The points ( 4,0 ) and ( 7, 6) lie on a particular line What is its equation in slope-intercept form of this line?

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:

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

Step-by-step explanation:

Answer:

y = -4x - 3

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

Answer:

26

Step-by-step explanation:

a^2-(b+c)= (-8)^2-(17+21)=64-38=26

[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

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

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:

75/96 or in its simplest form, 25/32

Step-by-step explanation:

1. Convert both fractions into improper fractions

2. Use KFC

15/8 ÷ 12/5 = 15/8 × 5/12

Hope this help!

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:

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

Answer:the 3rd one

Step-by-step explanation:

Answer:

use graphs

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer:

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

Answer:

-2

Step-by-step explanation:

rise over run = 4/-2 = -2

Answer:

Wrong order!

Step-by-step explanation:

There's a reason why coordinates are called an "ordered pair", and for every point (a, b) a is the x coordinate and b is the y coordinate. The calculations are correct, the way reporting them are not: the point should be (3.0) and (0,2) - in fact, all points on the x axis are of the form (p, 0) and all points on the y axis of the form (0,q)

Step-by-step explanation:

cross multiply

so it will be

2y= -1x+5

2y+x=5

thats the only part i know

Answer:

a

Step-by-step explanation:

The transformation from Figure 1 to Figure 2 is:

The transformation of 5 units to the right and 3 units down.

Option C is the correct answer.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

A B C D E has points (-3, 5), (-2, 5), (-1, 4), (-2, 3), and (-5, 3).

A' B' C' D' E' has points (2, 2), (3, 2), (4, 1), (3, 0), and (0, 0).

Now,

A = (-3 + 5, 5 - 3) to A' = (2, 2)

B = (-2 + 5, 5 - 3) to B' = (3, 2)

C = (-1 + 5, 4 - 3) to C' = (4, 1)

D = (-2 + 5, 3 - 3) to A' = (3, 0)

E = (-5 + 5, 3 - 3) to E' = (0, 0)

We see that,

There is a translation of 5 units to the right and  3 units to the down.

Thus,

The transformation of 5 units to the right and 3 units down.

Learn more about translation here:

https://brainly.com/question/12463306

#SPJ1

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.

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

Hope this helps!

Answer:

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

Step-by-step explanation:

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!

The answer is 18, 0

You gotta trust me

Answer:

Step-by-step explanation:

(1+25 /100) (1-20/100) (1-50/100)  <1

5/4 x 4/5 x 1/2 <1

Decrease in volume (in percent)

(1+25 /100) (1-20/100) (1-50/100)  x 100

=48.8%

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

Answer:

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Answer:

y + 5x = -7

Step-by-step explanation:

Hello there?

y + 3 = -5(x + 2)

LHS

Open the brackets

= -5x - 10

RHS remains

Combine the two:

y + 3 = -5 - 10

Collecting the like terms and taking the value of x to the LHS

=> y + 5x = - 7

I hope this helps. Have a nice studies

Answer:

The correct answer is D) y = 2x - 5

To find the equation of the line, start by finding the slope. You can do this by using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (1 - -3)/(3 - 1)

m = 4/2

m = 2

Now that we have the slope, we can use it along with either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5

Answer: y=2x-5

the points are 4 points away from each other vertically, and 2 away horizontally. This makes the slope 4/2 or just 2.

take the slope and go backwards until you hit the y axis and the y-intercept is -5

this means the equation is y=2x-5

Answer:

5x pounds

Step-by-step explanation:

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