Solve 9x - 8y = 19 for y

The value of each share of common stock, rounded to the nearest penny, is approximately $66.61 according to the given information and values in the question.

step by step:

To calculate the value of each share of common stock using the Discounted Cash Flow (DCF) valuation model, we need to discount the expected future cash flows to their present value and subtract the market value of the outstanding debt. The formula for calculating the value of each share of common stock is:

Value per Share = (Present Value of Future Cash Flows - Debt) / Number of Common Shares

To calculate the present value of future cash flows, we discount each cash flow using the cost of capital.

Let's calculate the present value of future cash flows and the value per share of common stock:

Year 1: FCF = $250,000

Year 2: FCF = $300,000

Year 3: FCF = $350,000

Year 4: FCF = $400,000

Year 5: FCF = $450,000

\(Year 6 onwards: FCF = $450,000 * 1.022^(Year - 5)\)

Cost of Capital = 6.65%

Outstanding Debt = $3,833,340

Number of Common Shares = 60,797

First, let's calculate the present value of future cash flows:

\(PV = FCF / (1 + r)^n\)

where:

PV = Present Value

FCF = Future Cash Flow

r = Cost of Capital

n = Number of years

\(Year 1:PV1 = $250,000 / (1 + 0.0665)^1 ≈ $234,837.45Year 2:PV2 = $300,000 / (1 + 0.0665)^2 ≈ $268,084.17Year 3:PV3 = $350,000 / (1 + 0.0665)^3 ≈ $301,706.42Year 4:PV4 = $400,000 / (1 + 0.0665)^4 ≈ $335,693.63Year 5:PV5 = $450,000 / (1 + 0.0665)^5 ≈ $369,035.06Year 6 onwards:PV6 = $450,000 * 1.022^(Year - 5) / (1 + 0.0665)^Year\)

Now, let's calculate the total present value of future cash flows:

\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)\)

∑(PV6) represents the sum of present values for Year 6 onwards, up to infinity. Since we have a constant growth rate of 2.2%, we can use the perpetuity formula to calculate this sum:

\(∑(PV6) = PV6 / (r - g)\)

where:

r = Cost of Capital

g = Growth rate

\(∑(PV6) = PV6 / (0.0665 - 0.022) = PV6 / 0.0445Now, let's calculate PV6 and ∑(PV6):PV6 = $450,000 * 1.022^1 / (1 + 0.0665)^6 ≈ $303,212.65∑(PV6) = $303,212.65 / 0.0445 ≈ $6,820,510.11\)

Next, let's calculate the total present value:

\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)Total PV = $234,837.45 + $268,084.17 + $301,706.42 + $335,693.63 + $369,035.06 + $6,820,510.11Total PV ≈ $8,329,866.84\)

Finally, let's calculate the value per share of common stock:

Value per Share = (Total PV - Debt) / Number of Common Shares

Value per Share = ($8,329,866.84 - $3,833,340) / 60,797

Value per Share ≈ $66.61

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The mean number of students in the class is 2.4 siblings.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = total sum of siblings / number of students

[(0 x 4) + ( 1 x 4) + ( 2 x 2) + ( 3 x 8) + ( 4 x 4) ] / ( 2 + 4 + 2 + 8 + 4)

= 48 / 20 = 2.4 siblings

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The sketch to illustrate the question is given below

Since each of the bags are filled equally with 2 kilograms 450 grams of sand

Then we can sum two bags and compare the mass with 5 kilogram

We can see that the sum of two bags weighs 4 kilograms and 900 grams (4.90 kilograms) which is 100 grams less than 5 kilograms.

Thus we can conclude that the mass of 2 bags is LESS THAN 5 kilograms

Answer:

minimum: 3

q1: 9

q3: 16

median: 13

max: 20

Step-by-step explanation:

the image attached below will help you read a box and whisker plot

From the logarithm quotient rule

we can see that

Therefore, expressions a and b are equivalent.

We can corroborate this result because:

Answer:

It is equal to 1 cup

Step-by-step explanation:

In the household measurement system, 8 oz is equivalent to: c. 1 tbsp.

In the United States customary system of measurement, which is commonly used in household cooking and baking, the abbreviation "oz" stands for ounces, and "tbsp" stands for tablespoons.

1 tablespoon (tbsp) is equivalent to 0.5 fluid ounces (fl oz), and since 8 fluid ounces is equivalent to 16 tablespoons, we can conclude that 8 oz is equal to 1 tablespoon (tbsp).

A tablespoon (tbsp) is a unit of volume commonly used in cooking and culinary measurements. It is part of the household measurement system, also known as the United States customary system, which is predominantly used in the United States for recipes and cooking measurements.

1 tablespoon is equal to approximately 14.79 milliliters (ml) or 0.5 fluid ounces (fl oz). It is typically abbreviated as "tbsp" or "T" (capital T) in recipes and on measuring spoons.

In cooking, tablespoons are often used to measure ingredients such as spices, oils, sauces, and other liquids. They provide a convenient way to measure small to moderate amounts of ingredients more accurately than using just a teaspoon or a cup.

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The test statistic for testing the claim of a population mean body temperature of 98.5 °F is approximately -0.169.

The value of the test statistic for testing the claim that the mean body temperature of the population is equal to 98.5 °F can be determined using the formula:

Test statistic
=
Sample mean
−
Population mean
Standard deviation
/
Sample size
Test statistic=
Standard deviation/
Sample size
​

Sample mean−Population mean
​


In this case, the sample mean is 98.3 °F, the population mean is 98.5 °F (as claimed), the standard deviation is 0.5 °F, and the sample size is 76. Plugging these values into the formula, we can calculate the test statistic.

Test statistic = (98.3 - 98.5) / (0.5 / sqrt(76)) ≈ -0.169

The test statistic is approximately -0.169 (rounded to two decimal places).

The test statistic measures the difference between the sample mean and the hypothesized population mean, in terms of the standard deviation and sample size. A negative test statistic indicates that the sample mean is slightly lower than the claimed population mean. By comparing this test statistic with critical values from the t-distribution at a 0.05 significance level, we can determine whether the difference is statistically significant or simply due to chance.

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The sampling technique used in the first scenario is stratified random sampling. Where as for the second and third scenario convenience sampling and systematic sampling are used.

i) In the first scenario, where 20 randomly selected households are interviewed from every grid in a disaster area, the sampling technique employed is stratified random sampling. The area is divided into 100 equal grids, and households are randomly selected from each grid. This approach ensures representation from each grid and provides a comprehensive view of the residents' needs.

ii) In the second scenario, where students are questioned as they leave the university's computer lab, the sampling technique used is convenience sampling. The researcher selects students conveniently available in the lab without following a specific randomization process. While this approach is convenient and easily accessible, it may introduce bias since it relies on the availability and willingness of students to participate.

iii) In the third scenario, where a researcher draws a sample from sequentially numbered invoices by selecting a random starting point and then drawing every 50th invoice, the sampling technique employed is systematic sampling. This technique involves selecting elements at fixed intervals from an ordered list. By randomly choosing a starting point and sampling every 50th invoice, the researcher ensures a systematic and evenly spaced sample.

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Answer:

3/19

Step-by-step explanation:

A box contains 20 balls: 10 are yellow , 6 are red and 4 are grey.

P(yellow) = yellow balls / total balls

         = 10/20 = 1/2

Now there are only  19 balls: 9 are yellow , 6 are red and 4 are grey.

P(red) = red balls/ total

          =6/19

Multiply the two probabilites together

P(yellow) * P(red) = 1/2 * 6/19 = 3/19

Answer:

I will assume you mean 0.015 out of 1.

It is 0.985

Step-by-step explanation:

Answer:

0.985

Step-by-step explanation:

The probability that a new fridge does not have a fault = 1 - 0.015

                                                = 0.985

Answer:

25 days old

Step-by-step explanation:

7 days = 1 week

3 x 7 = 21

21 + 4 = 25

25 days old

Answer 2 is 12

Step-by-step explanation:

more than 11 is 12

Answer:

x = - 0.9

Step-by-step explanation:

- 5.4 = 4x - 1.8 ( add 1.8 to both sides )

- 3.6 = 4x ( isolate x by dividing both sides by 4 )

\(\frac{-3.6}{4}\) = x , that is

x = - 0.9

Answer:       0.9                                                                                                                                                                                                                                         Step-by-step explanation:

Answer:

It depends on the type of numbers that are acceptable. If you state your problem in words

x - y =8

x + y = 1

The answers are    x = 4.5

                           y = -3.5

Answer:

  2.76×10^-3 m/s²

Step-by-step explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

The acceleration of one body by another is ...

  a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

  a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

  a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²

Answer:

The answer is A. 1/5 of an hour per truck.

Step-by-step explanation:

25/5=5 so that means 5 trucks per hour, or 1/5 of an hour per truck.

Hope this helps!! :)

Answer: 12. X = 14

Step-by-step explanation:

10x + 17 = 87 + 5x

10x = 70 + 5x

5x = 70

X = 14

Answer:a=18

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

The power series ∑k=0[infinity] is convergent. The radius of convergence is infinite.

The diameter of the largest disc at the series' convergence point is known as the radius of convergence of a power series in mathematics.

A power series is any series that can be written in the form:

\(\Sigma ^{infinity} n = 0 C_n (x - a)^n\)

The radius of convergence “R” is any number such that the power series will converge for |x – a| < R and diverge for |x – a| > R. The power series may not converge for |x – a| = R.

a – R < x < a + R (Power series converges)

x < a – R and x > a + R (Power series diverges)

Therefore, the radius of convergence is infinite.

