Daily math problems for November 3, 2026 — Descriptive Statistics & Sampling, Fundamental Algebra, Algebra & more

Add every value in the set.

$$6+8+11+15+20=60$$

Divide the total by the count of numbers, which is $5$.

$$\frac{60}{5}=12$$

The mean is $12$. (Note $11$ is the median and $14$ is the range — different measures.)

$10ab+15a=5a(2b+3)$.

${\displaystyle \frac{\pi }{6}}={30}^{\circ }$, and $\sin {30}^{\circ }={\displaystyle \frac{1}{2}}$.

$\widehat{2}\cdot \widehat{3}=\widehat{6}=\widehat{0}$. (${\mathbb{Z}}_6$ has zero divisors!)

$\mathbb{Q}$ has all the field axioms — every non-zero rational has a rational reciprocal. It's a field.

$\det (AB)=3\cdot (-2)=-6$.

With $r=2$ and $n=5$: ${\displaystyle \frac{2^6-1}{2-1}}={\displaystyle \frac{63}{1}}=63$. (Check: $1+2+4+8+16+32=63$.)

The sum telescopes: ${\sum }_{k=1}^{99}({\displaystyle \frac{1}{k}}-{\displaystyle \frac{1}{k+1}})=1-{\displaystyle \frac{1}{100}}={\displaystyle \frac{99}{100}}$.

$\mathrm{\Delta }=16-4=12$, $a=-1$, so $f_{\max }=-{\displaystyle \frac{\mathrm{\Delta }}{4a}}=-{\displaystyle \frac{12}{-4}}=3$. The image is $(-\mathrm{\infty },3]$.

A ring homomorphism preserves both operations: addition AND multiplication.