# Examples for 9th grade - page 55

- Sum 10

What is the probability that two dice throw twice in a row will result the sum of 10? - Land areas

Two land areas is 244 m^{2.}The first parcel is 40 m^{2}less than twice of the second one. What have acreage of each parcel? - Tickets

On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)? - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum - Forces

Determine the resultant of two perpendicular forces F_{1}= 560 N and second force of 25% smaller. - Three numbers

Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67. - Locomotive

Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done? - Rectangle - desc circle

Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter. - Chimney

Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney. - The cone

The lateral surface area of the cone is 4 cm^{2,}the area of the base of the cone is 2 cm^{2.}Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci - Triangle SSA

Construct a triangle ABC if |AB| = 5cm v_{a}= 3cm, CAB = 50 °. It is to create the analysis and construction steps. - Bath salts

Bath salt A weighs 900 grams and costs 36,40 CZK. Bath Salts B weighs 1000 grams, but costs 85 CZK. How much is a bath salt A cheaper than B one? - Two boxes-cubes

Two boxes cube with edges a=74 cm and b = 91 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge? - Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part? - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 8 days? - Positive number z

Positive number z is 10% greater than the number y. How many % is y smaller than z? Report the result rounded to one decimal place. - Surface area

The volume of a cone is 1000 cm^{3}and the content area of the axis cut is 100 cm^{2.}Calculate the surface area of the cone. - Chord 3

What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm? - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2.}What were the original dimensions of the hall?

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