Find two numbers whose sum is 28 and whose product is the maximum possible value. What two numbers yield this product?

There are no fallacies of relevance committed by the given argument.

The following arguments commits fallacy: argumentum ad baculum. Argumentum ad baculum is a Latin phrase which means argument from a stick or appeal to force. It is a type of logical fallacy in which someone tries to persuade another person by using threats of force or coercion rather than using evidence or reasoning.

The above statement is an example of the argumentum ad baculum fallacy as it tries to use fear to convince people to join their protective organization. They are using the threat of potential losses to convince people to join. It is a manipulative strategy that attempts to scare people into joining by threatening the safety of their business.No fallacy is committed. There are no fallacies of relevance committed by the given argument.

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4x - 4/4x² + x is the value of linear equation.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

28x³ - 28x²/28x⁴ + 7x³

= 28x²( x - 1 )/7x³( 4x + 1)

= 4( x - 1)/x( 4x + 1)

= 4x - 4/4x² + x

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9 hikers are the bare minimum that might have covered the range of 6 to 17 miles because that distance falls inside the typical interval of 10 x 15 miles.

Rearrange the function using fundamental algebraic concepts to determine the value of x when the derivative equals 0.

This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur.

To determine the minimum or maximum, rewrite the solution into the original function.

The greatest and smallest values of a function, either within a specific range (the local or relative extrema) or throughout the entire domain, are collectively referred to as extrema (PL: extrema) in mathematical analysis.

b)  the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

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Answer:

If the GM between √2 and 2√2 is a find the value of a.​

Step-by-step explanation:

To find the geometric mean between two numbers, we simply take the square root of their product.

In this case, we want to find the geometric mean between √2 and 2√2.

Their product is:

√2 * 2√2 = 2√4 = 2*2 = 4

So, the geometric mean between √2 and 2√2 is the square root of 4, which is:

√4 = 2

Therefore, the value of a is 2.

a) With the following probability table F F, Let’s apply the formula for the intersection of events to solve the first part of the problem.

P(EF) = P(E) x P(F|E).We know that P(E) = 0.1 and that P(F|E) = 0.3. Therefore,P(EF) = P(E) x P(F|E) = 0.1 x 0.3 = 0.03.b) Two events E and F are independent if and only if their intersection is equal to the product of their individual probabilities.

P(EF) = P(E) x P(F) if and only if E and F are independent. We know that P(E) = 0.1 and that P(F) = 0.1 + 0.3 = 0.4. Therefore, P(EF) = 0.03, which is different from 0.1 x 0.4 = 0.04.

Since P(EF) is different from P(E) x P(F), it means that E and F are not independent.c) Two events E and F are mutually exclusive if and only if their intersection is the null set.P(EF) = ∅ if and only if E and F are mutually exclusive. We know that P(EF) = 0.03, which is not equal to the null set. Therefore, E and F are not mutually exclusive.

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Answer:

The 2nd equation is false.

Step-by-step explanation:

You don't even have to solve. DE is not 58, it's 40.

The 2nd equation is false.

Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]

Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.

A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.

we can cross-multiply,

[tex]7(x+1) = 11(18)[/tex]

Expanding the left side,

[tex]7x + 7 = 198[/tex]

Subtracting [tex]7[/tex] from both sides,

[tex]7x = 191[/tex]

Dividing both sides by [tex]7[/tex],

[tex]x = 191/7[/tex]

Therefore, the solution to the proportion is

[tex]x = 27.2857[/tex]

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The Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.

