Which is an equation of a line with a slope of 1/2 that contains the point (-4,7)?

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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The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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The area of a circle in polar coordinates can be calculated as an integral, where r = 4sinθ is  2π.

The region encircled by a circle with radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

We know that the area of a polar curve can be calculated using the formula:

A = ½ ∫ [f(θ)]² dθ

where f(θ) is the radial function.

In this case, the radial function is r = 4 sin θ. Substituting this into the formula, we get:

A = ½ ∫ [4 sin θ]²dθ

= ½ ∫ 16 sin² θ dθ

= ½ [8θ - 4 sin 2θ] from 0 to π/2

= 2π

Therefore, the area of the circle r = 4 sin θ is 2π.

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Answer:

15000 pay on the ship for me

Answer:

i’m struggling on this

Step-by-step explanation:

if anybody gets the answer please let me know

1. The prime cost per cleaning is $249,900 / 9,000 = $27.77

2. The conversion cost per cleaning is $243,600 / 9,000 = $27.07

3. The total variable cost per cleaning is $262,500 / 9,000 = $29.17

4. The total service cost per cleaning is $276,900 / 9,000 = $30.77

5. The fixed overhead cost would increase by $900.

1. Prime cost per cleaning:

Prime cost includes direct materials and direct labor.

Prime cost = Direct materials + Direct labor

Prime cost = $18,900 + $231,000

Prime cost = $249,900

Therefore, the prime cost per cleaning is $249,900 / 9,000 = $27.77 (rounded to the nearest cent).

2. Conversion cost per cleaning:

Conversion cost includes direct labor and variable overhead.

Conversion cost = Direct labor + Variable overhead

Conversion cost = $231,000 + $12,600

Conversion cost = $243,600

Therefore, the conversion cost per cleaning is $243,600 / 9,000 = $27.07 (rounded to the nearest cent).

3. Total variable cost per cleaning:

Total variable cost includes direct materials, direct labor, and variable overhead.

Total variable cost = Direct materials + Direct labor + Variable overhead

Total variable cost = $18,900 + $231,000 + $12,600

Total variable cost = $262,500

Therefore, the total variable cost per cleaning is $262,500 / 9,000 = $29.17 (rounded to the nearest cent).

4. Total service cost per cleaning:

Total service cost includes direct materials, direct labor, variable overhead, and fixed overhead.

Total service cost = Direct materials + Direct labor + Variable overhead + Fixed overhead

Total service cost = $18,900 + $231,000 + $12,600 + $14,400

Total service cost = $276,900

Therefore, the total service cost per cleaning is $276,900 / 9,000 = $30.77 (rounded to the nearest cent).

5. If the rent on the office increased by $900, it would affect HHH's fixed overhead cost. The fixed overhead cost would increase by $900. This would lead to an increase in the total service cost per cleaning, as the fixed overhead is a component of the total service cost.

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Answer:

25.12 in^3.

Step-by-step explanation:

Volume of the cylinder = 3.14 * r^2 * h

= 3.14 * 2^2 * 8

The volume of the preserve

= 1/4 * 3.14 * 4 * 8

= 25.12 in^3.

Answer:

2 in

Step-by-step explanation:

so the original height is 8 in and you need to find the height if the jar was 1/4 full

half of 8 is 4

and half of 4 is 2

your final answer is 2 in

good luck :)

i hope this helps

have a nice day !!

m > 650 miles

A mileage over 650 miles makes company A cheaper than B.

1) Gathering the data

Company A

$127 (unlimited mileage)

Company B

$75 + 0.08m

2) To find out the mileage that makes Company A cheaper than Company B, we can write out the following:

3) Hence when we drive over 650 miles the Company A becomes cheaper than B.

the best would be the first choice because it's 7 dollars less than the second choice

Answer:

IM A PLAYA FORGIVE ME LOLOL

Answer:

Step-by-step explanation:

taxable income x social security tax rate = social security tax

taxable income x .062(6.2%) = 4873

taxable income = 4873/.062

taxable income = 78596.77

The standard deviation of a point estimator is a measure of the variability or precision of the estimator.

In statistics, a point estimator is a function that uses sample data to estimate an unknown parameter of a population. The standard deviation of a point estimator quantifies how much the estimates from different samples are expected to deviate from the true value of the parameter. A smaller standard deviation indicates a more precise estimator, as the estimates are expected to be closer to the true value. Conversely, a larger standard deviation suggests a less precise estimator with estimates that are more spread out. By calculating the standard deviation of a point estimator, we can assess its reliability and determine the level of confidence we can have in the estimated parameter value.

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What is the definition or meaning of the standard deviation of a point estimator?

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Answer:

6 possible outcomes

Step-by-step explanation:

To solve this problem, we have to make use of the Fundamental Counting Principle formula.

The formula counting principle states that when we are given two or more distinct events, in order to get the total number of possible outcomes, we multiply such events together.

In the above question, we are given two events.

Event 1

3 varieties of cheese: Cheddar, Gouda, and Swiss.

Event 2

2 styles of cheese: Shredded and Sliced

The possible outcomes for the variety and style of cheese = Event 1 × Event 2

= 3 × 2

6 possible outcomes.

