Imagine that the price per gallon of gas with a $7 car wash is $3. 19 and the price without the car wash is $3. 39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

The value of the coordinates of point D is, (3, - 1)

We have to given that;

All the coordinates of rectangles are,

A(-2,1), B(-6, -9), C(-1, -11)

Now, Let the fourth coordinate of rectangle is,

D (x, y)

Hence, Midpoint of AC and BD are same.

So., Midpoint of AC is,

⇒ AC = (- 2 + (- 1))/ 2, (1 + (- 11))/2

          = (- 3/2 , - 5)

And, Midpoint of BD,

⇒ BD = (- 6 + x)/2, (- 9 + y)/2

By comparing;

⇒ (- 6 + x)/2 = - 3/2

⇒ - 6 + x = - 3

⇒ x = - 3 + 6

⇒ x = 3

⇒ (- 9 + y)/2 = - 5

⇒ - 9 + y = - 10

⇒ y = -10 + 9

⇒ y = - 1

Thus, The value of the coordinates of point D is, (3, - 1)

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A graph of the points that represent this data are shown on the coordinate plane attached below.

In this scenario, the week number would be plotted on the x-axis (x-coordinate) of the scatter plot while the amount of money (in dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the week number and the amount of money (in dollars), a linear equation for the line of best fit is as follows:

y = 1.19x + 1.05

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The cost of the Portrait frame cost is: $32.8

The formula for the perimeter of a rectangle is given by the expression:

A = 2(L +  W)

Where:

L is Length

W is Width

We are given that:

Width: W = 4 ft

Height: H = 6 ft

Thus:

Perimeter = 2(6 + 4)

= 20 ft

Cost of the rectangular portrait per foot is $1.64

Thus:

Total cost = 20 * 1.64

= $32.8

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Answer:

k = -3.

Step-by-step explanation:

To answer this question, we need to use our own knowledge and information. Adding a constant k to a function f(x) shifts the graph of f(x) vertically by k units. If k is positive, the graph moves up. If k is negative, the graph moves down. The value of k can be found by comparing the y-coordinates of corresponding points on the graphs of f(x) and g(x). For example, if g(x) = f(x) + 2, then the graph of g(x) is 2 units above the graph of f(x), and any point (x, y) on f(x) corresponds to a point (x, y + 2) on g(x). Therefore, the answer is: k is the vertical shift of the graph of f(x) to get the graph of g(x). It can be found by subtracting the y-coordinate of a point on f(x) from the y-coordinate of the corresponding point on g(x).

Looking at the graph given, we can see that the graph of g(x) is below the graph of f(x), which means that k is negative. We can also see that one point on f(x) is (0, 3), and the corresponding point on g(x) is (0, 0). Using the formula above, we get:

k = y_g - y_f

k = 0 - 3

k = -3

Therefore, the correct option is k = -3.

Walter can stay within his budget by dropping Fes (option ii).

Walter's original itinerary includes trips to Marrakech, Fes, Kenitra, and Oujda, which will cost him a total of 478 + 478 + 778 + 683 = MAD 2,417. This exceeds his budget of MAD 2,500.

Option i suggests replacing Kenitra with Tangier and Oujda with Casablanca, which will cost a total of 610 + 466 + 610 + 466 = MAD 2,152. However, this still exceeds Walter's budget.

Option iii suggests replacing Marrakech with Casablanca, which will cost a total of 965 + 466 + 778 + 683 = MAD 2,892, which is over Walter's budget.

Therefore, the only option that allows Walter to stay within his budget is to drop Fes from his itinerary, which will cost a total of 478 + 778 + 683 = MAD 1,939. This is well within his budget of MAD 2,500. So optio 2 is correct.

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For series Σ a(-1)^(k+1)k!, convergence depends on the limit of |a(k+1)/a(k)|. For series Σ ka sin(2), it diverges.

Consider the series Σ a(-1)^(k+1)k!, where a is a sequence of real numbers.

To determine the convergence of this series, we can use the ratio test

lim┬(k→∞)⁡〖|a(k+1)(-1)^(k+2)(k+1)!|/|ak(-1)^(k+1)k!| = lim┬(k→∞)⁡〖(k+1)|a(k+1)|/|a(k)||〗

If this limit is less than 1, then the series converges absolutely. If the limit is greater than 1, the series diverges. If the limit is equal to 1, then the test is inconclusive.

Let's evaluate the limit

lim┬(k→∞)⁡〖(k+1)|a(k+1)|/|a(k)||〗 = lim┬(k→∞)⁡〖(k+1)!/(k!k)|a(k+1)/a(k)||〗 = lim┬(k→∞)⁡〖(k+1)/(k)|a(k+1)/a(k)||〗

Since lim┬(k→∞)⁡〖|a(k+1)/a(k)||〗 exists, we can apply the ratio test again:

if the limit is less than 1, the series converges absolutely.

if the limit is greater than 1, the series diverges.

if the limit is equal to 1, the test is inconclusive.

Therefore, we can classify the series Σ a(-1)^(k+1)k! as either absolutely convergent, conditionally convergent, or divergent depending on the value of the limit.

Consider the series Σ ka sin(2), where a is a sequence of real numbers.

To determine the convergence of this series, we can use the alternating series test, which states that if a series Σ (-1)^(k+1)b(k) is alternating and |b(k+1)| <= |b(k)| for all k, and if lim┬(k→∞)⁡〖b(k) = 0〗, then the series converges.

In this case, we have b(k) = ka sin(2), which is alternating since (-1)^(k+1) changes sign for each term. We also have

|b(k+1)|/|b(k)| = (k+1)|a|/k < k|a|/k = |b(k)|/|b(k-1)|

Therefore, |b(k+1)| <= |b(k)| for all k. Finally, we have

lim┬(k→∞)⁡〖b(k) = lim┬(k→∞)⁡〖ka sin(2)〗 = ∞〗

Since the limit does not exist, the series diverges.

Therefore, we can classify the series Σ ka sin(2) as divergent.

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The expression for the given statement is √3².

We have,

The expression that can be written from the statement.

3 square root = √3

Second power of x = x²

Now,

We can write the expression as,
= √3²

Thus,

The expression for the given statement is √3².

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To find the answer, we need to identify the quartiles of the data set and use them to construct the box plot.

First, we need to order the data set in increasing order:

10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Next, we need to find the median (Q2) of the data set. Since we have an even number of data points, we take the average of the two middle values:

Q2 = (25 + 30) / 2 = 27.5

This value represents the median of the data set.

To find Q1 and Q3, we divide the data set into two halves:

10, 15, 20, 25, 30 | 35, 40, 45, 50, 55

Q1 is the median of the lower half:

Q1 = (15 + 20) / 2 = 17.5

Q3 is the median of the upper half:

Q3 = (45 + 50) / 2 = 47.5

We can now use this information to construct the box plot:

     |         -------

     |        /

     |    -------

     |   /

     |-------

     |         10    20    30    40    50

            Q1          Q2         Q3

The box represents the middle 50% of the data (from Q1 to Q3), while the whiskers represent the minimum and maximum values that are not outliers.

Since we want to find the paint time for a student who is slower than 75% of the other students, we need to look at the upper quartile (Q3) of the data set. 75% of the data is contained between Q1 and Q3, so a student who is slower than 75% of the other students would have a paint time greater than Q3.

Therefore, the answer is 46 minutes, which is greater than Q3 (47.5 minutes).

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The probability is 0.125

There are a total of 2 × 2 x 2 = 8 possibilities of one plate, one cup, and one bowl that Kyra can select if she has two plates, two cups, and two bowls.

We need to figure out how many combinations fit this requirement because we are interested in the likelihood that all three objects are blue. There are 2 × 2 x 2 = 8 potential color combinations if we assume that each item can be either blue or not blue.

There is only one of these eight color pairings in which all three components are blue. P(all three are blue) = 1/8 = 0.125 is the likelihood that Kyra will select one blue plate, one blue cup, and one blue bowl.

So, the probability is 0.125.

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Step-by-step explanation:

= sqrt ( 28 ÷7) = sqrt (4) = 2

Answer:

2

Step-by-step explanation:

First we put the two equations together so it would be like this

[tex]\sqrt \frac{28}{7}[/tex]

the square root of that is 4 because 7 goes into 28 four times

so now we have this [tex]\sqrt{4}[/tex]

and the square root of 4 is 2

It would take approximately 20 hours for the bacteria to triple in number.

Given that the bacteria population doubles every 10 hours, we can use exponential growth to determine the time it would take for the population to triple.

Let's represent the initial population as P0 and the time it takes for the population to triple as t.

Using the concept of exponential growth, we can express the population at time t as P(t) = P0 * 2^(t/10).

Since we want the population to triple, we set P(t) = 3 * P0:

3 * P0 = P0 * 2^(t/10).

We can cancel out P0 from both sides of the equation:

3 = 2^(t/10).

To solve for t, we can take the logarithm of both sides. Using the base-2 logarithm (log2) gives us:

log2(3) = t/10.

Using a calculator, we find that log2(3) is approximately 1.585.

Now, we can solve for t:

1.585 = t/10.

Multiplying both sides of the equation by 10 gives us:

15.85 = t.

Rounding to the nearest hour, the time it would take for the bacteria population to triple is approximately 16 hours.

Therefore, the bacteria population would take approximately 20 hours to triple in number.

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An American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.

To find the amount of cheese consumed by an American in the middle 70% of cheese consumption, we need to find the z-scores that correspond to the lower and upper bounds of the middle 70% and then convert those z-scores back to the original scale of measurement.

First, we need to find the z-score that corresponds to the 15th percentile (lower bound) and the z-score that corresponds to the 85th percentile (upper bound) of the normal distribution. We can use a standard normal table or a calculator to find these values. Using a calculator, we get:

z_15 = invNorm(0.15) = -1.036

z_85 = invNorm(0.85) = 1.036

Next, we can use the formula:

z = (x - mu) / sigma

where x is the amount of cheese consumed by an American, mu is the mean amount of cheese consumed (32.3 lbs), and sigma is the standard deviation (8.7 lbs), to convert the z-scores back to the original scale of measurement:

For the lower bound:

-1.036 = (x - 32.3) / 8.7

x = -1.036 * 8.7 + 32.3 = 23.1 lbs

For the upper bound:

1.036 = (x - 32.3) / 8.7

x = 1.036 * 8.7 + 32.3 = 41.5 lbs

Therefore, an American in the middle 70% of cheese consumption consumes between 23.1 lbs and 41.5 lbs of cheese per year.

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Answer:

Step-by-step explanation:

In this set,

the maximum is 35

the minimum is 6

So, we can cross out options A, B

the median is 14

The only option that works for this set is option D

Answer:

A dilation always produces a similar figure. Similar figures have the same shape but different sizes.

In a dilation, each point of the original figure is transformed by multiplying its coordinates by a scale factor, which determines the change in size. However, the shape and proportions of the figure remain unchanged. Therefore, the figures obtained through dilation are similar, meaning they have the same shape but different sizes.

Therefore, the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form is:

y = -3/2 x + 3/2

Step-by-step explanation:

To find the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form (y = mx + b), we need to first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-3, 6) and (x2, y2) = (-5, 9).

m = (9 - 6) / (-5 - (-3))

m = 3 / (-2)

m = -3/2

Now that we have the slope, we can use either of the two given points and the slope to find the y-intercept (b) of the line:

y = mx + b

6 = (-3/2)(-3) + b

6 = 9/2 + b

b = 6 - 9/2

b = 3/2

If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:

58 m / 40.6 cm

To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:

58 m = 58 × 100 cm = 5800 cm

Now we can divide:

5800 cm / 40.6 cm = 142.857...

Rounding to the nearest thousandth, we get:

142.857... ≈ 142.857

Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

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The sample mean difference in heights for these 24 pairs of siblings is 1.79 inches. So the third option is correct.

The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in the population was (–0.76, 4.34).

This means that if we were to repeat this sampling process many times, we would expect 95% of the resulting confidence intervals to contain the true mean difference in heights for all brother-and-sister pairs in the population.

To find the sample mean difference from these 24 pairs of siblings, we take the midpoint of the confidence interval. The midpoint is the average of the lower and upper bounds, which is:

(-0.76 + 4.34) / 2 = 1.79

Therefore, the sample mean difference in heights for these 24 pairs of siblings is 1.79 inches.

So the correct answer is third option.

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The expression for the area of the flower garden is (45+2x)(20+2x) - 900.

Area of vegetable garden:

[tex]A_v = 45 ft * 20 ft[/tex] = 900 sq ft

Dimensions of entire garden:

Length = 45 ft + 2x

Width = 20 ft + 2x

Area of entire garden:

[tex]A_e = (45+2x)(20+2x)[/tex]

Area of flower garden:

[tex]A_f = A_e - A_v = (45+2x)(20+2x) - 900 sq ft[/tex]

So, the expression for the area of the flower garden is (45+2x)(20+2x) - 900.

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Answer:

Si hoy es martes en 300 días será lunes.

⭐Vamos a considerar que una semana tiene 7 días, es decir, cada 7 días será martes.

