= a) Prove that the given function u(x, y) = -8x3y + 8xy3 is harmonic b) Find v, the conjugate harmonic function and write f(z).

Answer:

x = 12

Step-by-step explanation:

10x+24 = 6x+72

10x - 6x = 72 - 24

4x = 48

x = 12

Answer:

144

Step-by-step explanation:

10x+24=6x+72

-6x          -6x

4x+24=72

     -24  -24

4x=48

/4   /4

x=12

<A=10(12)+24

<A=120+24

<A=144

The probability that fewer than 3 of the 8 sampled people are unemployed is approximately 0.91, indicating that there is a high chance of having at least 3 employed people in the sample.

It can be solved using the binomial distribution formula.

Let X be the number of unemployed people in a sample of 8 from the city.

Then X follows a binomial distribution with parameters n = 8 and p = 0.16, since the probability of an individual being unemployed is 0.16.

The probability of fewer than 3 people being unemployed is the probability of X = 0, 1, or 2.

We can compute this probability as:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)}

We can compute each term separately:

P(X = 0) = (8 choose 0) * 0.16⁰ * 0.84⁸ ≈ 0.3252

P(X = 1) = (8 choose 1) * 0.16¹* 0.84⁷ ≈ 0.3772

P(X = 2) = (8 choose 2) * 0.16² * 0.84⁶ ≈ 0.2035

Therefore,

P(X < 3) ≈ 0.3252 + 0.3772 + 0.2035 ≈ 0.906

Rounding to two decimal places, the probability that fewer than 3 of the 8 sampled people are unemployed is approximately 0.91.

To learn more about binomial distribution:

https://brainly.com/question/15246027

#SPJ11

Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line

Answer:

$ 7,299.92

Step-by-step explanation:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Answer:

1548.66 feet

Step-by-step explanation:

We can draw a straight line down the middle to form two right triangles

This will split the 70 degree angle into two 35 degree angles

We now have two 90-35-55 right triangles

Now we can use cos(55) * the hypotenuse on both sides to get the distance across the lake

Thus we have:

1200cos(55 = 688.29

1500cos(55 = 860.36

Best of luck

The theory which was first developed by Karl Marx is Conflict Theory. The legal process through which one becomes a legally recognized citizen is called naturalization.

Karl Marx was a German philosopher, economist, historian, sociologist, political theorist, journalist, and socialist revolutionary. He is known as one of the founders of social sciences. His theory was based on the conflict between the two classes of society: the proletariat (working class) and the bourgeoisie (ruling class).

The legal process through which one becomes a legally recognized citizen is called naturalization. Naturalization is the process by which foreign individuals become citizens of a new country.

To learn more about conflict theory visit:

https://brainly.com/question/30396865

#SPJ11

Answer:

1/2

Step-by-step explanation:

Given:

(2 cubed) (2 superscript negative 4)

= (2³)(2^-4)

= (2³) (1 / 2⁴)

= (2³ * 1) / 2⁴

= 2³ / 2⁴

Both numerator and denominator has the same base. Thus, pick one of the bases

Also, in indices, division sign can be translated to subtraction

Therefore,

2³ / 2⁴

= 2^3-4

= 2^-1

= 1/2¹

= 1/2

(2³)(2^-4) = 1/2

Answer:

D

Step-by-step explanation:

bc i said so

(a) The spring oscillating most quickly (with the shortest period) is represented by the differential equation: s" + 36s = 0.

(c) The spring oscillating most slowly (with the longest period) is represented by the differential equation: s" + 16s = 0.

Among the given differential equations, the spring oscillating most quickly with the shortest period is represented by the equation s" + 36s = 0. This equation describes simple harmonic motion with a high frequency due to the coefficient of the second derivative (s") term. The larger the coefficient, the faster the oscillations occur, resulting in a shorter period.

(b) To determine which spring has the largest amplitude, we need to examine the coefficients in front of the s (position) term in each differential equation. Unfortunately, there seems to be an error in the provided equations where some terms are repeated or inconsistent, making it impossible to accurately identify the spring with the largest amplitude.

(c) The spring oscillating most slowly with the longest period is represented by the differential equation s" + 16s = 0. A lower coefficient for the second derivative term results in slower oscillations and thus a longer period.

Learn more about properties of oscillating

brainly.com/question/30111348

#SPJ11

Considering the vertex of a quadratic equation, the greatest rectangular area that the farmer can enclose with 100 m is of 625 m².

A quadratic equation is modeled by the rule presented as follows:

y = ax^2 + bx + c

The vertex has these following coordinates.

\((x_v, y_v)\)

In which:

Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point in the function, as follows::

In this problem, the coefficients of the quadratic equation representing the area are given as follows:

a = -1, b = 50.

The greatest rectangular area that the farmer can enclose with 100 m is the y-coordinate of the vertex of the quadratic equation, hence:

\(y_v = -\frac{50^2 - 4(-1)(0)}{4(-1)} = 625\)

The area is of 625 m².

The quadratic equation for the area is:

A(w) = -w² + 50w

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

#SPJ1

Answer:

625

explanation:

trust

Answer:

the first one is correct and the second one is where you set them equal to 180 and slove for x and the third one is you set that equal to 180.

Step-by-step explanation:

The area of the triangular yard is 7000 ft².

The entire area enclosed by three sides of a triangle is the area of it.

Given,

The base of the triangle is 200 feet and the height of the triangle is 70 feet.

Therefore, the area of the triangle

= (1/2) × base of the triangle × height of the triangle =  (1/2) × 200 × 70 ft² = 7000 ft².

Learn more about the area of a triangle here: https://brainly.com/question/22625791

#Tag #SPJ2

Answer:

125+2x=y   (take 125 add 2x for $2 a day and then = y for amount saved)

Points on Graph:

(125,0)

(135,5)

(145,10)

(155,15)

(165,20)

(175,25)

(185,30)

(195,35)

(205,40)

(215,45)

(225,50)

Answer:

Step-by-step explanation:

Answer:

37 is the correct answer

The maximum number of ordered pairs possible in the relation is 22.

To find the maximum number of ordered pairs possible in the relation, we examine the sizes of each equivalence class.

In the given question, we have a set A with n elements and an equivalence relation R on A. Let's assume that R has m equivalence classes, and the sizes of those classes are denoted as n1, n2, n3, ..., nm.

To find the maximum number of ordered pairs possible in the relation, we examine the sizes of each equivalence class. In the given scenario, e1 has 8 ordered pairs, e2 has 10 ordered pairs, and e3 has 4 ordered pairs.

To maximize the number of ordered pairs, we consider a scenario where e1, e2, and e3 are the only equivalence classes, each containing its ordered pairs. In this case, the total number of ordered pairs would be 8 + 10 + 4 = 22.

Therefore, the maximum number of ordered pairs possible in the relation is 22.

Learn more about equivalence relations:

https://brainly.com/question/30956755

#SPJ11

The probability that more than 20% of the sample are from poverty households is approximately 0.8365.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

We can use the normal approximation to the binomial distribution to solve this problem, given that the sample size is relatively large (n=300) and the probability of success (p=0.22) is not too close to 0 or 1.

Let X be the number of children in the sample who live in poverty households. Then X follows a binomial distribution with parameters n=300 and p=0.22.

The mean of X is given by μ = np = 300 x 0.22 = 66, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(300 x 0.22 x 0.78) ≈ 6.23.

We want to find the probability that more than 20% of the sample are from poverty households, which is equivalent to finding P(X > 0.2n) = P(X > 60).

To use the normal approximation, we can standardize X as follows:

Z = (X - μ) / σ

Then, we have:

P(X > 60) = P(Z > (60 - 66) / 6.23) ≈ P(Z > -0.96)

Using a standard normal table or calculator, we can find that the probability of Z being greater than -0.96 is approximately 0.8365.

Therefore, the probability that more than 20% of the sample are from poverty households is approximately 0.8365.

To learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer:

Step-by-step explanation:

The graph has negative leading coefficient as

It is of the odd degree, and the degree is most probably 5

Answer:

Its A

Step-by-step explanation:

3.2 + 4.2= 7.4

10^5 x 10^8 = 10^13

Since your final answer is in scientific notation, its 7.4 x 10^13

Given function f(x) is as follows;f(x) = (916x³)/3 - 4x² + 6x - 13To find out the value of x for which the given function has a tangent line of slope 5, we need to use the concept of derivative. Since, the slope of the tangent line to the curve at a point on it is the value of the derivative at that point.

So, first we need to take the derivative of f(x). Differentiating the given function, we get;f'(x) = 916x² - 8x + 6Now, we need to find the value of x for which the slope of the tangent is equal to 5.We can form an equation by equating f'(x) to 5;916x² - 8x + 6 = 5Or, 916x² - 8x + 1 = 0.

We can solve the quadratic equation for x using quadratic formula  Therefore, the value(s) of x for which f(x) has a tangent line of slope 5 is (52/1832) or (-58/1832).

