If f(x) = (2x + 1)2 – 3 and g(x) = 2(2x2 + 3), which statement is true?
A. f(-5) = g(4)
B. f(3) = g(0)
C. f(1) = g(1)
D. f(-3) = g(-2)

The synergy from the merger is the increase in annual after-tax cash flow, which is $345,000. To determine the cost of acquisition using stocks, we need to calculate the value of 35% of Firm A's stock.

The synergy from the merger is the increase in annual after-tax cash flow, which is $345,000. To calculate the value of Firm T to Firm A, we need to determine the present value of this increased cash flow. Using the discounted cash flow method with a discount rate of 8%, we divide the increased cash flow by the discount rate to get the value: $345,000 / 0.08 = $4,312,500.

If Firm A chooses to acquire Firm T using 35% of its stock, we need to calculate the value of this stock. The value of Firm A's stock is $19 million, so 35% of that is 0.35 * $19 million = $6.65 million.

To calculate the NPV for the cash acquisition, we subtract the cost of acquisition ($11.5 million) from the present value of the increased cash flow ($4,312,500). The NPV is then $4,312,500 - $11.5 million = -$7,187,500.

For the equity acquisition, we subtract the value of Firm T to Firm A ($4,312,500) from the value of Firm A's stock used for acquisition ($6.65 million). The NPV is $6.65 million - $4,312,500 = $2,337,500.

Based on the NPV calculations, the cash acquisition has a negative NPV of -$7,187,500, while the equity acquisition has a positive NPV of $2,337,500. Therefore, Firm A should choose the equity acquisition approach, as it results in a positive NPV and is more financially advantageous.

Therefore, the value of T to A is $4,312,500, the cost to A for acquisition using stocks is $6.65 million, and the NPV for the equity acquisition is $2,337,500, indicating that Firm A should proceed with the equity acquisition approach.

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If on january 1, year 1, billy co signed a three-year lease for office space The amortization expense on this leasehold improvement that Billy should  record for Year 2 is: $1,000.

Since we were told that the new overhead lighting fixtures is the amount of $2,000 now let determine the  Amortization expense using this formula

Amortization expense = New overhead lighting fixtures / 2 years

Let plug in the formula

Amortization expense =  $2,000 /2

Amortization expense = $1,000

Therefore the  Amortization expense  is the amount of $1,000.

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The complete question:

On January 1 , Year 1, Billy Co. signed a three year lease for office space. The lease required monthly rent of 8,000 for the first year. 8,100 for the second year and 8,200 for the 3rd year. Billy has the option to renew the lease for a fourth year at 8,300 per month. On January 1, Year 2, Billy permanently installed new overhead lighting fixtures at a cost of $2,000. How much amortization expense on this leasehold improvement should Billy record for Year 2?

The solution to the system of equation y = 9x + 2 and 7y = 63x + 14 is x = -1 and y = -7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

y = 9x + 2

multiply the equation by 7:

7y = 63x + 14

-63x + 7y = 14          (1)

And:

-2x + 7y = -47     (2)

To solve by elimination method, subtract equation 2 from 1 to get:

-61x = 61

x = -1

Put x = -1 in the equation:

y = 9x + 2

y = 9(-1) + 2 = -9 + 2 = -7

The solution to the equation is x = -1 and y = -7

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Answer:

Step-by-step explanation:

Given

Solving in steps

Answer:

by using 1 to divide the value

Step-by-step explanation:

the inverse of 5/8 is 8/5.

Answer:

240

Step-by-step explanation:

Answer:

A= 3, 6, 9

B= 7, 14, 21

maybe?

The horizontal distance for the flared sides with a vertical distance of 4 inches must be 40 inches.

In this question, we are dealing with a ramp that smoothly connects to the sidewalk through flared sides. The guidelines state that the flared sides must have a slope of no more than 5.7 degrees, which means that for every 10 units of horizontal distance, there can be no more than 1 unit of vertical distance.

Now, let's talk about the given vertical distance of 4 inches. To find the horizontal distance for the flared sides, we need to use the 1:10 ratio. We can set up a proportion:

1 unit of vertical distance : 10 units of horizontal distance = 4 inches : x

To solve for x, we can cross-multiply:

1 x x = 10 x 4

x = 40 inches

This ensures that the slope of the flared sides does not exceed 5.7 degrees and meets the guidelines for safe and accessible ramp construction.

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Answer:

The value representing one standard deviation  to the right of the mean is 55.

