B

1103148604

Level: 
B
The total mechanical energy \( E \) of an object is given by the formula \( E=mgh+\frac12mv^2 \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity (about \( 10\,\mathrm{m}/\mathrm{s}^2 \)), \( h \) is the height of the object above the ground and \( v \) is the velocity of that object. Suppose that an object of the fixed mass \( m \) moves horizontally in the constant height \( h \) above the ground. Choose the graph, which could represent the dependence between the total mechanical energy (\( E \)) and velocity (\( v \)) of the object.

1003177802

Level: 
B
Choose the domain of the expression \( \ln\!⁡\left(-|3-2x|+6\right) \).
\( \left(-\frac32;\frac92\right) \)
\( \left(-\infty;-\frac32\right)\cup\left(\frac92;\infty\right) \)
\( \left(-\infty;\frac32\right)\cup\left(\frac92;\infty\right) \)
\( \left(\frac92;\infty\right) \)

1003143202

Level: 
B
What is the total count of all integer solutions of the all following equations? \[ \begin{aligned} \log_{\frac12}\!\left(\log_2⁡x\right)&=-1 \\ \log_5\!\left(\log_{\frac15}⁡x\right)&=0 \\ -\log_{\frac13}\!\left(\log_{\frac12}⁡x\right)&=1 \end{aligned}\]
\( 1 \)
\( 2 \)
\( 3 \)
\( 0 \)

1003134407

Level: 
B
In the tables below the absent hours in lessons of \( 16 \) boys and \( 14 \) girls from one class for half of a year are listed. Use the variance of the number of absent hours to find out the students of which gender had the absence more balanced. I.e. choose the group with more balanced absence and the correct variance of the number of absent hours. The variance is rounded to two decimal places. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Girl's ID} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text{Absent hours} & 27 & 61 & 38 & 61 & 17 & 39 & 61 \\\hline \\\hline \text{Girl's ID} & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\\hline \text{Absent hours} & 25 & 21 & 52 & 16 & 34 & 9 & 25 \\\hline \end{array} \] \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text{Boy's ID} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \text{Absent hours} & 67 & 56 & 26 & 36 & 27 & 55 & 17 & 34 \\\hline \\\hline \text{Boy's ID} & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\\hline \text{Absent hours} & 54 & 46 & 13 & 48 & 21 & 49 & 18 & 14 \\\hline \end{array} \]
boys: \( \sigma^2= 285{.}34\,\mathrm{lessons}^2 \)
girls: \( \sigma^2= 297{.}35\,\mathrm{lessons}^2 \)
boys: \( \sigma^2= 16{.}89\,\mathrm{lessons} \)
girls: \( \sigma^2= 17{.}24\,\mathrm{lessons} \)