Math practice for 13 year olds - page 402 of 414
Number of problems found: 8279
- Bath
There are 30 liters of hot water in the bath. Then we added 39 liters of cold water at a temperature of 19 °C and decreased the temperature of the water to 45 °C. What was the initial temperature of the hot water? - Solution
In 201 l, the red solution is 143 l in red color, and in 227 l, the blue solution is 112 l in blue color. How many l of red and blue l color solution must be mixed to get a mixture of 242 l to contain 121 l of color? - Warehouses
To four warehouses is going cement in 50 kg bags, from first one third to the second quarter of the total. The third store got two-thirds of the rest, and the last 120 tons came to fourth. How much cement is in all warehouses, and how much got everyone? - IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Scrap
From 18 products are 5 scraps. What is the probability that the random pick of 2 products has no defective product? - Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm. - Tape
Video is 199% more expensive than a tape recorder. How many percent is a tape recorder less expensive than a video? - Spherical cap
From a sphere with radius 26, a spherical cap was cut. Its height is 2. What part of the volume is a spherical cap from the whole sphere? - Elections
The elections attended a total of 1450 voters. First-day 48 men more than women, the second-day 16 women more than men. How many women attended elections? - Rectangular cuboid
The rectangular cuboid has a surface area 4131 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Troops
The route is 175 long km. On the first day, the first regiment went at an average speed of 14 km/h and back at 24 km/h. On the second day, the second regiment went on the same route at an average speed of 25 km/h there and back. Which regiment will take t - Pizza
A school survey found that 10 out of 15 students like pizza. If 5 students are chosen randomly, what is the probability that all 5 students like pizza? - 2x cone
A circular cone of height 36 cm is cut by a plane parallel to the base, dividing it into two smaller cones of equal volume. Calculate the height of the smaller cone. - Pediatrician
Pediatrician, this month of 20 working days takes 4 days holidays. What is the probability that it will be at work on Monday? - Work
The first paving machine can pave a pavement in 28 hours, and the second in 26 hours. The first machine started working, and after 2 hours the second machine joined it. How long after the second machine starts will they finish the job together? - Cone
A circular cone of height 14 cm and volume 4396 cm³ is cut at one third of its height (measured from the base) by a plane parallel to the base. Calculate the radius and circumference of the circular cross-section. - 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 - 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.
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