find the first partial derivatives of the function. (sn = x1 2x2 ... nxn; i = 1, ..., n. give your answer only in terms of sn and i.) u = sin(x1 2x2 ⋯ nxn)

Answers:

========================================================

Explanations:

Part (a)

The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.

Note: Amplitude is always positive as it measures a distance.

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Part (b)

For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.

The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8

So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi

The graph repeats itself every pi units, so the period is pi.

---------------------

Part (c)

The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.

---------------------

Part (d)

This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.

The parent sine function y = sin(x) goes through the origin (0,0)

However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)

This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2

This must mean we need to shift the sine graph 3pi/8 units to the right.

---------------------

Part (e)

Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).

So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.

Overall, one full cycle is between 0 and 2pi.

---------------------

Part (f)

Again I'm going to use sine instead of cosine. Refer back to part (d).

The general sine curve equation is

y = A*sin(B(x-C))+D

where

In this case, we found that

So,

y = A*sin(B(x-C))+D

will update to

y = 2*sin(2(x-3pi/8))-2

which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).

The standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients is 1.6487.

Given that a healthcare research agency reported that 41% of people who had coronary bypass surgery in 2008 were over the age of 65 and twelve coronary bypass patients are sampled.

To determine the mean number of people over the age of 65 in a sample of 12 coronary bypass patients, we use the formula below:

Mean = np

Where n = 12 and p = 0.41.

Mean = 12(0.41)

Mean = 4.92

Therefore, the mean number of people over the age of 65 in a sample of 12 coronary bypass patients is 4.92.

To determine the standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients, we use the formula below:

Standard deviation, σ = √(n p q)

Where n = 12, p = 0.41, and q = 1 - p.

Standard deviation, σ = √(12 × 0.41 × 0.59)

Standard deviation, σ = √2.71948

Standard deviation, σ = 1.6487 (rounded to four decimal places).

Therefore, the standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients is 1.6487.

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Report on Commonalities Among Three Chosen Regions

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

Answer:

For this assignment, three regions of the world have been selected to identify commonalities among them. The chosen regions are North America, Europe, and East Asia. Through internet research, several commonalities have been identified that are shared among these regions. Below are five commonalities found:

Economic Development:

All three regions, North America, Europe, and East Asia, are characterized by significant economic development. They are home to some of the world's largest economies, such as the United States, Germany, China, and Japan. These regions exhibit high levels of industrialization, technological advancement, and trade activities. Their economies contribute significantly to global GDP and are major players in international commerce.

Technological Advancement:

Another commonality among these regions is their emphasis on technological advancement. They are known for their innovation, research and development, and technological infrastructure. Companies and industries in these regions are at the forefront of technological advancements in fields such as information technology, automotive manufacturing, aerospace, pharmaceuticals, and more.

Cultural Diversity:

North America, Europe, and East Asia are culturally diverse regions, with a rich tapestry of different ethnicities, languages, and traditions. Immigration and historical influences have contributed to the diversity seen in these regions. Each region has a unique blend of cultural practices, cuisines, art, music, and literature. This diversity creates vibrant multicultural societies and fosters an environment of cultural exchange and appreciation.

Democratic Governance:

A commonality shared among these regions is the prevalence of democratic governance systems. Many countries within these regions have democratic political systems, where citizens have the right to participate in the political process, elect representatives, and enjoy individual freedoms and rights. The principles of democracy, rule of law, and respect for human rights are important pillars in these regions.

Education and Research Excellence:

North America, Europe, and East Asia are known for their strong education systems and institutions of higher learning. These regions are home to prestigious universities, research centers, and educational initiatives that promote academic excellence. They attract students and scholars from around the world, offering a wide range of educational opportunities and contributing to advancements in various fields of study.

In conclusion, the regions of North America, Europe, and East Asia share several commonalities. These include economic development, technological advancement, cultural diversity, democratic governance, and education and research excellence. Despite their geographical and historical differences, these regions exhibit similar traits that contribute to their global significance and influence.

