# College math questions and answers

Recent questions in Post Secondary
Thomas Hubbard 2022-05-24 Answered

### What is the mean, median, and mode of 1, 4, 5, 6, 10, 25?

Cara Duke 2022-05-24 Answered

### What is the mean of 58, 76, 40, 35, 46, 45, 0, and 100?

wanaopatays 2022-05-24 Answered

### Prove combinatorially the recurrence ${p}_{n}\left(k\right)={p}_{n}\left(k-n\right)+{p}_{n-1}\left(k-1\right)$ for all $0Recall that ${p}_{n}\left(k\right)$ counts the number of partitions of k into exactly n positive parts (or, alternatively, into any number of parts the largest of which has size n).

skottyrottenmf 2022-05-24 Answered

### Why are measures of central tendency essential to descriptive statistics?

Mauricio Hayden 2022-05-24 Answered

### Acos 90 degree matrix transformation.I'm writing a program that transforms a matrix of points by 90°. In it, I have two vectors from which I am performing the rotation. Both vectors are normalized:$A:x:\sqrt{\left(}\frac{1}{3}\right),y:\sqrt{\left(}\frac{1}{3}\right),z:-\sqrt{\left(}\frac{1}{3}\right)\phantom{\rule{0ex}{0ex}}B:x:\sqrt{\left(}\frac{1}{3}\right),y:\sqrt{\left(}\frac{1}{3}\right),z:\sqrt{\left(}\frac{1}{3}\right)$As I visualize it, these two vectors are separated by 90°, but the dot product of these vectors comes out to $\frac{1}{3}$$\sqrt{\left(}\frac{1}{3}\right)\ast \sqrt{\left(}\frac{1}{3}\right)+\sqrt{\left(}\frac{1}{3}\right)\ast \sqrt{\left(}\frac{1}{3}\right)+\sqrt{\left(}\frac{1}{3}\right)\ast -\sqrt{\left(}\frac{1}{3}\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{3}+\frac{1}{3}-\frac{1}{3}\phantom{\rule{0ex}{0ex}}=\frac{1}{3}\phantom{\rule{0ex}{0ex}}$My code is then supposed to use arc-cos to come up with 90° from this number, but I believe arc-cos needs an input of 0 in order to produce a result of 90°. What am I missing here?

patzeriap0 2022-05-24 Answered

### The mean length of 6 rods is 44.2 cm. The mean length of 5 of them is 46 cm. How long is the sixth rod?

osmane5e 2022-05-24 Answered

### Bounding $A\left(n,d\right)=max\left\{M|$ exists a code with parameters n,M,d}I would like to prove that this lower bound of $A\left(n,d\right)=max\left\{M|$ exists a code with parameters n,M,d} (where n is the length of the block code, M the number of words of the code, and d, the minimal distance of the code), holds:$\frac{{2}^{n}}{\sum _{i=0}^{d-1}\left(\genfrac{}{}{0}{}{n}{i}\right)}\le A\left(n,d\right)$For trying to see this, I have tried to connect this inequality with the cardinal of the ball of radius $d-1$, that is $\sum _{i=0}^{d-1}\left(\genfrac{}{}{0}{}{n}{i}\right){2}^{i}$, so for sure, that quantity is less than ${2}^{n}\sum _{i=0}^{d-1}\left(\genfrac{}{}{0}{}{n}{i}\right)$. But I don't see if this is or not helping me at all... I would appreciate some guidance, help, hint,... Thanks!

Quintacj 2022-05-24 Answered

### How to solve this differential equation:$x\frac{dy}{dx}=y+x\frac{{e}^{x}}{{e}^{y}}?$I tried to rearrange the equation to the form $f\left(\frac{y}{x}\right)$ but I couldn't thus I couldn't use $v=\frac{y}{x}$ to solve it.

cricafh 2022-05-24 Answered

### Let $\mathcal{g}$ be a Lie algebra and let $a,b,c\in \mathcal{g}$ be such that $ab=ba$ and $\left[a,b\right]=c\ne 0$. Let . How to prove that $\mathcal{h}$ is isomorphic to the strictly upper triangular algebra $\mathcal{n}\left(3,F\right)$?Problem: If $\mathcal{h}\cong n\left(3,F\right)$ then $\mathrm{\exists }{a}^{\prime },{b}^{\prime },{c}^{\prime }\in \mathcal{n}\left(3,F\right)$ with ${a}^{\prime }{b}^{\prime }={b}^{\prime }{a}^{\prime }$ and $\left[{a}^{\prime },{b}^{\prime }\right]={c}^{\prime }$ as in $h$ But then ${c}^{\prime }$ must equal $0$ whereas $c\in h$ is not $0$?

Nylah Burnett 2022-05-24 Answered

### Let $R$ be a commutative finite dimensional $K$-algebra over a field $K$ (for example the monoid ring of a a finite monoid over a field). Assume we have $R$ in GAP. Then we can check whether $R$ is semisimple using the command RadicalOfAlgebra(R). When the value is 0, $R$ is semisimple. Thus $R$ can be written as a finite product of finite field extensions of $K$.Question: Can we obtain those finite field extensions of $K$ or at least their number and $K$-dimensions using GAP?

