Maths practice for 14 year olds - page 67 of 370

Number of problems found: 7400

Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri
Eighty-two 80493
The sports club has 302 members. Ten times more members play soccer than tennis. Just one of the sports (F and T) is played by 222 members. Eighty-two members do not play football. How many members of the club play football? How many members play tennis?
The electric motor
The electric motor winding's copper wire (alpha=4*10^-3 1/K) has a resistance of 42 ohms at a temperature of 18 degrees. What is its resistance at an operating temperature of 50 degrees?
Nikelin and brass
Calculate the length of brass wire (ró=0.08 microohm m) and nickel (ró=0.4 microohm m) with a diameter of 0.5 mm, which has a resistance of 1 ohm
Resistivity 80483
The heating coil of the cooker has a resistance of 70.5 ohms and is made of a wire with a diameter of 0.30 mm and a length of 9.8 m. Determine the resistivity of the material from which it is made.
The grocery
Susan has decided to make grocery combos for her shop. The wholesaler she buys from sells sugar in packets of 20 in a carton, flour in packets of 12 a carton, and 15 bags of rice in a carton. How many of each item should she buy so there are an equal numb
Conductor 80474
A constant current of 80mA passes through the wire. What charge passes through the conductor in 1 h?
The sum 28
The sum of the age of a girl and her mother is 38. Next year the mother will be four times as old as her daughter. How old was the mother when her daughter was born?
Calculate 80467
Calculate the current I that would race through resistor R5 (720 ohms), resistor R2 (220 ohms), and an LED (U=2V) at a DC 6V source. The resistors are connected in series.
Ava bought
Ava bought snacks for her team's practice. She bought a bag of oranges for $2.71 and a 4-pack of juice bottles. The total cost before tax was $6.75. Write and solve an equation that can be used to determine juice cost, how much each bottle of juice cost
Martin: 80465
Kuba, Martin, and Pepa earned CZK 1,813. They divided them in the ratio Cuba: Martin 6:5. Martin: Pepa 2:3. How many crowns did each of them get?
Perpendicular 80464
A group of tourists split up at the intersection of two perpendicular paths. One group walked at a speed of 5.3 km/h. Second group 4.1km/h. How far were the two groups from each other after 1h 25min?
Hypotenuse 80461
The ratios of the sides of a right triangle are 3: 4: 5. How long is the hypotenuse if the entire perimeter of the triangle is 48 cm?
Arranged 80453
There are 390 trees arranged in rows in the orchard. How many rows are there if each row has the same number of trees greater than 30 and less than 40?
Coordinates 80452
A (a1, 4) B(7, -2) segment AB has a center where both coordinates are equal
The ages 2
The ages of the two persons differ by 18 years. Twelve years ago, the elder one was 4 times as old as, the younger one. The present age of the elder one is:
Grazing 80444
Forty sheep graze in the meadow. There are 4 times more whites than blacks. How many white and how many black sheep are grazing in the meadow?
Approximately 80443
The 94 m² flower bed is to be planted with begonias. An area of 2 dm² is needed for one seedling. How many grams of seeds should be sown if 1 g of seeds contains approximately 5000 seeds? Losses when growing seedlings are usually 30%.
Average 80442
The daily need for fat for a person is 80g on average. Almonds contain 45% fat. How many grams of almonds would a person have to eat if he wanted to cover his daily need for fats by eating only almonds?
Decrease 80441
By what percent does a cube's volume decrease if its edge length is reduced by a quarter?

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