Answer:

Step-by-step explanation:

First we need to find the slope of the given line;

Given the line 2x + 5y= -10, we need to write it in standard form of y = mx+c

Make y the subject of the formula;

2x + 5y= -10

5y = -2x-10

y = -2x/5-10/5

y = -2x/5 - 2

Hence the slope of the line m = -2/5

Since the equation of the line we need is parallel to this line, hence they will have the same slope.

The slope of the required line = -2/5

Get the intercept;

Substitute the point (10,4) and m = -2/5 into the equation y = mx+c

4 = -2/5(10)+c

4 = -4 + c

c = 8

Get the required equation;

y = mx+c

y = -2/5 x + 8

Hence the equation of a line parallel to the given line and contains the given point is y = -2/5 x + 8

Answer:

7/5 is the constant variation.

Hope this helps! Have a great day!

Answer:

f(-8) = 64

Step-by-step explanation:

Since x =-8, we need to use x^2 since -8 <0

(-8)^2 = 64

When x = -8 f(-8) = 64

Answer:

B

Step-by-step explanation:

There are 2 functions, one if x > 0 and one if x < 0

The x we are given is -8, and -8 is less than 0

Plug -8 into the function for if x < 0, which is x^2

(-8)^2=64

ANSWER:

The total surface area of the triangular prism is 69.77 square millimeters

STEP-BY-STEP EXPLANATION:

We have that the formula surface area of the remaining prism is the following

Replacing:

s1, s2 and s3 are the sides of the triangle, the base and the height are of the triangle and L is the length of the rectangle.

Answer:

\(y=\frac{1}{2}x+1\)

The slope is 1/2.

The y-intercept is 1.

Step-by-step explanation:

We have:

\(x-2=2(y-3)\)

Let’s divide both sides by 2. This gives us:

\(\frac{x}{2}-\frac{4}{2}=y-3\)

Simplify:

\(\frac{1}{2}x-2=y-3\)

Add 3 to both sides:

\(\frac{1}{2}x+1=y\)

Flip:

\(y=\frac{1}{2}x+1\)

This is in the slope-intercept form:

\(y=mx+b\\\)

Where m is the slope and b is the y-intercept.

Hence, our slope m is 1/2 and our y-intercept b is 1.

Answer:

D

Step-by-step explanation:

The equation would be y = -2x+3. If we take y+2x=3, and subtract 2x from both sides, we get y = -2x+3, which is the right equation.

Answer:

2x+y =3

Step-by-step explanation:

The line is given by slope intercept form

y = mx+b  where is the slope and b is the y intercept

The slope is -2 and the y intercept is 3

y = -2x +3

Add 2x to each side

2x+y =3

Answer:

v=5

Step-by-step explanation:

you are trying to make 4v into v right ?

so simply divide it by 4 - the same if it was 4a or 7a or 9k, always start by dividing by the number

then you need to balance the two sides - so whatever number you divide the letter by (which is the 4 in this case) , you do the same with the other side , so whatever number is after the equal sign , divide it by 4

PART ONE                                      ↓ 4v  =   20  

           DIVIDE BY 4                       →  v   =    20

PART TWO                                          v   =   20 ↓

                                                            v   =     5 ←           DIVIDE BY 4

The given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

What is a correlational study?                                                                                                                                                                         Correlational study is a research design that helps to measure and describe the relationship between variables without the researcher influencing or manipulating any variables. Correlation allows researchers to test how variables are related to one another, providing a way to find new relationships, understand phenomena, and make predictions.

Classify each statistical study as experimental or correlational. According to the given problem, data are collected on the dollar amount withdrawn for a sample of college students using the ATM in the campus center. As there is no manipulation of variables involved and no control group is assigned, this is a correlational study.

Therefore, the given statistical study - "For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn" is a correlational study.

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The coordinates of C are (-9, 8).

What are the coordinates?

If C' (-8,-9) is the image of C after a reflection across the line y = x, then the midpoint M of CC' must lie on the line y = x, since the midpoint of a line segment is equidistant from its endpoints.