Pensamos una aproximación de semanas, al dividir 300 entre 7:

300 ÷ 7 = 42,85 ≈ 42 semanas completas

Cantidad de días que hay en 42 semanas:

7 × 41 = 294 días

Cantidad de días que faltan para completar 300:

300 - 294 = 6 días

El día 294 será martes

6 días después (para completar 300) será lunes ✔️

Step-by-step explanation:

Brainlist porfavor

Answer:

Si hoy es martes en 300 días será lunes.

You can drive at most 700 miles within the $180 budget for weekly transportation.

To determine how many miles can be driven with a budget of $180 for weekly transportation, we'll use the given information: $75 per week for car rental and $0.15 per mile driven. First, subtract the weekly rental cost from the total budget:

$180 - $75 = $105

Now, divide the remaining budget by the cost per mile to find the maximum number of miles that can be driven:

$105 ÷ $0.15 ≈ 700 miles

So, you can drive at most 700 miles within the $180 budget for weekly transportation.

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The term "mapping" refers to the process of creating a mathematical correspondence between points or objects in two different sets. In this case, the mapping found in part b tells us that there exists a one-to-one correspondence between the points in Circle A and the points in Circle B.

There is a one-to-one correspondence between the points in Circle A and the points in Circle B, and that this correspondence preserves distance.

This means that for every point in Circle A, there is exactly one corresponding point in Circle B that is the same distance away from the center of the circle as the original point.

Since the correspondence is one-to-one, it follows that the two circles have the same number of points. That is, if Circle A has n points, then Circle B also has n points.

Therefore, we can conclude that the two circles have the same size.

Furthermore, because the correspondence preserves distance, any transformation that maps one circle onto the other must be a rigid motion, meaning it preserves angles and distances.

In particular, the transformation must be an isometry.

Therefore, we have shown that the two circles are congruent. That is, they have the same size and shape, and can be transformed onto one another by a combination of translations, rotations, and reflections.

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Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.

Total number of students is 22.

To find the percentage of students who collected between 49 and 98 kilograms of newspapers, we first need to count the number of students who collected within this range. From the given data, we can see that the following students collected between 49 and 98 kilograms of newspapers

87, 64, 90, 76, 60, 55, 57, 75, 56, 88

Percentage of students = (number of students in range / total number of students) x 100

= (10 / 22) x 100

= 45.45%

Therefore, approximately 45.45% of students collected between 49 and 98 kilograms of newspapers.

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The total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.

According to the question the hydrogen peroxide in the first container weighed 6.4 ounces, and the hydrogen peroxide in the second container weighed 4.07 ounces.

According to the rules of significant digits, the numbers after the decimal point in a sum of difference is the least of that of the numbers to be added or subtracted.

This means that when 6.4 and 4.07 is added, then we will see numbers of decimal places in each number. 6.4 has 1 number after decimal point and 10.47 has 2.

Hence the result of 6.4 + 10.47 will have a minimum of 2 which is 1 decimal place.

Now, 6.4 + 4.07

= 10.47

Rounding it off from the above-mentioned criteria gives us 10.5 ounces.

Therefore, the total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.

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Answer: yes, the game is fair.

Step-by-step explanation:

The game is fair because:

a. you are playing with multiple players, and they have equal odds

b. the odds of winning are higher, so there is balance since you earn less points.

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The value of the distance you will run is 5.62500 miles

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

This means that

Speed = 7.5 miles per hour

Time = 45 minutes

The distance you will run is calculated as

Distance = Speed * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = 7.5 miles per hour * 45 minutes

Evaluate the product

Distance = 5.62500 miles

Hence, the distance is 5.62500 miles

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The expression that represents the amount of money Amelia would have saved in w weeks is: $9w + $100

Amelia starts with $100 and saves an additional $9 per week for 6 weeks. To find the total amount of money she has after 6 weeks, you can use this formula:

Total money = Initial amount + (Weekly savings × Number of weeks)

Total money = $100 + ($9 × 6)
Total money = $100 + $54
Total money = $154

So, Amelia would have $154 after 6 weeks of saving.

For an expression representing the amount of money Amelia would have saved in w weeks:

Total money (w) = $100 + ($9 × w)

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The equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].

Let V(0) be the value of the stock in 1940, which is given as $1.25. Then, the value of the stock after t years (t > 0) can be found by multiplying the initial value with the growth factor of 1.07 raised to the power of the number of years of growth. Thus, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is:

V(t) = V(0) * [tex](1 + 0.07)^t[/tex]

Substituting the given value of V(0) = $1.25, we get:

V(t) = $1.25 * [tex](1 + 0.07)^t[/tex]

Simplifying this expression, we get:

V(t) = $1.25 * [tex]1.07^t[/tex]

Therefore, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].

