Find the product and explain the process and reasoning. 0.79 x 3.7

The value of a house decreases at a steady rate of 20% each year. What is the total percentage loss (to the nearest integer) in

Westkost [7]

Answer: The total percentage loss would be 67%.

Step-by-step explanation:

Since we have given that

Rate of decline each year = 20%

Number of years = 5

We need to find the total percentage loss in value of the house at the end of 5 years.

So, Total percentage loss would be

$1-(1-\dfrac{r}{100})^5\\\\=1-(1-\dfrac{20}{100})^5\\\\=1-(\dfrac{4}{5})^5\\\\=1-(0.8)^5\\\\=0.67\\\\\approx 67%$

Hence, the total percentage loss would be 67%.

8 0

3 years ago

100, percent is shown on the following tape diagram.How many feet are in 3 miles?

lbvjy [14]

Answer: 15840

Step-by-step explanation:

8 0

2 years ago

Find the slope of the line passing through the points (−3,−8) and (5,6)

Mrac [35]

The line passing through it is y=7/4x-11/<span>4</span>

7 0

3 years ago

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Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

a.

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

Which of the following statements could be true when a transversal crosses parallel lines? Select all that apply.

bezimeni [28]

<span>Complementary angles are formed.
</span>

4 0

3 years ago

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