# Examples for 9th grade

- Gold, silver, bronze

How many ways can we divide gold, silver, bronze medails if there are 6 people competing? - The angles

The angles in the triangle are in the ratio 12: 15: 9. Find the angles. - The manufacturer

The manufacturer found that 3% of the plates produced had a malfunction. Of the compliant, 75% are first and 25% second. What is the probability of producing first and second class plates? - Probability

How probable is a randomly selected three-digit number divisible by five or seven? - The coal

The coal stock would be enough to heat a larger room for 12 weeks, a smaller one for 18 weeks. It was heated for four weeks in both rooms, then only in a smaller one. How long was the coal stock enough? - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - Cllub flag

The children had the club flag sewn on. The red color covered 2/20 of the total area of the flag, the blue area a fifth, the yellow 19% of the total area. What% is the green area occupied? - The four

The four pirates divided 65 coins to each other. They were sorted by age, the youngest receiving the least number of coins, each half more than the previous one. How many coins did the oldest pirate receive? - In a

In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - Five letters

How many ways can five letters be arranged? - Digging

The first worker would dig a trench in 6 hours. For the second, the same work would take 4 hours. How long did it take for the trench to be dug if they worked together? - Closed circuit

In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage. - Flakes

A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips? - Price reduction

The product is sold for 360 CZK and the sales profit is 30%. By what percentage the sales profit will be reduced if I reduce the price of the product by 10%? - Energy consumption

The device is connected to 230V and draws 3.5A current. Power consumption is 1932kJ. How many minutes has this device been in operation? - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - Double price reduction

The price of TV has been reduced twice. First by 15% and later by another 10% of the reduced price. After this double price reduction, the TV was sold for 8,874 crowns. What was the original price of the TV? - Annulus from triangle

Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm - The conical

The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?

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