Daily Math · 2026-06-19

Question 1

Calculați $\log_5 5^{12} - \log_7 1$.

Accepted Answer

Avem $\log_5 5^{12} = 12$ și $\log_7 1 = 0$. Deci expresia este $12 - 0 = 12$.

Answer

$0$

Answer

$5$

Answer

$11$

Answer

$12$

Question 2

A square matrix $A$ is invertible iff:

Accepted Answer

Invertibility ⇔ non-zero determinant.

Answer

$\det(A) = 0$

Answer

$A$ is symmetric

Answer

$\det(A) 
e 0$

Answer

all entries are non-zero

Question 3

Two boxes — Box A has $3$ red and $1$ blue; Box B has $1$ red and $3$ blue. A box is chosen at random and a ball is drawn. Given the ball is red, the probability it came from Box A is:

Accepted Answer

$P(A) = P(B) = \dfrac{1}{2}$, $P(R|A) = \dfrac{3}{4}$, $P(R|B) = \dfrac{1}{4}$.

$P(A|R) = \dfrac{\dfrac{3}{4} \cdot \dfrac{1}{2}}{\dfrac{3}{4} \cdot \dfrac{1}{2} + \dfrac{1}{4} \cdot \dfrac{1}{2}} = \dfrac{3/8}{4/8} = \dfrac{3}{4}$.

Answer

$\dfrac{1}{4}$

Answer

$\dfrac{1}{2}$

Answer

$\dfrac{3}{4}$

Answer

$\dfrac{3}{8}$

Problems & worked solutions

Problem 1 — Logarithms

Problem 2 — Determinants

Problem 3 — Probability