# Tutor profile: Ngan H.

## Questions

### Subject: Basic Math

Solve this system of equations: $$ \left\{ \begin{array}{ccc} \displaystyle 3(e+f) & = & 5e + f + 2\\\\ \displaystyle 4(f-e) & = & e + 2f - 4 \end{array} \right. $$

Solving the first equation for $f$ gives \begin{align*} 3(e+f) & = 5e + f + 2\\ \Longrightarrow ~ 3e + 3f & = 5e + f + 2\\ \Longrightarrow ~~ 3f - f & = 5e - 3e + 2\\ \Longrightarrow \quad\quad\quad f & = e+1 \end{align*} Substituting for $f$ in the second equation gives \begin{align*} 4(f-e) & = e + 2f - 4\\ \Longrightarrow ~ 4((e+1) - e) & = e + 2(e+1) - 4\\ \Longrightarrow ~~\quad\quad\quad\quad\quad 4 & = e + 2e + 2 - 4\\ \Longrightarrow ~~\quad\quad\quad\quad\quad e & = 2 \end{align*} This means, $f = e + 1 = 2 + 1 = 3$.\\\\ Thus, $e = 2$ and $f = 3$.

### Subject: Statistics

In a poll conducted by the General Social Security, 81\% of respondent said that their jobs were sometimes or always stressful. Ten workers are chosen at random. \begin{enumerate}[(a)] \item Let $X$ be the number of respondents who find their job stressful among ten selected workers. Does $X$ follow a Bernouli or binomial distribution?\\ \item What is the probability that \underline{exactly} 7 of them find their jobs stressful?\\ \item What is the probability that \underline{no more than} 7 of them find their jobs stressful?\\ \item What is the probability that \underline{more than} 7 find their jobs stressful?\\ \item What is the mean number who find their jobs stressful in this study?\\ \item What is the standard deviation of the number who find their jobs stressful in this study?\\ \end{enumerate}

In a poll conducted by the General Social Security, 81\% of respondent said that their jobs were sometimes or always stressful. Ten workers are chosen at random. \begin{enumerate}[(a)] \item Let $X$ be the number of respondents who find their job stressful among ten selected workers. Does $X$ follow a Bernouli or binomial distribution?\\ {\color{red} $X$ follows a binomial distribution. } \item What is the probability that \underline{exactly} 7 of them find their jobs stressful?\\ {\color{red} $P(X=7) = $ binompdf$(10,\ 0.81,\ 7)=0.1883$ } \item What is the probability that \underline{no more than} 7 of them find their jobs stressful?\\ {\color{red} $P(X \leq 7) = $ binomcdf$(10,\ 0.81,\ 7)=0.2922$ } \item What is the probability that \underline{more than} 7 find their jobs stressful?\\ {\color{red} $P(X > 7) = 1 - P(X \leq 7) = 1-0.2922 = 0.7078$ } \item What is the mean number who find their jobs stressful in this study?\\ {\color{red} $\mu = np = 10 \times (0.81) = 8.1$ } \item What is the standard deviation of the number who find their jobs stressful in this study?\\ {\color{red} $\sigma^2 = np(1-p)=10\times(0.81)\times(1-0.81)=1.539 \quad\Longleftrightarrow \sigma = \sqrt{\sigma^2} = \sqrt{1.539}=1.2406 $ } \end{enumerate}

### Subject: Algebra

Given a quadratic function $\displaystyle p(x) = 2.019 x^2 - 20.19 x + 2019$. Evaluate $p(3-4a)$ and \underline{simplify} as much as it can be \textit{(you have to show your work)}.

\begin{align*} \displaystyle p(3-4a) &=2.019(3-4a)^2-20.19(3-4a) + 2019\\ &=2.019(3-4a)(3-4a)-20.19(3-4a) + 2019\\ &=2.019(9 - 24a + 16a^2) - (60.57 - 80.76a) + 2019\\ &=18.171 - 48.456a + 32.304a^2 - 60.57 + 80.76a + 2019\\ &=32.304a^2+32.304a+1976.601 \end{align*}