Select all that apply. Which of the following name an angle in the drawing? ACB CDE ECB BDA

Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Answer:

67.5 kgs.

Step-by-step explanation:

1 pound = 0.45 kg

1 1/2 pounds = 0.45 + 1/2 * 45

= 67.5 kgs.

Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

\((10x - 20) + (6x + 8) = 180\)

First, combine like terms. Like terms are terms that share the same amount of the same variables:

\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)

Next, divide 16 from both sides of the equation:

\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)

12 is your answer.

~

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Answer:

70 students

Step-by-step explanation:

If 40% of all students in Mrs. Well's class got an A, and 28 students got an A, that means that 28 = 40%

To find the total number of students, we need to find 100%

40% = 28

Divide by 4

10% = 7

Multiply by 10

100% = 70

So there are 70 students in Mrs. Well's class.

Hope this helps you! :D

Answer:

p =4

q = -2

Step-by-step explanation:

To mirror is to reflect.  See the picture

⇒I will use the laws of exponents. When you multiply powers of the same base you keep one base and add the exponents.

Below are all the steps in details

\(=9^{-8+(-2)} \\=9^{-8-2} \\=9^{-10} \\=\frac{1}{9^{10} } \\=\frac{1}{3486784401}\)

Answer:

No real solutions

Step-by-step explanation:

Discriminant

\(b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0\)

\(\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}\)

\(\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}\)

\(\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}\)

Given equation:  \(6x^2+6x+3=0\)

\(\implies a=6, \quad b=6, \quad c=3\)

Inputting these values into the discriminant:

\(\implies (6)^2-4(6)(3)=-36 < 0\implies \textsf{no real solutions}\)

Since a kite is a quadrilateral, it has the value of 360 total degrees.

The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

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Answer:

a. unbounded

e. x ≤ 9

Step-by-step explanation:

The interval means all real numbers less than or equal to 9.

Since all numbers to negative infinity are included, it is unbounded.

a. unbounded

e. x ≤ 9

A sketch looks like a number line with a solid dot at 9 and an line pointing left with an arrowhead at the left pointing left.

Answer:

b. unbounded

e. x ≤ 9

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

A bounded interval is an interval that includes both its endpoints.

For the interval (-∞, 9]:

Therefore, the given interval is unbounded.

Inequality notation

Therefore, the given interval is represented by the inequality x ≤ 9.

To sketch the graph on a number line:

To sketch the graph on a coordinate plane:

Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

The probability that less than five items will be sold from the items during the week will be 0.67.

From the complete question, the number of items that were sold in a week was given in a distribution table.

From the table, the probability that there will be less than a total of 5 items sold during that week will be:

= P(3 or 4 items sold) / P(3 or more items sold)

= (0.15 + 0.05) / (0.15 + 0.05 + 0.05 + 0.05)

= 0.20/0.30

= 0.67

In conclusion, the probability is 0.67.

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Answer:

Number 1

Step-by-step explanation:

Vertex is (−1,−13)

\(~~~~~6x^2 +12x -7 =0\\\\\implies x^2 +2x - \dfrac 76=0\\\\\implies x^2+2x = \dfrac76\\\\\implies x^2 +2x +1 = \dfrac 76 +1\\\\\implies (x+1)^2 = \dfrac{13}6\\\\\implies x+1 = \pm \sqrt{ \dfrac{13}6}\\\\\implies x = -1 \pm\sqrt{\dfrac{13} 6}\\\\\text{Hence,}~ x = -1 +\sqrt{\dfrac{13} 6}~~ \text{and}~~ x = -1-\sqrt{\dfrac{13} 6}\)

The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

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The critical value of that used in constructing the confidence interval is (42.512 , 31.688)

We have the following information from the question:

Sample mean, x(bar) = 37.1 bushels per acre

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 5.91 bushels per acre

Degree of freedom = n - 1 = 9

We have to determine the 98% confidence interval for the true mean yield.

We use the formula:

x(bar) ± \(t_c_r_i_t_i_c_a_l\)\(\frac{s}{\sqrt{n} }\)

Plug all the values in above formula:

37.1 ± 2.896\((\frac{5.91}{\sqrt{10} } )\)

37.1 ± 5.412 = (42.512 , 31.688)

Hence, The critical value of that used in constructing the confidence interval is (42.512 , 31.688).