Let (x, y) be the coordinates of C. Then the coordinates of the midpoint M are:

M = [(x - 8)/2, (y - 9)/2]

Since M lies on the line y = x, we have:

(x - 8)/2 = (y - 9)/2

Simplifying this equation, we get:

x - y = -1

So the coordinates of C must satisfy the equation x - y = -1 and also the reflection condition. To find the coordinates of C, we need to solve these two equations simultaneously.

Since C' is the image of C after reflection across the line y = x, we know that the line passing through C and C' is perpendicular to the line y = x. The slope of the line passing through C and C' is:

m = (y + 9)/(x + 8)

The slope of a line perpendicular to y = x is -1, so we have:

(y + 9)/(x + 8) = -1

Solving for y, we get:

y = -x - 17

Substituting this equation into x - y = -1, we get:

x - (-x - 17) = -1

Simplifying this equation, we get:

2x + 17 = -1

Subtracting 17 from both sides, we get:

2x = -18

x = -9

Substituting this value into y = -x - 17, we get:

y = -(-9) - 17 = 8

Therefore, the coordinates of C are (-9, 8).

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The general solution of the differential equation \(2xe^(x²y²) + xy² + 4y = 4cos²(212)\)  is \(y(x) = (e^(-x^3y^2) - 4y^3/3 - 4cos²(212)y + C) / (4/3).\)

To find dz/dt using the chain rule, we first differentiate z with respect to x (denoted as dz/dx) and multiply it by dx/dt. Since x = 32² is a constant, dx/dt = 0.

Next, we differentiate z with respect to y (denoted as dz/dy) and multiply it by dy/dt. Since y = t, dy/dt = 1. Therefore, dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = dz/dy.

Moving on to the differential equation, we aim to find the general solution. We begin by rearranging the equation to isolate the term involving y, which gives us:

\(2xe^(x²y²) + xy² + 4y - 4cos²(212) = 0.\)

Now, we integrate both sides of the equation with respect to y. This involves treating x as a constant, so we get:

∫(2xe^(x²y²) + xy² + 4y - 4cos²(212)) dy = 0.

Therefore, the general solution of the differential equation\(2xe^(x²y²) + xy² + 4y = 4cos²(212)\)  is \(y(x) = (e^(-x^3y^2) - 4y^3/3 - 4cos²(212)y + C) / (4/3)\), where C is the constant of integration.

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Answer:

-36uw

132b

hjk

-abc

Step-by-step explanation:

When you multiply a negative by another negative, the negative is cancelled out.  When you multiply a negative by a positive, the negative is kept.

1.) -9u(-4)(-w)

36u(-w)

-36uw

2.) -b(-12)(11)

12b(11)

132b

3.) -h(-jk)

hjk

4.) -1(-a)(-bc)

1a(-bc)

-1abc

-abc

Hope this helps! :)

Answer:

D. Irrational

Step-by-step explanation:

\( \sqrt{13} \: is \: an \: \purple{\bold {irrational}} \: number.\)

Answer:

The answer is 0.16

Step-by-step explanation:

Just divide 88 (the total number of students that walk) by 550 (total number of juniors+seniors) since its not asking about a certain grade level

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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The answers are :a) k = 6b) P(0.4 ≤ Y ≤ 1) = 1/5c) P(0.4 ≤ Y < 1) = 1/5d) P(Y ≤ 0.4 | Y ≤ 0.8) = 6/13e) P(Y < 0.4 | Y < 0.8) = 6/13

a) Value of k that makes f(y) a probability density function: It is known that the probability density function f(y) of a continuous random variable is said to be a probability density function if it satisfies the following two conditions: Integrating f(y) over the entire range of the random variable y should give 1. ∫(-∞ to +∞) f(y) dy = 1The probability density function should be non-negative for all possible values of y. f(y) ≥ 0Now, f(y) = ky(1 - y)0 elsewhere.

Therefore,\(0≤y≤1∫(0to1)f(y)dy=∫(0to1)ky(1−y)dy=1\).