Sweet 'n Low - Modified SugarSweet 'n Low is an artificial sweetener that is made from modified sugar. Sweet 'n Low is not as sweet as some other artificial sweeteners like Splenda and Truvia. However, Sweet 'n Low is still used in many products like gum, candy, and other sweet treats. Sweet 'n Low has been around since the 1950s and is still used today as a low-calorie alternative to sugar.Splenda - 600 times sweeter than sugarSplenda is a popular artificial sweetener that is around 600 times sweeter than sugar. Splenda is often used in diet drinks, desserts, and other sweet products. Splenda is made from sugar but is modified to be much sweeter. Splenda is a low-calorie alternative to sugar and can be used by people who are trying to reduce their sugar intake.Stevia - Made from the Stevia PlantStevia is an artificial sweetener that is made from the Stevia plant. Stevia is a natural sweetener and is often used in tea and other drinks. Stevia is not as sweet as some other artificial sweeteners, but it is still a popular alternative to sugar. Stevia is also used in some foods and desserts. Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.

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The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.

Statistical analysis is the method of using statistical techniques to collect and analyze data, evaluate its reliability and determine its statistical significance. The following are the primary purposes of statistical analysis:Provide summaries and descriptions of data: One of the most important applications of statistical analysis is to present data in a clear and concise manner. Summarizing the data can assist people in making sense of the data and drawing inferences from it.

For example, data can be summarized using graphs, charts, or tables. Identify patterns and relationships: The goal of statistical analysis is to identify any patterns or relationships that exist within the data. For example, statistical analysis can be used to determine if a product's sales are correlated with a specific time of year.

Test hypotheses and draw conclusions: Statistical analysis is used to test hypotheses and draw conclusions about a population or phenomenon. This is accomplished by using statistical techniques to determine whether or not the data supports a particular hypothesis. Statistical analysis can also be used to determine the probability of an event occurring in the future.

The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.

The complete question is as follows:

The primary purpose of statistical analysis is to:

a)transform information into data.
b)select samples and make inferences about populations
c)convert data into useful desicion-making information
d)perform statistical computations

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Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b) .

A graph that displays the distribution of a collection of continuous data is called a histogram. It is composed of a number of bars, each of which represents a set of values, and whose height denotes the frequency or number of data points that lie within a given range. Histograms are used to depict a distribution's shape, centre, and spread graphically. They are frequently used to find patterns and trends in data in areas like statistics, data analysis, and scientific study.

given

(A) We must first identify the data's range before dividing it into 5 intervals of equal width in order to construct a frequency table with 5 classes. The values are in the range of 0 to 18.

(b) We plot the class intervals on the x-axis and the frequency on the y-axis to generate a histogram from the frequency chart. The counts are used to illustrate how frequently each class interval occurs.

Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b).

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Answer:

C = 21,309.4

Step-by-step explanation:

Diameter of moon is miles is,

d = 2159.8 miles

We have,

The circumference of the moon is, 6783 miles

Since, We know that,

the circumference of circle is,

C = 2πr

Substitute given values,

6783 miles = 2 × 3.14 × r

6783 = 6.28 × r

r = 6783 / 6.28

r = 1079.9 miles

Therefore, Diameter of moon is miles is,

d = 2 x r

d = 2 x 1079.9

d = 2159.8 miles

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As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).

The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).

Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).

function result = myta(f,n,a,b)

   syms x; % define x as symbolic variable

   g = f(a); % initialize g as f(a)

   for i=1:n % iterate from 1 to n

       deriv = diff(f,x,i-1); % calculate the ith derivative of f

       term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series

       g = g + term; % add the ith term to g

   end

   result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)

end

This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".

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There are several predictions that the food service manager may make based on the data from the survey of 200 students regarding their preference for new lunch menu items. Let's examine some of these predictions and see if they are supported by the data.

The majority of students will like the new menu items.

The food service manager may predict that the majority of students in the school will like the new menu items, based on the positive responses from the 200 surveyed students. However, it's important to note that the sample size of 200 is relatively small compared to the total student population of 1,500. Therefore, it's possible that the preferences of the 200 surveyed students may not be representative of the preferences of the entire student population. To make a more accurate prediction, the manager may need to conduct a larger survey or pilot program to test the new menu items with a larger group of students.

Certain menu items will be more popular than others.

