B

9000153701

Level: 
B
The picture shows a square pyramid. The side of a base square is \(a = 4\, \mathrm{cm}\) and the height of the pyramid is \(v = 6\, \mathrm{cm}\). Find the angle \(\varphi \).
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6} {2}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 71^{\circ }34^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \varphi = \frac{6} {2\sqrt{2}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 64^{\circ }46^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi } {2} = \frac{2} {6}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 36^{\circ }52^{\prime}\)
\(\mathop{\mathrm{tg}}\nolimits \frac{\varphi } {2} = \frac{2} {2\sqrt{10}}\mathrel{\implies }\varphi \mathop{\mathop{\doteq }}\nolimits 35^{\circ }6^{\prime}\)

9000153304

Level: 
B
Two students performed repeated measurements of the same length. After evaluating statistical characteristics they got equal means of the length. Which of the following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
Both students did their measurements with the same accuracy.

9000151302

Level: 
B
Find the angle \(\varphi \) between the lines \(p\) and \(q\) given by their parametric equations. \[ p\colon \begin{aligned}[t] x& = 1 + 2t, & \\y& = 3 - 3t,\ t\in \mathbb{R}, \\ \end{aligned}\qquad q\colon \begin{aligned}[t] x& = 2 - k, & \\y& = 3 + k,\ k\in \mathbb{R} \\ \end{aligned} \]
\(11^{\circ }19'\)
\(88^{\circ }41'\)
\(45^{\circ }45'\)
\(54^{\circ }12'\)

9000153305

Level: 
B
Two students performed repeated measurements of the same length. After evaluating statistical characteristics they got equal standard deviations. Which of the following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
Both students did their measurements with the same accuracy.

9000151306

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

9000153306

Level: 
B
Two students performed repeated measurements of the same length. After evaluating statistical characteristics they got equal means and also equal standard deviations. Which of the following statement is true? (Remark: The accuracy is determined by the coefficient of variation.)
Both students did their measurements with the same accuracy.
There is not enough information to compare the accuracy of both measurements.
One of the students measured with a better accuracy than the other.
The stated question is irrelevant, two different statistical files cannot share their means and their standard deviations.

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. \[ p\colon \begin{aligned}[t] x& = 2 + t,& \\y& = 5,\ t\in \mathbb{R} \\ \end{aligned} \]
\(30^{\circ }\)
\(90^{\circ }\)
\(60^{\circ }\)
\(45^{\circ }\)

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

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.