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To find the volume of the solid generated by revolving the region bounded by the curve y=7secx and the line y=72 over the interval − π/4≤x≤π/4 about the​ x-axis, we can use the method of cylindrical shells.

First, we need to find the equation of the curve of the region being revolved. We have y=7secx and y=72, so at the intersection point, we have 7secx=72, which gives us secx=10.285. Taking the inverse secant function of both sides, we get x=1.37 (approximately).

Now, we can set up the integral for the volume using cylindrical shells. The radius of each shell is y-72, and the height of each shell is 2π times the distance from x to the intersection point, which is x-1.37. The integral is:

V = ∫(2π)(y-72)(x-1.37) dx, from -π/4 to π/4

We can substitute y=7secx into the integral:

V = ∫(2π)(7secx-72)(x-1.37) dx, from -π/4 to π/4

Using integration by parts, we can evaluate the integral:

V = (2π)[(7/2)ln|secx+tanx| - 72x + (1.37)(7/2)ln|secx+tanx| + 46.8] from -π/4 to π/4

V = (2π)(7/2)(ln|11+6√3| + ln|11-6√3| + 1.37ln|11+6√3| + 1.37ln|11-6√3| - 144)

V ≈ 305.64 cubic units.

Therefore, the volume of the solid generated by revolving the region bounded by the curve y=7secx and the line y=72 over the interval − π/4≤x≤ π/4 about the​ x-axis is approximately 305.64 cubic units.
To find the volume of the solid generated by revolving the region bounded by the curve y=7sec(x) and the line y=72 over the interval -π/4≤x≤π/4 about the x-axis, you can use the disk method. The formula for the disk method is:

Volume = π * ∫[R(x)² - r(x)²] dx from a to b

In this case, R(x) represents the outer radius, which is given by y=72, and r(x) represents the inner radius, which is given by y=7sec(x). The limits of integration are a=-π/4 and b=π/4. Therefore, the volume can be calculated as:

Volume = π * ∫[72² - (7sec(x))²] dx from -π/4 to π/4

Now, evaluate the integral and multiply by π to find the volume of the solid.

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To evaluate the indefinite integral of 3x^2 – 3x +1/ x^3 + 2, we can use partial fraction decomposition.

First, we factor the denominator: x^3 + 2 = (x + ∛2)(x^2 – ∛2x + 2).

Next, we can write the fraction as:

3x^2 – 3x +1/ x^3 + 2 = A/x + B(x^2 – ∛2x + 2) + C(x + ∛2)

Multiplying both sides by the denominator, we get:

3x^2 – 3x + 1 = A(x^2 – ∛2x + 2)(x + ∛2) + Bx(x + ∛2) + C(x^2 – ∛2x + 2)

To solve for A, B, and C, we can plug in specific values of x. For example, if we plug in x = -∛2, we get:

-2√2 + 1 = A(4√2) + C(0)

Therefore, A = (2 – √2)/8.

If we plug in x = 0, we get:

1 = A(2√2) + B(0) + C(√2)

Therefore, C = 1/√2.

Finally, if we plug in x = 1, we get:

1 = A(3√2) + B(1 – √2) + C(1 + √2)

Therefore, B = (-1 + √2)/4.

Now that we have A, B, and C, we can write the original fraction as:

3x^2 – 3x +1/ x^3 + 2 = (2 – √2)/8 * 1/x + (-1 + √2)/4 * (x^2 – ∛2x + 2) + 1/√2 * (x + ∛2)

Using this partial fraction decomposition, we can now integrate each term separately.

Integrating the first term, we get:

∫(2 – √2)/8 * 1/x dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + C

Integrating the second term, we can complete the square to get:

∫(-1 + √2)/4 * (x^2 – ∛2x + 2) dx = (-1 + √2)/4 * ∫(x – ∛1/2)^2 + 3/2 dx = (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + C

Integrating the third term, we get:

∫1/√2 * (x + ∛2) dx = (1/2√2) * (x^2/2 + ∛2x) + C

Putting it all together, we have:

∫(3x^2 – 3x +1)/ (x^3 + 2) dx = (1/8)(2ln|x| – √2 ln|x^2 + 2|) + (-1 + √2)/4 * ((x – ∛1/2)^2 + 3/2) + (1/2√2) * (x^2/2 + ∛2x) + C

where C is the constant of integration.

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