Examples for 9th grade - page 33

Train from Brno
First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
TV diagonal
Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
Flowerbed
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m² =.
Simple interest 2
Find the simple interest if 13905 USD at 4.5% for 6 months.
Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
Mushrooms from the forest
Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda?
Lathe
Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
Raffle
How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.
Skier
At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first?
The professor's birthday
Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc
Squaring the Circle
Calculating side of the square with the same area as the circle of radius 18.
Triangle
Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
ISO Triangle V2
Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
Again saw
From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
3sides prism
The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
Pennies
800 pennies have the same value as 100 ducats. 100 pennies have the same value as 250 tolars. How many ducats has the same value as 100 tolars?
Gon functions
Decide which of the numbers (values of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
Retail
At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 4% of weight of the goods and retail still have a profit of 6.3%? Goods are sold at retail for 25 euro per kg.
Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
Math logic
There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w

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