Write the fraction 36/27 in simplest form

A one-sample t-test was conducted to determine if the temperature increased in the first week of October 2019 compared to the average temperature from the previous 10 years. The result showed a p-value of 0.032, indicating a significant increase in temperature.

To determine if there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years, we can conduct a one-sample t-test with a null hypothesis that the population mean temperature this year is equal to the average temperature data from the previous 10 years (75) and an alternative hypothesis that the population mean temperature this year is greater than 75.

Using a statistical software, the calculated t-value is 2.17 with a corresponding p-value of 0.032. Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years. The p-value of 0.032 indicates that the probability of observing a sample mean temperature as extreme as 79.29 (the calculated sample mean temperature this year) or greater, assuming that the population mean temperature is equal to 75, is 0.032.

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1 standard deviation =  8 inches. the answer is OPTION E

We know that 99.7% of American men have heights between 5'0" and 7'0". Since height is normally distributed, we can use the empirical rule to estimate the standard deviation.

According to the empirical rule, 99.7% of the data falls within 3 standard deviations of the mean. Therefore, we can say that the range of heights from 5'0" to 7'0" is 3 standard deviations.

We can use this information to estimate the standard deviation as follows:

Range of heights = 7'0" - 5'0" = 2 feet

3 standard deviations = 2 feet

1 standard deviation = 2/3 feet

1 foot = 12 inches

Therefore, 1 standard deviation = 2/3 * 12 inches = 8 inches

So, our estimate of the standard deviation of the height of American men is 8 inches. Therefore, the answer is OPTION E in the given options.

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Complete question

If the heights of 99.7% of American men are between 5'0"

and 7'0", what is your estimate of the standard deviation of

the height of American men? (Assume the heights of

American Men are Normally Distributed).

A.) 1"

B.) 2"

C.) 4"

D.) 6"

E.) 8"

Rectangle X has a length of 17 meters and a width of 9 meters. Rectangle Y has a length of 17 meters and a width of 12 meters. You place both rectangles side-by-side to create a new rectangle Rectangle Z, 76 meter is the perimeter of Rectangle Z

The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths. By multiplying the lengths of all the sides of a form, the perimeter is always determined. The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible.

Rectangle X has a length of 17 meters and a width of 9 meters

Rectangle Y has a length of 17 meters and a width of 12 meters.

So, perimeter of rectangle Z = 2 (length + width)

= 2 [17 + (9 +12)]

= 2 × 38

= 76 meters.

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D is the correct fraction

Probabilities are used to determine the chances of an event.

The probability that there are 2 male and 2 female kittens is 0.375

The male and female kitten have an equal probability.

This is represented as:

\(\mathbf{p = 0.5}\) ---- probability of male kitten

\(\mathbf{q = 0.5}\) ---- probability of female kitten

The question is an illustration of binomial probability, and it is represented as:

\(\mathbf{Pr = ^nC_xp^xq^{n -x}}\)

In this case:

\(\mathbf{n = 4}\) --- number of kittens

\(\mathbf{x = 2}\) --- number of male kitten

So, we have:

\(\mathbf{Pr = ^4C_2 \times (0.5)^2 \times 0.5^{4 -2}}\)

\(\mathbf{Pr = 6 \times (0.5)^2 \times 0.5^2}\)

\(\mathbf{Pr = 0.375}\)

Hence, the probability that there are 2 male and 2 female kittens is 0.375

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Answer:

36,000

Step-by-step explanation:

Area formula- A=LW (length x width)

450 (length) x 80 (width)

450

 80

-------

36,000

(45 x 8 and add two zeros :))

Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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Answer:

Mean: 5

Median: 5

Mode: 6

Step-by-step explanation:

Mean: Add 6+9+2+4+3+6+5=35, then divide it by the number of numbers in the set (7). 35/7 = 5

Median: Order the numbers from least to greatest (2, 3, 4, 5, 6, 6, 9), then remove one number from the left-most then the right-most and see which number you end up with in the middle.

Mode: Find which number occurs the most times in the set of data (6).

Hope this helps! :)

It is not an entity that can take on different values, the consistency in measurement, the strength of the relationship between variables, or the truth of a measurement.

