$29,000;$4 decrease find the new amount given the original amount and the percent of change.

A, B & C form the vertices of a triangle.

Savatey [412]

Answer:

BC = 17.2.

Step-by-step explanation:

Since CAB = 90º, this is a right triangle.

The triangle format is given below:

C

A B

We have that AB = 8.6, and angle B measures 60º.

Length of BC:

BC is the hypotenyse.

Side AB is adjacent to angle B = 60º.

In a right triangle, angle $\alpha$ , it's adjacent side with length s and the hypotenuse h are related by the cosine of the angle, that is:

$\cos{\alpha} = \frac{s}{h}$

In this question, we have an angle of 60º, with has cosine 0.5. We also have that side AB = s = 8.6, and the hypotenuse h is side BC. So

$\cos{\alpha} = \frac{s}{h}$

$0.5 = \frac{8.6}{h}$

$0.5h = 8.6$

$h = \frac{8.6}{0.5}$

$h = 17.2$

BC = 17.2.

4 0

3 years ago

PLEASE HELP! A campground rents bicycles by the hour. The total cost y to rent a bicycle, including deposit, is presented by the

Lelu [443]

The domain and the range of the function are all possible values of the x and y, respectively, that function can take.
The range is given by:

$y_{o}= \frac{3}{3} +12 \\ y_{o}=12 \\ \\ y_{e}= \frac{27}{3} +12 \\ y_{e}=21 \\ \\ \boxed {Im=(y\in R \mid 12\leq y \leq 21)}$

The domain is given by:

$\boxed {D=(x\in R \mid 3\leq y \leq 27)}$

4 0

3 years ago

The body of a 154 pound person contains approximately 2×10-1 milligrams of gold and 6×101 milligrams of aluminum. Based on this

charle [14.2K]

Answer:

300

Step-by-step explanation:

6 × 10¹ ÷ 2 × 10-¹

= 300

no of aluminium is 300 times more than that of gold

7 0

3 years ago

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

About 7 of 10 U.S. households have TV remote controls. There were

julia-pushkina [17]

<span>Total households = 127,900,000 Proportion of households having remote control and not 7 : 3 7x + 3x = 127,900,000 10x = 127,900,000 x = 12,790,000 Households having remote control = 7x = 7 X 12,790,000 = 89,530,000 Answer: 89,530,000 households have TV remote controls.</span>

6 0

3 years ago