# 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 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 x3=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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