Based on the survey data, the food service manager may be able to identify which new menu items are more popular among the surveyed students. For example, if a majority of students indicate that they would like to see more vegetarian options, the manager may predict that introducing more vegetarian menu items will be popular among the broader student population. However, it's important to keep in mind that the preferences of the 200 surveyed students may not be representative of the preferences of the entire student population, so the manager may need to conduct additional research or testing to confirm these predictions.

The introduction of new menu items will increase overall satisfaction with the school lunch program.

If the survey data shows that a significant number of students are excited about the new menu items, the food service manager may predict that introducing these items will increase overall satisfaction with the school lunch program. However, it's important to note that satisfaction is a complex concept that can be influenced by many factors beyond just the menu items, such as the quality of service, cleanliness of the cafeteria, and overall atmosphere. Therefore, the manager may need to consider these other factors when predicting the impact of the new menu items on overall satisfaction with the lunch program.

In summary, while the data from the survey of 200 students can provide valuable insights into student preferences for new lunch menu items, it's important to interpret these results with caution and consider additional factors that may influence the broader student population. Conducting further research or testing can help to confirm these predictions and make more accurate decisions about the school lunch program.

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Answer:

[tex]{ \rm{s = 12( v_{0} + v_{1} )t}} \\ \\{ \boxed { \rm{t = \frac{s}{12(v_{0} + v_{1})} \: \: }}}[/tex]

Answer:

Rs 750

Step-by-step explanation:

Given, No. of kurtas: 18, Each with CP = Rs 1000.

So, SP of 18 kurtas: 18*1000 = Rs. 18000

Also, 3 sets of kurtas were damaged.

Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.

SP of 15 kurtas: 15*1250 = Rs. 18750

So, Clearly SP>CP, Profit.

We know Profit= SP-CP

= 18750-18000 = Rs 750

The value of  y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF

For similar triangle we can write,

⇒ CE/CF = AE/BF

⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5

So, y = 2.34

Similarly,

⇒ CF/CB = EF/AB

⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8

⇒ x = 18.5/8 = 2.31

Therefore, The value of  y = 2.34 and x = 2.31

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According to the question the value of triangles y = 2.34 and x = 2.31

Similar triangles are a pair of triangles that have the same shape but may differ in size. This means that their corresponding angles are congruent, and their corresponding sides are proportional. Similar triangles are an important concept in geometry.

Here two similar triangles are given below, ΔABC ≈ ΔCEF
For similar triangle we can write,
⇒ CE/CF = AE/BF
⇒ 3.9/5 = y/3    ⇒ y = (3×3.9)/5
So, y = 2.34
Similarly,
⇒ CF/CB = EF/AB
⇒ 5/8 = x/3.7    ⇒ x = (5×3.7)/8
⇒ x = 18.5/8 = 2.31
Therefore, The value of  y = 2.34 and x = 2.31

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The lower the p-value, the more likely it is that the results are not due to chance. In this case, the p-value is 0.0683 This means that the researchers can conclude that drivers are significantly more distracted while driving when using a cell phone than when talking to a passenger in the car.

There is a difference in the proportion of drivers who missed the exit between the two groups.
The conditions required for a two-proportion z-test to be appropriate include that the data is collected independently, both groups are independent, the data should come from a normal population, and the sample sizes should be greater than 10.
The data was collected independently, both groups are independent, and the sample sizes are greater than 10. Therefore, these conditions are met. It is not clear if the data is from a normal population or not, but the test can still be used if the sample sizes are large enough.
The p-value of 0.0683 measures the probability that the results observed are due to chance. Therefore ,the lower the p-value, the more likely it is that the results are not due to chance.

In this case, the p-value is 0.0683, which is considered to be a small enough value that it indicates a statistically significant difference between the two groups.

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The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.

The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.

Thus, Option B and Option D are correct.

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  

A. F(x)= 2 square x has the same domain and range as f(x)= square x.

B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.

D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.

Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).

Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).

Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.

Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).

Therefore, Option B and Option D are correct.

