Answers
First, we can find the value of "a" by using the fact that the function is quadratic. We know that the second differences between the values of f(x) are constant, which means that a = 1/2(16 - 2(15) + 12) = -1/2.
Next, we can use the point (0, 15) to find the value of "c". Plugging in x = 0 and f(x) = 15, we get:
15 = (-1/2)(0)^2 + b(0) + c
So c = 15.
Finally, we can use another point, such as (-4, 12), to find the value of "b". Plugging in x = -4 and f(x) = 12, we get:
12 = (-1/2)(-4)^2 + b(-4) + 15
Simplifying this equation, we get:
12 = 8 - 4b + 15
-11 = -4b
b = 11/4
Putting it all together, we get the equation:
f(x) = -1/2x^2 + 11/4x + 15
Related Questions
How yo write 0.044 as a fraction
Answers
The decimal number 0.044 in the fraction form will be 11/250.
Given that:
Decimal number = 0.044
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Multiply and divide the decimal number by 1,000. Then we have
⇒ 0.044 x 1,000 / 1,000
⇒ 44 / 1,000
⇒ 11 / 250
The decimal number 0.044 in the fraction form will be 11/250.
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$4,028 is invested, part at 14% and the rest at 7% . If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 7% by $313.39 , how much is invested at each rate?
Answers
$2,835 is invested at 14% and $1,193 is invested at 7%.
We have,
Let x be the amount invested at 14% and y be the amount invested at 7%.
We know that x + y = 4,028 and that the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 7% by $313.39.
The interest earned on x is 0.14x and the interest earned on y is 0.07y.
We can set up an equation based on the given information:
0.14x - 0.07y = 313.39
We can solve for one of the variables in terms of the other:
y = 4,028 - x
Substitute this into the equation we just created:
0.14x - 0.07(4,028 - x) = 313.39
Simplify and solve for x:
0.14x - 281.96 + 0.07x = 313.39
0.21x = 595.35
x = 2,835
Now we can find y:
y = 4,028 - x = 4,028 - 2,835 = 1,193
Therefore,
$2,835 is invested at 14% and $1,193 is invested at 7%.
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5. Find x.
Trapezoids Worksheet
Answers
Answer:
(1/2)(x + 4 + 100) = 3x
x + 104 = 6x
5x = 104, so x = 20.8
what is the answer to this
Answers
The area of the given square is 10 cm².
Given that,
The one square grid is of 1 cm²
Now labeling the figure
Since length of each side of square are equal
Therefore the length of sides of square is nothing but distance between the points (2,5) and (3,2).
Use distance formula
⇒[tex]\sqrt{(3-2)^{2} +(2-5)^{2} }[/tex]
⇒√10
So side of square = √10 cm
Thus area of square = side x side
= √10 x √10
= 10 cm²
Hence area = 10 cm²
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Margo borrows $500, agreeing to pay it back with 6% annual interest after 7 months. How much interest will she pay?
Answers
Margo will pay an interest of $17.50.
To calculate the interest that Margo will pay, we first need to find the interest rate for 7 months.
The annual interest rate is 6%, so the monthly interest rate is:
6% / 12 months = 0.5% per month
Now, we can calculate the interest that Margo will pay on the $500 loan:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the monthly interest rate, and Time is the time period in months.
Plugging in the values, we get:
Interest = $500 x 0.5% x 7 months = $17.50
Therefore, Margo will pay $17.50 in interest.
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Find the volume of the rectangular prism. 5 yd 5 yd 5 yd
Answers
Answer:
To find the volume of a rectangular prism, we multiply its length by its width by its height.
Here, the length, width, and height are all 5 yards, so we have:
Volume = length x width x height
Volume = 5 yd x 5 yd x 5 yd
Volume = 125 cubic yards
Therefore, the volume of the rectangular prism is 125 cubic yards.
PLEASE HELP ME :((
What vector describes the translation from
R
a) shape R to shape T?
b) shape T to shape R?
Y
6-
5 & 3
4-
2-
1-
-6 -5 -4 -3 -2 -1 0
-1-
-2-
--3+
-4-
-5-
-6+
1
+
T
2 3 4 5 6
X
Answers
The vectors that describe the translation between the shapes are <-6, -6> and <6, 6>
What vector describes the translation between the shapesa) shape R to shape T
We are given shapes R and T
The shape R is translated down by 6 units and translated right by 6 units
As a vector, we have the following representation <-6, -6>
b) shape T to shape R?
This is the reverse of the above transformation
i.e. the shape T is translated up by 6 units and translated left by 6 units
As a vector, we have the following representation <6, 6>
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Given the exponential growth function f ( x ) = 81 ( 1.0225 ) x What is the initial value of the function? What is the growth factor, or growth rate of the function (as a percent)?
