# College math questions and answers

Recent questions in Post Secondary
Neliswa Dlamini 2022-05-21

### Probability or expected value of hirings the company will make?A company is hiring for an open position and has n interviews set up, one per day. Each day, if the candidate is better than the current employee, the employee is fired and the candidate is hired. Otherwise, the current employee keeps the job. What is the expected number of hirings the company will make?I got the answer of $\frac{1+\left(n-1\right)}{2}$. Is this correct? I used the probability of no new hires and all new hires.

Mauricio Hayden 2022-05-21 Answered

### Let $A$ be a ${C}^{\ast }$-algebra. We say $A$ is “commutative“ if $a{b}^{\ast }c=c{b}^{\ast }a$ for all $a,b,c\in A$ and define “center” of $A$ as$Z\left(A\right)=\left\{v\in A:a{v}^{\ast }c=c{v}^{\ast }a\mathrm{\forall }a,c\in A\right\}$Are these notions of “commutativity“ and “center” same as usual notions of commutativity and center in ${C}^{\ast }$-algebras?

Laurel Yoder 2022-05-21 Answered

### The Relation between Setsif I have a relation between $A×A$if $A=\left\{1,2,3\right\}$if $B=\left\{1,2,3\right\}$$R=\left\{\left(1,1\right),\left(2,2\right),\left(3,3\right)\right\}$can I say that the Relation R is Reflexive and also a Symmetric because I have (a,b) and (b,a) and also (a,a).

Liberty Mack 2022-05-21 Answered

### Partitions of n where every element of the partition is different from 1 is $p\left(n\right)-p\left(n-1\right)$I am trying to prove that p(n| every element in the partition is different of $1\right)=p\left(n\right)-p\left(n-1\right)$, and I am quite lost... I have tried first giving a biyection between some sets, trying to draw an example in a Ferrers diagram and working on it... Nevertheless, I have not obtained significant results. Then, I have thought about generating functions; we know that the generating function of $\left\{p\left(n\right){\right\}}_{n\in \mathbb{N}}$ is $\prod _{i=1}^{\mathrm{\infty }}\frac{1}{1-{x}^{i}}$, so $\left\{p\left(n-1\right){\right\}}_{n\in \mathbb{N}}$ will have $\prod _{i=1}^{\mathrm{\infty }}\frac{x}{1-{x}^{i}}$ as generating function. So, what we have to prove is that $\prod _{i=1}^{\mathrm{\infty }}\frac{1}{1-{x}^{i}}-\prod _{i=1}^{\mathrm{\infty }}\frac{x}{1-{x}^{i}}=\left(1-$-x). $\prod _{i=1}^{\mathrm{\infty }}\frac{1}{1-{x}^{i}}$ is the generating function of p(n|every element in the partition is different of 1)... but i'm am not seeing why! Any help or hint will be appreciate it!

Riley Yates 2022-05-21 Answered

### In rational homotopy theory, one uses various algebras and coalgebras to model (simply connected) spaces (topological spaces or simplicial sets, usually) up to rational equivalences.Two types of models one can use are dg cocommutative algebras (Quillen) and dg commutative algebras (Sullivan). I will leave the dg implicit from now on. The dual of a cocommutative coalgebra is always a commutative algebra (while the converse is only true in the finite dimensional case). I have the following question.Let $X$ be a simply connected space, and suppose $C$ is a cocommutative rational model for $X$. Under what assumptions is its linear dual ${C}^{\vee }$ a commutative rational model for $X$?

Erick Clay 2022-05-21 Answered

### The random variable X has homogeneous distrigutionI have a problem with exercise:The random variable X has a homogeneous distribution in the interval [0,1]. Random variable $Y=max\left(X,1/2\right)$. Please find the expected value of a random variable Y. I need to do this for discrete variables and also for continuous variable

Denisse Valdez 2022-05-21 Answered

### Find matrix of linear transformation with respect to the basis of eigenvectorsThe transformation ${R}^{2}->{R}^{2}$ is represented by the matrix $\left(\begin{array}{cc}1& 2\\ 1& 0\end{array}\right)$.

Aiden Barry 2022-05-21 Answered

### There is a subset $T\subset S$ with $|T|=k+1$ such that for every $a,b\in T$, the number ${a}^{2}-{b}^{2}$ is divisible by 10.Let $k\ge 1$ be an integer.If S is a set of positive integers with $|S|=N$, then there is a subset $T\subset S$ with $|T|=k+1$ such that for every $a,b\in T$, the number ${a}^{2}-{b}^{2}$ is divisible by 10.What is the smallest value of N as a function of k so that the above statement is true?Step 2I have observed that perfect squares end with 0,1,4,5,6 and 9. If we have two perfect squares that end with the same as one of 0,1,4,5,6 and 9, then we are done.I think by PHP we should have $⌈\frac{N}{k}⌉=6$

Elisha Kelly 2022-05-21 Answered

### Discrete Mathematics what exactly does from A to B mean?Like if there's some relation R from a set A to a set B what exactly does this mean?I know it's just a subset of the Cartesian product $A×B,$, but what exactly does from A to B mean..? Like obviously from B to A is different so can anyone explain what the FROM really means here?

Landon Bonilla 2022-05-21 Answered

### I'm trying to solve this differential equation:$\frac{dy}{dx}=\frac{x-\mathrm{exp}\left(y\right)}{y+\mathrm{exp}\left(y\right)}$I thought I could use separation of variable, but I'm unable to isolate x.Could you please help me get started on this differential equation?

Jaidyn Bush 2022-05-21 Answered

### The test statistic is z = 2.75, the critical value is z = 2.326. The probability value is_________.Select one:a. not measurableb. greater than the significant levelc. equal to the significant leveld. less than the significant level

Kendrick Pierce 2022-05-21 Answered

### Reflect a point about a plane using matrix transformationGiven the plane equation $ax+by+cz=d$ and an arbitrary point in 3D space $\left(i,j,k\right)$, how do I find a homogenous transformation matrix that is used to reflect this point about the plane?

Isaiah Farrell 2022-05-21 Answered

### What happens to the mean, median and mode for the data 14, 15, 22, 15, 2, 16, 17, and 13 if the outlier is eliminated?

Simone Werner 2022-05-21 Answered

### Proof that $⌊-x⌋=-⌈x⌉$I wanted to ask if this kind of reasoning for proving the result in the title could be considered correct:We know that: $⌈x⌉=n$ if and only if $n-1Then $-⌈x⌉=-n$ if and only if $-n-1Then multiplying by -1 the formula $-n-1 we get $n+1>-x\ge n$, inverting the sign.But $n+1>-x\ge n$ is equivalent to $n\le -x.We know that $⌊x⌋=n$ if and only if $n\le x.So from $n\le -x we can infer that $⌊-x⌋=$ $n=-⌈x⌉$

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