Jordan and Taylor agree to meet at the gym. Jordan arrives uniformly between 8:00AM and 8:50AM. Taylor arrives uniformly be- tween 8:00AM and 8:30AM. Their arrival times are independent of one another. Jor- dan is impatient and will leave if Taylor is not there. Taylor will wait up to 10 minutes for Jordan. Determine the probability that they meet. 1. At least 29% 2. At least 16%, but less than 22% 3. At least 22%, but less than 29% 4. Less than 10% 5. At least 10%, but less than 16%

To develop an estimated regression with family-sedan and upscale-sedan as independent variables for treating cost/mile as the dependent variable, we can use a multiple linear regression model. The regression equation can be written as:

Cost/mile = β0 + β1 * Family-sedan + β2 * Upscale-sedan + ɛ

Here, β0 is the intercept, β1 is the coefficient of the Family-sedan variable, β2 is the coefficient of the Upscale-sedan variable, and ɛ is the error term.

After running the regression, we can examine the coefficients and their corresponding p-values to determine the significance of the independent variables. If the p-value is less than 0.05, we can conclude that the variable is statistically significant.

The findings of the regression will depend on the data used and the specific coefficients and p-values obtained. However, in general, we can expect that the cost/mile will be higher for upscale sedans compared to family sedans. This is because upscale sedans tend to have higher prices and higher maintenance costs. Additionally, we can expect that the coefficients of both variables will be positive, indicating that an increase in family-sedan or upscale-sedan ownership will result in an increase in cost/mile.

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The value of q' as a decimal, rounded to the nearest hundredth, is 0.23.

To find the value of q', we need to first understand what it represents. q' is the complement of the proportion of executives who want to strengthen innovation, i.e., the proportion of executives who do not want to strengthen innovation.

Since the survey showed that 23% of executives want to strengthen innovation, we can calculate the proportion of executives who do not want to strengthen innovation as:

q = 1 - 0.23 = 0.77

Therefore, q' can be calculated as:

q' = 1 - q = 1 - 0.77 = 0.23

Rounding to the nearest hundredth, we get:

q' ≈ 0.23

Therefore, the value of q' as a decimal, rounded to the nearest hundredth, is 0.23.

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The integral on the right-hand side of the given equation depends only on the area of the region R enclosed by C and not on the shape of C or its location in the plane.

We can use Green's theorem to show that the line integral ∫C zd(x) - 2x(d(y)) + 3y(d(z)) depends only on the area of the region enclosed by C and not on the shape of C or its location in the plane.

Green's theorem states that for a simple closed curve C in the xy-plane that encloses a region R, and for a vector field F = P(x, y)i + Q(x, y)j, we have

∫C P(x, y)d(x) + Q(x, y)d(y) = ∫∫R (∂Q/∂x - ∂P/∂y)dA

where dA = dxdy is the area element in the xy-plane.

In our case, the curve C lies in the plane x + y + z = 1. We can rewrite this equation as z = 1 - x - y, so we have a parametric representation of C

r(t) = (x(t), y(t), z(t)) = (t, 1 - t - u, u)

where t and u are parameters that vary along C.

Now, we can calculate the curl of the vector field F = z(x)i - 2x(j) + 3y(k)

∂P/∂y - ∂Q/∂x = -2 - 0 - 1 = -3

Since the curl is a constant (-3) and does not depend on the variables x, y, or z, we can apply Green's theorem to find the line integral of F along C

∫C zd(x) - 2x(d(y)) + 3y(d(z)) = ∫∫R (-3)dA

Therefore, we have shown that the line integral ∫C zd(x) - 2x(d(y)) + 3y(d(z)) depends only on the area of the region enclosed by C and not on the shape of C or its location in the plane.

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If 6 ounces of fish has 36 grams of protein, then the fish has 6 grams of protein per ounce.

To find the weight of protein per-ounce, we divide total number of grams of protein by the total number of ounces of fish.

We know that 6 ounces of fish has 36 grams of protein, so to find the number of grams of protein per ounce, we divide the total number of grams of protein by the total number of ounces;

⇒ grams of protein per ounce = (total grams of protein)/(total ounces of fish),

The total number of grams of protein is = 36, and the total number of ounces of fish is 6,

So, grams of protein per-ounce = 36/6 = 6,

Therefore, the fish has 6 grams of protein per ounce.

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The given question is incomplete, the complete question is

If 6 ounces of fish has 36 grams of protein, then the fish has ____ grams of protein per ounce.

If rectangular pyramid has length as 20 in., width as 10 in., and height as  25 in., then the lateral surface area of pyramid is (b) 1000 in².

