# Examples for secondary school students - page 47

- Three friends

Divide 570 euros to three friends so that first will get 50 euros less than the second and third twice more than the first. How many euros will get everyone? - Nuts

Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts. - Ladder slope

What is the slope of a ladder 6.2 m long and 5.12 m in height. - Sphere vs cube

How many percent of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Crystal water

The chemist wanted to check the content of water of crystallization of chromic potassium alum K_{2}SO_{4}* Cr_{2}(SO_{4}) 3 * 24 H_{2}O, which was a long time in the laboratory. From 96.8 g of K_{2}SO_{4}* Cr_{2}(SO_{4}) 3 * 24 H_{2}O prepared 979 cm^{3}solution of base. S - Numbers at ratio

The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers? - Lines

How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line? - Variations

Determine the number of items when the count of variations of fourth class without repeating is 42 times larger than the count of variations of third class without repetition. - Billiard balls

A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T - Pentagon

Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm. - 3s prism

It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism. - Normal Distribution

At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5? - Quatrefoil

Calculate area of the quatrefoil which is inscribed in a square with side 6 cm. - Candies

If Alena give Lenka 3 candy will still have 1 more candy. If Lenka give Alena 1 candy Alena will hame twice more than Lenka. How many candies have each of them? - Doctor 2

A doctor noted the Diastolic Blood Pressure (DBP) of a large number of patients. Later, he scrambled the data to keep the privacy of his patients. Based on the scrambled dataset, he finds that the lower inner fence is equal to 50 and the upper inner fenc - Truncated cone 5

The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone? - Water tank

The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second? - Three friends

Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much. - Roots

Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ? - Store

Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store?

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