A

2010013605

Level: 
A
The wooden cube with the edges of length \( 4\,\mathrm{cm} \) has faces painted in blue. Suppose we cut the cube into small unit cubes (the edge length is \( 1\,\mathrm{cm}\)) and select one of the unit cubes at random. What is the probability that the selected cube has at most one face painted in blue?
\( 0.5 \)
\( 0.375 \)
\( 0.438 \)
\( 0.75 \)

2010013603

Level: 
A
There are \( 28 \) students in the class, one of them is Boris. The teacher picks randomly four students to be tested. What is the probability that Boris is among them?
\( \frac{\binom{27}3}{\binom{28}4}\doteq 0.143 \)
\( \frac{\binom{27}4}{\binom{28}4}\doteq 0.857 \)
\( \frac{\binom{27}3}{\binom{28}3}\doteq 0.893 \)
\( \frac{\binom{27}{3}\binom{4}1}{\binom{28}{4}}\doteq 0.571 \)

2010013601

Level: 
A
Little John plays a dice game against Robin Hood. To win, he needs to get the sum of \(7\) by rolling two dice. What is the probability that he wins over Robin right on the first roll? Round your result to three decimal places.
\(0.167\)
\(0.833\)
\(0.083\)
\(0.139\)

2010018205

Level: 
A
The number of traffic accidents in the monitored cities changed year on year. It increased by \(20\%\) in city A and decreased by \(1\%\) in city B. Decide which of the following statements is correct: \[ \begin{array}{l} \text{X: The same number of accidents occurred in city A as in city B the last year.} \\ \text{Y: There were more accidents in city A than in city B the last year.} \\ \text{Z: There have been fewer accidents in city B than in city A this year.}\\ \end{array} \]
The correctness of any of the above statements cannot be verified from the given data.
Only statement X is true.
Only statement Y is true.
Only statement Z is true.

2010013504

Level: 
A
The average price of a pork meat increased by \(15\%\) in the year \(2018\), by \(13\%\) in the year \(2019\) and by \(28\%\) in the year \(2020\). Find the average percentage growth of the price of the pork meat per one year in the period \(2017\)-\(2020\). Round your result to the nearest percent.
\(18\%\)
\(19\%\)
\(20\%\)
\(17\%\)

2010013503

Level: 
A
Four seamstresses sew doll dresses in a sheltered workshop. During the six-hour working hours, the first seamstress sewed \(4\) dresses, the second \(5\), the third \(7\) and the fourth \(4\) dresses. What was the average time needed to sew one dress on this day?
\( 1\,\mathrm{h}\ 12\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 20\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 10\,\mathrm{min} \)
\( 1\,\mathrm{h}\ 24\,\mathrm{min} \)

2010013502

Level: 
A
The annual production of a business is recorded in the following table. Find the compound annual rate of decline in production for a given period \( 2017 \) - \( 2020 \). (I.e., the average annual coefficient of the production decline, i.e., the ratio that provides a constant decline rate over the time period.) Round the result to four decimal places. \[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & 2017 & 2018 & 2019 & 2020 \\\hline \text{Production (pcs)} & 55\: 000 & 50\: 000& 47\: 000 & 45\: 000 \\\hline \end{array}\]
\( 0.9353 \)
\( 0.9225 \)
\( 0.9898 \)
\( 0.9535 \)

2010013501

Level: 
A
Two years ago, a family business reported gross profit of \(3.5\) million euros. During the pandemic, the company got into trouble so that its last year gross profit fell by \(20\%\) and its gross profit of this year was \(1\) million euros lower than of the last year. What was the average annual decrease in the gross profit reported by the company during the priod under review? Round the result to the tenth of a percent.
\(28.3\%\)
\(27.9\%\)
\(26.7\%\)
\(28.2\%\)