A

1003029503

Level: 
A
Paul drove the first halfway of a test track at a constant speed of \( 20\,\mathrm{kph} \) and the second halfway at a constant speed of \( 30\,\mathrm{kph} \). We wish to know Paul's average speed. What type of the average do we need to use?
Harmonic mean
Arithmetic mean
Geometric mean
Weighted arithmetic mean

1003029502

Level: 
A
Two employees work in a factory workroom. The first one completed an assigned task in \( 20 \) minutes, the second one completed the same task in \( 10 \) minutes. We are interested in the average time of the task completion. What type of the average do we need to use?
Arithmetic mean
Harmonic mean
Geometric mean
Weighted arithmetic mean

1003029501

Level: 
A
In a toy-factory four workers make the same toys manually. In one \( 8 \) hour shift the first worker produced \( 12 \) toys, the second \( 10 \) toys, the third \( 16 \) toys and the fourth \( 12 \) toys. What was the average time to produce a toy on that work shift?
\( 38\,\mathrm{min}\ 24\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 40\,\mathrm{s} \)
\( 39\,\mathrm{min}\ 30\,\mathrm{s} \)
\( 38\,\mathrm{min}\ 58\,\mathrm{s} \)

1103048503

Level: 
A
Let \( f \) be a periodic function with period \( 4 \). The diagram shows a part of the graph of \( f \). Identify which of the following statements is false.
The function \( f \) is an odd function.
The function \( f \) is increasing in the interval \( [14,15] \).
The function \( f \) has maximum at \( x=-5 \).
The function \( f \) is a bounded function.

1003048501

Level: 
A
Let \( f \) be a periodic function with period \( 5 \). The table below shows some input and corresponding output values of \( f \). \[\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -1.5 & -1 & 0 & 1 & 2 & 3 & 4 \\\hline f(x) & 0 & 4 & 1 & -1 & 3 & 2 & 4 \\\hline \end{array}\] Identify which of the following statements is false.
\( f(-12)=3 \)
\( f(5)=1 \)
\( f(12)=3 \)
\( f(3.5)=0 \)

1003029202

Level: 
A
In a set of \( 100 \) items, \( 15 \) are defective. We pick randomly \( 10 \) items from this set. First eight items were not defective. Find the probability that the ninth item selected is not defective too. Results are rounded to two decimal places.
\( \frac{77}{92}=0{.}84 \)
\( \frac{85}{92}=0{.}92\)
\( \frac{15}{92}=0{.}16 \)
\( \frac7{92}=0{.}08 \)

1003029201

Level: 
A
Three dice are thrown together. Let \( A \) be the event “the sum is \( 5 \)” and \( B \) be the event “the sum is \( 16 \)”. Which of the following statements is true?
Events \( A \) and \( B \) have the same probability of occurrence.
Event \( A \) is more likely to occur than event \( B \).
Event \( B \) is more likely to occur than event \( A \).