the volume of the solid obtained by rotating the region enclosed by y=1/x4,y=0,x=2,x=4 y=1/x4,y=0,x=2,x=4 about the line x=−2x=−2 can be computed using the method of cylindrical shells via an integral

The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Answer:

put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges

Step-by-step explanation:

The appropriate alternative hypothesis would be that the market share percentage is 60%.

This is the left-tailed test.

The null and alternative hypothesis is

H0 :  p =60%

Ha : p <60%

answer most 60%

Speculation in a scientific context is a testable declaration about the connection among two or extra variables or a proposed reason for some located phenomenon. For a hypothesis to be a systematic hypothesis, the medical method calls for you could test it. Scientists typically base clinical hypotheses on preceding observations that can't satisfactorily be explained with the available scientific theories. despite the fact that the words "speculation" and "idea" are frequently used interchangeably, a systematic hypothesis isn't the same as a scientific theory.

In not unusual usage in the 21st century, speculation refers to a provisional idea whose advantage calls for assessment. for correct evaluation, the framer of a hypothesis needs to outline specifics in operational terms. Speculation requires greater work through the researcher with a view to both affirm or disprove it.

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Complete Question:

A marketing research firm is planning a study to test whether the market share that a new product will capture during its first year on the market is at most 20 percent. After setting up the null and alternative hypotheses, the appropriate alternative hypothesis would be that the market share percentage is:

Group of answer choices

at most 20%

at least 20%

greater than 20%

not equal to 20%

less than 20%

The p-value for testing the hypothesis H0: p = 0.45 versus H1: p < 0.45, with a sample size of n = 150, observed proportion x = 62, and a significance level α = 0.05, is approximately 0.0014.

The p-value approach is used to assess the strength of evidence against the null hypothesis (H0) based on the observed data. In this case, the null hypothesis states that the true population proportion (p) is equal to 0.45, while the alternative hypothesis (H1) suggests that p is less than 0.45.

To perform the test using the p-value approach, we calculate the test statistic and then determine the corresponding p-value. The test statistic for testing a proportion is given by z = \(\frac{ (p-hat - p0) }{\sqrt{\frac{(p0 * (1 - p0))}{n} } }\), where p-hat is the observed proportion, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.

Given n = 150 and x = 62, we calculate the observed proportion as p-hat = \(\frac{x}{n}= \frac{62}{150}= 0.4133\). Plugging in these values, we find the test statistic as z = \(\frac{(0.4133 - 0.45)}{\sqrt{\frac{(0.45 * (1 - 0.45))}{150} } } = -2.455\).

Next, we determine the p-value, which is the probability of obtaining a test statistic as extreme as or more extreme than the observed test statistic, assuming the null hypothesis is true. Using a standard normal distribution table or calculator, we find the p-value to be approximately 0.0014.
Since the p-value (0.0014) is less than the significance level \((\alpha = 0.05)\), we have strong evidence to reject the null hypothesis. This suggests that the observed proportion is significantly less than the hypothesized proportion, supporting the alternative hypothesis.

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Answer:

40 + 2r

Step-by-step explanation:

Well an hour has 60 minutes.

So 60 x 1/30 = 60/30 = 2 minutes for each person that didn't get into the job

60 x 1/3 = 60/3 = 20 minutes for the people that made it into the job.

20 x 2 = 40 minutes in total for the people that made it into the job.

We don't know how much people got rejected so:

The answer is

40 + 2r

Answer:

m=20

Step-by-step explanation:

m-9=11

m-9+9=11+9

m=20

Answer:

m=20

Step-by-step explanation:

brainliest plz

Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°

Answer:

0.5 m

Step-by-step explanation:

5÷20=0.25

0.25×2=0.5

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.

About the Distribution of Data:

The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.

The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.

Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.

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Step-by-step explanation:

Given

11x - 6 = 3 - 10x

11x + 10x = 3 + 6

21x = 9

x = 9/ 21 (divide both numerator and denominator by 3)

x = 3 / 7

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click the text to get your answer

Answer:

3855.25???

Step-by-step explanation:

Given :

To Find :

Solution :

Let the original price before the discount be x . Then the discount offered would be ,

→ 20% of x

→ 20x/100

So the Selling price would be ,

→ x - 20x/100

→ 80x/100

According to the question ,

→ 80x/100 = $28.80

→ x = $28.80 *100/80

→ x = $36

Hence the original price was $36 .

Answer:

original price = $36

Step-by-step explanation:

if she got discount: 100% - 20% = 80%

so,

80% ---> $28.80

1% --> $28.80 / 80

We know original is 100%:

100% --> ($28.80 / 80) * 100  =  $36

Answer:

Step-by-step explanation:

3/4 + 3/4 + 3/4 + 3/4 = 12/4 = 3. She will walk 3 miles in an hour.

