# Examples for 9th grade - page 16

- Compass

What angle are between directions W (West) and SE (SouthEast) on the compass? - Shooter

The shooter fired to a target from distance 9 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 16'(angle degree minutes). How many points should win his shot? - Triangle angles

The angles α, β, γ in triangle ABC are in the ratio 10:5:6. Calculate size of angles. - 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. - Scrap

From 8 products are 2 scrap. What is the probability that the random pick of 2 products have no defective product? - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - XY triangle

Determine area of triangle given by line -7x+7y+63=0 and coordinate axes x and y. - Coin and die

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

Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo - Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm^{2.}What is the area of the trapezoid? - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 40 m. Water depth at beginning of pool is 1.15 m (for children) and depth at end is 1.92 m (for swimmers). Slope express as percentage and as angle in degrees. - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3} - 3y inflation

Price of the medicament rise in the first year by 8%, the second year fell by 4% and in the third year increased by 10%. Calculate the average annual increase in price of the medicament. - Road

Average climb of the road is given by ratio 1:29. By what angle road average climb? - Black building

Jordan built building with a rectangular shape 5 m × 5.1 m. Calculate how much percent exceeded the limit 25 m^{2}for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenching - Mystery of stereometrie

Two regular tetrahedrons have surfaces 56 cm^{2}and 126 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Divisibility

Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Drunk man

Drunkman has 2.1‰ of alcohol in the blood. How many grams of alcohol has in blood, if he have 6 kg of blood? - Lid

What is the weight of concrete cover (lid) to round shape well with a diameter 1.3 m, if the thickness of the cover is 15 cm? 1 m^{3}of concrete weighs 2190 kg.

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