Maths practice for 14 year olds - page 188 of 370

Number of problems found: 7395

Five numbers in ratio
Five integers are in the ratio 1:2:3:4:5. Their arithmetic mean is 12. Determine the smallest of these numbers.
AM of three numbers
The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
Frustum of a cone
A reservoir contains 28.54 m³ of water when complete. The diameter of the upper base is 3.5 m, while the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone.
What 11781
What is greater: 2/5 of 10, or 20% of 4000?
Mathematicians 11761
The top five mathematicians in the class took on the teacher's help in calculating the paper's average grade. They dictated the following results: Mischa: "I came up with 3.30. " Dasha: "That's weird because it worked out precisely at 3.45. " Jana: "You p
Alcohol
6l 48% alcohol, how much must we add 52% alcohol to give 50% alcohol?
Distance 11711
The observer sits in a room 2 m from a 50 cm wide window. A road runs parallel at a distance of 500 m. What is the cyclist's average speed on this road when the observer sees him at 15 seconds?
Cost reduction
Fourteen pieces of goods cost just as much as 21 pieces before the discount. The price of one piece after the discount is CZK 1.50 lower than before the price reduction. How much was one piece before the discount?
Cylinder and its circumference
The height of a cylinder is four times its circumference, c. What is the volume of the cylinder in terms of its circumference c?
Propeller
The aircraft propeller rotates at an angular speed of 200 rad/s. A) What is the speed at the tip of the propeller if its distance from the axis of rotation is 1.5 m? B) What path does the aircraft travel during one propeller revolution at a speed of 540 k
Reducing balance method
A company buys an item having a useful life of 10 years for 1,000,000. If the company depreciates the item by the reducing balance method, a. find the depreciation for the first year. b. Estimate the depreciation for the second and third years. c. What is
Pozdechodim 11611
Mr. Pozdechodim missed the bus at 10.05. At 10.10, he passed Jindra. The bus travels at an average speed of 60 km/h and Jindra at 80 km/h. Will they catch the bus, which is 20 km from the next stop?
Budějovice 11601
At midnight, a 40km/h truck will leave České Budějovice for Turnov. At 1.5 hours after midnight, a 70 km/h car drove against him. The distance between České Budějovice and Trutnov is 223 km. At what time and how far from Trutnov will the two cars meet?
Surface of the cylinder
Calculate the surface of the cylinder for which the shell area is Spl = 20 cm² and the height v = 3.5 cm.
Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
Boys and girls
There are 20 boys and ten girls in the class. How many different dance pairs can we make of them?
Compound interest 3
After eight years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly? (interest is now a dream - in the year 2019)
Minutes 11521
The road from Brno to Hodonin is 60 km long. Lenka left Hodonin at a speed of 4 km/h, and at the same time, Jonas left Brno on a moped for her. What was the moped's speed if Jonas and Lenka met in 1 hour and 30 minutes?
Construct rhombus - MO
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all possibilities. How long is a side of a rhombus?
Z8–I–5 MO 2019
For eight different points as shown in the figure, points C, D, and E lie on a line parallel to line AB, F is the midpoint of line AD, G is the midpoint of line AC, and H is the intersection of lines AC and BE. The area of triangle BCG is 12 cm² and the

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