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The discount rate Karissa received is 12% discount.

In a discounted cash flow (DCF) analysis, the interest rate used to calculate the present value of future cash flows is known as the discount rate. This aids in determining if the present-day capital outlay required to fund a project or investment will be greater than the value of the projected future cash flows from that project or investment.

The WACC and adjusted present value are the two main formulas for calculating the discount rate (APV).

WACC = E/V x Ce + D/V x Cd x (1-T) is the formula for the WACC discount, and

APV = NPV + PV of the impact of financing is the formula for the APV discount.

Take the change in price

65 - 57.20 =7.80

And divide by the original price

7.80/65=.12

Change to percent form

12%

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Answer:

11

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

Currently, there is 1 red circle and 3 blue circles, making the ratio 1: 3.

The ratio 12:3 can be simplified to get 4:1.

Therefore, you will need to add 11 red circles to get the ratio 4: 1.

Answer:

Step-by-step explanation:

Answer:

w ≈ 12.14 cm

Step-by-step explanation:

using the tangent ratio in the right triangle on the left.

let vertical height be x

tan56° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.2}[/tex] ( multiply both sides by 3.2 )

3.2 × tan56° = x , then

x ≈ 4.744

using the cosine ratio in the right triangle on the right

cos67° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{w}[/tex] = [tex]\frac{4.744}{w}[/tex] ( multiply both sides by w )

w × cos67° = 4.744 ( divide both sides by cos67° )

w = [tex]\frac{4.744}{cos67}[/tex] ≈ 12.14 cm (to 2 decimal places )

Answer:

w = 12.14 cm

Step-by-step explanation:

See the attached image. Trigonometric functions will be used

James needs to invest $83226.33 as his principal in order to achieve this goal.

How to Work Out How Much

An asset or item purchased with the intention of generating income or appreciation is referred to as an investment. The term "appreciation" describes a rise in an asset's value over time. When a person buys a product as an investment, they don't intend to use it right away; instead, they plan to use it to make money later on.

Here is the basic interest calculation formula:

I, or simple interest, is equal to PRT/100.

Where:

P represents the primary amount.

R represents the rate.

The letter T represents time.

Modify the values.

2496.79 = P × 1 × 3/ 100

Multiplying by two

3 P = 249679

Create "P" as the formula's

P = 249679/ 3

Count through

P = $ 83226.33

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - [tex]\frac{3}{2}[/tex] x

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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = [tex]\frac{0-3}{0-(-2)}[/tex] = [tex]\frac{-3}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex] , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

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

using (0, 0 )

0 = - [tex]\frac{3}{2}[/tex] (0) + c = 0 + c , so

c = 0

y = - [tex]\frac{3}{2}[/tex] x + 0 , that is

y = - [tex]\frac{3}{2}[/tex] x

The required, each student will pay $10, as per the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The question seems to be incomplete,
Let's assume that the bill is of $50 excluding taxes

Now, each student has to pay = 50 / 5
                                                  = $10 per head

Thus, the required, each student will pay $10, as per the given condition.

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Answer: [tex]10\sqrt{2}[/tex]

Step-by-step explanation:

Angles in an isosceles right triangle are: 90, 45, 45.

The ratio of the sides are: [tex]1:1:\sqrt{2}[/tex]

Side of 90° = 20

Side of 45° = [tex]\frac{20}{\sqrt{2} }[/tex]

[tex]\frac{20}{\sqrt{2} } =[/tex] [tex]\frac{20\sqrt{2} }{\sqrt{2} ^{2} } = \frac{20\sqrt{2} }{2} = 10\sqrt{2}[/tex]

Step-by-step explanation:

No vertical reflection, stretch, or compression has been applied.

Horizontal translation: The graph has been shifted to the right by 122 units.

Vertical translation: The graph has been shifted up by 2 units.

Answer:

Step-by-step explanation:

The cost has two parts; a fixed cost of $29 and a variable cost of $0.12 per minute. So, the total monthly cost for 50 minutes is $35.

Let t be the time elapsed in hours, starting at 8:00 A.M. So t = 0 at 8:00 A.M. and t = 3 at 11:00 A.M. The distance traveled by the train can be expressed as the definite integral of its velocity with respect to time:

distance = ∫(87 mph) dt from t = 0 to t = 3

Since mph is a unit of speed, we need to convert it to a unit of velocity (feet per second) in order to evaluate the integral:

87 mph = 87 miles/hour × 5280 feet/mile = 454840 feet/hour

distance = ∫(454840 ft/hr) dt from t = 0 to t = 3

distance = 454840 ft/hr * t from t = 0 to t = 3

distance = 454840 ft/hr * 3 hours

distance = 1364520 feet

So, the train travels a distance of 1364520 feet from 8:00 A.M. to 11:00 A.M.

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Answer:

Below

Step-by-step explanation:

(5x2 + 2x + 11) − (7 + 4x − 2x2) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2 =

                                                     (5x^2 + 2x^2 ) + ( 2x-4x) +(11-7) =

                                                                7x^2     - 2x   + 4

0.15 cups of flour will be in each pancake.

As per the given data:

Desmond is making chocolate chip pancakes for his whole family.

He uses 3 cups of flour to make the 20 equal-sized pancakes.

Here we have to determine that how many cups of flour will be in each pancake.

Here we use the unitary method to find the number of cups of flour will be in each pancake.

Unitary method: The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Number of cups of flour in each pancake = [tex]$\frac{3}{20}[/tex]

= 0.15

Therefore 0.15 cup of flour in each pancake.

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The radius of the cylinder is 3 cm and the height of the cylinder is 1.27 cm.

The radius of the cylinder is half of the diameter of the cylinder and the value of the radius is calculated as follows;

r = d / 2

where;

r = ( 6 cm ) / ( 2 )

r = 3 cm

The height of the cylinder is calculated as follows;

V = πr²h

where;

h = ( V ) / ( πr² )

h = ( 36 ) / ( π x 3² )

h = 1.27 cm

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Ricky should place the ball along 2nd diamond of top rail from right.

Aim should be towards the 2nd diamond of right rail.

Distance-angle commonly refers to the horizontal distance of an angle that reaches a certain height, which in turn forms a triangle.

Given,

In the Diagram,

Shot of Montana Mike is shown,

Montana started the shot with the ball against the top rail and the ball hit the bottom rail three diamonds from the right rail.

By the figure,

To repeat Montana shot,

Hence, the shot will be repeated by Ricky if ball is placed along the 2nd diamond of top rail from right and aim towards 2nd diamond of right rail.

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Answer:

You should use  [tex]\frac{1}{3}[/tex] orange juice.

Step-by-step explanation:

Set up a proportion

[tex]\frac{3}{5}[/tex] = [tex]\frac{\frac{1}{5} }{x}[/tex]  
This is lime juice  to orange juice.  Cross multiply and solve for x.

3x = [tex]\frac{5}{1 }[/tex] x [tex]\frac{1}{5}[/tex]

3x = 1  Divide both sides by 3

x = [tex]\frac{1}{3}[/tex]

Answer: 1/3 cup of oj

Step-by-step explanation:

Lines r and s have the same slope of 4/9, therefore, they are parallel.

To determine if two lines are parallel or perpendicular, you can use the slope formula. If the slopes of the two lines are equal, the lines are parallel. If the product of the slopes of the two lines is -1, the lines are perpendicular.

The slope formula is: m = (y2 - y1) / (x2 - x1)

For line r:

m = (4 - 8) / (1 - 10) = -4 / -9 = 4/9

For line s:

m = (5 - 9) / (1 - 10) = -4 / -9 = 4/9

Since the slopes of the two lines are equal, they are parallel.

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Answer:

below

Step-by-step explanation:

2x-y =14

-3x+y = -6     add these two equations together....this will 'eliminate' y

-x = 8

x = -8    use this value of x in one of the equations to find y = -30

Answer:

Sharon needs to receive a score of 43 on the final to have an average score of 80.

Step-by-step explanation:

First, let's understand what is being told to us. We are being asked to find the score Sharon needs on the final, or x. Since the final is worth 2 tests, the final is equal to twice the score she receives, or 2x. Next, we need the average of all the tests, including the final, to be equal to 80. It's important to also note that we will be taking the average of 6 scores. Now, let's use all of our information to write an equation to solve:

( 77 + 84 + 72 + 65 + 96 + 2x ) / 6 = 80.   [Combine like terms]

( 394 + 2x ) / 6 = 80   [Multiply by 6]

394 + 2x = 480   [Subtract 394 from both sides'

2x = 86   [Divide both sides by 2]

x = 43

So, Sharon needs to receive a score of 43 on the final to have an average score of 80.

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Composite Functions for : f [ g (x) ] = 3 g(x) + 7 will be f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8

Common functions typically have a subset of the real numbers as their domain. Any integer from the domain may be used to replace a variable.

The domain of a composite function is determined by another function, not by a collection of numbers. We refer to it as "a result of another function. Example:

If: . f (x) = 3x + 7 . f [g(x)] must be found and simplified. g(x) = 5x - 5. Due to the fact that the domain of this function is a function of another function, f (x) is a simple function or just a function.

Let's make the example I gave previously simpler.

G (x) signifies in f "Replace x with g (x) in the function f (x). The Composite function f [g (x)]

we have : f [ g (x) ] = 3 g(x) + 7 . but . g( x) = 5x - 5

replace x in f[ g(x ) ] . by. 5x - 5 and simplify

f [ g(x) ] = 3 ( 5x - 5) + 7 = 15x - 8 **

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The question seems to be wrong

Evaluating Composite Functions for : f [ g (x) ] = 3 g(x) + 7

Answer:Fixed expenses are those that do not change regardless of the level of production or consumption. Variable expenses are those that change in proportion to the level of production or consumption.

Based on the table provided, the following expenses can be considered fixed:

$4,640

$10,304

$2,500

$3,998

These expenses could be considered fixed because they do not appear to be directly related to the level of production or consumption. For example, $4,640 could be tuition fees, which remain the same regardless of how many classes a student takes or how much they use campus facilities.

The following expenses can be considered variable:

$3,000

$700

These expenses could be considered variable because they may be directly related to the level of production or consumption. For example, $3,000 could be the cost of books, which may change depending on the number of classes a student takes. $700 could be spending money for daily needs like food, transportation, or entertainment, which would likely vary depending on how much a student spends.

In conclusion, the distinction between fixed and variable expenses is based on the relationship between expenses and the level of production or consumption. The expenses listed above have been categorized as fixed or variable based on this relationship.

Draw a line connecting the two perpendicular lines, creating a triangle. Calculate the two remaining unknown sukutes, subtract 62 from 180 to get 118 degrees, and divide this by two to get 59 degrees.

What are perpendicular lines?

Perpendicular lines are described in geometry as line segments that join or overlap at right angles. The word 'perpendicular' comes from the Latin word 'perpendicularis,' which means a plumb line.  If two lines AB and CD are parallel, we may express them as AB and CD. The sign indicates that the lines are perpendicular.

Step 1: Draw a line from the center of the windshield to the left side of the windshield. This line should be 90 degrees.

Step 2: Draw another line perpendicular to the first line, going from the center of the windshield to the right side of the windshield. This line should also be 90 degrees.

Step 3: Draw a line connecting the two perpendicular lines, creating a triangle. This line should be 62 degrees.

Step 4: Calculate the two remaining unknown sukutes. To do this, subtract 62 from 180 to get 118 degrees. Then divide this by two to get the two remaining unknown sukutes, which should both be 59 degrees.

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The equation that best represents the relationship is 7x - 4y = -20

From the question, we have the following parameters that can be used in our computation:

x      y

5     13.75

10    22.50

15    31.25

In the above table, we can see that

As x increases by 5

y increases by 8.75

So, the slope is

m = 8.75/5 = 1.75

A linear equation is represented as

y = mx + c

so, we have

y = 1.75x + c

Using the ordered pair, we have

1.75 * 5 + c = 13.75

Evaluate

c = 5

So, we have

y = 1.75x + 5

Express as

4y = 7x + 20

This gives

7x - 4y = -20

Hence, the relaionship is 7x - 4y = -20

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Among the given, only 0.5 can be exactly represented in binary notation with a finite number of bits

Hence, option (d) is the correct choice.

Binary is a base-2 number system in which a number is represented by two states: 0 and 1. We can also refer to it as a true and false condition. A binary number is constructed in the same manner as a decimal number.

Binary data is information expressed or displayed using the binary number system. Binary data is the only type of data that a computer can directly understand and execute. It is represented numerically as a series of zeros and ones.

The binary representation of 0.5 is 0.1_2, and it is the only terminating fraction among the available possibilities.

As a result, it is the only fraction that can be expressed precisely.

All of the other possibilities have a non-terminating fraction portion and hence cannot be expressed accurately with a limited amount of bits.

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The complete question may be:

Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits?

(a) 0.1

(b) 0.2

(c) 0.4

(d) 0.5

(e) All the above

The equation of the circle will be x² +y² +7x +11.

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).

The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.

The general form of the equation of a circle is x² + y² + 2gx + 2fy + c = 0.

The equation can be written as:-

( x - x₁)( x - x₂) + ( y - y₁) ( y - y₂)

( x + 4 ) ( x + 3) + ( y + 1) ( y -1)

x² +7x +12 + y² - 1

x² + 7x + y² +11

Hence, the equation of the circle is x² + 7x + y² +11.

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The instantaneous rate of change of g(x) = 2/(x + 6) at x = 3 is given as follows:

g'(3) = -0.025.

The function for this problem is defined as follows:

g(x) = 2/(x + 6).

The instantaneous rate of change at x = a is defined as follows:

g'(a).

In exponent format, the function is defined as follows:

g(x) = 2(x + 6)^(-1).

Applying the chain rule, the derivative of g(x) is given as follows:

g'(x) = -2(x + 6)^(-2)[x + 6]'

g'(x) = -2/(x + 6)².

At x = 3, the numeric value of the derivative is given replacing the lone instance of x by 3, hence:

g'(3) = -2/(3 + 6)²

g'(3) = -2/81

g'(3) = -0.025.

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Equation for charges of first plan

C₁ = 24.t

Equation for charges of second plan

C₂ = 9t + 2995

If we talk for _199.7__ minutes the two plans will cost the same.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

First plan charges rate of 24 cents per minute

C₁ = 24.t

C₁ is the charge of first plan

t is the number of minutes

Second plan charges $29.95 plus 9 cents per minute.

C₂ = 9t + $29.95

1 dollar = 100 cents

C₂ = 9t + 2995

Where C₂ is the charge of first plan

t is the number of minutes.

Let after x minutes the cost of both plans will be same

C₁ = C₂

24x = 9x + 2995

24x - 9x = 2995

15x = 2995

x = 2995/15

x = 199.667 ≈ 199.7 minutes

Hence, C₁ = 24.t and C₂ = 9t + 2995 are the equations for the charges of first plan and second plan respectively.

After talking 199.7 minutes the cost of two plans will be same.

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