# Examples for 9th grade - page 71

1. Two numbers We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
2. Land - isosceles trapezoid Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
3. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
4. Timber log The ship goes from point x to y. Downstream it takes 4 hours, upstream 6 hours. How long does it take from a point x to y a log?
5. Roof 8 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
6. Glass Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?
8. Chord circle The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
9. Church roof 2 The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
10. Tickets On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
11. Three numbers What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
12. Balls The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
13. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
14. Three-digit How many three-digit natural numbers do not have the number 7?
15. 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.
16. Cuboid enlargement By how many percent increases the volume of cuboid if its every dimension increases by 30%?
17. 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?
18. 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.
19. Divisible by 5 How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
20. AP 6 Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38

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