Dragon Company just issued a dividend of $2. 85 per share of its common stock. The company is expected to maintain a constant 3. 6 percent growth rate. If the stock sells for $58 a share what is the company's cost of equity?

Using Scientific notation, the expression (6.1 * 10⁴) + (5.2 * 10⁴) can be written as;  11.3 * 10⁴

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 × 10⁸.

Now, we want to use scientific notation to simplify;

(6.1 * 10⁴) + (5.2 * 10⁴)

Using distributive property of equality, we can say that the expression can be broken down as;

10⁴(6.1 + 5.2)

= 11.3 * 10⁴

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The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots

To find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation

2x² + 10x + 9 - 2x = 0

Simplifying the left-hand side, we get:

2x² + 8x + 9 = 0

Now, we can use the quadratic formula to find the roots of the equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 8, and c = 9.

Substituting these values into the formula, we get:

x = (-8 ± √(8² - 4(2)(9))) / 2(2)

Simplifying the expression under the square root, we get:

x = (-8 ± √-8) / 4

The square root of -8 is not a real number

So, the equation has no real root

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The 3 different formulas for area of triangle are :

\(A = \frac{1}{2}* b* h\)

\(A = \frac{\sqrt{3}}{4} * side^2\)

\(A =\sqrt{s(s-a)(s-b)(s-c)}\)

In a 2-D plane, the area of a triangle is the region enclosed by it. A triangle, as we all know, is a closed shape with three sides and three vertices. The general formula for calculating the area of a triangle is half of the product of its base and height.

To calculate the area of a triangular polygon, we must first determine its base (b) and height (h).

Area of triangle is  \(A = \frac{1}{2}* b* h\).

When all sides of triangle, then the triangle is called equilateral triangle.

Area of an Equilateral Triangle ,\(A = \frac{\sqrt{3}}{4} * side^2\)

Heron's formula can be used to calculate the area of a triangle with three sides of varying lengths. The first step is to calculate the semi-perimeter of a triangle by adding all three sides and dividing by two. The following step is to use the semi-perimeter of a triangle value in the main formula known as "Heron's Formula" to calculate the area of a triangle.

\(A =\sqrt{s(s-a)(s-b)(s-c)}\)

Where, \(s=\frac{a+b+c}{2}\)

Thus, there are many ways to determine the area of triangle.

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For the Poisson distribution, E(X+1) equals A + 1, while for the binomial distribution, E(X+1) equals np + 1.

(a) In the case where X follows a Poisson distribution Po(A), where A > 0, we want to evaluate the expectation E(X+1).

The Poisson distribution is commonly used to model the number of events occurring within a fixed interval of time or space, given the average rate of occurrence (A). The probability mass function of the Poisson distribution is given by P(X=k) = (e^(-A) * A^k) / k, where k is a non-negative integer.

To evaluate E(X+1) for the Poisson distribution, we need to find the expected value of X+1. Using the properties of expectation, we can express it as E(X) + E(1).

The expected value of X from the Poisson distribution is given by E(X) = A, as it corresponds to the average rate of occurrence. The expected value of a constant (in this case, 1) is simply the constant itself.

Therefore, E(X+1) = E(X) + E(1) = A + 1.

(b) In the case where X follows a binomial distribution B(n, p), where n is a positive integer and p is a probability value between 0 and 1, we want to evaluate the expectation E(X+1).

The binomial distribution is commonly used to model the number of successes (X) in a fixed number of independent Bernoulli trials, where each trial has a probability of success (p).

To evaluate E(X+1) for the binomial distribution, we need to find the expected value of X+1. Again, using the properties of expectation, we can express it as E(X) + E(1).

The expected value of X from the binomial distribution is given by E(X) = np, where n is the number of trials and p is the probability of success in each trial. The expected value of a constant (in this case, 1) is simply the constant itself.

Therefore, E(X+1) = E(X) + E(1) = np + 1.

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The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

The cost function and demand function of a monopolist can be found in the question. These can be used to derive the marginal revenue and marginal cost.

The optimal level of output and profit can be derived using the marginal revenue and marginal cost equations. After that, you can confirm that the demand is elastic at the optimal output.

