C

1003082606

Level: 
C
How many of the following inequalities have the same solution set? \[ \begin{aligned} 2\left(\frac14\right)^{2x-1}-\left(\frac12\right)^{4x-2}-\frac14&\leq 0 \\ 2^{4x+4}-15\cdot4^{2x}&\geq 2^4 \\ 9^{2x+1}-2\cdot3^5&\geq3^{4x+1} \end{aligned} \]
\( 3 \)
\( 2 \)
\( 1 \)
\( 0 \)

1003082605

Level: 
C
Solve the following system of two inequalities. \begin{align*} \left(\frac12\right)^{x+1}-3\left(\frac12\right)^{x+2}+\frac12&\geq0\\ 4^{x+2}-3\cdot4^{x+1} &< 1 \end{align*}
The system of inequalities has no solution.
\( x\in(-\infty;\infty) \)
\( x\in(-\infty;-1) \)
\( x\in(-\infty;-1] \)

1003029206

Level: 
C
In the hospital, \( 22 \) boys and \( 18 \) girls were born in one month. Babies were listed in the register by their date of birth. Find the probability that there are at least three boys in the first five places of the register. The results are rounded to four decimal places.
\( \frac{\binom{22}3\cdot\binom{18}2+\binom{22}4\cdot\binom{18}1+\binom{22}5\cdot\binom{18}0}{\binom{40}5} = 0{.}5982 \)
\( \frac{\binom{22}3+\binom{22}4+\binom{22}5}{\binom{40}5} = 0{.}0535 \)
\( \frac{22^3\cdot18^2+22^4\cdot18^1+22^5\cdot18^0}{40^5}=0{.}1252 \)
\( \frac{\binom{22}3\cdot\binom{18}2+\binom{22}4\cdot\binom{18}1+\binom{22}5\cdot\binom{18}0}{40^5} = 0{.}0038 \)
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