The "Lateral-Surface-Area" of a rectangular pyramid is the sum of the areas of the four triangular faces that connect the base to the top of pyramid.

Each of these triangular-faces has a base that is equal to the length or width of the rectangular base, and a height that is equal to the overall height of the pyramid.

The base length is = 20 in., the base width is = 10 in., and the overall height is 25 in.

The height of each triangular face is equal to the overall height of the pyramid, which is = 25 in,

To find the lateral surface area, we find the area of one triangular face and multiply it by 4.

So, Area of one triangular face = (1/2) × base × height,

⇒ Area = (1/2) × 20 × 25,

⇒ Area = 250 in²,

So, the area of one triangular face is 250 in².

Since there are 4 triangular faces, the lateral surface area of the pyramid is:

⇒ Lateral surface area = 4 × Area of one triangular face,

⇒ 4 × 250 in²,

⇒ 1000 in²,

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

A rectangular pyramid has a base length of 20 in., base width of 10 in., and an overall height of 25 in.

What is the lateral surface area of the pyramid?

(a) 500 in²

(b) 1000 in²

(c) 750 in²

(d) 950 in²

The scale will read the weight of the water displaced by the cube.

To calculate the weight of the water displaced, we can use Archimedes' principle which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The weight of the water displaced by the cube can be calculated using the formula:

W = density of water x volume of water displaced x acceleration due to gravity

The volume of water displaced is equal to the volume of the cube, which is 0.3 x 0.3 x 0.3 = 0.027 cubic meters.

The density of water is 1000 kg/m³.

The acceleration due to gravity is 9.8 m/s².

Therefore, the weight of the water displaced is:

W = 1000 x 0.027 x 9.8 = 264.6 N

So, the scale will read 264.6 N.

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The proportion of students who score between 400 and 600 on the SAT-M is approximately 68.27%.

To find the proportion of students who score between 400 and 600 on the SAT-M, we need to use the standard normal distribution.

First, we need to calculate the z-scores for the lower and upper limits of the range. To do this, we use the formula:

z = (x - μ) / σ

where x is the value we're interested in (400 or 600), μ is the mean score for the SAT-M (which we'll assume is 500), and σ is the standard deviation (which we'll assume is 100).

For 400:
z = (400 - 500) / 100
z = -1

For 600:
z = (600 - 500) / 100
z = 1

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

Using a table or calculator, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 1 is 0.8413. To find the area between these two z-scores, we subtract the smaller area from the larger area:

0.8413 - 0.1587 = 0.6826

So the proportion of students who score between 400 and 600 on the SAT-M is approximately 0.6826, or 68.26%.
Hi! To find the proportion of students who score between 400 and 600 on the SAT-M (math section), you need to look at the distribution of scores. The SAT-M scores typically follow a normal distribution with a mean (µ) of 500 and a standard deviation (σ) of 100.

To find the proportion of students who score between 400 and 600, we can use the Z-score formula to standardize the scores:

Z = (X - µ) / σ

For 400: Z1 = (400 - 500) / 100 = -1
For 600: Z2 = (600 - 500) / 100 = 1

Now, we need to find the probability between these two Z-scores, which can be represented as P(-1 < Z < 1). You can find this probability using a standard normal distribution table or a calculator with a normal distribution function. The result is approximately 0.6827, or 68.27%.

So, the proportion of students who score between 400 and 600 on the SAT-M is approximately 68.27%.

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The population and may need to be approximated using other methods such as t-distribution or bootstrapping.

Population is a group of individuals of the same species living in the same area at the same time. It is a term used in biology, sociology and other fields of study.

Without knowing the specific characteristics of the population, it is difficult to determine the exact distribution of the sample mean of a simple random sample of size 15 drawn from that population.

However, if the population is approximately normally distributed or if the sample size is large enough (usually considered to be n > 30), the sample mean will follow a normal distribution. This is known as the Central Limit Theorem.
Hence, If the population is not normally distributed and the sample size is small, the distribution of the sample mean will depend on the specific characteristics of the population and may need to be approximated using other methods such as the t-distribution or bootstrapping.

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The expression representing the volume of the cylinder in cubic units is 2πx^3.

Given that the height of a cylinder is 2x and its radius is x, we can find the volume of the cylinder using the formula for the volume of a cylinder:

Volume = π * (radius)^2 * height

In this case, the radius is x, and the height is 2x. We can plug these values into the formula:

Volume = π * (x)^2 * (2x)

Now, we can simplify the expression:

Volume = π * x^2 * 2x

Volume = 2πx^3

So, the expression representing the volume of the cylinder in cubic units is 2πx^3.

