In a parking lot,there are 16 silver cars, 8 blue cars ,and 10 red cars . A car leaves the parking lot. What is the probability that it is
a: a silver car?
b: a blue car?
c: a red car?
d: suppose that the first car that leaves is a silver car . What is the probability that the second car that leaves is not a silver car?

Just break it up,

12*6 + 3*9 + 2*2

72 + 27 + 4

103 yd^2 <--

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:

Step-by-step explanation:

Answer:

2/4

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

0.2x = 12

Same as: 1/5x = 12

Multiply both sides by 5

x = 60

0.3 * 60 = 18

The number of hydrogen atoms present in the sculpture of earth if the mass of earth is 829 kg is 4.145 × 10²⁹.

Given that,

Mass of the sculpture of the earth = 829 kg

We know that,

Mass of an hydrogen atom = 2 × 10⁻²⁷ kg

Number of hydrogen atoms = Mass of earth / Mass of hydrogen atom

                                              = 829 / 2 × 10⁻²⁷

                                              = 414.5 × 10²⁷

                                              = 4.145 × 10²⁹

Hence the required number of atoms is 4.145 × 10²⁹.

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Answer: a

Step-by-step explanation:

Answer:the answer is The container on the left is made of 2 centimeters squared more plastic.

Step-by-step explanation:

i took the test

The container on the right is made of 2 centimeters squared more plastic.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given two rectangular containers.

We have to find the surface area of both the containers.

Surface area of a rectangular prism = 2[(l × w) + (w × h) + (l × h)]

Here l, w and h are the length, width and height of the rectangular prism.

For the first rectangular prism,

Surface area = 2 [(5 × 4) + (4 × 7) + (5 × 7)] = 166 cm²

For the second rectangular prism,

Surface area = 2 [(4 × 3) + (3 × 10) + (4 × 10)] = 164 cm²

Hence the container on the right is made of 2 centimeters squared more plastic.

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Answer:

The area of the shaded region is 36.

In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. This means that line segment AE is parallel to line segment CD and is half as long, and line segment BE is parallel to line segment AD and is also half as long.

Since AE is half as long as CD, and CD is twice as long as AE, we can say that CD is equal to 2 * AE. Similarly, since BE is half as long as AD, and AD is twice as long as BE, we can say that AD is equal to 2 * BE.

Since AD is equal to 2 * BE and CD is equal to 2 * AE, the lengths of AD and CD are equal. This means that the shaded region is a parallelogram with sides of equal length.

The area of a parallelogram is equal to the product of its base and height. In this case, the base of the parallelogram is 6 (the length of side BC) and the height is AE + BE (the combined length of the two sides of the parallelogram).

We know that AE is half as long as CD, and CD is twice as long as AE, so CD is equal to 2 * AE. Since CD is equal to 2 * AE, AE is equal to CD / 2. Since CD is equal to 11 (the length of side AB), AE is equal to 11 / 2 = 5.5.

Similarly, we know that BE is half as long as AD, and AD is twice as long as BE, so AD is equal to 2 * BE. Since AD is equal to 2 * BE, BE is equal to AD / 2. Since AD is equal to 6 (the length of side BC), BE is equal to 6 / 2 = 3.

The combined length of AE and BE is 5.5 + 3

Answer:

no

Step-by-step explanation:

in the first equation you would be distributing so it would be 5a+5b but in the second its just 5a+b

Answer:

x= 8.9 cm

Step-by-step explanation:

First, since we know that the radius of the circle is 5 centimeters, we know that the diameter of the circle and the hypotenuse of the triangle is 10 centimeters long. Then you use the pythagorean theorem to find out the length of side x. The equation would be: 4.5^2 + x^2= 10^2. Next, you simplify the equation by squaring the squares to get. 20.25 + x^2= 100. Finally, you would subtract 100 and 20.25 to get 79.75 and take the square root of that number to get your x value. x= \(\sqrt{79.75}\). When you do this equation you come out with x=8.93028554975 and then round it to the nearest tenth which is 8.9 cm.

Answer:

So you need to solve for x and y so to find x and y you do -3+3 and that would get you to -1 so that would mean that y=3 and x=2 because 3+2+-1=4 then in the second problem thing it would be x+y to get 3 i hope that this makes sence now. :)

Step-by-step explanation:

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

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Answer:

1 = 58°

2 = 32°

3 = 32°

Step-by-step explanation:

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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The form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

To evaluate the polynomial \(y = x^3 - 5x^2 + 6x + 0.55\)at x = 1.37 using 3-digit arithmetic with chopping, we substitute x = 1.37 into the expression:

\(y = (1.37)^3 - 5(1.37)^2 + 6(1.37) + 0.55\)

Calculating each term;

\((1.37)^3\)= 2.559

5\((1.37)^2\)= 9.415

6(1.37) = 8.22

Substituting these values into the expression for y,

y = 2.559 - 9.415 + 8.22 + 0.55

y = 1.914

Now, let's move on to part (b).

We will express y as y = ((x - 5)x + 6)x + 0.55,

Now using 3-digit arithmetic with chopping.

Then, we substitute x = 1.37 into the expression:

y = ((1.37 - 5) 1.37 + 6) 1.37 + 0.55

Calculating each term separately:

(1.37 - 5) = -3.63

-3.63 x 1.37 = -4.98

-4.98 + 6 = 1.02

1.02 x 1.37 = 1.3974

Finally, adding 0.55:

y = 1.3974 + 0.55

y = 1.9474

Now, let's compare the percent relative round-off errors in both cases.

In part (a), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was also 1.914. Therefore, the percent relative round-off error is:

(1.914 - 1.914) / 1.914 x 100 = 0%

In part (b), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was 1.9474.

Therefore, the percent relative round-off error is:

(1.9474 - 1.914) / 1.914 x 100 ≈ 1.741%

Therefore, in this comparison, we can conclude that the form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

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a : 10<x<=20

b: 20<x<=30

Answer:

D) -6 meters per minute

Step-by-step explanation:

\(\mathsf{rate \ of \ change =\dfrac{change \ in \ y}{change \ in \ x}}\)

\(\implies \mathsf{rate \ of \ change =\dfrac{250-280}{5-0}=-6 \ meters \ per \ minute}\)

\(↬rate \: of \: change = \frac{change \: in \: y }{change \: in \: x}\)

\(↬rate \: of \: change = \frac{250 - 280}{5-0} = -6 \: meters \: per \: minute \)

Answer :- \(\small\bold\red{-6 \: meters \: per \: minute}\)

Answer:

1.75x?

Step-by-step explanation:

I'm not sure if it has to be multiple numbers

Answer:

9

Step-by-step explanation:

x/9 = 1

Multiply both sides by 9

x = 9

Also, any number over itself is equal to 1.

no

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

6^-2 = 1/6^2 = 1/36.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Answer:

14⁻⁵

Step-by-step explanation:

Dividing two exponents with the same base has the effect of subtracting the bottom exponent from the top one. Following that rule, we can simplify our fraction like this:

\(\dfrac{14^{-3}}{14^2}=14^{-3-2}=14^{-5}\)

Answer:

1/14^5

Step-by-step explanation:

14^-3 can be rewritten as 1/14^-3

When doing so you are left with 1/(14^2)(14^3)

Simplify: 1/(14^5) because when multiplying exponents with common bases, you add the exponents.

Answer:

2x - 12

Step-by-step explanation:

Given:

-3(6x+4)+20x

Distribute:

-18x-12+20x

Combine like terms:

2x-12

Hope this helps, have a nice day :))

Answer:

3 8 + 1 2

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