How do you write a rule to represent the relationship between the number of typed words and the time in which they are typed if a typist types 45 words per minute?

How do you ddd: $3a^2+8a-6$ and $4a^2-9a+11$?

$X$ is a discrete uniform distribution on $1,2,\dots ,n$. I know that the median is $\frac{n+1}{2}$ for odd $n$. I need to find median when $n$ is even. Would it be $\frac{n}{2}$ or $\frac{n}{2}+1$, whichever is greater?
Also, is every point mode as PDF has highest values there? So there are $n$ modes - $1,2,\dots ,n$?

Given the mean, median and mode of a function and have to find the probability density function.
mean: $\gamma -\beta {\mathrm{\Gamma }}_1$
median: $\gamma -\beta (ln2{)}^{1/\delta }$
mode: $\gamma -\beta (1-1/\delta {)}^{1/\delta }$
Also given that
${\mathrm{\Gamma }}_k=\mathrm{\Gamma }(1+k/\delta )$
$\mathrm{\Gamma }(z)={\int }_0^{\mathrm{\infty }}{t}^{z-1}dt$
$-\mathrm{\infty }<x<\gamma ,\beta >0,\gamma >0$
Now I understand how to calculate the mean, mode and median when given a probability density function. However I'm struggling to go backwards. I initially tried to "reverse" the process by differentiating the mean or median however I know this is skipping the substitution over the given limit.
I then looked for patterns with known distributions and realised they are from Weibull distribution however $\gamma -$. Does this mean essentially this is a typical Weibull distribution however shifted by $\gamma$ and therefore the pdf will be $\gamma -Weibullpdf"$

Prove that if diam(G)=3 for a regular graph G, then $diam(\overline{G})=2.$.
I know that without using regularity one can show that if $diam(G)\ge 3,\text{then }diam(\overline{G})\le 3$. How do I use regularity to show that it must be exactly 2?

What is the difference between categorical (qualitative) data and numerical (quantitative) data?

According to the definition I read, it came to my notice that the number with highest frequency has to be a mode for a given data set, but then what if I have all the numbers as distinct... In that scenario we won't have a particular number having a frequency more than other elements in the data set... Now if I consider a case when we have 2 numbers in a dataset with same max number of occurrences like:
$2,3,4,5,3,2$
Here 2, 3 both happen to have same maximum frequency and thus we say there are 2 modes... The above is stated similar in case we have 3 modes or multi modes ... So if there are all distinct numbers then we would have each number having the same maximum frequency as 1 ..so we can say all the numbers are modes...for that dataset...But then I have seen on some websites claiming that such data sets have "NO MODE".

Is age a discrete or continuous variable? Why?