Ill mark you brainlist plz help if you put something random I will report you!

5. Each pair of polygons below are similar. Show your work! Solve for x:

Stella [2.4K]

Since they are similar, you need to find the ratio of similarity (I made up the term, there is probably a correct one that I can’t remember).

If you divide 16/40, you’ll find that that ratio is 2.5. So then you just multiply 16 x 2.5. You’ll get 18.

18 is the length of the top of the trapezoid.

You set 18=2x+4 and solve it algebraically. Subtract 4 from both sides.

14=2x
Divide by 2 and x=7

(You can also check that the ratio is right by 16/18 is the same decimal value as 40/45. You’ll get .88888...)

4 0

3 years ago

Let U1, ..., Un be i.i.d. Unif(0, 1), and X = max(U1, ..., Un). What is the PDF of X? What is EX? Hint: Find the CDF of X first,

Kryger [21]

Answer:

$E(X)= n \int_{0}^1 x^n dx = n [\frac{1}{n+1}- \frac{0}{n+1}]=\frac{n}{n+1}$

Step-by-step explanation:

A uniform distribution, "sometimes also known as a rectangular distribution, is a distribution that has constant probability".

We need to take in count that our random variable just take values between 0 and 1 since is uniform distribution (0,1). The maximum of the finite set of elements in (0,1) needs to be present in (0,1).

If we select a value $x \in (0,1)$ we want this:

$max(U_1, ....,U_n) \leq x$

And we can express this like that:

$u_i \leq x$ for each possible i

We assume that the random variable $u_i$ are independent and $P)U_i \leq x) =x$ from the definition of an uniform random variable between 0 and 1. So we can find the cumulative distribution like this:

$P(X \leq x) = P(U_1 \leq 1, ...., U_n \leq x) \prod P(U_i \leq x) =\prod x = x^n$

And then cumulative distribution would be expressed like this:

$0, x \leq 0$

$x^n, x \in (0,1)$

$1, x \geq 1$

For each value $x\in (0,1)$ we can find the dendity function like this:

$f_X (x) = \frac{d}{dx} F_X (x) = nx^{n-1}$

So then we have the pdf defined, and given by:

$f_X (x) = n x^{n-1} , x \in (0,1)$ and 0 for other case

And now we can find the expected value for the random variable X like this:

$E(X) =\int_{0}^1 s f_X (x) dx = \int_{0}^1 x n x^{n-1}$

$E(X)= n \int_{0}^1 x^n dx = n [\frac{1}{n+1}- \frac{0}{n+1}]=\frac{n}{n+1}$

6 0

3 years ago

What is the volume of the base of a pyramid is 18 square yards. The height of the pyramid is 5 feet tall if its base is a square

satela [25.4K]

Use the equation for volume of a pyramid (base x width x height)

8 0

3 years ago

Find the equation of a line that passes through the point (2,1) and has a gradient of 2. Leave your answer in the form ax + by =

Arte-miy333 [17]

Step-by-step explanation:

normally, if we have the gradient (or slope of inclination or change rate) and a point, we start using the point-slope form :

y - y1 = a(x - x1)

with (x1, y1) being a point on the line, and a being the slope of gradient (or ... however you want to call it).

y - 1 = 2(x - 2) = 2x - 4

y + 3 = 2x

2x - y = 3

8 0

2 years ago

Select the best answer that defines the circumference of a circle.

Zigmanuir [339]

Answer:

The circumference is the distance around the circle, similar to the perimeter of a polygon.

Step-by-step explanation:

The term "circumference" is often used to refer to the once-around length of any circular or roughly-circular object. One can refer to the circumference of an ellipse or of one's head, for example.

8 0

3 years ago