The distance that Anusha covered in one hour is 3 miles

If Anusha is walking on a hiking trail at a rate of three-fourths miles in One-fourth hour, this is expressed as:

3/4 miles = 1/4 hours

We need to get the rate of Aisha that is the distance traveled in an hour

x = 1 hour

Divide both expressions

3/4x = 1/4

Cross multiply

4x = 3 * 4

4x = 12

x = 12/4

x = 3

Hence the distance that Anusha covered in one hour is 3 miles

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The  speed on the plane is 104mph while that of the wind is 78mph

The formula for calculating distance is expressed as:

Speed = Distance/Time

If the plane is flying with the wind;

3(r+ w) = 312

r + w = 104 ................... 1

If against the wind

4(r - w )= 312

r- w = 78 .................. 2

Add both equations

2r = 104  + 78

2r = 182

r = 91

Since r + w = 104

w = 104 - 91

w = 13

Speed on the plane  = r + w  = 91 + 13 = 104mi/hr

Speed on the wind = 91 - 13 = 78mi/hr

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Answer:

A

Step-by-step explanation:

The entire circle has an area of pi * r^2

r = 10

pi = 3.14

Area = 3.14 * 10^2

Area = 314 cm^2

But that is the whole circle. What is shaded is 1/4 of the circle which 314/4

which = 78.5 cm^2

Answer: A

Answer:

A) 78.5 cm^2

Step-by-step explanation:

1. To find the shaded part of the circle (1/4), we can use a formula similar to the one we use to find the area of a whole circle, but in this case, for the 1/4 part that's shaded: \(\frac{1}{4} \pi r^2\). Keep in mind that pi is approximated to 3.14.

2. (Solving)

Step 1: Plug in the values.

Step 2: Simplify.

Therefore, the answer is A) 78.5 cm^2.

may be this helpfulness!

Answer:

y=2x+3

Step-by-step explanation:

The theoretical probability of an event is the likelihood of that event occurring. Knowing the theoretical probability of an event can help people make informed decisions in their lives.

It is calculated by dividing the number of desired outcomes by the total number of possible outcomes. For example, if a wheel is spun once, the probability of getting the number zero is 1/8. This is calculated by dividing the number of desired outcomes (1) by the total number of possible outcomes (8). Mathematically, this can be written as: P(zero) = 1/8.In this equation, P stands for probability and zero is the desired outcome. The probability of getting the number zero is 1/8, or 12.5%. This means that there is a 12.5% chance of getting the number zero when spinning the wheel once. Theoretical probability is an important concept in mathematics and is used in many different applications. It is used to calculate the odds of winning in games of chance, the likelihood of a certain outcome in an experiment, and the expected value of investments. Knowing the theoretical probability of an event can help people make informed decisions in their lives.

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The total area of the regions between the curves is 8 square units

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

y = 6x² - 9x and y = 3x

With the use of graphs, the curves intersect ar

x = 0 and x = 2

So, the area of the regions between the curves is

Area = ∫6x² - 9x - 3x

This gives

Area = ∫6x² - 12x

Integrate

Area =  2(x - 3)x²

Recall that x = 0 and x = 2

So, we have

Area =  2(0 - 3) * 0² - 2(2 - 3) * 2²

Evaluate

Area =  8

Hence, the total area of the regions between the curves is 8 square units

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- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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The value of x is 10.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given;

Base=6

Perpendicular=8

Now

x^2=6^2+8^2

X^2=36+64

X^2=100

x=10

Therefore, by pythagoras theorem the answer will be 10.

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

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The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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The correct option is (B) 1/3.

The value of fraction m/k = 1/3.

The term "percentage" comes from latin "per centum," which implies "by the hundred." Percentages seem to be fractions with a denominator of 100.

Calculating a percentage means determining a portion of a whole in terms of 100. A percentage can be calculated in two ways:

It needs to be mentioned that second method of percentage calculation is not used when the denominator does not have a factor of 100. In such cases, we employ the unitary method.

Now, according to the question;

Given that 75% of m is equivalent to k% of 25,

Formally, the above equation can be written as

75%(m) = k%(25)

or,

(75/100) × m = (k/100) × 25

Simplifying;

m/k = 25/75

m/k = 1/3.

Therefore, the value of fraction m/k is 1/3.

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The equation of the plane orthogonal to the line (x, y, z) = (9, 5, 7) + t(-2, -4, 4) and passing through the point (5, 7, 9) can be written as -2x - 4y + 4z = 36.

To find the equation of a plane orthogonal (perpendicular) to a line, we need a direction vector of the line and a point that lies on the plane. In this case, the given line has a direction vector of (-2, -4, 4) and passes through the point (9, 5, 7).

We can start by finding a normal vector to the plane by taking the cross product of the direction vector of the line and a vector formed by subtracting the given point (5, 7, 9) from any point on the line (9, 5, 7). The cross product of (-2, -4, 4) and (4, 2, 2) gives us a normal vector of (4, 0, 0).

Using the normal vector (4, 0, 0) and the coordinates of the point (5, 7, 9), we can write the equation of the plane in the form ax + by + cz = d. Plugging in the values, we get -2x - 4y + 4z = 36.

Therefore, the equation of the plane orthogonal to the given line and passing through the point (5, 7, 9) is -2x - 4y + 4z = 36.

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Answer:

58-17.4=40.6

8%=3.25

43.86

Step-by-step explanation: