Find the measure of
m

The length of the bridge is 12.12 feet, the length the dog swam is 32.36 feet.

tan 68 = 30 / x

cross mulitply

x = 30 / tan 68

x = 12.12 feet

sin 68 = 30 / h

h = 30 / sin 68

h = 32.36

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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The vertex is (0, 4), the domain is {x | -3 ≤ x ≤ 3}, and the range is {y | y ≤ 4}.

Given points on the coordinate plane, a parabola opens down with solid circles at (−3, −5), (−2, 0), (−1, 3), (0, 4), (1, 3), (2, 0), (3, −5).

To determine the vertex, domain, and range, we can use the following steps:

Step 1: Graph the points on the coordinate plane to create the parabolic curve. By plotting these points, we can see that the curve is a downward-opening parabola with a minimum point (vertex) at (0, 4).

Step 2: The vertex of the parabola can be determined by looking at the x-coordinate of the minimum point of the curve. Therefore, the vertex of this parabola is at (0, 4).

Step 3: To find the domain of the parabola, we need to determine the range of possible x-values. By examining the x-coordinates of the given points, we can see that the domain is {x | -3 ≤ x ≤ 3}.

Step 4: To find the range of the parabola, we need to determine the range of possible y-values. By examining the y-coordinates of the given points, we can see that the range is {y | y ≤ 4}.

Thus, the vertex is (0, 4), the domain is {x | -3 ≤ x ≤ 3}, and the range is {y | y ≤ 4}.

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A graph of quadrilateral DEFG with points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9) is shown on the coordinate plane in the image below.

In Mathematics and Geometry, a quadrilateral can be defined as a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.

In this scenario, we would use an online graphing tool to plot quadrilateral DEFG based on the given coordinates or its points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9).

Based on the graph of quadrilateral DEFG with points D (−4, 4), E (1, −4), F (9, 1), and G (4, 9), this quadrilateral is composed of two pairs of opposite sides that are parallel and as such, we can logically deduce that it most likely represents a square.

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Therefore, the painting should be placed 5/4 feet on each side of the wall.

In the given problem, a 5-foot wide painting should be centered on a 15-foot wide wall. We can determine the length of each side of the painting by subtracting x from each side of the wall.

Therefore, the left side of the equation can be written as:

[tex]15 - x - 5 - x[/tex]

The physical situation given is that the painting is to be centered on the wall. This means that each side of the wall will have the same amount of space as the painting.

Therefore, the length of each side of the painting can be determined by subtracting x from each side of the wall. The total width of the wall is 15 feet, and the painting is 5 feet wide.

Therefore, the total length of the space on each side of the painting is 5 + x.To find the value of x, we can equate the length of each side of the painting. Therefore, the equation can be written as:

[tex]15 -x - 5 - x = 5 + x + x[/tex]

Simplifying the equation, we get:

[tex]10 - 2x = 2x + 5[/tex]

Solving for x, we get:

[tex]4x = 5x = \frac{5}{4}[/tex]

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Answer:

No.

Explanation:

Any number times an even number is even by definition.

Let's call the even factor 2n, and the other factor (odd or even) x. 2n × x = 2nx. Because it is multiplied by 2, it must still be even. The factors of an odd number are all odd.

The equation of the line that passes through [tex]$(6, -2)$[/tex] and is parallel to [tex]$y = \frac{1}{2}x - 3$[/tex] is [tex]$y = \frac{1}{2}x - 5$[/tex]

To find the equation of a line parallel to another line, we need to know that parallel lines have the same slope. The given line has a slope of [tex]$\frac{1}{2}$[/tex]. Therefore, the parallel line we are looking for will also have a slope of [tex]$\frac{1}{2}$[/tex].

Using the point-slope form of a linear equation, we can write the equation of the line as:

[tex]$y - y_1 = m(x - x_1)$[/tex]

where [tex]$(x_1, y_1)$[/tex]represents the given point and [tex]$m$[/tex] is the slope.

Substituting the values we have,[tex]$(x_1, y_1) = (6, -2)$[/tex] and [tex]$m = \frac{1}{2}$[/tex], we get:

[tex]$y - (-2) = \frac{1}{2}(x - 6)$[/tex]

Simplifying further:

[tex]$y + 2 = \frac{1}{2}x - 3$[/tex]

[tex]$y = \frac{1}{2}x - 5$[/tex]

This equation represents a line with the same slope and a different y-intercept, resulting in a parallel line.

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Answer:

The area of the trapezium is 40 cm².

