Find the answer please

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

Kym is wrong because instead of 25% it would be 50 percent

Step-by-step explanation:

Answer:

Sample Response: The ratio of boys to total students was 25:50. Written as a fraction, this is 25/50. Rewrite the fraction with a denominator of 100 to 50/100. So 50% of the students were boys.

You might wanna change up some words so the teacher doesn't know your cheating lol

The answer is D. The samples do not need to be drawn from a population that is Normal in order to apply the central limit theorem. Option C is correct in stating that either the population distribution is Normal or the sample size is large. As long as the sample size is sufficiently large, the central limit theorem allows for the distribution of sample means to be approximately Normal, regardless of the distribution of the population from which the samples were drawn. However, options A and B are also important conditions that must be met before applying the central limit theorem.

The condition that is not necessary to check before applying the Central Limit Theorem is option D: "The samples must be drawn from a population that is Normal."

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that, under certain conditions, the sampling distribution of the mean of a sufficiently large sample will approximate a normal distribution, regardless of the shape of the population distribution.

Options A, B, and C represent the conditions that must be checked before applying the CLT. Option A states that the population should be at least 10 times larger than the sample size when the sample is collected without replacement.

Option B emphasizes the importance of random sampling and independence of observations within the sample. Option C states that either the population distribution should be normal, or the sample size should be large. However, option D is not a necessary condition for applying the CLT.

The CLT holds even if the population distribution is not normal. This is one of the key strengths of the CLT as it allows for the approximation of the sampling distribution of the mean for various population distributions, as long as the other conditions (A, B, and C) are satisfied.

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woah this looks hard

Two of the diagonal elements being zero will result in the determinant being zero.

For square matrices of size n, with zeros anywhere possible off the diagonal and along their diagonal, we call these diagonal matrices.

(a) For the 2-by-2 case, the determinant of a 2-by-2 diagonal matrix is given by:

det(A) = a11 a22

If a11 or a22 is zero, then the determinant is zero. Therefore, if one of the diagonal elements is zero, the determinant will be zero.

(b) For the 3-by-3 case, the determinant of a 3-by-3 diagonal matrix is given by:

det(A) = a11 a22 a33

If a11, a22, or a33 is zero, then the determinant is zero. Therefore, if one of the diagonal elements is zero, the determinant will be zero.

(c) For the 4-by-4 case, the determinant of a 4-by-4 diagonal matrix is given by:

det(A) = a11 a22 a33 a44

If a11, a22, a33, or a44 is zero, then the determinant is zero. Therefore, if one of the diagonal elements is zero, the determinant will be zero.

If a22 and a33 are both zero, then the determinant of the 4-by-4 matrix is given by:

det(A) = a11 * 0 * 0 * a44 = 0

Therefore, two of the diagonal elements being zero will result in the determinant being zero.

In general, for an n-by-n diagonal matrix, if k diagonal elements are zero, then the determinant is zero if k > n-1, and non-zero if k ≤ n-1.

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Answer:

Step-by-step explanation:

Because changing from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964.

The effect does have on the correlation of the two variables should be that it remain the same i.e. 0.964.

Since there is the changing from centimeters to meters so this does not impact the correlation value due to which it remain the constant i.e. 0.964.

Also, the correlation coefficient should be unit -less and the value should always ranged between -1 to 1.

Therefore, it remains the constant.

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A regression model allows us to examine how the probability distribution of a dependent variable, Y, might be related to one or more independent variables (collectively called X). Therefore, the correct answer is (a) regression model.

A regression model is a statistical tool used to model the relationship between a dependent variable (often denoted as Y) and one or more independent variables (often denoted as X). It can help us understand how changes in the independent variables affect the values of the dependent variable, and can be used to make predictions or estimate values of the dependent variable based on specific values of the independent variables.

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Answer:

The equation for the nth term of the arithmetic sequence is:

\(a_{n} = a + (n-1)d\\\)

The \(a_{30}\) is 140

Step-by-step explanation:

"a" represents the first term which is -5.

"d" represents the common difference which is 5.

To find the common difference, just subtract the 2nd and 1st term.

0 - (-5) = 5

Now put the values in the equation:

\(a_{n} = a + (n - 1)d\\a_{n} = (-5) + (n - 1)5\)

We are finding the 30th term so just put 30 to the "n" to help us find the 30th term of the sequence.

