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3 years ago

Find the value of x. Select one: a. 2.3 inches b. 3.3 inches c. 4.1 inches d. 6.1 inches

Mathematics

1 answer:

spayn [35]3 years ago

6 0

Answer:

c 4.1 inches

Step-by-step explanation:

The circumference of a circle is given by

C = 2*pi*r

The sector is only 78 degrees

Take the fraction of a circle and multiply by the circumference to find the length x

x = C* 78/360

= 2 * pi *r * 78/360

= 2 * pi *3 * 78/360

Using 3.14 for pi

= 4.082

Rounding to the nearest tenth

x = 4.1 inches

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A movie rental company offers a membership plan that costs $10/month and charges $2 to rent each movie. How many movies can a me

Brums [2.3K]

Answer:

See below

Step-by-step explanation:

linear equation: y=2x+10

x=cost per movie rented

10=$10 for the membership

24=2x+10 (24 being total you want to spend)

subtract 10 from each side

14=2x

divide by 2

7=x

He can rent no more than 7 movies if he want to spend $24 or less in the month

8 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]

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

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

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Marta_Voda [28]

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