To know more about value visit :

https://brainly.com/question/30035551

#SPJ11

The correct answer is $56,000.the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables

To determine the total profit for Pinewood Furniture Company, we need to calculate the profit generated from producing 200 chairs and 400 tables.

Each chair generates a profit of $80, and if 200 chairs are produced, the total profit from chairs would be:

200 chairs * $80/profit per chair = $16,000.

Similarly, each table generates a profit of $100, and if 400 tables are produced, the total profit from tables would be:

400 tables * $100/profit per table = $40,000.

Therefore, the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables, would be:

$16,000 (profit from chairs) + $40,000 (profit from tables) = $56,000.

Hence, the correct answer is $56,000.

Learn more about Macroeconomics

brainly.com/question/30268833

#SPJ11

Answer (Please mark as brainliest):

x^2 - 9

Step-by-step explanation:

To distribute (x+3) (x-3), we use the FOIL method:

(x+3)(x-3) = x(x) + x(-3) + 3(x) + 3(-3)

= x^2 - 3x + 3x - 9

= x^2 - 9

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0.

In this case, the equation is already in standard form since there is only one term with x^2 and no x or constant terms:

x^2 - 9

When you see the symbol "△", this denotes a triangle. Now combine the symbol with the letters FGH, this becomes △FGH, meaning a triangle FGH, with F, G, and H as the three points.

Now, the symbol "∠" means angle and "m∠" means the measure of an angle. So m∠F means the angle at the point F, m∠G means the angle at the point G, and m∠H means the angle at the point H. (I'll attach a diagram of this triangle).

Now we have to determine m∠H, which is the angle at point H. To do that, we have to find the value of \(x\). To do that, we have to use one of the laws of a triangle, which is:

The sum of angles in a triangle = 180°. This means when we add all the angles in a triangle, it sums up to 180°. Let's do that.

\(\angle F + \angle G + \angle H = 180\textdegree \\\angle F = (5x - 6)\textdegree, \angle G = (3x + 16)\textdegree, \angle H = (x + 8)\textdegree \\(5x - 6) + (3x + 16) + (x + 8) = 180\\5x + 3x + x - 6 + 16 + 8 = 180\\9x + 18 = 180\\9x = 180 - 18\\9x = 162\\x = 18\textdegree\)

Now that we have found the value of x as 18°, we can substitute its value to determine the angle H.

\(m\angle H = (x + 8), x = 18\\m\angle H = 18 + 8\\m\angle H = 26\textdegree\)

I hope you understand the explanation.

The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

To learn more about the limit from the given link

https://brainly.com/question/29013259

#SPJ4

Answer:

5/24 more

Step-by-step explanation:

1/3 turns into 8/24

and

1/8 turns into 3/24

so eric has read 5/24 more

Answer:

5/24

Step-by-step explanation:

1/8×3=3/24

1/3×8=8/24

8/24-3/24=5/24.

Answer:

The area is the product of length and width, which is to say that the length and width are factors of the area.

Assuming the dimensions are integers, you want factors of 84 that differ by 5.

Step-by-step explanation:

... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12

The last of these pairs differ by 5, so ...

the length is 12 inches

the width is 7 inches.

The answer is l=12, w=7

Answer:

Step-by-step explanation:

Givens

Let the width be w

Let the length be w + 5

Let the area = 84

Equation

A = L*w

Solution

x(x + 5) = 84              Remove the brackets

x^2 + 5x = 84            Subtract 84 from both sides

x^2 + 5x - 84 = 0      This will factor

(x - 7)(x + 12) =0

x + 12 has no meaning. Geometry does not use negative numbers.

x - 7 = 0                      Add 7 to both sides

x = 7

The width = 7

The length = 7 + 5 = 12

Answer:

45 girls

Step-by-step explanation:

since the ratio is 3:5, 3 being the boys, we can divide 27 by 3. We get nine, which is the number we multiply 5 with. 9*5=45 girls

Answer:

f(x) = 8 + x

f(5) = 8 + 5

[What I just did there: I replaced x with 5]

f(5) = 13!

Answer: sorry took look long F(5)= 13

Step-by-step explanation:

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

no solution, you have "9x -" on both sides, so the equation is false and has no solution

Step-by-step explanation:

How many solutions are there to the equation below?

9x - 16 = 9x - 23

take off 9x from both side

-16 = -23

no solution, you have "9x -" on both sides, so the equation is false and has no solution