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Answer:

142 sq cm

Step-by-step explanation:

A= 2(lh + wh + lw)

2(7*3+5*3+7*5)

2(21+15+35)

2(71)

A= 142 sq cm

The probability of someone returning exactly 1 of the 3 packages can be calculated as:P(1 out of 3 packages is returned) = C(3, 1) × P(0 or 1 diskette is defective)¹ × (1 - P(0 or 1 diskette is defective))²P(1 out of 3 packages is returned) = C(3, 1) × (0.9043820371)¹ × (0.0956179629)²P(1 out of 3 packages is returned) = 0.2448700124Therefore, the required probability of someone returning exactly 1 of the 3 packages is 0.2448700124.

The given data from the question is that the company produces diskettes which have the probability of being defective as 0.01. The packages that are sold have a size of 10 and the guarantee says that there can be at most one defective diskette in the package. Now, the question is to find the probability of someone returning exactly 1 of the 3 packages that they have bought.  So, the given data can be summarized as:Given:Probability of the diskette being defective, p = 0.01Guarantee: At most one diskette in the package of size 10 is defective.Now, let's solve the problem using probability theory

Probability of 1 diskette being defective in a package of size 10 can be calculated as:P(defective) = p = 0.01P(non-defective) = 1 - p = 0.99Using the given guarantee, probability of at most one defective diskette in a package of size 10:P(0 or 1 diskette is defective) = P(0 defective) + P(1 defective)P(0 or 1 diskette is defective) = C(10, 0) × (0.99)¹⁰ + C(10, 1) × (0.99)⁹ × (0.01)P(0 or 1 diskette is defective) = 0.9043820371Using the above probability

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the only option that satisfies both conditions is option B:[tex]y = 12 \sqrt{(x)} - 1[/tex]. Its range is all real numbers and its graph is decreasing from left to right.

What is quadratic equation?

A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x^2).

To determine which of these functions has a range of all real numbers and a graph that is decreasing from left to right, we can examine the behavior of the functions as x approaches positive or negative infinity.

For option A, we see that the term (x+7) inside the square root will approach infinity as x approaches infinity, and since the term is subtracted from 3 and multiplied by -6, the y-values will approach negative infinity.

For option B, as x approaches infinity, the square root term will also approach infinity, and since it is being multiplied by 12 and subtracted by 1, the y-values will approach positive infinity.

For option C, as x approaches negative infinity, the term (x+1) inside the cube root will approach negative infinity, and since it is being multiplied by 3 and subtracted by 4, the y-values will approach negative infinity.

For option D, as x approaches negative infinity, the cube root term will approach negative infinity, and since it is being multiplied by -5 and added to 15, the y-values will approach positive infinity.

Therefore, the only option that satisfies both conditions is option B: y = [tex]12 \sqrt{(x)} - 1.[/tex] Its range is all real numbers and its graph is decreasing from left to right.

For the first question, we know that the given square root function has an endpoint at (-4, 19). Let's substitute these values into the function to solve for the unknown parameter 'a':

[tex]y = a\sqrt{(x-h)}+k[/tex]

[tex]19 = a \sqrt{(-4-h)}+k[/tex]

We also know that the square root function has a domain of all values of 'x' such that the expression inside the square root is non-negative. Therefore:

(x-h) >= 0

x >= h

Combining the two equations, we get:

[tex]19 = a\sqrt{(-4-h)}+k[/tex]

h <= x

Since we have only one equation with two unknowns ('a' and 'k'), we cannot solve for the exact values of 'h' and 'a'. However, we can eliminate some of the answer choices based on the domain condition:

For the second question, we need to find a function that has a range of all real numbers and a graph that is decreasing from left to right. Let's analyze each option:

Option A: y=-6√x+7+3 has a maximum value of 3 and a decreasing graph from left to right, but its range is limited to y <= 3, so it does not satisfy the range condition.

Option B: y = 12-1 has a constant value of 11, so its range is limited to y = 11, which does not satisfy the range condition.