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The correct option is

e. $27,343.75; $39,062.50; $58,593.75.

To determine how much each partner should pay for the renovations while maintaining their investments in the same ratio, we need to calculate the amounts based on their initial investment ratios.

The total ratio is 3.5 + 5 + 7.5 = 16.

To find the amount each partner should pay, we divide the renovation cost by the total ratio and then multiply it by each partner's respective ratio:

On: (125,000 * 3.5) / 16 = $27,343.75

Luc: (125,000 * 5) / 16 = $39,062.50

Isaac: (125,000 * 7.5) / 16 = $58,593.75

Therefore, each partner should pay the following amounts for the renovations:

On: $27,343.75

Luc: $39,062.50

Isaac: $58,593.75

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

10x - 12x - 3 does not equal -5x. Looks like what she did wrong was treating -3 as -3x and got her incorrect result that way

Part B

10x - 12x - 3 = (10-12)x - 3 = -2x - 3

To calculate the interest owed after 93 days, we use the formula for simple interest: Interest = Principal x Rate x Time. Substituting the given values, the interest amounts to $624.49.

This is the total interest that Melissa will owe to the bank after 93 days.Melissa took out a loan of $15,400 from a bank for home renovations. The bank charges a simple interest rate of 16% per year If Melissa doesn't make any payments towards the loan, the total amount owed after 93 days is obtained by adding the principal and the interest together.

Therefore, the total amount owed would be $16,024.49. This means that if Melissa does not make any payments during the 93-day period, her loan balance will increase to approximately $16,024.49, including both the original principal amount and the accrued interest.

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Answer:

(-2,1 ) (1,4) (-2,4)

Step-by-step explanation:

The ordered pair of one of the zeros for the following function is (x +8)

We have that the function is a quadratic function written as;

f(x)=x2+7x−8

Using the factorization method of solving quadratic functions;

Multiply the coefficient of  x squared by the constant in the expression, we have;

1(-8) = -8

Now, find the pair factors of the product that sum up to give 7, we have;

8x and -x

Substitute the values

x² + 8x - x - 8

group in pairs

(x² + 8x) - (x - 8)

factorize

x(x + 8) - 1(x + 8)

Then, we have;

x = 1

x = -8

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Multiple questions are included, and the answers vary for each question.

The given paragraph consists of multiple questions related to proof techniques and statements.

The questions ask for selecting the applicable proof techniques or true statements based on constructive proof of existence, plausible first steps in proving a statement, and different proof techniques mentioned in Epp's book.

Each question requires careful reading and understanding of the provided options and statements in order to determine the correct answers.

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Answer:

-x + 1

Step-by-step explanation:

First, rewrite 2x +3 - 3x + (-2) as 2x +3 - 3x - 2.  Note that +(-2) = -2.

Next, combine like terms.  We get -x + 1.  

Double check to determine whether this is one of the given possible answers.

piping would not occur. c = void ratio at critical state

ϕ = angle of shearing resistance

Substituting the given values in equation (3), we get:

\(i_c = (0.55 – 1)tan(0)\)

The pore water pressure at any point in the soil mass is given by the expression: p = hw + σv tanϕ ……(2)where,σv = effective vertical stressh

w = pore water pressureϕ = angle of shearing resistanceσv = σ – u (effective overburden stress)

p = total pressureσ = effective stressu = pore water pressure

From the figure shown above, the pore water pressure distributions on the upstream and downstream faces of the wall are given as below: On the upstream face: h

w = 6 m (above water level)p = hw = 6 m

On the downstream face:h\(w = 0p = σv tanϕ = (10)(0.55) = 5.5 md.\)

The critical hydraulic gradient can be obtained using the following formula:

i_c = (e_c – 1)tanϕ ……(3

)where,e_

Critical hydraulic gradient is given as\(,i_c = -0.45 < 0\)

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Answer:

Pour déterminer le nombre de gélules de 500 mg de paracétamol que l'usine de fabrication peut produire à partir de 5 tonnes de paracétamol, nous devons effectuer quelques conversions.

Tout d'abord, nous devons convertir les 5 tonnes en milligrammes, car la quantité de paracétamol par gélule est exprimée en milligrammes.

1 tonne équivaut à 1 000 000 de grammes (ou 1 000 000 000 de milligrammes). Donc, 5 tonnes équivalent à 5 000 000 de grammes (ou 5 000 000 000 de milligrammes).

Maintenant, pour déterminer le nombre de gélules de 500 mg que nous pouvons produire, nous divisons la quantité totale de milligrammes par le dosage de chaque gélule.

Nombre de gélules = Quantité totale de milligrammes / Dosage par gélule

Nombre de gélules = 5 000 000 000 mg / 500 mg

Nombre de gélules = 10 000 000

Donc, à partir de 5 tonnes de paracétamol, l'usine de fabrication peut produire 10 000 000 de gélules de 500 mg chacune.