B

9000153301

Level: 
B
A student performed repeated measurements of a length (in meters) and evaluated the main statistical characteristics: mean, standard deviation, variance and the coefficient of variation. Which of these characteristics has it's unit square meter?
variance
standard deviation
mean
coefficient of variation

9000150501

Level: 
B
A man of height \(180\, \mathrm{cm}\) casts a \(200\, \mathrm{cm}\) shadow. At the same moment, a tree of an unknown height casts a \(35\, \mathrm{m}\) shadow. Find the height of the tree.
\(\frac{63} {2} \, \mathrm{m}\)
\(\frac{350} {9} \, \mathrm{m}\)
\(\frac{72} {7} \, \mathrm{m}\)
\(\frac{36} {35}\, \mathrm{m}\)

9000153308

Level: 
B
Statistical file contains repeating measurements of a body mass in kilograms. Find the change in the coefficient of variation if we convert all data in the file to grams.
The coefficient of variation does not change.
The coefficient of variation becomes bigger.
The coefficient of variation becomes smaller.

9000151307

Level: 
B
Find the angle \(\varphi \) between the line \(x + \sqrt{3}y - 6 = 0\) and the line \(p\) given by it's parametric equations. \[ p\colon \begin{aligned}[t] x& = 2 + t,& \\y& = 5;\ t\in \mathbb{R} \\ \end{aligned} \]
\(30^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(45^{\circ }\)

9000151306

Level: 
B
Find the angle \(\varphi \) between the lines \(p\) and \(q\) given by their parametric equations. \[ p\colon \begin{aligned}[t] x& = 1 - t, & \\y& = 2 + t;\ t\in \mathbb{R}, \\ \end{aligned}\qquad q\colon \begin{aligned}[t] x& = 4 - k, & \\y& = 5 + k;\ k\in \mathbb{R}. \\ \end{aligned} \]
\(0^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(30^{\circ }\)

9000150107

Level: 
B
Evaluate the following integral on the interval \((3;+\infty)\). \[ \int \frac{x^{3} - 27} {x - 3} \, \mathrm{d}x \]
\(\frac{x^{3}} {3} + \frac{3x^{2}} {2} + 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}} {3} -\frac{3x^{2}} {2} + 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}} {3} -\frac{3x^{2}} {2} - 9x + c,\ c\in \mathbb{R}\)
\(\frac{x^{3}} {3} + \frac{3x^{2}} {2} - 9x + c,\ c\in \mathbb{R}\)

9000153606

Level: 
B
Give a verbal description to the angle shown in the picture.
The angle between the edge on triangular face and the base edge from the same face.
The angle between the triangular face and a base edge not in this face.
The angle between two triangular faces having a common edge.
The angle between a triangular face and square base.

9000153603

Level: 
B
Give a verbal description to the angle shown in the picture.
The angle between two opposite triangular faces.
The angle between a triangular face and the base.
The angle between two edges in the same triangular face.
The angle between two triangular faces having a common edge.