After that, you need to calculate the markup and the DWL associated with the monopoly output. Finally, you need to find the new optimal output and determine if the DWL increases or decreases.

Given:Cost Function C(Q) = ¼ Q2 Marginal cost MC(Q) = ½ Q Demand P = 100 – ¼ Q. a.

Sketch the market demand, marginal costs, and marginal revenues.

Market demand:Marginal cost:Marginal revenue: b. What is the monopolist’s optimal level of output and profits?In the monopolistic market, the optimal level of output and profits are given by the condition that Marginal Revenue = Marginal Cost.

Marginal Revenue is the derivative of Total Revenue with respect to Quantity, which can be found by using the demand equation and solving for Q:TR(Q) = P × Q = (100 – ¼ Q)Q = 100Q – ¼ Q2MR(Q) = dTR(Q)/dQ = 100 – ½ QMarginal Cost is given by the question as MC(Q) = ½ Q.

The monopolist's optimal level of output and profits can be found by equating MR and MC:100 – ½ Q = ½ Q => Q = 66.67 units of outputWhen Q = 66.67, the price is given by the demand equation:P = 100 – ¼ Q => P = 83.33.

Therefore, the monopolist's optimal output is 66.67 and optimal profits are (P – MC) × Q = (83.33 – 33.33) × 66.67 = $2,000.

Confirm that demand is elastic at the optimal output.The demand is elastic at the optimal output if the absolute value of the price elasticity of demand is greater than one.

The price elasticity of demand is given by:Ed = (% Change in Quantity Demanded)/(% Change in Price) = (dQ/Q)/(dP/P) × P/QSince MR = P(1 - 1/Ed), MR is greater than MC if Ed is less than 1 and less than MC if Ed is greater than 1. Therefore, the optimal output occurs where Ed is equal to
Substituting the values of P and Q, we get:Ed = (dQ/Q)/(dP/P) × P/Q = -1.47Therefore, demand is elastic at the optimal output.

Calculate the firm’s markup.The markup is given by the formula (P - MC)/P.Substituting the values of P and MC, we get:(83.33 - 33.33)/83.33 = 0.6 = 60% markup .

What is the DWL associated with the monopoly output?DWL (Deadweight Loss) is the difference between the total surplus in a competitive market and the total surplus in a monopoly market.

The formula for DWL is:DWL = (1/2)(Pmon - Pcomp)(Qcomp - Qmon)DWL can be calculated by using the demand equation and finding the quantity demanded at the monopoly price and the competitive price. At the monopoly price of $83.33, the quantity demanded is 66.67.

At the competitive price of $66.67, the quantity demanded is 100. Therefore, DWL can be calculated as follows:DWL = (1/2)(83.33 - 66.67)(100 - 66.67) = $1,111.1 f.

Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output?The new optimal output will be where the new marginal cost equals the original marginal revenue.

The subsidy reduces the marginal cost to (1/2) Q - $10.

Therefore, the monopolist's new optimal output can be found by solving for Q:100 - 1/2 Q + 10 = 1/2 Q => Q = 74.07 units of outputWhen Q = 74.07, the price is given by the demand equation:P = 100 - 1/4 Q => P = $81.48 g. Does the DWL fall or rise?The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

Therefore, the deadweight loss falls.

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Math textbook with double-digit number of pages split into sections. each section with exactly 12 pages long, with the exception of the epilogue, which is 11 pages long and a trivia fact is presented on the bottom of the 5th page, has total of 35 pages.

Let's assume the number of sections in the math textbook is represented by the variable "n". Each section is 12 pages long, except for the epilogue, which is 11 pages long. Therefore, the total number of pages in the textbook can be calculated as:

Total pages = (12 * n) + 11

Now, let's consider the trivia facts presented on the bottom of every 5th page. If a trivia fact appears on the second-to-last page, it means that the total number of pages in the textbook is a multiple of 5 minus 1.

So, we need to find a value for "n" that satisfies the equation:

(12 * n) + 11 = 5k - 1

Where "k" is an integer representing the number of sets of 5 pages. Rearranging the equation, we get:

12n = 5k - 12

Now, we can start substituting different values of "k" to find a solution that satisfies the equation and gives a double-digit number of pages.