Let's solve the integration,∫(0 to 1) ky(1 - y) dy= k[(y²/2) - (y³/3)] [0,1]= k(1/2 - 1/3)= k/6Using this equation, we have:k/6 = 1 => k = 6

b) Probability that .4 ≤ Y ≤ 1:∫(0.4 to 1) f(y) dy= ∫(0.4 to 1) 6y(1 - y) dy= 1/5

c) Probability that .4 ≤ Y < 1:∫(0.4 to 1) f(y) dy= ∫(0.4 to 1) 6y(1 - y) dy= 1/5

d) Probability that Y ≤ .4 | Y ≤ .8:To compute P(Y ≤ 0.4 | Y ≤ 0.8), we require to calculate the conditional probability P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)P(Y ≤ 0.4 and Y ≤ 0.8) = ∫(0 to 0.4) f(y) dy = ∫(0 to 0.4) 6y(1 - y) dy= 0.192P(Y ≤ 0.8) = ∫(0 to 0.8) f(y) dy = ∫(0 to 0.8) 6y(1 - y) dy= 0.416Therefore, P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8) = 0.192 / 0.416 = 12 / 26 = 6 / 13e)

Probability that Y < .4 | Y < .8:To compute P(Y < 0.4 | Y < 0.8), we require to calculate the conditional probability P(Y < 0.4 and Y < 0.8) / P(Y < 0.8)P(Y < 0.4 and Y < 0.8) = ∫(0 to 0.4) f(y) dy = ∫(0 to 0.4) 6y(1 - y) dy= 0.192P(Y < 0.8) = ∫(0 to 0.8) f(y) dy = ∫(0 to 0.8) 6y(1 - y) dy= 0.416Therefore, P(Y < 0.4 | Y < 0.8) = P(Y < 0.4 and Y < 0.8) / P(Y < 0.8) = 0.192 / 0.416 = 12 / 26 = 6 / 13Hence, the answers are:a) k = 6b) P(0.4 ≤ Y ≤ 1) = 1/5c) P(0.4 ≤ Y < 1) = 1/5d) P(Y ≤ 0.4 | Y ≤ 0.8) = 6/13e) P(Y < 0.4 | Y < 0.8) = 6/13.

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Therefore, the range of the relation 2x + y = 3 for the given domain {-3, 0, 6} is {9, 3, -9}.

To determine the range of the relation 2x + y = 3 for the given domain {-3, 0, 6}, we need to find the corresponding range values when we substitute each value from the domain into the equation.

Substituting -3 into the equation, we have 2(-3) + y = 3, which simplifies to -6 + y = 3. Solving for y, we get y = 9.

Substituting 0 into the equation, we have 2(0) + y = 3, which simplifies to y = 3.

Substituting 6 into the equation, we have 2(6) + y = 3, which simplifies to 12 + y = 3. Solving for y, we get y = -9.

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Algebra

The formula to find the coordinate is (x,y)

Meaning, point D is (1,4)

Hi there!  

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I believe your answer is:  

(1,4)  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

(5,3)

Step-by-step explanation:

I took the test and go it right!

The coordinate point for D is (5, 3). Therefore, option C is the correct answer.

A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square. That is why it is also known as a tilted square. Look at the image below to understand the relationship of rhombus shape with parallelogram and square.

Given that, Point A (2,2), Point B (3,4) and Point C (4,1)

The coordinate point for D that would make ABDC a rhombus.

So, the coordinate point for D is (5, 3).

Therefore, option C is the correct answer.

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Answer:

It should be Volume of water

The margin of error of this poll is

Given that 230 people were asked if they liked dogs, and 90% said they did.

In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.

Sample size (N)=230

Sample proportion  \((\hat{p})\) = 90% = 0.90  and

confidence interval = 99%

The critical value at 99% confidence interval with α=0.01 is

\(\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end\)

This value is taken from the Standard normal distribution table.

Now, we will calculate the margin of error (E) by using the formula

\(E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}\)

Substituting the values in the formula, we get

\(\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end\)

Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.

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Answer:

x= 82°

Step-by-step explanation:

According to the angle sum property, sum of all angle in a triangle is 180°

45°+53°+x= 180°

98°+x= 180°

x= 180-98

x= 82°

Answer:

0.04

Step-by-step explanation:

es la respuesta válida

Answer:

-17/8

Step-by-step explanation:

Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.

Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.

Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.

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