Option C: y=3x+1-4 has a graph that is increasing from left to right, so it does not satisfy the decreasing graph condition.

Option D: y=-5 +15 has a constant value of 10, so its range is all real numbers, and its graph is decreasing from left to right (a horizontal line).

Therefore, the answer is Option D: y=-5 +15.

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Answer:

The submarine travels 100 ft / min.

Step-by-step explanation:

To determine how long it will take the submarine to reach the lab from the surface of the ocean, we need to know how far it is from the surface of the ocean to the lab. Since this is not given, let us present the distance as D

The submarine travels at 100ft/min

He also travels a distance of D ft

Then  the ratio below is correct:1/100 = x/Dx = D/100

Where the x is the time we want to find. If you have omitted the distance D by mistake, all you need to do is divide it by 100 to get the time you are looking for.

It will take 29.2 minutes in order for the submarine to reach the lab from the surface of the​ ocean.

Solution

To determine how long it will take the submarine to reach the lab from the surface of the ocean, we need to know how far it is from the surface of the ocean to the lab. Since this is not given, let us present the distance as D.

The submarine travels at 100ft/min

He also travels a distance of Dft

Then the ratio below is correct:

[tex]1/100 = x/D[/tex]

[tex]x = D/100[/tex]

Where x is the time we want to find.

If you have omitted the distance D by mistake, all you need to do is divide it by 100 to get the time you are looking for.

Answer:

13

Step-by-step explanation:

distance formula:

=[tex]\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }[/tex]

=[tex]\sqrt{(5--2)^{2}+(-5-6)^{2} } \\\sqrt{170} \\13[/tex]

Anna should use 10 mL of the 72% salt solution and 20 mL of the 54% salt solution to make 30 mL of a 60% salt solution

Let's assume that Anna will use x mL of the 72% salt solution, and therefore she will use (30 - x) mL of the 54% salt solution (since the total volume is 30 mL).

To find out how much of each solution Anna should use, we can set up an equation based on the amount of salt in each solution.

The amount of salt in x mL of 72% salt solution is

= 0.72x

The amount of salt in (30 - x) mL of 54% salt solution is

= 0.54(30 - x)

To make a 60% salt solution, the total amount of salt in the final solution should be

0.6(30) = 18

So we can set up an equation

0.72x + 0.54(30 - x) = 1

Simplifying the equation

0.72x + 16.2 - 0.54x = 18

0.18x = 1.8

x = 10 ml

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The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

An inequality is a mathematical statement that cοmpares twο values οr expressiοns and indicates whether they are equal οr nοt, οr which οne is greater οr smaller.

Since the shading is nοt included, we will need tο use the lines themselves tο determine the cοrrect regiοn οf the cοοrdinate plane.

The first inequality y > (3/2)x - 5 has a slοpe οf 3/2 and a y-intercept οf -5. This means the line will have a pοsitive slοpe and will be lοcated belοw the pοint (0,-5).

The secοnd inequality y < (-1/6)x - 6 has a negative slοpe οf -1/6 and a y-intercept οf -6. This means the line will have a negative slοpe and will be lοcated abοve the pοint (0,-6).

Tο find the pοint that satisfies BOTH inequalities, we need tο lοοk fοr the regiοn οf the cοοrdinate plane that is belοw the line y = (3/2)x - 5 AND abοve the line y = (-1/6)x - 6. This regiοn is the triangular-shaped area that is bοunded by the twο lines and the x-axis.