These 6 Possible outcomes are listed below:

1) Cheddar cheese , Shredded

2) Cheddar cheese , Sliced

3) Gouda cheese , Shredded

4) Gouda cheese , Sliced

5) Swiss cheese , Shredded

6) Swiss cheese , Sliced

The number of square tiles needed is 24 tiles

The formula for calculating the area of a rectangle is expressed as:

A = LW where:

L is the length

W is the width

For the rectangle:

Area = 12 feet × 8 feet

Area = 96ft²

For the square:

Area of a square = L²

Area of a square = 2²

Area of a square = 4ft²

Determine the number of square tiles that will cover the patio.

Number of square tiles needed = Area of rectangle/Area of square

Number of square tiles needed = 96/4

Number of square tiles needed = 24

Hence the number of square tiles needed is 24 tiles.

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Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Arithmetic progression is S = 1/2n[2a+(n-1)d]

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

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Geometric progression is Uₙ = arⁿ ⁻ ¹

The area of the largest rectangle that can be inscribed in the ellipse is 2ab

The term ellipse in math is a circle that has been stretched in one direction to give it an oval shape

Here we have given the following equation x²/a² + y²/b² = 1

Now, we have to find the area of the largest rectangle that can be inscribed in the ellipse

Here we all know that the Area of rectangle = 4xy

That can be written as A = 4xy

Now, we have to differentiate the given expression then we get,

=> dA/dx = 4xdy/dx  + 4y ----------------------(1)

Here we have given an equation  x²/a² + y²/b² = 1

Now, we have to differentiate this one also, then we get,

=> 2x/a²  + 2y(dy/dx)/b² = 0

If we equate both of the equation then we get the value as.

=> dy/dx = - xb²/a²y

Now, substitute the values on equation (1), then we get,

=> dA/dx = 4x( - xb²/a²y)  + 4y

Equate the expression with 0, then we get the value of

=> a²y² = b²x²

=> x²/a² = y²/b²

When we simplify this one then we get the value of x as (a/√2) and  y as b/√2

Therefore, the Area is calculated as,

=> 4xy  =  4(a/√2)(b/√2)  = 2ab

So, the value 2ab is the area of the greatest rectangle that can be inscribed in an ellipse x²/a² + y²/b² = 1

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

1/4

Step-by-step explanation:

Given:

Two angles form a linear pair.

It means sum of their measures = 180°.

And,

Measure of one angle is 24° greater than the other.

Let the other angle be x.

→ First angle = (x + 24)

According to the question,

→ 2x = 180 - 24

→ 2x = 156

→ x = 156/2

Therefore,

An explanation of an event that is based on repeated observations and experiments is a scientific theory

A thorough, well-researched explanation of a natural occurrence constitutes a scientific theory.

We frequently use the word "theory" to refer to a hypothesis or informed guess in common speech, but in science, a theory is an explanation that is the result of a substantial and repeated investigation. The purpose of theories is to explain a broad concept; they are not intended to establish facts

Some of the most well-known and complicated events are explained by scientific theories. The theories of relativity, evolution, and gravity are a handful of the most well-known scientific concepts.

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Answer:

She will save 62.40

Step-by-step explanation:

First find the total amount she makes

hours times hourly rate

19.5 * 12.80

249.60

She saves 1/4 of this, so multiply by 1/4

1/4 * 249.60

62.40

She will save 62.40

Answer:

62.40

Step-by-step explanation:

Answer: X equals 11.

Step-by-step explanation:

2600 = 235x + 15

2585 = 235x (subtract 15)

11 = x (divide 2585 by 235)

Answer:

11

Step-by-step explanation:

Answer:

Yes they are equivalent

Answer:

575.2m

Step-by-step explanation:

1- inch to cm

22647 × 2.54 = 57523cm

2- cm to meter

57523 / 100 = 575.2m

As the number of degrees of freedom become large, the t distribution actually approaches the normal distribution, not

the binomial distribution. The correct answer is false.

The t distribution is used when the sample size is small and the population standard deviation is unknown, while the

binomial distribution is used for discrete data where there are only two possible outcomes.

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of

independent trials with a constant probability of success, whereas the t distribution is a continuous probability

distribution that models the variability of sample means from a normal population.

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a) For an abelian group of order 80, the invariant factors are \(2^4,\) \(2^3\), \(2^2\), 2, and 5. These correspond to the elementary divisors of the group.

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b) For an abelian group of order 3969, the invariant factors are \(3^4\), \(3^3\),\(3^2\), 3, \(7^2\), 7, and 1. These represent the elementary divisors of the group.

c) For an abelian group of order 70, the invariant factors are 2 * 5 * 7, 2 * 5, 2 * 7, 5 * 7, 2, 5, 7, and 1. These are the elementary divisors of the group.

d) For an abelian group of order 22500, the invariant factors are \(2^2\) * \(3^2\) * \(5^4\), \(2^2\)  *d)

For an abelian group of order 22500, the invariant factors are \(2^2\) * \(3^2\) * \(5^2,\)d) For an abelian group of order 22500, the invariant factors are \(2^2\) * \(3^2\)  * \(5^2,\)  \(2^2\)  *  \(5^2,\),  \(2^2\) * d)

For an abelian group of order 22500, the invariant factors are \(2^2\) * \(3^2\) ,  \(5^2,\),d) For an abelian group of order 22500, the invariant factors are \(2^2\) * \(3^2\) , \(2^2\) , 5, 3, and 1. These represent the elementary divisors of the group.

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Answer:

1187.52

Step-by-step explanation:

2 π r h + 2 π r² = 2·π·7·20+2·π·7² ≈ 1187.52202