B

1003037501

Level: 
B
The difference of one-fifth of the unknown number and one-half of the number is greater than the difference of the number and thirteen. How many natural numbers do satisfy the given condition? (Note: Natural numbers are corresponding to positive integers.)
\( 9 \)
\( 10 \)
infinity
\( 18 \)

1003046904

Level: 
B
We are given the inequality \( \frac1x+1 > \frac3{2x} \). Decide which of the following inequalities has the different solution set than the given inequality has, i.e. choose the inequality which is not equivalent to the given inequality.
\( 1+x > \frac32 \)
\( \frac2x+2>\frac3x \)
\( 1>\frac3{2x}-\frac1x \)
\( \frac1x-\frac3{2x}>-1 \)

1003046903

Level: 
B
We are given the inequality \( 3x+\frac{5-6x}2 > -2 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 0\cdot x > -9 \)
\( 0\cdot x > 9 \)
\( 0\cdot x < -9 \)
\( 3\cdot x > -9 \)

1003046902

Level: 
B
We are given the inequality \( 5-\frac{x+2}3 \leq \frac{2-x}6 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 26-2x \leq 2-x \)
\( 34-2x \leq 2-x \)
\( 26-2x \geq 2-x \)
\( 28-2x \leq 2-x \)

1003046901

Level: 
B
We are given the inequality \( -2x-\frac52 > 5-\frac x3 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 12x+15 < 2x-30 \)
\( 12x+15 > 2x-30 \)
\( 12x-15 > 2x-30 \)
\( 12x-15 < 2x+30 \)

1003030807

Level: 
B
The function \( f(x) \) is increasing in the interval \( J \). Identify which of the following statements is false.
The function \( h(x) = -2 f(x) \) is increasing in the interval \( J \).
The function \( g(x) = 2 f(x) \) is increasing in the interval \( J \).
The function \( m(x) = f(x)+2 \) is increasing in the interval \( J \).
The function \( n(x) = f(x)-2 \) is increasing in the interval \( J \).

1003029402

Level: 
B
A sample of \( 50 \) pieces of pears was selected randomly from the production of the plant breeding institute. The weights of these pears are recorded in the table. \[ \begin{array}{|c|c|} \hline \text{ Weight (g) }&\text{ Number of pears } \\\hline 26\text{ -- }30&8 \\\hline31\text{ -- }35&14 \\\hline 36\text{ -- }40&15 \\\hline 41\text{ -- }45&9 \\\hline 46\text{ -- }50&4\\\hline\end{array}\] Calculate the variance of pear weights and round the variance to the nearest hundredth. (To solve the task with help of calculator is recommended.)
\( 33{.}81\,\mathrm{g}^2 \)
\( 5{.}81\,\mathrm{g}^2 \)
\( 15{.}84\,\mathrm{g}^2 \)
\( 39{.}84\,\mathrm{g}^2 \)

1003029401

Level: 
B
Wooden boards were expected to be cut to the same length. After their cutting the resulting measured lengths are: \( 2{.}00,\ 2{.}02,\ 2{.}05,\ 2{.}02,\ 2{.}08,\ 2{.}11 \) (in meters). We use the standard deviation of board lengths to describe (quantify) the accuracy of cutting. Find the standard deviation of board lengths rounded to four decimal places.
\( 0{.}0382\,\mathrm{m} \)
\( 0{.}0381\,\mathrm{m} \)
\( 0{.}0014\,\mathrm{m} \)
\( 0{.}0015\,\mathrm{m} \)