# Examples for secondary school students

#### Number of problems found: 2186

- Trapezoid 15

Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4 - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it? - Birth

Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy? - Vertices of a right triangle

Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. - Circus

On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus? - Cube in sphere

The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius. - Variance and average

Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx). - Rectangle - sides 4

Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5. - Medicine

We test medicine on 6 patients. For all drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work? - Parallelogram

The parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides. - Decimal to fraction

Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures. - XY triangle

Determine the area of a triangle given by line 7x+8y-69=0 and coordinate axes x and y. - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Grandson and granddad

Grandson with grandpa, they counted how many years have together. Their product is 365. How many years is the sum of their years? - Against each other

From two points A, B distant 23 km at the same time started two cars against each other at speeds 41 km/h and 65 km/h. How long does cars meet and what distance passes each of them? - Equation

How many real roots have equation x^{3}=x ? - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Lion or virgin

We toss the coin, and every throw fits a lion or a virgin with an equal probability of 1/2. Determine how much we have to make throws that with probability 0.9 lion fell at least once. - Newtonmeters

The driver loosened the nut on the car wheel with a wrench that held 20 cm from the axis of the bolt. He acted on the key with a force of 320N. At what moment did he act on the bolt? - Friction coefficient

What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07

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