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AlekseyPX
3 years ago
14

An insured's roof cost $4,000 when installed 5 years ago. It has been damaged by hail and must be replaced. The new roof will co

st $6,000 at today’s prices. If the roof has been depreciating at $200 per year and the insured’s policy is written on the actual cash value(ACV), how much will the policy pay toward the insured's new roof?
Mathematics
1 answer:
hoa [83]3 years ago
5 0

Answer:

ACV=$4,500

Step-by-step explanation:

We have that the actual cash value (ACV) is defined as:

ACV=\dfrac{R\times(E-C)}{E}

Where:

ACV = actual cash value

R = replacement cost or purchase price of the item

E = expected life of the item

C = current life of the item

Then we have R=$6,000, C=5years, and to find the expected life of the item we can use the depreciating of the roof, then if the roof is depreciating $200 each year we just need to divide $4,000 by $200 to find the expected life of the roof:

\dfrac{4,000}{200}=20

Then the espected life of the roof is 20 years, with this result we have all the data, then:

ACV=\dfrac{\$6,000\times (20-5)}{20}=\dfrac{\$6,000\times (15)}{20}=\dfrac{\$90,000}{20}=\$4,500

Then the ACV is $4,500

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A triangle is placed in a semicircle with a radius of 5 yd, as shown below. Find the area of the shaded region.
Svetradugi [14.3K]

Answer:

  14.25 yd^2

Step-by-step explanation:

The triangle area is given by the formula ...

  A = 1/2bh

Here, the base is 10 yd, and the height is 5 yd, so ...

  triangle area = (1/2)(10 yd)(5 yd) = (5 yd)^2 = 25 yd^2

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The semicircle is half the area of a circle with radius 5 yd, so its area is ...

  semicircle area = (1/2)π(5 yd)^2 = 12.5π yd^2 ≈ 39.25 yd^2

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The shaded region is the difference between these areas:

  shaded area = 39.25 yd^2 -25 yd^2 = 14.25 yd^2

7 0
3 years ago
5. (05.03 LC) What is the simplified form of the quantity of x plus 5, all over the quantity of 3x plus 4 + the quantity of x pl
earnstyle [38]

Answer:

B. \frac{4x^{2}+24x+31}{3x^{2}+13x+12}

Step-by-step explanation:

We have been given a rational expression \frac{(x+5)}{(3x+4)}+\frac{(x+4)}{(x+3)} and we are asked to simplify our rational expression.

We can see that our denominators are not equal. Since the two denominators do not share any common factors, the common denominator is simply the product of these two denominators.      

To keep the value of expression same we will multiply the same quantity with numerators and denominators.

\frac{(x+5)(x+3)}{(3x+4)(x+3)}+\frac{(x+4)(3x+4)}{(x+3)(3x+4)}  

Now let us simplify our expression using FOIL.  

\frac{x^{2}+3x+5x+15}{3x^{2}+9x+4x+12}+\frac{3x^2+4x+12x+16}{3x^{2}+4x+9x+12}

\frac{x^{2}+8x+15}{3x^{2}+13x+12}+\frac{3x^2+16x+16}{3x^{2}+13x+12}    

Now we have same denominators, so we can add our numerators.

\frac{x^{2}+8x+15+3x^2+16x+16}{3x^{2}+13x+12}    

Now let us combine like terms.

\frac{(1+3)x^{2}+(8+16)x+15+16}{3x^{2}+13x+12}  

\frac{4x^{2}+24x+31}{3x^{2}+13x+12}  

Therefore, the simplest form of our given rational expression will be \frac{4x^{2}+24x+31}{3x^{2}+13x+12}  and option B is the correct choice.

8 0
3 years ago
1/4 + 7/8 = ?<br> 2/3<br> 5/8<br> 1 1/8<br> 13/4
Marta_Voda [28]

Answer:

c

Step-by-step explanation:

1/4 + 7/8 =

2/8 + 7/8    Convert the 1/4 to the denominator as 8 so we can add the top number.

9/8      Add the top number.

1 1/8     Simplifly the result.

4 0
2 years ago
Read 2 more answers
A number added to itself is one
Ivenika [448]
The number would be .5 I'm pretty sure
6 0
3 years ago
Solve using the Distributive Property
diamong [38]

Answer:

6(5)+(2)5

Step-by-step explanation:

5 0
2 years ago
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