# Grade - examples - page 144

- Bags

The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights. - Hypotenuse

Calculate the length of the hypotenuse of a right triangle with a cathetuses 71 cm and 49 cm long. - Cuboid enlargement

By how many percent increases the volume of cuboid if its every dimension increases by 30%? - Cuboid surface

Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm. - Working together

One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together? - Cars 6

At 9:00 am two cars started from the same town and traveled at a rate of 35 miles per hour and the other car traveled at a rate of 40 miles per hour. After how many hours will the cars be 30 miles apart? - Televisions

Television is the fifth most expensive and tenth cheapest TV. How many different TVs are in stores? - Divisible by 5

How many three-digit odd numbers divisible by 5, which are in place ten's number 3? - Water reservoir

The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used. - De Moivre's formula

There are two distinct complex numbers z such that z^{3}is equal to 1 and z is not equal 1. Calculate the sum of these two numbers. - Circle - simple

The circumference of a circle is 930 mm. How long in mm is its diameter? - Calculation

How much is sum of square root of six and the square root of 225? - Two-digit number

I am a two-digit number less than 20. When I divided by three, then you get the rest 1 and when you divide me by four you get also rest 1. What number am I? - Family

Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother? - AP 6

Calculate the first five items of an arithmetic sequence if it is given: a_{2}– a_{3}+ a_{5}= 20 a_{1}+ a_{6}= 38 - Angles in ratio

The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z. - Scale 3

Miriam room is 3.2 meters wide. It is draw by line segment length 6.4 cm on floor plan. In what scale it is plan of the room? - Equation

? - Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter. - Four friends

Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together?

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