Answers
The initial value of the function is 81.
The growth factor, or growth rate of the function is 2.25%.
How to the initial value of the function?
An exponential function is a type of function which involves exponents. The general form of the exponential function is f(x) = a(1 + r)ˣ.
Where a is the initial value of the function and r is growth factor, or growth rate of the function.
We have the exponential growth function f(x) = 81(1.0225)ˣ.
Comparing f(x) = 81(1.0225)ˣ with f(x) = a(1 + r)ˣ. We can say:
a = 81
Thus, the initial value of the function is 81.
comparing again, we can say:
1 + r = 1.0225
r = 1.0225 - 1
r = 0.0225
r = 0.0225 * 100
r = 2.25%
Thus, the growth factor, or growth rate of the function is 2.25%.
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A certain sum of money doubles itself in ten years, in how many years will it become two and half times at the same rate of simple interest?
Answers
Let P be the principal amount. After n years at a rate of 10%, the amount becomes:
A = P + (10/100)*P*n
A = P*(1 + 0.1n)
If the amount becomes two and a half times the principal, then:
2.5P = P*(1 + 0.1n)
Dividing both sides by P, we get:
2.5 = 1 + 0.1n
Subtracting 1 from both sides, we get:
1.5 = 0.1n
n = 15
Therefore, the sum of money will become two and a half times at the same rate of simple interest in 15 years.
Find the mode for the following group of data items. If there is no mode, so state.
21, 18, 17, 16, 22, 19, 15, 17
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The mode(s) is/are (Use a comma to separate answers as needed.)
B. There is no mode.
Answers
The mode of the given data set as required to be determined in the task content is; 17.
What is the mode of the data set as required?It follows from the task content that the mode of the given data set is to be determined.
Recall from definition that the mode of a given data set is the observation or data value which occurs most frequently; i.e with the highest frequency.in the data set.
On this note, since 17 appears most frequently in the data set; It follows that the mode is ; 17.
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What is the incorrect statement? Show your work
Answers
The incorrect statement regarding the dilation is given as follows:
3. The original figure was reduced to create the image.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
For this problem, we have that the original triangle was dilated by a scale factor of two, hence the original figure was enlarged to create the image.
(a figure is reduced when the scale factor is less than 1).
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Help please . Find the surface of the area
Answers
The surface area of this cuboid is 130 cm^2
What is a Cuboid?Cuboid is a closed three-dimensional structure surrounded by rectangular faces, which are rectangle plane sections.
How to determine this
The surface area of cuboid is the total area of all its 6 faces.
SA = 2{(Length * Height) + (Width * Length) + (Width * Height)
Where Length = 10 ft
Width = 5 ft
Height = 1 ft
SA = 2{(10*1) + (5*10) + (5*1)
SA = 2(10 + 50 + 5)
SA = 2(65)
SA = 2 * 65
SA = 130 ft^2
Therefore, the surface area of cuboid is 130 ft^2
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Can someone help me with this problem please? I'll give extra points :(
Answers
Answer:
y = 2x + 1.5
Step-by-step explanation:
You can find two points and derive an equation.
Two obvious points are (0, 1.5) and (2, 5.5).
Using the form y = mx + b, you can find the slope m by using the formula [tex](y_1-y_2)/(x_1-x_2)[/tex].
m = (1.5-5.5)/(0-2) = -4/-2 = 2.
You can find b by plugging in your m value and one of the two points.
y = 2x + b
1.5 = 2*0 + b
b = 1.5
Thus, your equation is y = 2x + 1.5.
Find the value of x.
2x +S
60°
Answers
The value of the variable is 11
How to determine the valueTo determine the value of the variable, we need to know the triangle sum theorem.
The triangle sum theorem states that the sum of the angles in a triangle is 180 degrees.
From the diagram shown, we have that;
The angles are;
90 degrees
60 degrees
2x + 8
add the values
90 + 60 + 2x + 8= 180
collect the like terms, we get;
158 + 2x = 180
then,
2x = 22
Make 'x' the subject
x = 11
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HELP EASY ALGEBRA 1 QUADRATICS
The profit P, in dollars, of a small business can be modeled by the function P(x) = 0.3x2 + 7x – 40, where x is the number of units sold. How many units need to be sold for the business to make a profit of $60?
Answers
The two number of units need to be sold for the business to make a profit of $60 is A = 10 units
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = 0.3x² + 7x - 40
At profit of $ 60 , y = 60
60 = 0.3x² + 7x - 40
Subtracting 60 on both sides , we get
0.3x² + 7x - 100 = 0
Multiply by 10 , we get
3x² + 70x - 1000 = 0
And , roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
On simplifying , we get
x = [ -70 ± √ ( 70 )² - 4 ( 3 ) ( -1000 ) ] / 2 ( 3 )
x = [ -70 ± √ ( 4900 + 12000 ) ] / 6
x = ( -70 ± √16900 ) / 6
On simplifying the equation , we get
x = ( -70 ± 130 ) / 6
x = 10 or x = -100/3
The number of units cannot be negative , so x = 10 units
Hence , the values of x at the business has a profit of $ 60 is x = 10 units
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What command bisects and divides angles?
A.
Line Command
B.
Midpoint object snap Command
C.
Endpoint object snap Command
D.
Copy Command
E.
Circle Command
Answers
The command that bisects and divides angles is: A. Line Command.
What is a line command?You must draw two lines starting at the angle's terminus and extending to any point on the angle in order to bisect an angle using the Line command. Next draw a line through the angle's vertex and the intersection of the two lines you just drew using the "bisector" tool from the "Object Snap" menu.
You can draw a line from the angle's vertex to any point on the angle and then use the "Divide" command to divide that line into the necessary number of segments to divide an angle using the Line command. Angles are divided into equal pieces at the spots where the divided line crosses them.
Therefore the correct option is A.
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a. What is the number of degrees of freedom that should be used for finding the critical value ta/2?
b. Find the critical value ta/2 corresponding to a 95% confidence level.
c. Give a brief general description of the number of degrees of freedom.
Answers
a. The number of degrees of freedom that should be used for finding the critical value to/2 is 49.
b. Using a t-distribution table or a calculator, we get: by/2 = 2.0096 (rounded to four decimal places)
c. The correct option is D. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
a. The number of degrees of freedom that should be used for finding the critical value to/2 is given by the formula df = n - 1, where n is the sample size.
Therefore, in this case, df = 50 - 1 = 49.
b. To find the critical value tα/2 corresponding to a 95% confidence level, we need to use a t-distribution table with 49 degrees of freedom.
For a two-tailed test at the 0.025 level of significance (α/2), we find that tα/2 = 2.0096 (rounded to four decimal places).
Therefore, by/2 = 2.0096.
c. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
This restriction is typically imposed when estimating a population parameter from a sample statistic. The number of degrees of freedom is determined by subtracting 1 from the sample size (n-1).
The concept of degrees of freedom is important in statistical inference and hypothesis testing, as it affects the critical value used in determining whether a hypothesis is statistically significant.
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An object is thrown upward from the top of a 64-foot building with an initial velocity of 48 feet per second. The height h of the
object after t seconds is given by the quadratic equation h= -16t² +48t+ 64. When will the object hit the ground?
The object will hit the ground when the time is how many seconds..
Answers
The object will hit the ground after 4 seconds.
We have,
The object will hit the ground when its height is zero.
So we need to solve the equation:
h = -16t² + 48t + 64 = 0
We can simplify this equation by dividing both sides by 16:
-t² + 3t + 4 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = -1, b = 3, and c = 4.
Plugging in these values, we get:
t = (-3 ± √(3² - 4(-1)(4))) / 2(-1)
t = (-3 ± √(9 + 16)) / -2
t = (-3 ± √(25)) / -2
t = (-3 ± 5) / -2
We get two possible solutions:
t = -1 and t = 4.
Since time cannot be negative, we can discard the negative solution.
Therefore,
The object will hit the ground after 4 seconds.
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Will mark brainliest.
Answers
The equation 2x + (2x + 8) + x + (x - 32) = 360° can be used to solve for x which makes option D correct. The variable x for the arc angles is equal to 64.
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
The arcs together is the circumference of the circle O and they subtends the angle at the center of the circle which is 360° so;
2x + (2x + 8) + x + (x - 32) = 360°
6x - 24 = 360
6x = 360° + 24 {collect like terms}
6x = 384
x = 384/6 {divide through by 6}
x = 64
Therefore, the equation 2x + (2x + 8) + x + (x - 32) = 360° can be used to solve for x, and the variable x for the arc angles is equal to 64.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
The correct option is the last one, if the lines are parallel, the system has no solutions.
For which graph the system of equations has no solutions?To solve a system of equations graphically, we need to graph both equations in the same coordinate axis and find the points where the two graphs intercept, these points are the solutions for the system.
so, if the two graphs never intercept, the system has no solutions, and that will be the case for two parallel lines (parallel lines don't intercept).
Then the correct option is the last one, a system of equations with two parallel lines has no solutions.
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Triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create Triangle 2. How is this done
Answers
The correct statement about the area and perimeter of Triangle 2 is true is:
The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1.
What are the coordinates after dilation of triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create Triangle 2.
Now, We get;
The Triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create Triangle 2.
Hence, The perimeter of triangle 2 is 4.1 times the perimeter of Triangle 1.
And, We know that;
Area of triangle = 1/2 x Base x Height
So, The area of triangle 2 is 16.81 times the area of Triangle 1.
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The missing options are:
A. The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 4.1 times the area of Triangle 1.
B. The perimeter is 8.2 times the perimeter of Triangle 1, and the area is 8.2 times the area of Triangle 1.
C. The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1.
D. The perimeter is 16.4 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1,
Darrell has $4,873 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 2 years?
Answers
Answer:
Darrell will earn $499.48---------------------
Use the formula for compound interest:
[tex]A = P(1 + r/n)^{nt}[/tex]where,
A = the future amount,P = $4873, the initial amount, r = 5% = 0.05, the annual interest rate,n = 1, the number of compounds per year,t = 2, the time in years.Plugging in the values given, we get:
[tex]A = 4873(1 + 0.05/1)^{1\cdot2} = 4873(1.05)^2 = 5372.48[/tex]To find the interest earned, subtract the principal from this amount:
Interest = 5372.48 - 4873 = 499.48please help me i just need this one more
Answers
The value of angle S and angle R is 95⁰ and 110⁰ respectively.
What is the value of angle S and angle R?The value of angle S and angle R is calculated as follows;
11y + 7y = 180 (opposite angles of cyclic quadrilateral are supplementary)
18y = 180
y = 180/18
y = 10
(3x - 5) + (3x + 5) = 180 (opposite angles of cyclic quadrilateral are supplementary)
6x = 180
x = 180/6
x = 30
Angle S = 3x + 5
= 3(30) + 5
= 95⁰
Angle R = 11y
= 11 x 10
= 110⁰
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Please answer all questions by today
Answers
Number 5 is 48, and B
the graph of -1.25x - 5y is shown on the grid. Which ordered pair is in the solution set of -1.25x-5y<2.5?
A. (-4,0.5)
B. (1.5,-2)
C. (-1,0)
D. (0,-1)
Answers
The ordered pair is in the solution set of -1.25x - 5y < 2.5 is (-1, 0) and (-1,0)
The function of -1.25x - 5y < 2.5
(A) (-4, 0.5)
The value of x = -4
The value of y = 0.5
-1.25(-4) - 5(0.5) < 2.5
5 - 2.5 < 2.5
2.5 < 2.5
Not true
(B) (1.5, 2)
The value of x = 1.5
The value of y = -2
-1.25(1.5) - 5(2) < 2.5
-1.875 + 10 < 2.5
8.125 < 2.5
Not true
(C) (-1, 0)
The value of x = -1
The value of y = 0
-1.25(-1) - 5(0) < 2.5
1.25 < 2.5
True
(D) (0,-1)
The value of x = 0
The value of y = -1
-1.25(0) - 5(-1) < 2.5
+5 < 2.5
Not true
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Futura Company purchases the 76,000 starters that it installs in its standard line of farm tractors from a supplier for the price of $10.70
per unit. Due to a reduction in output, the company now has idle capacity that could be used to produce the starters rather than
buying them from an outside supplier. However, the company's chief engineer is opposed to making the starters because the
production cost per unit is $11.10 as shown below:
Direct materials
Direct labor
Supervision
Depreciation
Variable manufacturing overhead
Rent
Total product cost
Per Unit
$ 4.00
3.20
1.70
1.30
0.50
0.40
$ 11.10
Total
$ 129,200
$ 98,800
$ 30,400
If Futura decides to make the starters, a supervisor would have to be hired (at a salary of $129,200) to oversee production. However,
the company has sufficient idle tools and machinery such that no new equipment would have to be purchased. The rent charge above
is based on space utilized in the plant. The total rent on the plant is $85,000 per period. Depreciation is due to obsolescence rather
than wear and tear.
Required:
What is the financial advantage (disadvantage) of making the 76,000 starters instead of buying them from an outside supplier?
The answer is not $158,160!
Answers
Financial advantage (disadvantage) of making the 40,000 starters instead of buying them from an outside supplier is: $89,700.
Here, we have,
Financial advantage (disadvantage)
First step is to calculate the relevant cost of making starters
Relevant cost= Direct materials+ Direct labor+ Variable manufacturing overhead+ Supervision
Relevant cost=($4×69,000)+ ($3.20×69,000) +($0.60×69,000) + $117,300
Relevant cost=$276,000+$220,800+$41,400+$117,300
Relevant cost=$655,500
Second step is to calculate the relevant cost of buying starters
Relevant cost=$10.80 × 69,000
Relevant cost=$745,200
Third step is to calculate the financial advantage
Financial advantage=$745,200-$655,500
Financial advantage=$89,700
Therefore the financial advantage is $89,700.
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What is the measure of angle k?
102
118
134
156
Answers
Answer:
118 degrees because it’s opposite of angle M which is also 118
Step-by-step explanation:
pls mark brainliest
118 degrees because it's opposite of angle M which is also 118
7. The table below represents the relationship
between cups of flour, fand cups of sugar, s
needed to make cookie dough.
Flour and Sugar in Cookie Dough
Cups of flour (f)
1
2
3.5
5.25
Cups of sugar (s)
2
4
7
10.5
Which equation correctly shows the relationship
between the cups of flour, fand cups of sugar, s
needed to make the cookie dough?
A f = 1/s
B s=²f
C s=3.5f
D f = 2s
Answers
The equation that correctly shows the relationship between cups of flour and sugar is f = 1/2s. Option A
How do we form the equation that represents the relationship between flour and sugar?if 1 cup of flour needs 2 cups of sugar.
2 cups of flour need 4 cups of sugar.
3.5 cups of flour need 7 cups of sugar.
5.25 cups of flour need 10.5 cups of sugar.
This only means that the size of sugar is twice the size of flour. Therefore to form our equation, we say
sugar = 2flour. But since the option is not there,
we can also go for
f = 1/2s
3.5 = 1/2 × 7
3.5 = 3.5
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Input Area
Shares outstanding 8,700,000
Share price $46.50
Purchase price of land $65,000,000
Perpetual earnings increase $14,000,000
Current cost of capital 12.50%
Cost of new debt 8%
Optimal equity weight 70%
Optimal debt weight 30%
Tax rate 21%
Output area:
1. If Stephenson wishes to maximize its total market value, would you recommend that it issue debt or equity to finance the land purchase? Explain.
Assets ?? Equity??
Total assets?? Debt & Equity ??
Perpetual aftertax earnings??
NPV of purchases??
3. Balance Sheet
Old assets??
NPV of Project?? Equity??
Total assets?? Debt & Equity ??
New share price? ?
Shares to issue? ??
4. Balance Sheet
Cash???
Old assets??
NPV of project?? Equity ??
Total assets ?? Debt & Equity ??
Total shares outstanding ? ?
Share price ?? ?
PV of earnings increase ?? ?
Balance Sheet
5. Old assets??
PV of project ??? Equity ?? ?
Total assets ?? ? Debt & Equity ??? ?
Value of levered company ?? ? <---VL = VU+TC*D Note*: TC = Tax rate
Balance Sheet
Value unlevered?? ? Debt ?? ?
Tax shield value?? ? Equity ?? ?
Total assets ?? ? Debt & Equity ?? ?
Stock share price???
6. Which method of financing maximizes the per share stock price of Stephenson's equity?
Answers
2.
- Assets: $65,000,000 (purchase price of land)
- Equity: $405,450,000 ($46.5 x 8,700,000)
- Total assets: $470,450,000 ($65,000,000 + $405,450,000)
- Debt & Equity: $470,450,000
- Perpetual aftertax earnings: $14,000,000 / (1 - 0.21) = $11,060,000
- NPV of purchases: -$65,000,000
3.
- Old assets: $405,450,000
- NPV of Project: -$65,000,000
- Equity: $340,450,000 ($405,450,000 - $65,000,000)
- Total assets: $470,450,000 ($405,450,000 + $65,000,000)
- Debt & Equity: $470,450,000
- New share price: $40.41
- Shares to issue: 1,607,166.24
4.
- Cash: -$65,000,000
- Old assets: $405,450,000
- NPV of project: -$65,000,000
- Equity: $275,450,000 ($340,450,000 - $65,000,000)
- Total assets: $340,450,000 ($405,450,000 - $65,000,000)
- Debt & Equity: $275,450,000
- Total shares outstanding: 8,700,000
- Share price: $31.67
- PV of earnings increase: $175,000,000 / 0.125 = $1,400,000,000
- Old assets: $405,450,000
- PV of project: -$65,000,000
- Equity: $340,450,000
- Total assets: $740,450,000 ($405,450,000 - $65,000,000 + $400,000,000)
Let [tex]f(x)=2(3)^x^+^1[/tex]. Evalulate [tex]f(2)[/tex] without using a calculator. Do not include [tex]f(2)[/tex] in your answer.
Answers
[tex]f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54[/tex]