Step-by-step explanation:

The formula for the area of a trapezium is:

[tex]\boxed{A=\dfrac{1}{2}(a+b)h}[/tex]

where:

Given the parallel bases are 13 cm and 7 cm in length, and the height is 4 cm, substitute these values into the formula and solve for A:

[tex]\begin{aligned}A&=\dfrac{1}{2}(13+7) \times 4\\\\&=\dfrac{1}{2}(20) \times 4\\\\&=10 \times 4\\\\&=40\; \sf cm^2\end{aligned}[/tex]

Therefore, the area of the trapezium is 40 cm².

Rounding to the nearest dollar, the move-in costs for the two-bedroom Hometown Apartment would be approximately $1,524. (none of the given options is correct)

To calculate the move-in costs for the two-bedroom Hometown Apartment, we need to consider the first and last month's rent, the security deposit, and the rental agent's fee.

The monthly rent for the apartment is $515, so the total rent for two months would be $515 * 2 = $1,030.

The security deposit is $185, and the rental agent's fee is 30% of the total rent. To find the agent's fee, we multiply the total rent by 30%: $1,030 * 0.3 = $309.

Adding up the first and last month's rent ($1,030), the security deposit ($185), and the rental agent's fee ($309), we get $1,030 + $185 + $309 = $1,524. (none of the given options is correct)

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The correct choice is "approximately Normal because the expected number of successes and failures for each sample are all at least 10."

The correct shape and justification of the sampling distribution of [tex]\bar p[/tex]F - [tex]\bar p[/tex]S can be determined based on the conditions for the approximate normality of the sampling distribution of the difference in proportions.

The conditions for the sampling distribution to be approximately normal are as follows:

The sampling method is random.

The samples are independent of each other.

The sample sizes are large enough.

In this scenario, 28 teachers and 100 students are selected randomly, satisfying the first condition.

For the second condition, we assume that the samples of teachers and students are independent of each other. While it's ideal to have truly independent samples, without further information about the sampling process, we can assume that the samples are relatively independent.

The third condition requires that the sample sizes are large enough. Specifically, for each sample, the expected number of successes and failures should be at least 10. Let's calculate the expected number of successes and failures for each group:

For the teachers:

Expected number of successes: 28 * 0.37 ≈ 10.36

Expected number of failures: 28 * (1 - 0.37) ≈ 17.64

For the students:

Expected number of successes: 100 * 0.89 ≈ 89

Expected number of failures: 100 * (1 - 0.89) ≈ 11

As we can see, both groups meet the criterion of having expected successes and failures of at least 10.

Based on these conditions, we can conclude that the sampling distribution of [tex]\bar p[/tex]F - [tex]\bar p[/tex]S is approximately normal.The answer that best fits the facts is "approximately Normal because the expected number of successes and failures for each sample are all at least 10."

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It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.

The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).

To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.

A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:

A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.

B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.

C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.

D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.

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If the sin of theta is equal to 3/5, we can determine the value of cos of theta using the Pythagorean identity. The Pythagorean identity states that s[tex]sin^2[/tex](theta) + [tex]cos^2[/tex](theta) = 1.

Given that sin(theta) = 3/5, we can square both sides of the equation to obtain [tex]sin^2[/tex](theta) = [tex](3/5)^2[/tex] = 9/25.

Substituting this value into the Pythagorean identity, we have 9/25 + [tex]cos^2[/tex](theta) = 1.

To solve for cos(theta), we subtract 9/25 from both sides of the equation:

[tex]cos^2[/tex](theta) = 1 - 9/25

[tex]cos^2[/tex](theta) = (25/25) - (9/25)

[tex]cos^2[/tex](theta) = 16/25

Taking the square root of both sides, we find that cos(theta) = ±(4/5).

Since cosine is positive in the first and fourth quadrants, we can conclude that cos(theta) = 4/5.

Therefore, the value of cos(theta) is 4/5.

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Adding and Subtracting Rational Expressions Adding and subtracting rational expressions require the following The rational expressions must have a common denominator.Add or subtract the numerators of the rational expressions and write the result over the common denominator.

Simplify the resulting expression if necessary. When adding or subtracting rational expressions, the common denominator is usually determined by finding the least common multiple (LCM) of the denominators.

The LCM is the smallest expression that can be divided evenly by the denominators.In the case of the addition and subtraction of rational expressions, the rational expressions must have a common denominator. When adding or subtracting rational expressions with the same denominator, add or subtract the numerators of the rational expressions and write the result over the common denominator.

