B

9000138304

Level: 
B
Two different dice (a white die and a black die) are rolled. Find the probability that we get the number \(3\) on the black die and a number different from \(3\) on the white die.
\(\frac{5} {36}\doteq 0{.}1389\)
\(\frac{3} {36}\doteq 0{.}0833\)
\(\frac{6} {36}\doteq 0{.}1667\)
\(\frac{1} {36}\doteq 0{.}0278\)

9000128803

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). The point \(M\) is the middle of the side \(CV \). Find the distance between the point \(M\) and the line \(AD\).
\(\frac{\sqrt{97}} {2} \, \mathrm{cm}\)
\(\frac{\sqrt{106}} {2} \, \mathrm{cm}\)
\(\frac{\sqrt{65}} {2} \, \mathrm{cm}\)

9000128804

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). Find the distance between the line \(AD\) and the plane \(BCV \).
\(\frac{24} {5} \, \mathrm{cm}\)
\(\frac{15\sqrt{34}} {5} \, \mathrm{cm}\)
\(6\, \mathrm{cm}\)

9000121803

Level: 
B
Consider a regular polygon with the central angle of \(24^{\circ }\). In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of diagonals in this polygon.
\(90\)
\(15\)
\(72\)
\(45\)

9000128805

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). Find the angle between the line \(BV \) and the plane \(ABC\). Round to two decimal places.
\(43.31^{\circ }\)
\(59.04^{\circ }\)
\(45^{\circ }\)

9000121809

Level: 
B
The number of diagonals in a regular polygon is \(2.5\)-times bigger than the number of the sides of this polygon. In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the central angle of the polygon.
\(45^{\circ }\)
\(50^{\circ }\)
\(135^{\circ }\)
\(35^{\circ }\)

9000128806

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). The point \(M\) is the middle of the side \(CV \). Find the angle between the line \(AM\) and the plane \(ABC\). Round to two decimal places.
\(17.45^{\circ }\)
\(34.50^{\circ }\)
\(18.32^{\circ }\)

9000128801

Level: 
B
The base \(ABCD\) of a square pyramid \(ABCDV \) has side \(6\, \mathrm{cm}\). The height of the pyramid is \(4\, \mathrm{cm}\). The point \(M\) is the middle of the side \(CV \). Find the distance between the point \(M\) and the plane \(ABC\).
\(2\, \mathrm{cm}\)
\(\frac{\sqrt{34}} {2} \, \mathrm{cm}\)
\(\frac{5} {2}\, \mathrm{cm}\)