\(a_{30} = -5 + (30-1)5\\a_{30} = -5 + (29)5\\a_{30} = -5 + 145\\a_{30} = 140\)

So the 30th term is 140

The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

Given that,

The set are U={22,23,24,25,26,27,28,29,30}

O={prime number}={23,29}

R={even numbers}={22,24,26,28,30}

We have to find (O∪R)',(O∩R)' and O∩R

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent elements can be anything, including people, alphabetic letters, numbers, shapes, variables, etc.

First,

O∪R= {23,29}∪{22,24,26,28,30}

O∪R= {22,23,24,26,28,29,30}

Now,

1. (O∪R)'=U-(O∪R)

(O∪R)'= {22,23,24,25,26,27,28,29,30} - {22,23,24,26,28,29,30}

(O∪R)'= {25,27}

2. O∩R={23,29}∩{22,24,26,28,30}

O∩R={Φ}

3. (O∩R)'=U-(O∩R)

(O∩R)'= {22,23,24,25,26,27,28,29,30} -{Φ}

(O∩R)'= {22,23,24,25,26,27,28,29,30}

Therefore, The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

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Answer:

The answer is A

Step-by-step explanation:

55mi x   1hr    x   1min  x 1.61*103m = 24.6m/s

1 hr     60min      60sec        1mi

And then you round 24.6 to 25 so your answer is A

Answer:

y=x^2+7x+4

Step-by-step explanation:

because the sign before x^2 is positive, the graph would concave up, if there's only one intercept, it has to be the vertex. the vertex is the critical point.

solve every make the derivative of each function equals zero, you get the x where the vertex shall be, then get this"x" into y=x-5 see if the y in y=x-5 is equal to y=x^2+6x+9 or other options.

let me give u an example.

for y=x^2+x-4, the critical point shall be 2x+1=0,x=-1/2, and the y is -4.25,

if you plug x=-1/2 into y=x-5, it's -5.5, -5.5 doesn't equal to -4.25

Answer:

D

Step-by-step explanation:

y = x2 + 7x + 4

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

Step-by-step explanation:

Because 2 1/4=2 2/8

so 2 2/8 - 1 1/8 equals 1 1/4

:)

Answer:

(x,y)=(-2,-1)

Step-by-step explanation:

4x - y = -7: 8x-2y=-14

8x-2y=-14

-8x + 4y = 12

add these two:

2y=-2

y=-1

plug in the y:

-8x-4=12

-8x=16

x=-2

The magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5.

The magnitude of an earthquake is the measured of the amplitude r the size of the seismic waves which is produced by the earthquake.

The magnitude, m, of an earthquake is defined to be

\(m = \log\left( \dfrac{I}{S}\right)\)

Here (I) is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and (S) is the intensity of a "standard" earthquake, which is barely detectable.

The magnitude of an earthquake that is 35 times more intense than a standard earthquake has to be find out. The Intensity of this earth quack can be given as,

\(I=35S\)

Put this values in the above formula as,

\(m = \log\left( \dfrac{35 S}{S}\right)\\m = \log\left( 35 \right)\\m\approx 1.5\)

Thus, the magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5.

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Answer:

c. or 1.5

Step-by-step explanation:

Step-by-step explanation:

9x + 1

This is the correct answer

Based on the information provided, we can infer that the average number of hours spent per week on household chores by all adults is 287, with a standard deviation of 7 hours. This means that most adults spend between 280 to 294 hours per week on household chores, assuming a normal distribution.

It's important to note that these figures may vary based on individual circumstances, such as the number of people in a household, their ages, and their responsibilities. Additionally, cultural and social factors can also influence how much time individuals spend on household chores. For example, in some cultures, women are expected to do most of the household work, while in others, it is a shared responsibility among all family members.
Overall, understanding the average amount of time spent on household chores can help us make informed decisions about how to allocate our time and resources. It can also shed light on important social and cultural dynamics that shape our everyday lives.

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Answer:

2.5

Step-by-step explanation:

2/3 *(3+3/4)=2.5

Answer:

\(\frac{5}{2}\) or \(2\frac{1}{2}\) or 2.5

Step-by-step explanation:

\(\frac{2}{3}*3\frac{3}{4}\)

Convert \(3\frac{3}{4}\) to an improper fraction. You can do this by multiplying the whole number by the denominator and add the numerator; all of this over the same denominator.

\(3\frac{3}{4}=\frac{3*4+3}{4} =\frac{12+3}{4} =\frac{15}{4}\)

Now work it out.