Step-by-step explanation:

The provided data set is:

S = {56, 54, 45, 52, and 48}

Compute the mean and standard deviation as follows:

\(\mu=\frac{1}{n}\sum X=\frac{1}{5}\times [56+54+45+52+48]=51\\\\\sigma=\sqrt{\frac{1}{n}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{5}\cdot {(56-51)^{2}+...+(48-51)^{2}}}=\sqrt{\frac{1}{5}\times 80}=4\)

Compute the value representing one standard deviation  to the right of the mean as follows:

\(X=\mu+1\cdot \sigma\)

    \(=51+(1\times 4)\\=51+4\\=55\)

Thus, the value representing one standard deviation  to the right of the mean is 55.

Answer:

20

Step-by-step explanation:

12 (2 + ) − (4 + )

24-4

=20

Answer:

20

Step-by-step explanation:

Answer:

A.  -5x = -23

Step-by-step explanation:

First you have to simplify the equation - 4(x - 5) + 8x = 9x - 3

-4x + 20 + 8x = 9x -3

9x - 4x = 20 + 3

5x = 23

=> equivalent to answer A.

The equivalent expression is,

⇒ - 5x = - 23

We have to given that,

An expression is,

- 4 (x - 5) + 8x = 9x - 3

Now, We can simplify the expression for equivalent expression,

- 4 (x - 5) + 8x = 9x - 3

Apply distributive property, we get;

- 4x + 20 + 8x = 9x - 3

4x + 20 = 9x - 3

4x - 9x = - 20 - 3

- 5x = - 23

Therefore, The equivalent expression is,

⇒ - 5x = - 23

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Answer:

1.17

Step-by-step explanation:

(MUCH BETTER!)

From the definition of the sin of an angle, you know:

sin(45°) = AC/AB = 4/AB   ⇒   AB = 4/sin(45°) ≈ 5.6569

sin(63°) = AC/AD = 4/AD   ⇒   AD = 4/sin(63°) ≈ 4.4893

Then the difference AB-AD is:

AB -AD = 5.6569 -4.4893 = 1.1676

AB -AD ≈ 1.17 units

Sorry this took me so long to answer!

The probability that exactly two of the orangutans at the zoo will survive is 0.302.

This problem can be solved using the binomial distribution formula, which calculates the probability of obtaining k successes (survivors in this case) in n trials (orangutans in this case) given a probability p of success (orangutan surviving in this case). The formula is:

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

In this case, n = 10, k = 2, p = 0.20 (the probability of an orangutan surviving is 1-0.80 = 0.20). Plugging these values into the formula, we get:

P(2) = (10 choose 2) * 0.20^2 * 0.80^8

P(2) = 45 * 0.04 * 0.16777216

P(2) = 0.302

Therefore, the probability that exactly two of the orangutans at the zoo will survive is 0.302, or approximately 30.2%.

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

Yes it does exist

Step-by-step explanation:

You must be able to add any two sides and get a number greater than the third side in order to be considered a triangle.

In this case that is possible.

Hope this helps!

Answer:

3/14

Step-by-step explanation:

You add!

1/7 + 1/14

= 2/14 + 1/14 // Change 1/7 to 2/14 by doing this: 1x2/7x2

= 3/14

Answer:

( -15, -16 )

Step-by-step explanation:

Plug in the given endpoint into the midpoint formula setting each equation equal to the corresponding midpoint.

\(\frac{-5+x}{2}=-10\\-5+x=-20\\x=-15\\\\\frac{4+y}{2}=-6\\4+y=-12\\y=-16\)

The strategy for generating a hypothesis that does not fit among the options provided is option C) Thinking of things unilaterally.

Introspection, finding exceptions to the rule, and thinking about variables in terms of amount or degrees are all valid strategies for generating hypotheses.

Introspection involves reflecting on personal experiences, thoughts, and observations to generate hypotheses about a particular phenomenon or question.

Finding exceptions to the rule involves identifying instances that do not conform to the expected pattern or generalization, which can lead to the formulation of alternative hypotheses.

Thinking about variables in terms of amount or degrees involves considering how varying levels or quantities of a particular variable may impact the outcome or relationship being studied, which can help generate hypotheses about the nature and direction of the relationship.

On the other hand, "thinking of things unilaterally" is not a recognized strategy for generating hypotheses. The term "unilaterally" typically refers to actions or decisions made by one side or party without considering others.

Hypothesis generation involves considering multiple perspectives, factors, and possibilities, rather than approaching it unilaterally.The correct answer is option c.