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Answer:

34

Step-by-step explanation:

4(2)-2(7)+40

8-14+40

-6+40=34

4a-2b+40

4x2-2x7+40

8-14+40

-6+40

34 is the answer.

Answer:

c=14•366

14•4 to the nearest tenth

Step-by-step explanation:

using Pythagoras theorem

c^2=a^2+b^2

c^2=7•9^2+12^2

c^2=62•41+144

c^2=206•41

take the square roots of both sides

c=14•3669

14•4 to the nearest tenth

Answer:

8x+12y=120

Step-by-step explanation:

i took the test

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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Answer:

-8

in this the arthmatic difference is table of 2

Answer:

the common d/f is that -2>-4>-6

The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's solve for x:

3(4x - 10) = 2(3x - 30)

First, we can simplify both sides by distributing the coefficients:

12x - 30 = 6x - 60

Next, we'll move all the x terms to one side of the equation and the constants to the other side:

12x - 6x = -60 + 30

Simplifying further:

6x = -30

Finally, we can solve for x by dividing both sides by 6:

x = -5

Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

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Answer:

 50,722 =

 50,000  

+ 0  

+ 700  

+ 20  

+ 2  

Step-by-step explanation:

Answer:

\(\csc(u).sec(u)\)

Step-by-step explanation:

\( \tan(u)+ \cot(u) \\ \\ = \frac{ \sin(u)}{ \cos(u)} + \frac{ \cos(u)}{ \sin(u)} \\ \\ = \frac{ { \sin}^{2} (u) + {\cos}^{2} (u)}{ \sin(u). \cos(u)} \\ \\ = \frac{1}{ \sin(u). \cos(u)} \\ ( \because \: { \sin}^{2} ( \theta) + {\cos}^{2} ( \theta) = 1) \\ \\ = \frac{1}{\sin(u)} \times \frac{1}{\cos(u)} \\ \\ = \csc(u).sec(u) \\ \\ \implies \: \purple{ \bold{ \tan(u)+ \cot(u) = \csc(u).sec(u)}}\)

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

(Sin²u + Cos²u) = 1

The final expression of the trigonometric expression tan(u) + cot(u) is

Cosec(u) x Sec(u)

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Tan (u) + Cot (u)

We know that,

Tan x = sin x / cos x

Cot x = cos x / sin x

Now,

Tan (u) + Cot (u)

= {Sin (u) / Cos (u) + Cos (u)}/ Sin (u)

Simplify by forming into a fraction.

= (Sin²u + Cos²u) / Sin(u)Cos(u)

[ sin² + cos² = 1 ]

So,

(Sin²u + Cos²u) = 1

= 1 / Sin(u)Cos(u)

= 1/Sin(u) x 1/Cos(u)

= Cosec(u) x Sec(u)

Thus,

The final expression of the trigonometric expression tan(u) + cot(u) is

Cosec(u) x Sec(u)

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Answer: 2488.14 m³

Step-by-step explanation:

Volume of the 2 ends make a sphere

V(sphere)= 4/3 \(\pi r^{3}\)       r=6

    =4/3\(\pi\)6³

    =904.779

V(cylinder)= Bh

        = \(\pi\)r²h

        =\(\pi\)6²(14)

        =1583.363

V(total) = V(cylinder) + V(sphere) = 904.779=1583.363

=2488.14 m³

The correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

The associative property of addition states that the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Given that, an expression, (5 + 9) + 10

According to associative property of addition, (a+b)+c = a+(b+c)

Therefore,

(5 + 9) + 10 = 5+(9+10)

= 5+19

= 24

Hence, the correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

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Answer:

\(\displaystyle Point \ A(-2, 5)\\Point \ B(5, 5)\\d = 7 \ units\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A(-2, 5)

Point B(5, 5)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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Answer:

9 dollars or B

Step-by-step explanation:

16.50 (hourly wage) x 6 (hours worked) = 99 dollars

$99/11 deliveries= 9 dollars per delivery.