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Base area and surface area of the cone with radius 4 inches and height 6.5 inches is equal to 146.1 and 16π square inches.

Dimensions of the cone are,

Cone radius  = 4 inches

Cone height  = 6.5 inches

Let 'r' be the radius of the cone

Let us consider 'h' be the height of the cone.

Apply formula of surface area of the cone ,

= πr ( r  + √ h² + r² )

And Base area of the cone

= πr²

Substitute the value of radius and height of the cone we have,

Surface area of the cone

= π × 4 ( 4 + √ ( 6.5 )² + ( 4 )² )

=4π ( 4 + √58.25 )

= 4 × 3.14 ( 4 + 7.63 )

=  12.56 × 11.63

= 146.072 square inches

= 146.1 in²

Base area of the cone

= π × (4)²

= 16π square inches

Therefore, the surface area  and base area of the cone is equal to 146.1 and 16π square inches.

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Answer:

Step-by-step explanation:

Step 1: Enter the circle centre and radius in the respective input field ; Step 2: Now click the button “Find Equation of Circle” to get the equation

According to the given information, about 95% of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution.

What is Normal distribution?

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that describes the random variation of a continuous variable in a population.

In a normal distribution, about 68% of the values lie within one standard deviation of the mean, about 95% of the values lie within two standard deviations of the mean, and about 99.7% of the values lie within three standard deviations of the mean.

Therefore, about 95% of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution.

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Question:

About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?(Enter an exact number as an integer, fraction, or decimal.)

Answer:

0.75

Step-by-step explanation:

On an 8-sided number cube, the set is {1, 2, 3, 4, 5, 6, 7, 8}

6/8 of these are greater than 2.

6/8 is equal to 3/4, which is equal to 0.75

The solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

(a - b) / (a + b) = 3/5

To solve for a in terms of b, we cross multiply:

5(a - b) = 3(a + b)

Expanding the brackets, we get:

5a - 5b = 3a + 3b

Simplifying the equation by combining like terms, we get:

5a - 3a = 8b

2a = 8b

Dividing both sides of the equation by 2, we get:

a = 4b

Therefore, the solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

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The complete question is:

The equation given is A = 4b. Please write an appropriate question related to this equation.

The p-value for a standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5 is 0.0322.

To find the p-value for the standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5, we need to find the area under the standard normal distribution curve to the left of z = -1.86.

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can use the following steps:

1) Calculate the cumulative distribution function (CDF) of the standard normal distribution at z = -1.86. This gives us the area under the curve to the left of z = -1.86.

CDF(-1.86) = 0.0322

2) Since the alternative hypothesis is one-tailed (p < 0.5), we need to find the area in the left tail of the standard normal distribution. Therefore, the p-value is the same as the area under the curve to the left of z = -1.86.

p-value = 0.0322

So the p-value for a standardized test statistic of z = -1.86 with the alternative hypothesis Ha: p < 0.5 is 0.0322.

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a. All states are positive recurrent, the Markov chain is recurrent.

b. The Markov chain has two absorbing states, it is transient.

c. All states are positive recurrent, the Markov chain is recurrent.

d. The Markov chain has one absorbing state, it is transient.

a. The Markov chain with transition matrix P1 has 3 states: state 1, state 2, and state 3. To determine if they are transient or recurrent, we need to check if any state is reachable from every other state. It can be shown that all states communicate with each other, so the Markov chain is irreducible. Moreover, since all states are positive recurrent, the Markov chain is recurrent.

b. The Markov chain with transition matrix P2 has 5 states: state 1, state 2, state 3, state 4, and state 5. To determine if they are transient or recurrent, we need to check if any state is reachable from every other state. However, it is clear that state 4 and state 5 are absorbing states and can only transition to themselves. Therefore, these states are not reachable from any other state, and the Markov chain is not irreducible. Moreover, since the Markov chain has two absorbing states, it is transient.

c. The Markov chain with transition matrix P3 has 5 states: state 1, state 2, state 3, state 4, and state 5. To determine if they are transient or recurrent, we need to check if any state is reachable from every other state. It can be shown that all states communicate with each other, so the Markov chain is irreducible. Moreover, since all states are positive recurrent, the Markov chain is recurrent.

d. The Markov chain with transition matrix P4 has 5 states: state 1, state 2, state 3, state 4, and state 5. To determine if they are transient or recurrent, we need to check if any state is reachable from every other state. However, it is clear that state 2 is an absorbing state and can only transition to itself. Therefore, this state is not reachable from any other state, and the Markov chain is not irreducible. Moreover, since the Markov chain has one absorbing state, it is transient.

