Expert Answers to Algebra 2 Problems

How can I find the roots of $x^3-<!--\; -\; -->3x+1$ using Cardano's formula?
So far, I found that
$x=\sqrt[3]{{\displaystyle \frac{-<!--\; -\; -->1+\sqrt{-<!--\; -\; -->3}}{2}}}+\sqrt[3]{{\displaystyle \frac{-<!--\; -\; -->1-<!--\; -\; -->\sqrt{-<!--\; -\; -->3}}{2}}}$
$x=\sqrt[3]{{\displaystyle \frac{-<!--\; -\; -->1+i\sqrt{3}}{2}}}+\sqrt[3]{{\displaystyle \frac{-<!--\; -\; -->1-<!--\; -\; -->i\sqrt{3}}{2}}}$
$x=\sqrt[3]{\frac{-<!--\; -\; -->1}{2}+\frac{i\sqrt{-<!--\; -\; -->3}}{2}}+\sqrt[3]{\frac{-<!--\; -\; -->1}{2}-<!--\; -\; -->\frac{i\sqrt{-<!--\; -\; -->3}}{2}}$
I am now trying to express each cubic radicand in their exponential form.

What is the response? When we round 25 off to the nearest ten?

Which one of the following statements is false?
A. If a number is divisible by two Co-Prime Numbers, then it is also divisible by the product of those Co-Prime Numbers.
B.2 is the only even and the smallest prime number.
C.Every number (except 1 and 2) will have at least 3 factors.
D.Prime Factorisation means using only Prime Numbers to write the Factors of a number.

A sequence is defined by the recursive function f(n+1)=f(n)−2. If f(1)=10 , what is f(3)?

What's the correct notation for log squared?
${\log }^2<!--\; \; -->(n)$ or $[\log <!--\; \; -->(n){]}^2$

What is the square root of the number 676.

Which is a solution to the equation?
$(x-<!--\; -\; -->2)(x+5)=18$

write this equation: $T=2\mathrm{\pi <!--\; \pi \; -->}\sqrt{\frac{m}{k})}$
in terms of m.

What are ALL the real zeros of $y=(x-<!--\; -\; -->12{)}^3-<!--\; -\; -->7$

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
F(x) = 0 x < 0 x2 25 0 ≤ x < 5 1 5 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(g) Calculate V(X) and σx. V(X) = σx =
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

The difference of two negative integers is always negative?

What is the value of 1 + infinity and 1- infinity?

How do you calculate $\log \left(0.1\right)$?

How do you write the first five terms of the sequence ${\displaystyle a_n=0.3}$?

Zero is a positive integer since it doesn't carry any negative sign.

The following data has been collected about Keller Company's stockholders' equity accounts: Common stock $10 par value 20,000 shares authorized and 10,000 shares issued, 9,000 shares outstanding $100,000 Paid-in capital in excess of par value, common stock 50,000 Retained earnings 25,000 Treasury stock 11,500 Assuming the treasury shares were all purchased at the same price, the cost per share of the treasury stock is:
$10.50.
$10.00.
$11.50.
$1.15.
$1.28.

An equation which one's root is $x=\sqrt{2}+\sqrt{3}+\sqrt{5}$ and coefficients are integer.
How many equation we can write for it?

Alternate proof for "${\log }_{10}<!--\; \; -->2$ is irrational"
I need to prove that ${\log }_{10}<!--\; \; -->2$ is irrational. I understand the way this proof was done using contradiction to show that the even LHS does not equal the odd RHS, but I did it a different way and wanted to check its validity!
Prove by contradiction: Suppose that $\log <!--\; \; -->2$ is rational - that is, it can be written as
$\log <!--\; \; -->2=\frac{a}{b}$
where a and b are integers. Then
$2={10}^{\frac{a}{b}}$
$2={10}^a{10}^{\frac{1}{b}}$
$\frac{2}{{10}^a}={10}^{\frac{1}{b}}$
Log both sides:
$\log <!--\; \; -->(\frac{2}{{10}^a})=\frac{1}{b}$
$\log <!--\; \; -->2-<!--\; -\; -->\log <!--\; \; -->({10}^a)=\frac{1}{b}$
$\log <!--\; \; -->2=\frac{1}{b}+a$
$\log <!--\; \; -->2=\frac{ab+1}{b}$
However we assumed that $\log <!--\; \; -->(2)=\frac{a}{b}$ and thus we have a contradiction.

Modeling phenomena using random variables
A load balancer in a cloud computing system is composed of N servers. The balancer, When assigning the connections to the servers, decide at random which one to use. But nevertheless, Due to some prioritization of the servers, 10% of them have a higher utilization level than the rest. Model the problem of access to the servers of the cloud computing system, for that purpose define clearly the sample space ($\mathrm{\Omega <!--\; \Omega \; -->}$), the observations in the sample space ($\mathrm{\omega <!--\; \omega \; -->}$) and the probability function of the events of the problem. Also define an impossible event. Finally, define the random variables X and Y, which respectively represent the events of accessing a system server and accessing any server of the most used. Which of these random variables gives more information about the problem?

Infinite series representation for root of polynomials?
Given a polynomial $p(x)=a_n{x}^n+\cdots <!--\; \cdots \; -->+a_{1}x+a_0$, can every root of the polynomial be represented as $\underset{k=0}{\overset{\mathrm{\infty <!--\; \infty \; -->}}{\sum <!--\; \sum \; -->}}{b}_k$ with the $b_k$'s being a function of $a_0,\dots <!--\; \dots \; -->,a_n$ using only elementary operations of arithmetic and taking roots?