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We can make 4 servings of chicken noodle soup using 20 oz of egg noodles.

To determine how many servings of chicken noodle soup can be made from 20 oz of egg noodles, we need to divide the total amount of noodles by the amount required for each serving.

Given that 5 oz of egg noodles are needed for one serving, we can divide 20 oz by 5 oz/serving to get the total number of servings.

20 oz ÷ 5 oz/serving = 4 servings

The serving size may vary depending on the recipe and the individual's appetite, so this calculation is an estimate. Other ingredients such as chicken, vegetables, and broth will also affect the overall serving size and number of servings.

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The graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

We have,

Graph is a type of data structure that consists of a set of nodes (also called vertices) and edges. Each node is connected to other nodes by edges. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. They are also very useful for visualizing relationships between data points in a variety of fields.

The translation of the parent graph of f(x)=√x+3+2 is a vertical shift upward 3 units, followed by a horizontal shift to the right 2 units. This is represented by the bold line in the graph. In terms of the equation, the translation is represented by the addition of the 3 and the 2 to the function. The 3 causes the graph to shift vertically upward and the 2 causes the graph to shift horizontally to the right. As a result, the graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

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complete question:

Below, the graph of f(x) = √x +3 + 2 is sketched in bold. Its parent function f(x)=√x is represented

by the thin curve.

1) Describe the

translation of the parent

graph.

2) How does the translation relate to the equation?

Answer: miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:miles per hour = mi/hr = 17.5mi/0.25hr = 17.5*4mi/0.25*4hr = 70mi/hr

Step-by-step explanation:

18.75 miles in 1/4 hour.

that is the ratio 18.75 / 1/4

but we want the miles in an hour.

so, how many 1/4 are in a whole ?

well, 4.

so we need to multiply the ratio by 4/4 (so that on one hand we multiply the denominator by 4 to make it a whole, and on the other hand we are not changing the value of the ratio) :

18.75 × 4 / (1/4 × 4) = 75 miles / 1 hour = 75 mph.

Answer:

A. $52.50

Step-by-step explanation:

$50 x .05 (5% as a decimal)

This gives you $2.50, add this to the cost of the dress.

Answer:

52.50

Step-by-step explanation:

Find the tax

50 * 5%

50 * .05

2.5

Add the tax to the price of the dress

50 +2.5

52.50

Answer:

♨ \( \text{Question} : \text{Simplify}\)

♨ \(\underbrace{ \text{Required \: Answer : } }\)

First , combine like terms :

Like terms are those which have the same base.

\( \longrightarrow{ \sf{ - 5x + 7x + 8x + 15 - 20}}\)

\( \longrightarrow{ \sf{2x + 8x + 15 - 20}}\)

\( \longrightarrow{ \sf{10x + 15 - 20}}\)

Remember : The negative and positive numbers are always subtracted but posses the sign of bigger integer.

\( \longrightarrow{ \boxed{ \bold{ \text{10x - 5}}}}\)

And we're done!

Hope I helped!

Best regards ! シ

~TheAnimeGirl

\( {m}^{2} + 5m + 7 \\ \\ put \: m = - 2 \\ \\ = {( - 2)}^{2} + 5 \times ( - 2) + 7 \\ = 4 - 10 + 7 \\ = 11 - 10 \\ = 1\)

\(\huge \boxed{\sf 1}\\\\\\\sf Evaluate\ for\ m=-2\\\\(-2)^2+5(-2)+7\\\\4+(-10)+7\\\\=1\)

Answer:

Should be a collective noun.

For example: In addition to those...

Answer:

C.

Step-by-step explanation:

A concave polygon must have atleast an internal angle which is greater than other angles.

\({ \underline{ \blue{ \sf{christ \: † \: alone}}}}\)

Based on the information provided, \(\overrightarrow{r}\) = at a bearing angle of = 59.88° .

We are requested to calculate the overall displacement of the ship, both in magnitude and direction, once it departs the harbor under the stated parameters. First, let's define a bearing.

Angles are generally measured anticlockwise from the positive x-axis, whereas bearing angles are evaluated clockwise from the positive y-axis. A bearing is NOT a standard angle measuring tool.

Therefore, a bearing of 44.0° indicates that this is an angle 90.0° - 44.0° = 46°. This is the angle to be used in the calculations.

We're given that the first displacement is 11.4° at an angle of 46° (which was computed earlier).

Step 1  - Split the above into components

x1 = 11.4 Cos 46°

= 7.92m

y1 = 11.4Sin 46.0°

= 11.4 * 0.71933980033

= 8.2m

The second displacement is a simple 6.2mi due east, that is, the positive

x-direction. The components are thus:

Δx = x1 + x2

= 7.92 + 6.2

= 14.12mi

Δy = 1 + y2

= 8.2 + 0

= 8.2

r = √(x total)² + (y total)²

=√[(14.21)²+(8.2)²]

= √(201.9241 +67.24)

= √269.1641

= 16.4mi

The direction of the displacement vector is given by:

tan Ф = (Δy)/(Δx)

= arctan (8.2/14.12)

= arctan (0.5807365439)

= 30.12°

Recall that we were asked for the bearing angle. The bearing angle is what we get when we subtract 30.12° from 90°.

That is:
= 90 - 30.12

= 59.88°

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Answer:

  72 square units

Step-by-step explanation:

The figure shown has a uniform horizontal cross section, so is equivalent to a rectangle with length 12 and height 6. Its area is given by the rectangle formula:

  A = LW

  A = (12)(6) = 72 . . . . square units

__

Additional comment

Essentially, the semicircle removed from the left side is tacked onto the right side. The rectangle area is unchanged by that.

We need to state the answer in years and months, so we'll convert the decimal part to months:0.419 years = 0.419 x 12 months/year = 5.028 month.

So the final answer is 4 years and 3 months.

To save $16,000 by making deposits of $95 at the end of every month into an account earning interest at 4.4% compounded semi-annually, it will take 4 years and 3 months.

Here's the solution:

First, we'll need to use the formula: \(P = (A / ((1 + r/n) ^{(nt)})) - (R / (r/n))\)

Where: P = the initial deposit

A = the total amount we want to save

R = the monthly deposit

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time (in years) So, for this problem,

we have:

P = 0 (since we don't have any money saved yet)

A = $16,000 R = $95 r = 0.044 (4.4% expressed as a decimal)

n = 2 (since the interest is compounded semi-annually)

t = ?

We'll start by solving for t:

P = (A / ((1 + r/n) ^ (nt))) - (R / (r/n))0 = ($16,000 / ((1 + 0.044/2) ^ (2t))) - ($95 / (0.044/2))

= \(16000 / (1.022 ^{(2t)}) - 4318.18\) (rounded to two decimal places)16000 / (1.022 ^ (2t))

= 4318.18 (rounded to two decimal places)1.022 ^ (2t)

= 3.7060 (rounded to four decimal places)2t

= log 1.022 3.70602t = 6.839t = 3.419

Now we know that it will take approximately 3.419 years to save $16,000 by making deposits of $95 at the end of every month into an account earning interest at 4.4% compounded semi-annually.

But we need to state the answer in years and months, so we'll convert the decimal part to months:0.419 years = 0.419 x 12 months/year = 5.028 month.

So the final answer is 4 years and 3 months.\(P = (A / ((1 + r/n) ^{(nt)})) - (R / (r/n))\)

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It will take approximately 46 years and 1 month (or 11 months) to save $16,000 by making monthly deposits of $95 into the account.

To determine how long it will take to save $16,000 by making monthly deposits of $95 into an account earning interest at 4.4% compounded semi-annually, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

FV is the future value (which is $16,000 in this case)

P is the monthly deposit ($95)

r is the annual interest rate (4.4% or 0.044)

n is the number of compounding periods per year (2, since it's compounded semi-annually)

t is the time in years

Plugging in the given values, we have:

16000 = 95 * ((1 + 0.044/2)^(2*t) - 1) / (0.044/2)

Simplifying the equation, we get:

16000 = 95 * (1.022^(2*t) - 1) / 0.022

Multiplying both sides of the equation by 0.022, we have:

352 = 95 * (1.022^(2*t) - 1)

Dividing both sides of the equation by 95, we get:

3.7052631579 = 1.022^(2*t) - 1

Adding 1 to both sides of the equation, we have:

4.7052631579 = 1.022^(2*t)

Taking the logarithm of both sides of the equation, we get:

log(4.7052631579) = log(1.022^(2*t))

Using logarithm properties, we can bring down the exponent:

log(4.7052631579) = 2*t * log(1.022)

Dividing both sides of the equation by 2 * log(1.022), we can solve for t:

t = log(4.7052631579) / (2 * log(1.022))

Using a calculator, we find:

t ≈ 46.08

Therefore, it will take approximately 46 years and 1 month (or 11 months) to save $16,000 by making monthly deposits of $95 into the account.

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