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The correct option is (b) all dots lie on the regression line.

What is regression line?

A regression line is a straight line that is used to model the relationship between two variables in a linear regression analysis. It is also known as the line of best fit, because it represents the line that minimizes the sum of the squared distances between the observed data points and the predicted values of the dependent variable based on the values of the independent variable.

The correct option is (b) all dots lie on the regression line.

If all dots lie on the regression line, it means that there is a perfect linear relationship between the variables, and one variable can be perfectly predicted from the other. This indicates a strong association between the variables, with no variability or error in the relationship.

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To yield a linear graph, the variables that should be plotted on the horizontal and vertical axes depend on the nature of the process being repeated by the student. If the process involves measuring the dependent variable y for different values of an independent variable x, then x should be plotted on the horizontal (x-axis) and y on the vertical (y-axis). This is because the independent variable is usually plotted on the x-axis, while the dependent variable is plotted on the y-axis. The resulting graph will show how y varies with respect to x, and if the relationship between x and y is linear, the graph will be a straight line.

On the other hand, if the process involves measuring the dependent variable y for different values of another independent variable z, then z should be plotted on the horizontal (x-axis) and y on the vertical (y-axis). This is because in this case, the variable being plotted on the x-axis is still the independent variable, while the dependent variable is still plotted on the y-axis.

In summary, the choice of variables to plot on the horizontal and vertical axes to yield a linear graph depends on the nature of the process being repeated by the student, and whether the process involves measuring the dependent variable y for different values of an independent variable x or another independent variable z.

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Answer:

1- red, green

2- blue, green

3- green, blue

Step-by-step explanation:

The underlined options should be your answers.

The two-way table allows us to calculate the joint distribution, marginal distributions, and conditional distributions for incidents of sexual harassment in middle and high schools. The most appropriate conditional distribution depends on the research question and the factors being considered.

In this study on sexual harassment in middle and high schools, the joint distribution of students who have witnessed sexual harassment in school is given in the two-way table in figure 9.9. We can use this table to calculate the marginal distributions for the number of times sexual harassment was witnessed, as well as the conditional distributions based on other factors, such as gender or grade level.

The two marginal distributions are the number of students who witnessed sexual harassment across all grades and genders. This allows us to see the total number of incidents of sexual harassment and how they vary by grade level or gender.

The conditional distributions are based on additional factors, such as gender or grade level. For example, we can calculate the percentage of female students who witnessed sexual harassment compared to the percentage of male students who witnessed it. We can also calculate the percentage of incidents that occurred in each grade level.

The preferred conditional distribution to explain the results of the analysis depends on the research question. If the research question is focused on gender differences, then the gender-based conditional distribution would be most useful. If the question is focused on grade level differences, then the grade-level based distribution would be more appropriate.

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Answer:

A. the number of degrees that the temperature changed

Because to answer the question, "How much did the patient's temperature rise between 9:54 and 10:41?" you need to know how much is changed.

The function C(x) = 24x - 12 gives us the number of muffins Chelsea can use for the bake sale in each batch she bakes, based on the number of muffins x she bakes.

The number 24 is the slope or rate of increase of the function, while -12 is the y-intercept or initial value of the function.

Chelsea is making muffins for the school bake sale, but her oven burns hotter on one side than the other. As a result, she ends up with burnt cupcakes in each batch she bakes that cannot be used for the sale. To determine how many muffins she can use for the bake sale in each batch, we have been given a function C(x) = 24x - 12.

Now, let's break down the given function C(x) = 24x - 12. The number 24 is the coefficient of x in the function, and it represents the rate of increase of the function. In other words, for each additional muffin Chelsea bakes in a batch, she can use 24 more muffins for the sale. Therefore, the number 24 is also called the slope of the function.

On the other hand, the value -12 is called the y-intercept of the function, which is the point where the graph of the function intersects the y-axis. It represents the initial number of muffins that Chelsea can use for the sale even if she doesn't bake any muffins. In this case, it means that Chelsea can use 12 muffins for the sale without baking any muffins.

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a. The margin of error for the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.017.

b. The correct choice is: "We are 90% confident that the observed proportion of adults that responded 'wrong track' is within 0.017 of the population proportion."

a) To calculate the margin of error for a 90% confidence interval, we need to use the formula:

[tex]ME = z\sqrt{ (pq/n) }[/tex]

where:

z = the z-score for a 90% confidence interval, which is 1.645

p = the proportion of adults who said things were going in the wrong direction, which is 0.44

q = the complement of p, which is 1 - 0.44 = 0.56

n = the sample size, which is 2306.

