Daily math problems for May 11, 2026 — Algebra, Integrals, Probability

$4+5=9$, and $9<mrow><mi\; mathvariant="normal">m</mi><mi\; mathvariant="normal">o</mi><mi\; mathvariant="normal">d</mi></mrow>6=3$. So the answer is $\widehat{3}$.

$\bullet$ Factor the numerator:

$$x^5+x^3+x=x(x^4+x^2+1)$$

$\bullet$ The integrand simplifies to $x$, which is odd, so by symmetry:

$${\int }_{-2}^{2}xdx=0$$

$\bullet$ Decode the second term:

$$i^{2026}=i^2=-1$$

$${\log }_{2}1024=10$$

$\bullet$ Combine:

$$0+(-1)(10)=-10$$

$P(A)=P(B)={\displaystyle \frac{1}{2}}$, $P(R\mathrm{\mid }A)={\displaystyle \frac{3}{4}}$, $P(R\mathrm{\mid }B)={\displaystyle \frac{1}{4}}$.

$P(A\mathrm{\mid }R)={\displaystyle \frac{{\displaystyle \frac{3}{4}}\cdot {\displaystyle \frac{1}{2}}}{{\displaystyle \frac{3}{4}}\cdot {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{4}}\cdot {\displaystyle \frac{1}{2}}}}={\displaystyle \frac{3\mathrm{/}8}{4\mathrm{/}8}}={\displaystyle \frac{3}{4}}$.