I need help with this Pre-Cal question

If P = (X, Y) is a point in the given square, then X and Y are i.i.d random variables each with distribution

[tex]\displaystyle P(X = x) = \begin{cases}\dfrac14 & \text{if } -2 \le x \le 2 \\ 0 & \text{otherwise}\end{cases}[/tex]

and so the joint density of X and Y is

[tex]\displaystyle P(X = x, Y = y) = \begin{cases}\dfrac1{16} & \text{if }-2 \le x \le 2 \text{ and } -2 \le y \le 2 \\ 0 &\text{otherwise}\end{cases}[/tex]

We want to find P(X² + Y² ≤ 1). Points that satisfy this inequality lie in the set

R = {(x, y) : -1 ≤ x ≤ 1 and -√(1 - x²) ≤ y ≤ √(1 - x²)}

but we can more easily describe the region in polar coordinates by setting

x = r cos(t) and y = r sin(t)

so that the set R is identical to

R' = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}

Integrate the joint density over R' :

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_R \frac1{16} \, dx \, dy[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \iint_{R'} \frac r{16} \, dr \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \int_0^1 \frac r{16} \, dr \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \int_0^{2\pi} \frac{1^2 - 0^2}{32} \, dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac1{32} \int_0^{2\pi} dt[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \frac{2\pi-0}{32}[/tex]

[tex]\displaystyle P(X^2 + Y^2 \le 1) = \boxed{\frac{\pi}{16}}[/tex]

Answer:

The answer is $2.52.

Step-by-step explanation:

56 x .045= $2.52

Answer:

I think its 5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

y=2/x=1    y=4/x=4

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

rise over run = 4/-2 = -2

Using the percentage method, the amount that Mitch's employer is going to withhold is $29.979

Now, the amount subject to withholding from his total wage payment is;

Provided that the weekly taxable wage is more than $195 but not up to $645; Then, by using the percentage method, the Federal income tax can be computed as:

Therefore, we can conclude that the amount that Mitch's employer is going to withhold is $29.979

Learn more about taxable income here:

https://brainly.com/question/17347618?referrer=searchResults

[tex]\huge\bold{\purple{\bold{⚡EuroNow⚡}}} [/tex]

[tex]\huge\underline\mathtt\colorbox{cyan}{Its easy}[/tex]

The function for EuroNow has a greater rate of change

Answer:

Hey just search up an algebraic calculator I finished my homework with it lol

Step-by-step explanation:

9514 1404 393

Answer:

  7

Step-by-step explanation:

Of the 9 2-digit numbers ending in 6, only 2 are perfect squares: 16 and 36. The other 7 are not perfect squares.

Answer:

positive; sence it's starting from the bottom and going up its positive

Answer:

y=15x

Step-by-step explanation:

Plug in the numbers given and the equation works.

Step-by-step explanation:

cross multiply

so it will be

2y= -1x+5

2y+x=5

thats the only part i know

Answer:

15/64

Step-by-step explanation:

Evaluate:

[(1/2)²-(1/4)³]

We have to find the value of expression ?

Explanation:-

Given that

[(1/2)²-(1/4)³]

⇛ [{(1/2)×(1/2)}-{(1/4)×(1/4)×(1/4)}]

⇛ [{(1×1)/(2×2)}-{(1×1×1)/(4×4×4)}]

⇛ [(1/4)-(1/64)]

LCM of 4 and 64 = 64

⇛ [(1×16)-(1×1)]/64

⇛ (16-1)/64

⇛ 15/64

The value of the given expression is 15/64.

Answer:

that you can define a tangent relationship between a line and an arc. If the adjoining elements change, the tangent relationship is maintained between the elements. Geometric relationships control how a sketch changes when edits are made.

Step-by-step explanation:

i took this i guess and it was gud

The answer is 18, 0

You gotta trust me

Answer:

49

Step-by-step explanation:

Multiply out (a+b)^2

(a+b)^2 = (a+b)(a+b) = a^2 + ab + ba + b^2 ; not ab = ba so,

= a^2 + 2ab + b^2 = a^2 + b^2 + 2ab ; now subtitue in given values

=25 + 2(12) = 25 + 24 = 49

So (a+b)^2 = 49

--------------------------------

32/48

2/3

<3

Answer:

A. 2/3

Step-by-step explanation:

32 = 2 x 16

48 = 3 x 16

32 / 48

= ( 2 x 16 ) / ( 3 x 16 )

= 2 / 3

Answer:

you have to show a diagram or I can't help you

Answer:

5x pounds

Step-by-step explanation:

Here's the solution if you need, hope it's help

Answer:

what type of math is this?

Step-by-step explanation:

Answer: In the tenth year your rent would be 2440 a month.

Hope this helps!

Answer:

y=x-1

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the points (7, 6) and (-2, -3)

There are 3 ways to write the equation of the line:

The most common (and usually, the easiest way) would be slope-intercept form, so let's write it that way

First, we'll need to find the slope of the line

The slope can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have two points, which is needed, but let's label their values in order to avoid any confusion:

[tex]x_1= 7\\y_1=6\\x_2=-2\\y_2=-3[/tex]

Now substitute these values into the formula to find the slope (m):

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-3-6}{-2-7}[/tex]

Subtract the numbers

m=[tex]\frac{-9}{-9}[/tex]

Divide

m=1

The slope of the line is 1

So far, we can write the equation of the line as this:

y=1x+b, or y=x+b

We'll need to find b

As the equation passes through both (7,6) and (-2, -3), we can use either one of them to solve for b

Taking (7, 6) for instance, substitute 7 as x and 6 as y:

6=1(7)+b

Multiply

6=7+b

Subtract 7 from both sides

-1=b

Now substitute -1 as b:

y=x-1

Hope this helps!

Distance:-

[tex]\\ \sf{:}\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf{:}\Rrightarrow \sqrt{(5+5)^2+(5-0)^2}[/tex]

[tex]\\ \sf{:}\Rrightarrow \sqrt{10^2+5^2}[/tex]

[tex]\\ \sf{:}\Rrightarrow \sqrt{125}[/tex]

[tex]\\ \sf{:}\Rrightarrow 11.2[/tex]

Answer:

8%

Step-by-step explanation:

4/50 = 0.08 = 8%

Steps to solve "what percent is 4 of 50?" If you are using a calculator, simply enter 4÷50×100 which will give you 8 as the answer.

Answer:

Step-by-step explanation:

Answer:

Scale factor = 2.5.

Step-by-step explanation:

Work out the lengths of the corresponding sides.

The scale factor is the ratio of one side to the other.

Take the smallest length in both triangles.

Blue triangle:

length = √((7.5-2.5)^2 + (12.5-5)^2) = 9.0139 units.

Red triangle:

length = √((3-1)^2 + (5-2)^2) =3.6056

So the scale factor

= 9.0139/ 3.6056

= 2.5.

Answer:

y = -4x - 3

Hope this helps and if it did maybe mark me as brainliest : ) ?

Answer:

i think i'ts D. (x +2)

Step-by-step explanation:

Answer:

the slope is 1/4. the equation would be y=1/4x-7 I think

Step-by-step explanation: