Examples for 9th grade - page 22
- Monty Hall
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
- Triangular prism
Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
Rhombus has two diagonals e=11 dm and f=17 dm. Calculate the side angle and height of the rhombus.
- Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix?
- Area codes
How many 6 digit area codes are possible if the first number can't be zero?
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
- Hexagon 5
The distance of parallel sides of regular hexagonal is 81 cm. Calculate the length of the radius of the circle described to this hexagon.
The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost
- Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
Determine the slope of the line perpendicular to the line p: y = 9x +7.
Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 352 dm and the other diagonal BD has length 148 dm.
- The car
The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B.
- Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
- Tank and water
Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in?
How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number.
Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it is
Line segments 52 cm and 7.6 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
- Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 2184. Calculate how many books Ladislav could buy at the price of 42 and 28 euros if he don't want fill whole home library and he can buy only 63 books?
- Rectangular trapezoid
The rectangular trapezoid having bases length 3.2 cm and 62 mm. The shorter arm has a length 0.25 dm. Calculate the lengths of the diagonals and the second arm.