Thomas Hubbard 2022-05-24 Answered

### What is the Z-score for a 10% confidence level (i.e. 0.1 pvalue)?I want the standard answer used for including in my thesis write up. I googled and used excel to calculate as well but they are all slightly different.Thanks.

Nerya Fozailov 2022-05-23
il2k3s2u7 2022-05-23 Answered

### In how many ways can we distribute 2 types of gifts?The problem: In how many ways can we distribute 2 types of gifts, m of the first kind and n of the second to k kids, if there can be kids with no gifts?From the stars and bars method i know that you can distribute m objects to k boxes in $\left(\genfrac{}{}{0}{}{m+k-1}{k-1}\right)$ ways. So in my case i can distribute m gifts to k kids in $\left(\genfrac{}{}{0}{}{m+k-1}{k-1}\right)$ ways, same for n gifts i can distribute them in $\left(\genfrac{}{}{0}{}{n+k-1}{k-1}\right)$ ways. So now if we have to distribute m and n gifts we can first distribute m gifts in $\left(\genfrac{}{}{0}{}{m+k-1}{k-1}\right)$ ways, then n gifts in $\left(\genfrac{}{}{0}{}{n+k-1}{k-1}\right)$ ways, so in total we have:$\left(\genfrac{}{}{0}{}{m+k-1}{k-1}\right)\cdot \left(\genfrac{}{}{0}{}{n+k-1}{k-1}\right)\phantom{\rule{1em}{0ex}}\text{ways.}$.Is my reasoning correct?What about when we have to give at least 1 gift to each kid, can we do that in$\left(\genfrac{}{}{0}{}{m-1}{k-1}\right)\cdot \left(\genfrac{}{}{0}{}{n+k-1}{k-1}\right)+\left(\genfrac{}{}{0}{}{n-1}{k-1}\right)\cdot \left(\genfrac{}{}{0}{}{m+k-1}{k-1}\right)\phantom{\rule{1em}{0ex}}\text{ways?}$

Timiavawsw9 2022-05-23 Answered

### Find the limit of:$\underset{x\to \frac{\pi }{3}}{lim}\frac{1-2\mathrm{cos}x}{\pi -3x}$

Landyn Jimenez 2022-05-23 Answered

### How to approach this discrete graph question about Trees.A tree contains exactly one vertex of degree d, for each $d\in \left\{3,9,10,11,12\right\}$.Every other vertex has degrees 1 and 2. How many vertices have degree 1?I've only tried manually drawing this tree and trying to figure it out that way, however this makes the drawing far too big to complete , I'm sure there are more efficient methods of finding the solution.Could someone please point me in the right direction!

Hailey Newton 2022-05-23 Answered

### If $\mathcal{A}$ is a commutative ${C}^{\ast }$-subalgebra of $\mathcal{B}\left(\mathcal{H}\right)$, where $\mathcal{H}$ is a Hilbert space, then the weak operator closure of $\mathcal{A}$ is also commutative.I can not prove this.

hushjelpw4 2022-05-23 Answered

### Representing a sentence with quantified statementsMy approach to this question: $\mathrm{\exists }x\left(P\left(x\right)\to R\left(x\right)\right)$I cannot verify if my answer is correct, any help to verify my answer would be appreciated and if I did wrong any help to explain why would also be appreciated.

Wayne Steele 2022-05-23 Answered

### How do you find the range of 4, 6, 3, 4, 5, 4, 7, 3?

res2bfitjq 2022-05-23 Answered

### I have a first order PDE:$x{u}_{x}+\left(x+y\right){u}_{y}=1$With the initial condition:I have calculated result in Mathematica: $u\left(x,y\right)=\frac{y}{x}$, but I am trying to solve the equation myself, but I had no luck so far. I tried with method of characteristics, but I could not get the correct results. I would appreciate any help or maybe even whole procedure.

groupweird40 2022-05-23 Answered

### Exercise involving DFTThe fourier matrix is a transformation matrix where each component is defined as ${F}_{ab}={\omega }^{ab}$ where $\omega ={e}^{2\pi i/n}$. The indices of the matrix range from 0 to $n-1$ (i.e. $a,b\in \left\{0,...,n-1\right\}$)As such we can write the Fourier transform of a complex vector v as $\stackrel{^}{v}=Fv$, which means that${\stackrel{^}{v}}_{f}=\sum _{a\in \left\{0,...,n-1\right\}}{\omega }^{af}{v}_{a}$Assume that n is a power of 2. I need to prove that for all odd $c\in \left\{0,...,n-1\right\}$, every $d\in \left\{0,...,n-1\right\}$ and every complex vectors v, if ${w}_{b}={v}_{cb+d}$, then for all $f\in \left\{0,...,n-1\right\}$ it is the case that:${\stackrel{^}{w}}_{cf}={\omega }^{-fd}\phantom{a}{\stackrel{^}{v}}_{f}$I was able to prove it for $n=2$ and $n=4$, so I tried an inductive approach. This doesn't seem to be the best way to go and I am stuck at the inductive step and I don't think I can go any further which indicates that this isn't the right approach.Note that I am not looking for a full solution, just looking for a hint.

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