Determine the solution, if any, to the system of equations below

In the year 1985, a house was valued at $120,000. By the year 2005, the value had appreciated exponentially to $145,000. What wa

11Alexandr11 [23.1K]

Answer:

The annual growth rate between 1985 and 2005 is 0.95%

The value of the house in the year 2010 is $152,018

Step-by-step explanation:

Let the annual growth rate = r

Value of the house in year 1985 = $120,000

Value of the house in year 2005 = $145,000

Time (t) = 2005 - 1985

= 20 years

A = P (1 + r)^t

145000 = 120000 (1 + r) ^20

(1 +r)^20 = 145000 / 120000

(1 +r)^20= 1.2083

(1 +r)^20= (1.2083)^1/20

(1 +r)^20= 1.0095

r = 1.0095 - 1

r = 0.0095

r% = 0.0095 x 100

= 0.95%

Value of the house in year 2010

=145000(1 + r)^5

=145000 (1 + 0.0095)^5

= 145000 x 1.0484

=$152,018

3 0

3 years ago

Which shape is similar to the original shape? A) A B) B C) C D) D

Anna35 [415]

Answer:

I think the answer is A.

Step-by-step explanation:

Original shape: 7 x 5 x 225 x 6 x 12 x 45 = 25,515,000

A: 9 x 5 x 225 x 6 x 35 x 12 = 25,515,000

B: 14 x 10 x 255 x 12 x 24 x 45 = 462,672,000

C: 9 x 7 x 225 x 8 x 15 x 45 = 76,545,000

D: 8 x 4 x 225 x 6 x 12 x 35 = 18,144,000

This is probably not the way you would solve it but this is how I did it. Basically I multiplied all the numbers in each shape together.

(also i'm not quite sure if this is right >.< sorry!)

8 0

2 years ago

Type the single exponent that would appear on the 7: *

liq [111]

You add the exponent. You never multiply it.

Hope this helps!

Say, mind doing me a favor and clicking the brainliest button for me? It would help me tons.

<h2>~~~PicklePoppers~~~</h2>

6 0

2 years ago

Let x denote the lifetime of a mcchine component with an exponential distribution. The mean time for the component failure is 25

aliina [53]

Answer:

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The mean time for the component failure is 2500 hours.

This means that $m = \frac{2500}, \mu = \frac{1}{2500} = 0.0004$

What is the probability that the lifetime exceeds the mean time by more than 1 standard deviations?

The standard deviation of the exponential distribution is the same as the mean, so this is P(X > 5000).

$P(X > x) = e^{-0.0004*5000} = 0.1353$

0.1353 = 13.53% probability that the lifetime exceeds the mean time by more than 1 standard deviations

4 0

2 years ago

Choose the polynomial written in standard form.

Semenov [28]

Answer:

$x^4 + 4x^3 + 10x$

Step-by-step explanation:

A polynomial written in decreasing order of the degree of its monomials ( or single term ) is called its standard form,

In polynomial,

$x^2 + 4x^4 + 10x^6$ ,

Degrees are written in increasing order,

⇒ It is not written in standard form,

In polynomial,

$x^4 + 4x^3 + 10x$ ,

Degrees are written in decreasing order,

⇒ It is written in standard form,

In polynomial,

$x^7 + 4x^3 + 10x^4$ ,

There is no order of degrees,

⇒ It is not written in standard form,

In polynomial,

$x^6 + 4x^3 + 10x^7$ ,

There is no order of degrees,

⇒ It is not written in standard form,

4 0

2 years ago

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