Validity is concerned with the degree to which a measure or conclusion accurately represents the concept or phenomenon it is intended to assess or describe. It focuses on the appropriateness and accuracy of inferences or interpretations based on the measurement or observation. Validity addresses the question of whether a measure or conclusion captures the intended construct or relationship and provides meaningful and reliable information.

Validity is distinct from other concepts mentioned. While an entity can take on different values, it is not synonymous with validity. Consistency in measurement refers to reliability, which is a separate concept related to the consistency and stability of measurements. The strength of the relationship between two variables is typically referred to as the correlation or association, but it is not directly related to validity. Lastly, the truth of a measurement is a broader philosophical concept, but validity specifically relates to the accuracy and appropriateness of a measure within a specific context or purpose.

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\(3/x - 2 -5/2 -4/x - 2\) is equivalent to \((-15x + 40)/2(x-2)(x-2)\)

\(3/x - 2 - 5/2 - 4/x - 2\) can be simplified by finding a common denominator:

LCD = 2(x-2)

So we need to multiply the first fraction by 2/2 and the second fraction by (x-2)/(x-2):

\(3/x - 2 * 2/2 - 5/2 - 4/x - 2 * (x-2)/(x-2)\)

\(= (6 - 2(x-2))/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14)/2(x-2) - 5/2 - (4x-8)/(x-2)(x-2)\\= (-2x + 14 - 5(x-2) - 2(4x-8))/2(x-2)(x-2)\\= (-2x + 14 - 5x + 10 - 8x + 16)/2(x-2)(x-2)\\= (-15x + 40)/2(x-2)(x-2)\)

Therefore, \(3/x - 2 -5/2 - 4/x - 2\) is equivalent to \((-15x + 40)/2(x-2)(x-2).\)

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The lines intersect at the point (3, 2). Therefore, the solution to the system of equations y = 2x - 4 and y = (-1/2)x + 1 is x = 3 and y = 2.

To solve the system of equations y = 2x - 4 and y = (-1/2)x + 1 using the graphing method, we can graph both equations on the same coordinate plane and find the point of intersection.

To graph y = 2x - 4, we can start by plotting the y-intercept, which is -4. From there, we can use the slope of 2 to plot additional points. For example, if we move one unit to the right along the x-axis, we would move two units up along the y-axis to get the point (1, -2). Similarly, if we move one unit to the left, we would move two units down to get the point (-1, -6). By connecting these points, we can graph the line y = 2x - 4.

To graph y = (-1/2)x + 1, we can start by plotting the y-intercept, which is 1. From there, we can use the slope of (-1/2) to plot additional points. For example, if we move two units to the right along the x-axis, we would move one unit down along the y-axis to get the point (2, 1/2). Similarly, if we move two units to the left, we would move one unit up to get the point (-2, 3/2). By connecting these points, we can graph the line y = (-1/2)x + 1.

The point where the two lines intersect is the solution to the system of equations. By looking at the graph, we can see that the lines intersect at the point (3, 2). Therefore, the solution to the system of equations y = 2x - 4 and y = (-1/2)x + 1 is x = 3 and y = 2.

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You can form two different types of quadrilaterals from the given sticks of 8cm,8cm,5cm,5cm.

A quadrilateral is a polygon with four sides and four angles. Quadrilaterals are two-dimensional shapes, meaning they exist on a flat surface and have length and width, but no depth. Some examples of quadrilaterals include rectangles, squares, parallelograms, and trapezoids.

You can form two different types of quadrilaterals using four sticks of 8cm, 8cm, 5cm, and 5cm in length such as a rectangle of the two 8cm sticks as the length and the two 5cm sticks as the width to create a rectangle, and you can also form a parallelogram by using the two 8cm sticks as the length, and the other two 5cm sticks as the width.

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Your question seems incomplete, but I assume the complete question was:

"How many types of quadrilaterals can be formed using these sticks of 8cm, 8cm, 5cm, 5cm?"

By the use of arithmethic, the final temperature in Sudbury is - 1 °C.

In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:

T = T' + ΔT₁ + ΔT₂

T = 4 °C + 5 °C - 10 °C

T = 9 °C - 10 °C

T = - 1 °C

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The volume is 1024. the base lengths are all 16 inches

Answer: 43.75%

Step-by-step explanation:

The percentage change is given by:

= [Final value - initial value / Initial value] x 100

The percentage increase in the average number of people from 2005 to 2012 is 56.25%.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

The average number of people in 2005 = 8000.

The average number of people in 2012 = 12500.

The change in the average number of people from 2005 to 2012.

= 12500 - 8000

= 4500

The percentage change in the average number of people at the games from 2005 to 2012.

= [Change in the average number of people / Average number of people in 2005] x 100

= (4500 / 8000) x 100

= 450/8

= 56.25%

Thus,

The percentage increase in the average number of people from 2005 to 2012 is 56.25%.

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A scatter plot would be the best type of plot to use to show the relationship between the price of Airbnb rentals and the room type.

A scatter plot shows the relationship between two variables by plotting each data point as a dot on the graph. In this case, the room type would be plotted on one axis and the price on the other axis, allowing you to see the distribution of prices for each room type.

By plotting the data in this way, you can see how one variable is related to another, and identify any patterns or trends in the data. This type of plot is particularly useful for exploring the relationship between two continuous variables.

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The correct question for the answer is

which plot would you use to plot prices of airbnb rentals as function of room type?

a) boxplot

b) scatter plot

c) bar plot

d) histogram

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To find the probability of the call lasting less than 230 seconds, we have to find P(X<230). Here X follows normal distribution with mean = 290

The given data: Meanμ = 290 seconds

Standard deviation σ = 30 seconds

Sample size n = 1000a) and

standard deviation = 30.

We get the value of 0.0228, which represents the area left (or below) to z = -2. Therefore, the probability that the call lasted less than 230 seconds is 0.0228 (or 2.28%). By using z-score formula;

Z=(X-μ)/σ

Z=(230-290)/30

= -2P(X<230) is equivalent to P(Z < -2) From z-table,

0.6384 (or 63.84%) P(230330) is equivalent to 1 - P(X<330)Here X follows normal distribution with mean = 290 and standard deviation = 30.From part b,

We already have P(X<330).Therefore, P(X>330) = 1 - 0.9082 = 0.0918, which is equal to 9.18%. Therefore, the probability that the call lasted more than 330 seconds is 0.1356 (or 13.56%).Answer: 0.1356 (or 13.56%). In parts a, b, and c, the final probabilities are rounded off to four decimal places as needed, as per the instructions given. However, these values are derived from the exact probabilities and can be considered accurate up to that point.

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a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

\(-\frac{5}{7}\)

Step-by-step explanation:

if we evaute the expression it will look like:

-6×7y=30

if we solve it :

(1) Simplify  −6×7y  to  -42y

-42y=30

(2) Divide both sides by -42

y=\(-\frac{30}{42}\)

(3) Simplify \(-\frac{30}{42} \\\)

​ \(-\frac{5}{7}\)

The probability that the temperature on a given day in February is 22º or lower is 0.16

The kind of distribution you'll choose as your foundation for your calculations will determine how to calculate probability with mean and deviation. We'll be working with scattered data in this case.

You can build models of your data using the usual distribution if you have data with a mean and standard deviation. By standardizing the normal distribution, we may determine the probability contained within this set of data based on its mean and standard deviation.

Given that: Average Temperature μ = 30.2°

Standard Deviation of Temperature σ = 8.5

Probability that the temperature is 22° or lower:

P[ X ≤ 22 ]

Let x be Temperature on a given day.

to calculate required probability.

Z = (x - μ)/σ

Z = (22-30.2)/8.5

Z = -0.965

First we convert X into Z using this relationship,

Now, Probability [ Z ≤ -0.965 ] = 0.16

The probability that temperature on a given day in February is 22º or lower is 0.16

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The word AND in probability implies that we use the​ multiplication rule.

The word OR in probability implies that we use the​ addition rule.

The statement "if two events are disjoint, then they are independent" - this statement is FALSE because those events that cannot occur simultaneously, and independent events are those events that do not affect the probability of each other's occurrence.

The word "AND" in probability implies that we use the "multiplication rule." This rule states that the probability of two events occurring together is the product of their individual probabilities.

The word "OR" in probability implies that we use the "addition rule." This rule states that the probability of at least one of the events occurring is the sum of their individual probabilities, minus the probability of both events occurring simultaneously.

Two events can be either disjoint or independent, but they cannot be both at the same time. For instance, let's say we are rolling a die. The events "getting a 1" and "getting an even number" are disjoint, as they cannot occur simultaneously. However, they are not independent, as the occurrence of one event affects the probability of the other event occurring. Specifically, if we get a 1, the probability of getting an even number reduces to zero.

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The word AND in probability implies the multiplication rule, while the word OR implies the addition rule. Disjoint events are not necessarily independent.

The word AND in probability implies that we use the multiplication rule. The word OR in probability implies that we use the addition rule.

However, it is FALSE that if two events are disjoint, then they are independent. Disjoint events mean that they have no outcomes in common, while independent events mean that the occurrence of one event has no effect on the probability of the occurrence of the other event.

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The correct answer from your group of answer choices is 1/36.

The probability of getting a 6 by throwing two dice is 1/36. When throwing two dice, there are 36 possible outcomes (6 outcomes for the first dice and 6 outcomes for the second dice). Out of these 36 outcomes, there is only one outcome where both dice show a 6 (6 on the first dice and 6 on the second dice). Therefore, the probability of getting a 6 by throwing two dice is 1/36.
The probability of getting a 6 by throwing two unbiased six-sided dice can be calculated as follows:

1. Determine the total number of possible outcomes when throwing two dice. Since each die has 6 sides, there are 6 * 6 = 36 possible outcomes.
2. Identify the combinations that result in a sum of 6. They are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). There are 5 such combinations.
3. Calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes: 1/36.

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Given the vector field F = <az, a² + 2y, e² - y²>, we can calculate its curl as follows:

curlF = (∂F₃/∂y - ∂F₂/∂z) i + (∂F₁/∂z - ∂F₃/∂x) j + (∂F₂/∂x - ∂F₁/∂y) k

     = (0 - 0) i + (0 - 0) j + (0 - 0) k

     = <0, 0, 0>

The curl of F is zero, indicating that the vector field is conservative.

Next, we need to determine a suitable surface S over which the integration will be performed. In this case, S is the portion of the ellipsoid 4x² + y² + 16z² = 64 that lies above the xy-plane. This surface S is an upward-oriented portion of the ellipsoid.

Since the curl of F is zero, the surface integral ∬_S curlF · dS is zero as well. This implies that the result of the evaluation is 0.

In summary, using Stokes' Theorem, we find that ∬_S curlF · dS = 0 for the given vector field F and surface S, indicating that the surface integral vanishes due to the zero curl of the vector field.

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The required answers are:

a) \(\(\frac{dy}{dx} = -\frac{2x}{(x^2 + 5)\ln^2(x^2 + 5)}\)\)

b) the derivative of \(\(x^n\)\) with respect to x is \(\(nx^{n-1}\)\), where n is a constant:

\(\(\frac{dy}{dx} = 4x^3\)\).

c) the expression is: \(\(\frac{dy}{dx} = \frac{3x^2}{2\sqrt{x^3 + \sqrt{2 - 7}}}\)\)

(a) To find the derivative of y with respect to x for \(\(y = \frac{1}{{\ln(x^2 + 5)}}\)\), we can use the chain rule.

Let's denote \(\(u = \ln(x^2 + 5)\)\). Then, \(\(y = \frac{1}{u}\)\).

Now, we can differentiate y with respect to u and then multiply it by the derivative of u with respect to x:

\(\(\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}\)\)

To find \(\(\frac{dy}{du}\)\), we differentiate y with respect to u:

\(\(\frac{dy}{du} = \frac{d}{du}\left(\frac{1}{u}\right) = -\frac{1}{u^2}\)\)

To find \(\(\frac{du}{dx}\)\), we differentiate u with respect to x:

\(\(\frac{du}{dx} = \frac{d}{dx}\left(\ln(x^2 + 5)\right)\)\)

Using the chain rule, we have:

\(\(\frac{du}{dx} = \frac{1}{x^2 + 5} \cdot \frac{d}{dx}(x^2 + 5)\)\\\\(\frac{du}{dx} = \frac{2x}{x^2 + 5}\)\)

Now, we can substitute the derivatives back into the chain rule equation:

\(\(\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = \left(-\frac{1}{u^2}\right) \cdot \left(\frac{2x}{x^2 + 5}\right)\)\)

Substituting \(\(u = \ln(x^2 + 5)\)\) back into the equation:

\(\(\frac{dy}{dx} = -\frac{2x}{(x^2 + 5)\ln^2(x^2 + 5)}\)\)

(b) To find the derivative of y with respect to x for \(\(y = x^4 + 1\)\), we differentiate the function with respect to x:

\(\(\frac{dy}{dx} = \frac{d}{dx}(x^4 + 1)\)\)

Using the power rule, the derivative of \(\(x^n\)\) with respect to x is \(\(nx^{n-1}\)\), where n is a constant:

\(\(\frac{dy}{dx} = 4x^3\)\)

(c) To find the derivative of y with respect to x for \(\(y = \sqrt{x^3 + \sqrt{2 - 7}}\)\), we differentiate the function with respect to x:

\(\(\frac{dy}{dx} = \frac{d}{dx}\left(\sqrt{x^3 + \sqrt{2 - 7}}\right)\)\)

Using the chain rule, we have:

\(\(\frac{dy}{dx} = \frac{1}{2\sqrt{x^3 + \sqrt{2 - 7}}} \cdot \frac{d}{dx}(x^3 + \sqrt{2 - 7})\)\)

The derivative of \(\(x^3\)\) with respect to x is \(\(3x^2\)\), and the derivative of \(\(\sqrt{2 - 7}\)\) with respect to \x is 0 since it is a constant. Thus, we have:

\(\(\frac{dy}{dx} = \frac{1}{2\sqrt{x^3 + \sqrt{2 - 7}}} \cdot (3x^2 + 0)\)\)

Simplifying the expression:

\(\(\frac{dy}{dx} = \frac{3x^2}{2\sqrt{x^3 + \sqrt{2 - 7}}}\)\)

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Answer:

Step-by-step explanation:

1.5x - 8 = 7

=> 1.5x = 7 + 8

=> 1.5x = 15

\( = > \frac{15x}{10} = 15\)

\( = > x = 15 \times \frac{10}{15} \)

=> x = 10 (Ans)

Answer:

x=10

Step-by-step explanation:

Simplifying

1.5x + -8 = 7

Reorder the terms:

-8 + 1.5x = 7

Solving

-8 + 1.5x = 7

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.

-8 + 8 + 1.5x = 7 + 8

Combine like terms: -8 + 8 = 0

0 + 1.5x = 7 + 8

1.5x = 7 + 8

Combine like terms: 7 + 8 = 15

1.5x = 15

Divide each side by '1.5'.

x = 10

Simplifying

x = 10

Answer:

a negative and a positive

Step-by-step explanation:

always equal a negative

and she put x next to 31.7 when x was not meant to be there

Answer:

She added before multiplying instead of multiplying before adding

Step-by-step explanation:

–31.7 + 4.5x

Let  x=2.1

–31.7 + 4.5(2.1)

We multiply before adding

-31.7 +9.45

-22.25

The antiderivative of f(x)=x^4 7sqrt(x) is with f(1) = -1 is f(x) = \(2x^{(\frac{7}{2})} - 2 - 2^{(\frac{1}{2})}\).

To find the antiderivative of the given function, we need to integrate it with respect to x. Let's begin by separating the terms:

f(x) = x⁴ * 7sqrt(x)

= 7x⁴ * sqrt(x)

Using the power rule of integration, we can integrate each term:

∫7x⁴ * sqrt(x) dx

= 7 ∫\(x^{(4+\frac{1}{2})}\) dx

= 7 * \(\frac{2}{7} x^{(\frac{7}{2})}\) + C

=\(2x^{(\frac{7}{2} )}\) + C

Here, C is the constant of integration. To determine its value, we use the given initial condition:

f(1) = \(2(1)^{\frac{7}{2} }\) + C = -1

Simplifying, we get:

C = -2 - \(2^{(\frac{1}{2} )}\)

Therefore, the antiderivative of f(x) with f(1) = -1 is:

f(x) = \(2x^{(\frac{7}{2})} - 2 - 2^{(\frac{1}{2})}\)

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