A

2010018103

Level: 
A
In February 2021, Aneta recorded an outdoor temperature in Ostrava-Poruba, always measured at \(2\) p.m. The results in \(^{\circ}\mathrm{C}\) are shown in the following table: \[ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Day} & 1. & 2. & 3. & 4. & 5. & 6. & 7. & 8. \\\hline \text{Temperature }(^{\circ}\mathrm{C}) & -1 & 3 & 7& 8 & 3 & 0 & -4 & -5 \\\hline \\\hline \text{Day} & 9. & 10. & 11. & 12. & 13. & 14. & 15. & 16.\\\hline \text{Temperature } (^{\circ}\mathrm{C}) & -4 & -3 & -6 & -4 & -3 & 2 & -2 & 0\\\hline \\\hline \text{Day} & 17. & 18. & 19. & 20. & 21. & 22. & 23. & 24. \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 3 & 8 & 4 & 5 & 5 & 8 & 5 & 16 \\\hline \\\hline \text{Day} & 25. & 26. & 27. & 28. & & & & \\\hline \text{Temperature } (^{\circ}\mathrm{C}) & 15 & 15 & 6 & 8 & & & & \\\hline \end{array} \] Determine the mode of the recorded temperatures.
\(8\,^{\circ}\mathrm{C}\)
\(3\,^{\circ}\mathrm{C}\)
\(-3\,^{\circ}\mathrm{C}\)
\(-4\,^{\circ}\mathrm{C}\)

2010018102

Level: 
A
The same component is manufactured simultaneously on two differently powerful machines. The first one makes \(1\) component in \(20\) minutes, the second one makes the same component in \(10\) minutes. We are interested in how long it takes on average to produce \(1\) component using these two machines. What type of average do we use for the calculation?
Harmonic mean
Geometric mean
Arithmetic mean
Weighted arithmetic mean

2010018101

Level: 
A
Andrea took part in a children's cycling race. The first part of the route led from the Lower Square to the Upper Square and Andrea completed it with an average speed of \(10\,\mathrm{km/h}\). Returning from the Upper Square to the Lower Square she rode the same route with an average speed of \(13\,\mathrm{km/h}\). We are interested in her average speed during the whole race. What type of average do we need to use?
Harmonic mean
Arithmetic mean
Geometric mean
Weighted arithmetic mean

2010013201

Level: 
A
Find the complex roots of the following quadratic equation. \[ 3x^2 + 8 = 0 \]
\( x_1=-\frac{2\sqrt{6}}3\mathrm{i},\ x_2=\frac{2\sqrt{6}}3\mathrm{i} \)
\( x_1=-\frac{\sqrt{6}}3\mathrm{i},\ x_2=\frac{\sqrt{6}}3\mathrm{i} \)
\( x_1=-\frac{\sqrt{12}}3\mathrm{i},\ x_2=\frac{\sqrt{12}}3\mathrm{i} \)
\( x_1=-\frac{\sqrt{6}}6\mathrm{i},\ x_2=\frac{\sqrt{6}}6\mathrm{i} \)

2010013021

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=5^{3-x}-4\) be translated to get the graph of the function \(f(x)=\left(\frac15\right)^{x+1}-6\)?
\(\vec{u}=\left(-4;-2\right)\)
\(\vec{u}=\left(4;2\right)\)
\(\vec{u}=\left(4;-2\right)\)
\(\vec{u}=\left(-4;2\right)\)

2010013020

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=5^{x+1}-6\) be translated to get the graph of the function \(f(x)=\left(\frac15\right)^{3-x}-4\)?
\(\vec{u}=\left(4;2\right)\)
\(\vec{u}=\left(-4;-2\right)\)
\(\vec{u}=\left(4;-2\right)\)
\(\vec{u}=\left(-4;2\right)\)

2010013019

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=\left(\frac14\right)^{5-x}-1\) be translated to get the graph of the function \(f(x)=4^{x-2}+3\)?
\(\vec{u}=\left(-3;4\right)\)
\(\vec{u}=\left(-3;-4\right)\)
\(\vec{u}=\left(3;4\right)\)
\(\vec{u}=\left(3;-4\right)\)

2010013018

Level: 
A
By what vector \(\vec{u}\) should the graph of the function \(f(x)=\left(\frac14\right)^{x-2}+3\) be translated to get the graph of the function \(f(x)=4^{5-x}-1\)?
\(\vec{u}=\left(3;-4\right)\)
\(\vec{u}=\left(-3;-4\right)\)
\(\vec{u}=\left(3;4\right)\)
\(\vec{u}=\left(-3;4\right)\)