# Examples for 9th grade - page 17

- Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9° - Amazing number

An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers. - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 14 days, B together with C for 23 days, A together with C for 13 days. How long it would take to complete the task every one of them alone? How long it would. - XY triangle

Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y. - Spherical segment

Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment. - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports? - Blueberries

Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter? - Heron backlaw

Calculate missing side in a triangle with sides 17 and 34 and area 275. - Coin and die

Flip a coin and then roll a six-sided die. How many possible combinations are there? - Leveling

Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m^{2}to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness. - Tractors

Six tractors plowing the field for 8 days. After two days, two tractors broke down. How many days were prolonged work in the field? - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees. - Drunk man

Drunkman has 2.6‰ of alcohol in the blood. How many grams of alcohol has in blood, if he have 5 kg of blood? - Wheat

The rectangle shaped field with dimensions 889 m and 1336 m harvested last year was 6235 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 3 m parallel to the side of the field 1336 m, where. - Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism! - Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16. - Shooter

The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot? - Wiring

Conduit has a cross section 48^{2}mm. Maybe put it into 6 conductors with a cross section S2 $mm^{2}? - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2}. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.

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