Let's try "k" equals 3. Substituting into the equation:

12n = (5 * 3) - 12

12n = 15 - 12

12n = 3

However, this doesn't give us a double-digit number of pages. Let's try a larger value of "k".

Let's try "k" equals 8:

12n = (5 * 8) - 12

12n = 40 - 12

12n = 28

n = 28 / 12

n = 2.33

Since "n" should be an integer representing the number of sections, we can see that "n" equals 2 satisfies the equation.

Therefore, the textbook has a total of:

Total pages = (12 * 2) + 11

Total pages = 24 + 11

Total pages = 35

So, the textbook has 35 pages.

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Answer:

It's the second one.

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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The option is B. Emerson is painting the outside of a cube for a math project. he knows the area of each face is 145 square inches.

the place is the quantity that expresses the quantity of vicinity on the plane or on a curved floor. The area of a plane vicinity or aircraft location refers to the area of a shape or planar lamina, while surface location refers to the region of an open floor or the boundary of a three-dimensional object. the place can be understood as the quantity of material with a given thickness that might be necessary to fashion a model of the shape, or the amount of paint essential to cowl the surface with a single coat. it's by far the 2-dimensional analog of the period of a curve (a one-dimensional concept) or the volume of a stable (a three-dimensional idea).

The region of a form can be measured by using comparing the form to squares of a set size. within the global system of devices (SI), the standard unit of the region is the rectangular meter (written as m²), which is the place of a rectangular whose aspects are one meter long. A shape with an area of 3 square meters might have an equal area to 3 such squares. In mathematics, the unit square is defined to have area one, and the place of some other form or floor is a dimensionless real number.

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The company survey 307 customers in order to get 98% confidence.

Sample proportion (p) = 0.5 (as no estimate is given)

α = 1 - 92% = 0.08.    Therefore, α/2 = 0.08/2 = 0.04

Z(α/2) = Z(0.04) = 1.751

Estimate = 5% = 0.05

Now, E = Z(α/2) * sqrt (p(1-p)/n)

n = (1.751/0.05)2 * 0.5 * (1-0.5)

n = 307

Hence, the company should survey 307 customers in order to be 98% confident that the estimated (sample) proportion is within 2 percentage points of the true population proportion of customers who are over the age of forty.

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Answer:

see below

Step-by-step explanation:

1 1/4 > z

Open circle and 1 1/4 since there is no equals sign

line goes to the left since z is less than the number

Since we are working with the ">" symbol, its going to be an open circle.

Since 5/4 is greater than z, that means that the lie will go on forever to the left.

The arrow second from last is the correct answer (the that is a left arrow with an open circle).

Best of Luck!

When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

We need to apply Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction for two different media.

Step 1: Calculate the angle of refraction in the first material using Snell's Law.
n1 * sin(i1) = n2 * sin(r1)
1 * sin(60°) = 1.20 * sin(r1)
sin(r1) = 0.5/1.20
r1 ≈ 25.4°

Step 2: Repeat the process for the remaining materials, using the previous angle of refraction as the new angle of incidence. Calculate the final angle of refraction in the last material.

For the second material:
1.20 * sin(25.4°) = 1.40 * sin(r2)
r2 ≈ 21.4°

For the third material:
1.40 * sin(21.4°) = 1.32 * sin(r3)
r3 ≈ 22.9°

For the fourth material:
1.32 * sin(22.9°) = 1.28 * sin(r4)
r4 ≈ 23.3°

Step 3: Calculate the angle of emergence in air.
1.28 * sin(23.3°) = 1 * sin(e)
e ≈ 29.4°

When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.

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Answer:

10 groups you need to make 200.

mark as brainlist

Answer:

3150 inches is the volume

Step-by-step explanation:

i hoped this helped

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac informs us about the nature of the zeros

• If b² - 4ac > 0 then 2 real and irrational zeros

• If b² - 4ac > 0 and a perfect square then 2 real and rational zeros

• If b² - 4ac = 0 then 2 real and equal zeros

• b² - 4ac < 0 then zeros are not real

Given

f(x) = 3(x - 4)² - 12 ← expand factor using FOIL

     = 3(x² - 8x + 16) - 12 ← distribute parenthesis by 3

     = 3x² - 24x + 48 - 12

     = 3x² - 24x + 36 ← in standard form

with a = 3, b = - 24 , c = 36 , then

b² - 4ac

= (- 24)² - (4 × 3 × 36

= 576 - 432      

= 144 ← a perfect square

Then 2 zeros are real and rational  and produce 2 x- intercepts

Answer: 7/25 or 28%

Step-by-step explanation:

28 (cherry) + 19 (strawberry) + 20 (orange) + 33 (lemon) = 100 (total)

so p(cherry), or the probability of getting cherry, is 28/100 (7/25)

that as a percent is 28%

Answer:

£177.92

Step-by-step explanation:

To increase something by 28% would be to multiply the original value by 1.28:

So to increase £139 by 28%, we do:

£139 × 1.28 = £177.92

So this is our final answer

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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Answer:

It would take 45 minutes to get 18 marks

Step-by-step explanation:

30 ÷ 12 = 2.5

2.5 x 18 = 45

It would take 45 minutes to get 18 marks

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

The probability that the married couple will have adjacent desks is 0.22.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.

= 8 x 7! x 2

= 80640

Ans the total number of possible arrangements is 362880.

= 9!

= 362880

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 80640/362880

probability = 0.22

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Answer:

hkfgyjfjyfj685

Step-by-step explanation:

rdytesrghd

Answer:

-2x+8

Step-by-step explanation:

(-x+3)-(x-5)

= -x+3-x+5

= -2x+8

Answer:

??????.

Step-by-step explanation:

????????????????

Answer: For #6, domain is {-3≤x<4}, range is {-3<y≤-1}

Step-by-step explanation: For #6 domain, the leftmost point on the graph is -3, with a closed circle. This means that x is greater than or equal to -3 (-3≤x). The rightmost point is 4, with an open circle, meaning that x is less than 4 (x<4). Put them together in the standard format, and you get {-3≤x<4}. Same principle for range; lowest point is -3, with an open circle (-3<y), and highest point is -1, with a closed circle (x≤-1). Result is {-3<y≤-1}.

I'm not sure whether you are a beginner at this or if it's just this one that you're stuck on, I hope my answer was sufficient.

Answer:

96 i think

Step-by-step explanation:

I think its 96. just multiply all the sides

Answer:

Infinitely many solutions

Step-by-step explanation:

Note that 2(2x+3y=12) is 4x+6y=24, which is the first equation. Therefore, by canceling the equations out, you have 0=0, which means whatever one side equals, the other side ALWAYS equals that.

The statement "you should perform x trials until you observe a success" is not a common characteristic of a binomial distribution.

In a binomial distribution, there are exactly two possible outcomes (success and failure), the probability of success is the same in all trials, there are a fixed number of observations, each trial is independent.

However, the number of trials required to observe a success is not a fixed characteristic of a binomial distribution. The number of trials may vary depending on the probability of success and the particular sequence of trials that occur. In a binomial distribution, we are interested in the probability of obtaining a specific number of successes in a fixed number of trials, rather than the number of trials needed to observe a success.

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The following confidence intervals could be valid for a 90% confidence level: A (0.52-0.60), B (0.53-0.61), and E (0.48-0.64).

To determine the valid confidence intervals, we need to consider the margin of error for a given confidence level. The formula for the margin of error is: margin of error = critical value * standard error.
Since the confidence level is 90%, the critical value (z-score) is approximately 1.645. The standard error can be calculated using the formula: standard error = sqrt((p * (1-p)) / n), where p is the sample proportion (0.56) and n is the sample size.
By substituting the given values, we can calculate the margin of error. The lower bound of the confidence interval is obtained by subtracting the margin of error from the sample proportion, while the upper bound is obtained by adding the margin of error.
After calculating the bounds for each option, we find that A (0.52-0.60), B (0.53-0.61), and E (0.48-0.64) are valid 90% confidence intervals for the population proportion.

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