# Examples for secondary school students

- Three reds

What is the probability that when choosing 3 carats from seven carats, all 3 reds will be red? - Regular n-gon

In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places. - Sequence 11

What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ? - Arithmetic progression

In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ? - Photocopier

A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page? - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo - Tricolors

From the colors - red, blue, green, black and white, create all possible tricolors. - Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm^{3}. - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Krkonose CZ

Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Cuboid height

What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic? - Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip? - Hollow sphere

The volume of the hollow ball is 3432 cm^{3}. What is its internal radius when the wall thickness is 3 cm? - Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate? - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - VCP equation

Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0 - BTC bubble

One of the world's experts in bubbles -- Prof. Robert Shiller, a Yale economist -- said Bitcoin "was an amazing example of a bubble" back in 2014. If you exchange fiat US dollar $100 to BTC in 2010, now in 2017 have value of 72.9 millions dollars. Find

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