Plugging in these values, we get:

ME = 1.645sqrt(0.440.56/2306) = 0.017

Therefore, the margin of error for the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.017.

b) The correct choice is: "We are 90% confident that the observed proportion of adults that responded 'wrong track' is within 0.017 of the population proportion."

This means that if we were to conduct the same survey many times and calculate the confidence interval each time, we would expect 90% of those intervals to contain the true proportion of adults who think things are going in the wrong direction.

The margin of error of 0.017 indicates the maximum amount by which the sample proportion may differ from the true population proportion.

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The value of P(number greater than 2) when rolling a fair, eight-sided number cube is 0.75

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

Rolling a fair, eight-sided number cube

The sample space of a eight-sided number cube is

S = {1, 2, 3, 4, 5, 6, 7, 8}

Where, the outcomes greater than 2 are

Outcomes = {3, 4, 5, 6, 7, 8}

Using the above as a guide, we have the following:

P(number greater than 2) = n(Outcomes)/n(S)

So, we have

P(number greater than 2) = 6/8

Evaluate

P(number greater than 2) = 0.75

Hence, the value of P(number greater than 2) is 0.75

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The average rainfall over 2 days as per given average rainfall is 6 inches in 30 days is equal to  0.4 inches

Average rainfall is 6 inches in 30 days,

find the average rainfall per day by dividing by 30.

average rainfall per day = 6 inches / 30 days

⇒average rainfall per day = 0.2 inches per day

To find the average rainfall over 2 days = multiply the average rainfall per day by the number of days.

⇒ average rainfall over 2 days = 0.2 inches per day x 2 days

⇒ average rainfall over 2 days = 0.4 inches

This is much less than the 14 inches of rain that Hurricane Katrina dropped in one 48-hour period.

Therefore, the average rainfall over 2 days is 0.4 inches.

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The phase described in the question is the Analyze phase of the Six Sigma DMAIC (Define, Measure, Analyze, Improve/Design, Control/Verify) methodology.

During this phase, teams analyze data collected during the Measure phase to develop hypotheses about the causal relationships between inputs and outputs. They narrow down the causation to the vital few factors that are most significant in affecting the output. Statistical analysis is used to validate the hypotheses and assumptions made during the Define and Measure phases.

The goal of the Analyze phase is to identify the root cause of the problem and establish a baseline performance for future comparison. Once the root cause is identified, the team can move on to the Improve/Design phase to develop and implement solutions to address the problem.

Finally, the Control/Verify phase is used to ensure that the improvements made are sustained and that the problem does not recur.

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Sure, the term you are referring to is called a sequence diagram. It is a graphical representation of a use-case that shows the interactions among different classes or objects along a time axis. Sequence diagrams are useful for visualizing the flow of messages or events between different parts of a system, and can be used to identify potential issues or bottlenecks in the system's design.

They are commonly used in software development to help teams understand and communicate complex interactions between different components of a system.
 In this context, the Sequence Diagram captures the behavior and communication between classes or objects, allowing developers to visualize the flow of control and understand the system's functionality more effectively.

this is a dynamic model fo a use-case showing the interaction among classes along a time axis

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The measure of the central angle of the circle is m∠DGF = 24°

Given data ,

Let the measure of the minor arc of the circle be DF = 48°

Let the measure of the central angle be ∠DGF

And , Central Angle = 2 x Angle in other segment

On simplifying , we get

m∠DGF = ( 1/2 ) ( 48 )°

So , the measure of m∠DGF = 24°

Hence , the angle is m∠DGF = 24°

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It should be noted that 5, 7, 9 forms an obtuse triangle.

Also, 5, 10, 5√3 forms an acute triangle.

a² + b² = c²

5² + 7² = 25 + 49 = 74

9² = 81

Since 74 < 81, we know that 5, 7, 9 forms an obtuse triangle.

Again, we apply the Pythagorean theorem.

5² + (5√3)² = 25 + 75 = 100

(2√13)² = 52

Since 100 > 52, we know that 5, 10, 5√3 forms an acute triangle.

Applying the Pythagorean theorem:

(√13)² + 10² = 13 + 100 = 113

12² = 144

Since 113 < 144, we know that √13, 10, 12 forms an obtuse triangle.

Applying the Pythagorean theorem:

16² + 30² = 256 + 900 = 1156

34² = 1156

Since 1156 = 1156, we know that 16, 30, 34 forms a right triangle.

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