Answer:
Let’s solve this problem step by step. Since a + b = 28 and a = 2b + 7, we can substitute the value of a in the first equation to get 2b + 7 + b = 28. Solving for b, we get 3b + 7 = 28, which means 3b = 21 and b = 7. So, the second number is 7.
Some friends start jumping rope during recess at 12:22.They jump rope for 24 minutes.Show and write the they stop jumping rope.Circle A.M or P.M.
Answer:
They would stop jumping rope at 12:46
Step-by-step explanation:
I'd probably say P.M considering the fact that I don't think kids would be having recess at midnight
i need the whole problem done plus the steps to it please, im stressed and its due soon
Total Surface Area of the Triangular prism = 30 ft².
Here, we have,
The triangular prism is attached.
The triangular prism shown has 2 triangular faces and 3 lateral faces.
here, we have,
Base of the triangle =2 ft
Height of the Triangle =3 ft
Area of one Triangular Face is:
A = 1/2 * 2 * 3 = 3 ft²
The dimensions of the lateral rectangles are:
2 ft by 3 ft
3 ft by height 3 ft
3 ft by height 3 ft
Therefore, total surface area of the triangular prism
=2(Area of one Triangular Face)+Area of 3 rectangular faces
= 2 *3 + ( 2*3 + 3*3 + 3*3)
= 6 + 24
= 30 ft²
Total Surface Area of the Triangular prism = 30 ft².
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Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
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 [tex]= $50,000 - $10,000 = $40,000[/tex]
Year 2:
Book value = Initial investment - (2 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (2 \times$10,000) = $30,000[/tex]
Year 3:
Book value = Initial investment - (3 [tex]\times[/tex] Depreciation expense per year)
Book value = $50,000 - (3 [tex]\times[/tex] $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (4 \times $10,000) = $10,000[/tex]
Year 5:
Book value = Initial investment - (5 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (5 \times $10,000) = $0[/tex]
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 [tex]\times[/tex] (Salvage value - Book value)
For Year 5:
Tax on salvage value[tex]= 0.30 \times ($10,000 - $0) = $3,000[/tex]
For Year 4 (if scrapped):
Tax on salvage value[tex]= 0.30 \times ($15,000 - $10,000) = $1,500[/tex]
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:
[tex]PV = CF / (1 + r)^t[/tex]
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 [tex]= $10,000 / (1 + 0.12)^1 = $8,928.57[/tex]
PV Year 2 [tex]= $0 / (1 + 0.12)^2 = $0[/tex]
PV Year 3 [tex]= $0 / (1 + 0.12)^3 = $0[/tex]
PV Year 4 [tex]= $13,500 / (1 + 0.12)^4 = $9,551.28[/tex]
PV Year 5 [tex]= $7,000 / (1 + 0.12)^5 = $4,474.39[/tex]
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%.
Which polynomial function could be represented by the graph below?
1. What are two significant advantages of a 401(k) over an IRA?
Here are two significant advantages of a 401(k) over an IRA:
Higher Contribution LimitsEmployer Contributions and MatchingThe two significant advantages of a 401(k) over an IRAHigher Contribution Limits: 401(k) plans allow for higher annual contributions compared to IRAs. The contribution limit for a 401(k) is $19,500 (or $26,000 for individuals aged 50 and older), while the limit for an IRA is $6,000 (or $7,000 for individuals aged 50 and older).
Employer Contributions and Matching: 401(k) plans often offer employer contributions and matching programs. Employers may contribute to an employee's 401(k) account, adding to their retirement savings without any direct cost to the employee.
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Which of the following represents the equation of the trigonometry function graphed below?
The equation of the trigonometric function graphed is A) f(x) = 3 sin (x) - 2.
Given a graph of the trigonometric function.
We have to find the equation of the trigonometric function.
For x = π/2, y = 1
Also, when x = 3π/2, y = -5
A) If the function is,
f(x) = 3 sin (x) - 2,
When x = π/2
f(x) = 3 sin (π/2) - 2
= 3(1) - 2
= 1
When x = 5π/2
f(x) = 3 sin (5π/2) - 2
= 3 (-1) - 2
= -5
Hence the correct option is A.
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Find the maximum for the profit function,
P = 2x+10y
subject to the following constraints.
4x + 2y ≤ 5
-3x+y 2-2
X>0
(y ≥0
4x + 2y ≤ 5
-3x + y 2 -2
Round your answer to the nearest cent (hundredth).
Answer:
The maximum value of the profit function occurs at the corner point with the highest value, which is P2 = 25.
Therefore, the maximum profit is $25.
Step-by-step explanation:
Which three lengths could be the lengths of the sides of a triangle?
Any three lengths that satisfy the triangle inequality theorem can form the sides of a triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In order for three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider three lengths: a, b, and c.
To determine if they can form a triangle, we need to check the following conditions:
a + b > c
a + c > b
b + c > a
If all three conditions are true, then the lengths a, b, and c can form a triangle.
For example, let's consider the lengths 3, 4, and 5.
3 + 4 > 5 (True)
3 + 5 > 4 (True)
4 + 5 > 3 (True)
Since all three conditions are true, the lengths 3, 4, and 5 can form a triangle.
Therefore, any three lengths that satisfy the triangle inequality theorem can be the lengths of the sides of a triangle.
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