The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

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The sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$

The given problem can be solved using algebraic and geometric methods. We can use algebraic methods, such as the equations given in the problem, and we can use geometric methods by visualizing what the problem is asking. To start, let's translate the given problem into mathematical equations. Let $z_0$ be the original complex number. We want to rotate this point by 90 degrees counter-clockwise about some complex number $c$ to get $z_2$. Thus,$$z_2 = c + i(z_0 - c)$$$$=c + iz_0 - ic$$$$= (1-i)c + iz_0.$$We also know that this transformation will rotate the point $z_1 = (z_0 + z_2)/2$ by 45 degrees. Thus, using similar logic,$$z_1 = (1-i/2)c + iz_0/2.$$Now let's use the formula for rotating a point about the origin by $\theta$ degrees (where $\theta$ is measured in radians) to find a relationship between $z_1$ and $z_0$.$$z_1 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c + iz_0/2 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c = (e^{i\theta/2} - 1)z_0/2.$$We can solve for $c$ by dividing both sides by $1-i/2$.$$c = \frac{e^{i\theta/2} - 1}{1-i/2}\cdot\frac{z_0}{2}.$$We can now use the information given in the problem to solve for the sum of the real and imaginary parts of $c$. We know that rotating $z_0$ by 90 degrees counter-clockwise will result in the complex number $z_2$. Visually, this means that $c$ is located at the midpoint between $z_0$ and $z_2$ on the line that is perpendicular to the line segment connecting $z_0$ and $z_2$. We can use this geometric interpretation to solve for $c$. The midpoint of the line segment connecting $z_0$ and $z_2$ is$$\frac{z_0+z_2}{2} = c + i\frac{z_0-c}{2}.$$Solving for $c$, we get$$c = \frac{z_0+z_2}{2} - \frac{i}{2}(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0- (e^{i\theta/2} - 1)(z_0/2)/(1-i/2)).$$We can now find the real and imaginary parts of $c$ and add them together to get the desired answer. Let's first simplify the expression for $c$.$$2c = z_0+z_2 - i(z_0 - (e^{i\theta/2} - 1)\cdot(z_0/2)\cdot(1+i)/2)$$$$= z_0 + z_2 - i(z_0 - z_0(e^{i\theta/2} - 1)(1+i)/4)$$$$= z_0 + z_2 - i(z_0 - z_0e^{i\theta/2}(1+i)/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0(1-e^{i\theta/2})/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0/4(1-e^{i\theta/2} + 1 - i))$$$$= z_0 + z_2 - i(z_0/2(1-\cos(\theta/2) - i\sin(\theta/2)))$$$$= z_0 + z_2 - i(z_0(1-\cos(\theta/2)) + z_0\sin(\theta/2) - i(z_0\cos(\theta/2))/2.$$Now we can find the real and imaginary parts of $2c$ and divide by 2 to get the real and imaginary parts of $c$. We have$$\operatorname{Re}(2c) = \operatorname{Re}(z_0+z_2) - \operatorname{Im}(z_0)(1-\cos(\theta/2)) - \operatorname{Re}(z_0)\sin(\theta/2)$$$$\operatorname{Im}(2c) = \operatorname{Im}(z_0+z_2) - \operatorname{Re}(z_0)(1-\cos(\theta/2)) + \operatorname{Im}(z_0)\sin(\theta/2).$$Thus, the sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$

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The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night

According to the given data,

Sample size n = 101

Sample mean x = 6.5

Standard deviation s = 2.14

Level of confidence C = 96%

Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.

Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081

Substituting the values in the above formula, we get:

Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28

Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72

Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.

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The Midpoint is the middle- point of the line member. The midpoint connecting two sides of a triangle is resemblant to the third side and half as long.

The midpoint is the middle of the line member. It's equidistant from both endpoints and is the centroid of the member and endpoints. Cut a member in two.

The midpoint theorem states that a line member drawn from the midpoint of two sides of a triangle is resemblant to the third side and half the length of the third side of the triangle.

The mean theorem helps us find the missing values for the sides of triangles. Connects the sides of a triangle with a line member drawn from the midpoints of two sides of the triangle.

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A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.

To determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.

We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).

Here's how to solve the problem:

1 pound = 16 ounces

Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces

The weight of one toy car is 7 ounces.

Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):

448 ÷ 7 = 64

Therefore, the bin can hold 64 toy cars.

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