\(\frac{2}{3}*\frac{15}{4}=\frac{30}{12}=\frac{15}{6}=\frac{5}{2}\)

In case you need a mixed number as the answer, we can convert from improper fraction to mixed number.

5/2=2

4

----

1

the 2 after the equal sign is the big number, the 1 is the numerator and the 2 before the equal sign in the denominator.

\(2\frac{1}{2}\)

Answer:

Yes, his expectation is reasonable

Step-by-step explanation:

Mathematically;

1 mile = 1.609344 km

If he runs this in 5 minutes;

his speed will be 1.609344/5 = 0.3219 km/m

Now he intends breaking the record of 5 kilometers in 15.25 minutes

Distance = speed * time

What we shall have in this case will be;

15.25 * 0.3219 = 4.908

Approximately this is 5 km

So we can conclude that he will break the record if he runs at this speed

In this assignment, we are given the goal of estimating the age of the universe based on an estimate of the Hubble constant, denoted as n. We also need to quantify the quality of the estimate.

The age of the universe can be expressed in years as 9 = c / (n * s), where c is a constant and s represents the scale parameter. To begin, we need to find the distribution of 6, which is the reciprocal of the Hubble constant. It can be shown that c-1H follows a gamma distribution with shape parameter na and scale parameter ne. The density function of c-1H can be derived based on the gamma distribution.

Next, we need to consider 6 = cH-1, which represents the reciprocal of the Hubble constant multiplied by the constant c. It can be shown that 6 has an inverse gamma distribution with shape parameter (cn)na and scale parameter na. The density function of 6, denoted as U ~ IG (na, cn), can be derived based on the inverse gamma distribution.

In summary, by analyzing the distribution of 6, we can estimate the age of the universe using the given equations and assumptions. The specific calculations and derivations of the density functions for the gamma and inverse gamma distributions would provide further insights into the estimation process.

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If the CAPM (Capital Asset Pricing Model) is valid, we would expect the estimated coefficient, g0, to be zero.

In the CAPM, the excess return of a stock (ri - rf) is modeled as a linear function of the stock's beta (bi), representing the systematic risk, and the nonsystematic variance (s2(ei)). The constant term in the regression equation, g0, represents the expected excess return when the beta and nonsystematic variance are both zero.

According to the CAPM, the expected excess return for a stock with zero systematic risk (beta) and zero nonsystematic variance should be equal to the risk-free rate (rf). Therefore, in the regression equation, the expected value of g0 would be zero.

So, if the CAPM is valid and the regression equation is estimated correctly, we would expect the estimated coefficient, g0, to be close to zero.

In practice, the estimated coefficient g0 is often found to be significantly different from the market risk premium. This is because the CAPM is a simplified model of the capital markets. It ignores factors such as investor risk aversion and transaction costs. As a result, the estimated coefficient g0 should be interpreted with caution.

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Data:

a=pound of strawberrys

d=amount of dollars

p= price of one pound

p= $2.50

To convert 750 ml to oz, multiply 750 by 0.033814. 750 ml is equal to approximately 25.36 oz.

Milliliters (ml) and ounces (oz) are both units of volume commonly used for measuring liquids. To convert milliliters to ounces, you can use the conversion factor of 0.033814.

This means that for every milliliter, there are 0.033814 ounces. To convert 750 ml to oz, simply multiply 750 by 0.033814, giving you a result of approximately 25.36 oz.

This conversion is useful for measuring the volume of liquids, especially for small quantities such as in cooking and baking. It is important to note that the conversion factor is an approximation and may vary based on the specific measurement standard used.

Nevertheless, the conversion factor is widely used and accurate for most practical purposes.

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Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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The number of intervals that feel that America is doing about the right amount to protect the environment is 0.487, and 0.551 intervals

To find the number of adults who feel that America is doing about the right amount to protect the environment, we need to use the confidence interval proportion formula

CI = p ± Zα/2 * √(p * (1-p)/n

where:

p = sample proportion = 519/1000 = 0.519

n = sample size = 1000

Zα/2 = the critical value for the desired confidence level = 1.96

By substuting the values, we get:

CI = 0.519 ± 1.96 * √(0.519 * (1-0.519) / 1000)

= 0.519 ± 0.032

= (0.487, 0.551)

Therefore,  (0.487, 0.551) interval feel that America is doing about the right amount to protect the environment.

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Answer:

Glad we helped

Step-by-step explanation:

Answer:

the answer is d.

Step-by-step explanation:

i whish it helps you.