1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dahasolnce [82]
2 years ago
12

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10

%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars? 1. 7 years 2. 0 years 3. 1 years 5. 0 years.
Mathematics
1 answer:
zvonat [6]2 years ago
4 0

The approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

<h3>What is depreciation?</h3>

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

FV=P\left(1-\dfrac{r}{100}\right)^n

Here, (<em>P</em>) is the price of the product, (<em>r</em>) is the rate of annual depreciation and (<em>n</em>) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is n_1. Thus, by the above formula for the first car,

0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}

Take log both the sides as,

\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85

Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is n_2. Thus, by the above formula for the second car,

0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}

Take log both the sides as,

\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14

The difference in the ages of the two cars is,

d=4.85-3.14\\d=1.71\rm years

Thus, the approximate difference in the ages of the two cars, which  depreciate to 60% of their respective original values, is 1.7 years.

Learn more about the depreciation here;

brainly.com/question/25297296

You might be interested in
If you own 3 traditional IRAs and you are 58 years old, your combined pre-tax contributions may be____.
amm1812
1/2 would be the answer

5 0
3 years ago
This is a linear equation/ graph quiz ! please help , my teacher makes no sense to me!
JulijaS [17]

Answer:

(8,5)

Step-by-step explanation:

5x - 2y = 30

coordinates are (x,y) so you plug in 8 for x and solve for y

5(8) - 2y = 30

40 - 2y = 30

subtract 40 from both sides to isolate y

-2y = -10

divide both sides by -2 to isolate y

y = 5

6 0
3 years ago
Read 2 more answers
Rectangle w/area of 91 has dimensions of (x+2) and (2x+3). Solve for dimensions.
Leviafan [203]

Answer:

5unit

Step-by-step explanation: since area of rectangle = length*width

Here length is (x+2) and width is(2x+3)

(x+2)(2x+3)=91

On further solving

2x^2+75x-85=0

2x^2-10x+17x-85=0

2x(x-5)+17(x-5)=0

(2x+17)(x-5)=0

x=5unit

8 0
3 years ago
Which is equivalent to x^3 y^-7
PilotLPTM [1.2K]

For this case we must find an expression equivalent to:

x ^ 3 * y ^ {- 7}

By definition of power properties we have to meet:

a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}

Then, we can rewrite the expression as:

x ^ 3 * \frac {1} {y ^ 7} =\\\frac {x ^ 3} {y ^ 7}

Answer:

\frac {x ^ 3} {y ^ 7}

8 0
2 years ago
Please help me I will give brainliest
andrew11 [14]

Answer:

1st one

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the amount of time.<br> I=$450, P=$2400, r=7.5%<br> Help!
    13·1 answer
  • Find the sum of the value of 8 in 387,562 and the value of 7 in 7,328,562
    9·1 answer
  • If x/3 = 18 then what is x?
    9·1 answer
  • Ashleigh rode her bicycle 26.5 miles in 4 hours.which gives best estimate of how far Ashleigh rode in 1 hour
    10·1 answer
  • Nick and Matt want to compare the size of their square computer screens. The only information they know is that Nick's computer
    13·1 answer
  • A theater company with 9 actors is putting on a play that has 3 roles. In how many different ways can the director assign actors
    10·2 answers
  • How long will it take for an airplane that averages 95 miles an hour to fly 1,710 miles?
    6·1 answer
  • Help us this correct
    15·2 answers
  • A store sold 550 video games during the month of December. If this made up 12.5% of its yearly video games scales, about how man
    5·1 answer
  • What are the domain and range?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!