Mathematics, 05.06.2020 03:59 BarcaOsama

A number is selected from the set {1, 2, 3, 5, 15, 21, 29, 38, 500}. If equal elemental probabilities are assigned, what is the probability that the number chosen is either less than 29 or odd? 6/9 7/9 8/9

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Answer from: DASASDAEDWEDA

The required probability is $\frac{7}{9}$ .

Step-by-step explanation:

Set given is:

S = {1, 2, 3, 5, 15, 21, 29, 38, 500}

Total number of elements in set, n(S) = 9

Let A be the event that the number is less than 29 ({1, 2, 3, 5, 15, 21}).

Number of items in the event A, n(A) = 6

Probability of event A,

$P(A) = \dfrac{n(A)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}$

Formula for probability of any event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Let B be the event that the number is odd (either of {1,3,5,15,21,29}).

Number of items in the event B, n(B) = 6

Probability of event B,

$P(B) = \dfrac{n(B)}{n(S)}}=\dfrac{6}{9} \Rightarrow \dfrac{2}{3}$

The event A and B have a few elements in common, i.e. numbers less than 29 which are odd as well.

The common elements are represented as:

$A \cap B = \{1, 3, 5, 15, 21\}$

$n(A\cap B) = 5$

$P(A \cap B ) = \dfrac{n(A \cap B)}{n(s)}\\\Rightarrow P(A \cap B) = \dfrac{5}{9}$

To find probability of selecting a number which is either less than 29 (event A) or odd (event B),

We have to find $P(A\ or \ B)$ which is represented as $P(A \cup B)$ and the formula is:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)\\\Rightarrow \dfrac{2}{3} + \dfrac{2}{3} - \dfrac{5}{9}\\\Rightarrow \dfrac{12-5}{9}\\\Rightarrow \dfrac{7}{9}$

The required probability is $\frac{7}{9}$ .

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

Answer from: Quest

Hello!

the answer is:

the correct option:

b. $x=2.23$

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

$7^{x}=77$

then, using placing logarith with base 7 on both sides of the equation, we have:

$7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322$

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

$x=2.23$

hence, we have that the correct option:

b. $x=2.23$

have a nice day!

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