known mean and standard deviation).

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The solution to the initial value problem dy/dФ + y = sin Ф is: y = (-cos Ф + 2)/e^Ф.

To solve the initial value problem dy/dФ + y = sin Ф, we first need to find the integrating factor, which is given by e^Ф. Multiplying both sides by the integrating factor, we get:

e^Ф(dy/dФ) + e^Фy = e^Фsin Ф

Now, we can use the product rule to simplify the left-hand side:

(d/dФ)(e^Фy) = e^Фsin Ф

Integrating both sides with respect to Ф, we get:

e^Фy = -cos Ф + C

where C is a constant of integration. Solving for y, we get:

y = (-cos Ф + C)/e^Ф

To find the value of C, we use the initial condition y(0) = 1. Substituting this into the equation above, we get:

1 = (-cos 0 + C)/e^0
1 = (-1 + C)/1
C = 2

Therefore, the solution to the initial value problem dy/dФ + y = sin Ф is:

y = (-cos Ф + 2)/e^Ф

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The value of l, k, and c are 1, 284.2 and 4.0000 respectively. When f = 10%, V = -0.0032 mV, When f = 50%, V = 0.0092 mV, When f = 90%, V = -0.0193 mV.

(a) The formula given for f(V) is the logistic function, which is of the form f(V) = L / (1 + C*e^(-kV)). Therefore, we can compare this to the given formula to obtain:
L = 1
k = 1421/5 = 284.2
C = 4
Rounding C to four decimal places, we get C = 4.0000.

(b) To find the voltages at which 10%, 50%, and 90% of the channels are open, we can use the logistic function formula and solve for V when f = 0.1, 0.5, and 0.9 respectively.
For f = 0.1:
0.1 = 1 / (1 + 4*e^(-284.2V))
0.9 + 4*e^(-284.2V) = 10
e^(-284.2V) = 1.525
-284.2V = ln(1.525)
V = -0.0032 mV
For f = 0.5:
0.5 = 1 / (1 + 4*e^(-284.2V))
1 + 4*e^(-284.2V) = 2
e^(-284.2V) = 0.25
-284.2V = ln(0.25)
V = 0.0092 mV
For f = 0.9:
0.9 = 1 / (1 + 4*e^(-284.2V))
4*e^(-284.2V) = 9
e^(-284.2V) = 2.25
-284.2V = ln(2.25)
V = -0.0193 mV
Rounding these answers to two decimal places, we get:
When f = 10%, V = -0.0032 mV.
When f = 50%, V = 0.0092 mV.
When f = 90%, V = -0.0193 mV.

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The equation of the plane tangent to the graph of f(x,y) at (1,0) is z = f(1,0) + 2(x - 1) + y.

a.) To find the equation of the plane tangent to the graph of f(x,y) at (1,0), we first need to find the partial derivatives of f(x,y) with respect to x and y. The partial derivative of f(x,y) with respect to x is 2xe^xy, and the partial derivative of f(x,y) with respect to y is x^3e^xy. Evaluating these at (1,0), we get 2(1)(1) = 2 and (1)^3(1) = 1. So the equation of the plane tangent to the graph of f(x,y) at (1,0) is z = f(1,0) + 2(x - 1) + y.

b.) The linear approximation of f(x,y) for (x,y) near (1,0) can be found using the formula L(x,y) = f(1,0) + fx(1,0)(x - 1) + fy(1,0)y, where fx and fy are the partial derivatives of f with respect to x and y evaluated at (1,0). We already found fx(1,0) to be 2 and fy(1,0) to be 1. Evaluating f(1,0), we get f(1,0) = 1, so the linear approximation of f(x,y) near (1,0) is L(x,y) = 1 + 2(x - 1) + y.

c.) The differential of f at point (1,0) is the linear transformation given by df(1,0)(x,y) = fx(1,0)x + fy(1,0)y. Plugging in fx(1,0) = 2 and fy(1,0) = 1, we get df(1,0)(x,y) = 2x + y.

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To find the integrating factor for the given

ODE

, we need to first rearrange the

equation

into the standard form of y' + p(x)y = q(x), where p(x) = 0 and q(x) = Ndx + x - t^3 + e^(-Nt^2).

Dividing both sides of the equation by N, we get:

dx/dt + (1/N)x = (1/N)t^3 - e^(-Nt^2)

Now, we can find the

integrating factor

by taking the exponential of the

antiderivative

of p(x), which is:

e^∫(1/N)dx = e^(x/N)

Therefore, the integrating factor for the given ODE is e^(x/N). Multiplying both sides of the ODE by this integrating factor, we get:

e^(x/N)dx/dt + (1/N)e^(x/N)x = (1/N)e^(x/N)t^3 - e^((x/N)-Nt^2)

Recognizing the left-hand side as the product rule of (e^(x/N)x), we can simplify the equation to:

d/dt(e^(x/N)x) = (1/N)e^(x/N)t^3 - e^((x/N)-Nt^2)

Integrating

both sides with respect to t, we get:

e^(x/N)x = (1/N)e^(x/N)(1/4)t^4 + (1/2N)e^((x/N)-Nt^2) + C

where C is the constant of integration. Solving for x, we get:

x = (1/N)(1/4)t^4 + (1/2N)e^(-Nx^2) + Ce^(-x/N)

where we have used the fact that e^(x/N) is never zero since x > 0. Therefore, we have found the

general solution

for the given ODE.

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Differential Equation

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