Examples for secondary school students - page 227 of 237
Number of problems found: 4730
- Sales
From statistics of sales goods, item A buys 77% of people, and item B buys 58% of people. What is the probability that from 15 people buy 8 item A and 7 item B? - TV fail
On average, a television set experiences 25 failures per 10,000 hours of use. Find the probability of a failure occurring within 400 hours of operation. - Earth's circumference
Calculate the length of the circle of latitude at 48°10′ on Earth. - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=19, a perpendicular is drawn from point A to diagonal BD, meeting it at point P. Determine the ratio r = (|PB|)/(|DP|). - Rhombus
A rhombus has a side length of a = 20 cm. The points where the inscribed circle touches the sides divide each side into segments of length a₁ = 13 cm and a₂ = 7 cm. Calculate the radius r of the inscribed circle and the lengths of the diagonals of the rho - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the centre S[x₀, y₀] and the radius r of the circle. - Freedom
In the city are 2/4 of women married for 4/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number. - Pine
How much of a mixed forest will a ranger cut down, given the following instructions: "We are cutting down only pine trees, which currently make up 97% of our mixed forest. After the cutting, pine trees should constitute 92% of all remaining trees." - Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube. - Trapezoid MO
Right-angled trapezoid ABCD has a right angle at vertex B. Given that |AC| = 12, |CD| = 8, and the diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Beer
After drinking three 10° beers in a short time, there are 5.2 g of alcohol in the blood of an adult weighing 5 kg. How much is this in per mille? - Ravens
In the tale of the Seven Ravens, there were seven brothers, each born exactly 4 years after the previous one. When the eldest was 4 times older than the youngest, their mother put a curse on all of them. How old were the seven brothers when their mother c - Area of RT
Calculate the area of a right triangle in which the hypotenuse has length 14 and one of the segments that the altitude creates on the hypotenuse has length 5. - Derivation
Does there exist a function whose derivative is the function itself? - Radians
Convert 90° to radians. Write the result as a multiple of π. - Discount
A ladies' sweater was discounted twice: first by 8%, then by 8% of the new price. Its final price was 66 €. Determine the original price of the sweater. - Permill
How many permills is 1141 from 98313? - Cotangent
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α. - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height hc = 70 cm. Determine the length of both triangle legs.
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