The resulting expression can then be simplified by factoring, canceling out, and then simplifying the factors that remain.If the rational expressions have different denominators, find the LCM of the denominators. The LCM is then used to create equivalent fractions with the same denominator.

After that, you can add or subtract the numerators and simplify the resulting fraction.For example, consider the addition of the rational expressions `3/x` and `2/x+3`.

To add these two rational expressions, the denominators of the two fractions must first be combined. This is done by finding the LCM of the two denominators, which is `x(x + 3)`

.Then, multiply the first fraction by[tex]\frac{`(x + 3)}{(x + 3)`}[/tex] and the second fraction by `x/x`.This results in [tex]\frac{`(3(x + 3) + 2x)} {x(x + 3)`}[/tex] after adding the numerators. Simplify by combining like terms and factoring the numerator, resulting in

[tex]\frac{x`(5x + 9 }{(x(x + 3))}`[/tex].

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The gradient of the given sequence is -5 for the decreasing section and +5 for the increasing section.

To determine the gradient of the given sequence of numbers, we need to calculate the rate of change between consecutive terms. The gradient, also known as the slope, represents the steepness of the line connecting these points.

Looking at the sequence: 50 45 40 35 30 - 25 20 15 10 5 - 0 5 10, we can observe that the sequence is decreasing from left to right, then increasing from right to left.

Let's focus on the decreasing section first: 50 45 40 35 30 - 25 20 15 10 5 - 0. The gradient of this section is negative, as the values are decreasing. The rate of change between consecutive terms is constant, and it is -5. Therefore, the gradient is -5 for this decreasing section.

Moving on to the increasing section: 0 5 10, the gradient is positive since the values are increasing. The rate of change between consecutive terms is also constant at +5. Hence, the gradient for this increasing section is +5.

The gradient of the given sequence is -5 for the decreasing section and +5 for the increasing section.

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However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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Answer:

[tex]\csc A = \dfrac{\sqrt{41}}{5}[/tex]

Step-by-step explanation:

To find the exact value of csc A in simplest radical form using a rational denominator, we can use the reciprocal identities of secant and cosecant:

[tex]\boxed{\sec A = \dfrac{1}{\cos A}}\;\;\;\boxed{\text{csc} A = \dfrac{1}{\sin A}}[/tex]

Given sec A = √(41)/4, we can use the definition of secant as the reciprocal of cosine to find the value of cos A:

[tex]\cos A=\dfrac{1}{\sec A}=\dfrac{1}{\frac{\sqrt{41}}{4}}=\dfrac{4}{\sqrt{41}}[/tex]

Since angle A is in Quadrant I, both sin A and cos A are positive.

Now we can substitute the value of cos A into the trigonometric identity to find sin A:

    [tex]\sin^2 A + \cos^2 A = 1[/tex]

[tex]\sin^2 A + \left(\dfrac{4}{\sqrt{41}}\right)^2 = 1[/tex]

         [tex]\sin^2 A + \dfrac{16}{41} = 1[/tex]

                  [tex]\sin^2 A = 1-\dfrac{16}{41}[/tex]

                  [tex]\sin^2 A =\dfrac{25}{41}[/tex]

                    [tex]\sin A=\sqrt{\dfrac{25}{41}}[/tex]

                    [tex]\sin A=\dfrac{5}{\sqrt{41}}[/tex]

Finally, we can substitute the value of sin A into the reciprocal identity to find csc A:

[tex]\text{csc} A = \dfrac{1}{\sin A} = \dfrac{1}{\frac{5}{\sqrt{41}}} = \dfrac{\sqrt{41}}{5}[/tex]

Therefore, the exact value of csc A in simplest radical form with a rational denominator is:

[tex]\boxed{\csc A = \dfrac{\sqrt{41}}{5}}[/tex]

The measure of the angle KWS in the circle is 70 degrees.

The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Therefore, let's find the central angle m∠KWS as follows:

Hence,

arc angle  = central angle

m∠KWS = 22 + 48

m∠KWS = 70 degrees

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Answer:

v=2144.66

Step-by-step explanation:

V=4/3πr^3
sub in r which is 8

V=4/3 * π * 8^3
V=4/3 * π * 512

Answer:

Day 1: 25, Day 2: 16, Day 3: 64

Step-by-step explanation:

First you need to form an equation using unknowns, below i have used x to represent the number of calls

Day 1: x+9

Day 2: x

Day 3: 4x

105-9 (as day 1 is x+9) = 96

4 + 1 + 1 = 6 (6x)

96/6 = 16

x = 16, so Day 2 = 16

16 + 9 = 25

16 x 4 = 64

To check, 16 + 25 + 64 = 105

Hope this helps :D

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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The correct option is A. Martha's error was that she should have rounded the dividend to 70.

