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3 years ago

What is the measure of each interior angle of a regular polygon with 5 sides?

Mathematics

2 answers:

Sedaia [141]3 years ago

5 0

108 degrees because of the equation 180(n-2)/n. 180(5-2)/5= 540/5= 108.

Ann [662]3 years ago

3 0

ANSWER

108°

EXPLANATION

The measure of each interior angle of a regular polygon is given by

$\theta = \frac{(n - 2) \times 180}{n}$

where n refers to the number of sides of the polygon.

From the question we have n=5 in this case.

We substitute to obtain;

$\theta = \frac{(5 - 2) \times 180}{5}$

$\theta = \frac{3\times 36}{1}$

This simplifies to:

$\theta = 108 \degree$

Hence each interior angles of a regular polygon with 5 - sides is 108°

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Taya2010 [7]

The bag contains,

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Total marbles (possible outcome) is,

$\text{Total marbles = (R) + (G) +(B) = 9 + 7 + 4 = 20 marbles}$

Let P(R) represent the probablity of picking a red marble,

P(G) represent the probability of picking a green marble and,

P(B) represent the probability of picking a blue marble.

Probability , P, is,

$\text{Prob, P =}\frac{required\text{ outcome}}{possible\text{ outcome}}$ $\begin{gathered} P(R)=\frac{9}{20} \\ P(G)=\frac{7}{20} \\ P(B)=\frac{4}{20} \end{gathered}$

Probablity of drawing a Red marble (R) and then a blue marble (B) without being replaced,

That means once a marble is drawn, the total marbles (possible outcome) reduces as well,

$\begin{gathered} \text{Prob of a red marble P(R) =}\frac{9}{20} \\ \text{Prob of }a\text{ blue marble =}\frac{4}{19} \\ \text{After a marble is selected without replacement, marbles left is 19} \\ \text{Prob of red marble + prob of blue marble = P(R) + P(B) = }\frac{9}{20}+\frac{4}{19}=\frac{251}{380} \\ \text{Hence, the probability is }\frac{251}{380} \end{gathered}$

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1 year 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: