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schepotkina [342]

3 years ago

11

In a circle, a central angle whose measure is pi/2 radians intercepts an arc whose length is 3pi/2 centimeters. How many centime

ters are in the radius of the circle?

1 answer:

ivann1987 [24]3 years ago

4 0

<span> $\frac{3\pi}{2}$ cm = quarter of circumference

$=\frac{2r\pi}{4} \\ \\=\frac{r\pi}{2} \\ \\ \Rightarrow r=3 \text{ cm}$ </span>

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Which best describes the transformation that occurs from the graph of f(x)=x^2 to g(x)=(x-2)^2+3??

Leokris [45]

answer right 2, up 3

any function with the following form is a transformation from f(x) = x²

g(x) = (x – a)² + b

were a moves the function to the right when a is a positive number and to the left when its a negative number, and b moves the function up when b is positive and down when its negative.

then for a=2 positive and b=3 positive, we have

right 2, up 3

3 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

I need help please and thank you

lys-0071 [83]

Answer: it’s 135

Step-by-step explanation:

4 0

3 years ago

Simplify: StartRoot 324 EndRoot 1. Write the prime factorization of the radicand. StartRoot 324 EndRoot = StartRoot 2 times 2 ti

Savatey [412]

Answer:

18

Step-by-step explanation:

To continue where you left off, ...

$\sqrt{2^2}\times\sqrt{3^2}\times\sqrt{3^2}=2\times 3\times 3=18$

The square root of 324 is 18.

3 0

3 years ago

Read 2 more answers

Pls help with math ASAP

Dafna11 [192]

Answer:

She will need 16 packages

6 0

3 years ago