To determine Martha's error, we need to analyze the steps she took to estimate the quotient of -71.81 and -8.02 using rounding to the nearest whole number.

First, Martha rounded -71.81 to the nearest whole number, which is -72. However, the error lies in her next step. Instead of considering the dividend as -72, she should have rounded it to the nearest whole number, which is -70. Rounding the dividend to -70 would have been the correct approach.

Then, she divided -70 by -8.02 to estimate the quotient. By performing the division, she obtained a quotient of 8. However, her error occurred in the rounding of the dividend, not in the division process itself.

Rounding the dividend to -70 instead of -72 would have resulted in a different quotient, which would have been closer to the actual value. Therefore, Martha's error lies in rounding the dividend incorrectly, and the correct statement is that she should have rounded the dividend to 70.

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Answer: its B

Step-by-step explanation:

Im in the asighnment rn

Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

[tex]y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x[/tex]

Part B

[tex]y=9(5)\\y=45[/tex]

Answer:

  a) 600 m

  b) 1200 m

Step-by-step explanation:

Given a distance-time graph of a motorcyclist's journey, you want to know the distance to the shop, and the distance traveled in the first 4 minutes.

The graph is the distance the motorcyclist is from home. Since the graph starts with the motorcyclist at the shop, and the starting value on the graph is distance from home = 600 m, we can conclude ...

  the shop is 600 m from the motorcyclist's home.

The graph tells us the motorcyclist is 1800 m from home after traveling 4 minutes. Since the start of the journey was 600 m from home, the distance traveled in that 4 minutes is ...

  1800 -600 = 1200 . . . . meters

The motorcyclist traveled 1200 meters in the first 4 minutes.

__

Additional comment

It's all about reading a graph, including the axis labels. Understanding the problem statement is helpful, too.

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The type of sampling used in the scenario where Christopher obtains a list of athletes and divides them into groups of varsity and junior varsity, then randomly selects a proportionate number of individuals from each group to study the eating habits of all athletes in his school is stratified random sampling.

Stratified random sampling is a sampling method used to divide a population into different strata or subgroups based on some characteristics or attributes such as gender, age, race, etc. in such a way that the members of each subgroup are homogeneous or similar in some specific ways.

Then a random sample is drawn from each subgroup or stratum in the population to obtain a representative sample of the entire population.

It is a more efficient and precise sampling method than simple random sampling, especially when there are significant differences or variability within the population being studied.

The stratified random sampling method is used in the scenario given because Christopher divided the athletes into two strata or groups based on their team's level (varsity and junior varsity) and then randomly selected a proportionate number of individuals from each group.

This will enable him to obtain a representative sample of the entire population of athletes in his school and study their eating habits accurately.

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The decimal 0.07183 can be written as the fraction 359/500.

To convert the decimal 0.07183 into a fraction, we need to determine the numerator and denominator that represent the decimal value accurately.

The decimal 0.07183 can be written as 0.07183/1, as any number divided by 1 equals itself.

To convert the decimal to a fraction, we remove the decimal point and place the numerator over the appropriate power of 10 in the denominator. In this case, since the decimal has five digits after the decimal point, we place the numerator over 10,000 (10 raised to the power of 5).

Thus, the fraction equivalent of 0.07183 is 0.07183/1 = 7183/10000.

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), we get:

7183/10000 = 359/500.

Therefore, the decimal 0.07183 can be written as the fraction 359/500.

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The equation that is equivalent to [tex]In7 + 3 ln x = 5 In 2 is x^3 = 32/7.[/tex]

To solve the given equation, In7 + 3 ln x = 5 In 2, we can use the properties of logarithms to simplify and rewrite it in a different form.

First, we can combine the logarithms on the left-hand side using the property of addition of logarithms:

[tex]In[/tex][tex]7 + ln(x^3) = In(2^5)[/tex]

Next, we can simplify further by applying the property of exponents of logarithms:

[tex]In(7x^3) = In(32)[/tex]

Now, since the natural logarithm function is a one-to-one function, we can equate the expressions inside the logarithms:

[tex]7x^3 = 32[/tex]

We can rearrange the equation to obtain it in the standard form:

[tex]x^3 = 32/7[/tex]

The equation that is equivalent to [tex]In7 + 3 ln x = 5 In 2 is x^3 = 32/7.[/tex]

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