# Examples for 9th grade - page 33

- A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 1. - Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 13 cm and one cathetus 2 cm. Height of the prism is equal to 10/7 of the perimeter of the base. Calculate the surface area of prism. - Triangle

The triangle has known all three sides: a=6.7 m, b=6.6 m, c= 11.5 m. Calculate area of this triangle. - Diameter

If the endpoints of a diameter of a circle are A(10, -5) and B (8, 7), what is the radius of the circle? - Car

The driver of a car is to get to 378 km distant city. From atlas found that 99 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 117 km/h. Calculate how many hours it will ta - Simple interest 4

Find the simple interest if 19590 USD at 4.6% for 242 days. Assume a 360-day year. - Rectangle - sides

What is the perimeter of a rectangle with area 1026 cm^{2}if length of the shorter side is 11 cm shorter than the length of the longer side? - Roller

Roller has a diameter of 0.97 m and a width 169 cm. How many m^{2}of road level when he turns 68-times? - Rectangle

Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees. - Driving school

Driving final exam involving 17 attendants. The exam consists of three parts. 4 fails at test (quiz) and 3 students fails on car skills test on playground (slalom between the cone). The practical part of the test - driving in town in the real traffic - al - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 11 cm? - Tank

In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank? - 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 - Free fall

Stephen fall from height 5 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s^{2} - Euler problem

Someone buys a 720 tolars towels. If it was for the same money of 6 more towels, it would be 6 tolars cheaper each. How many were towels? - Rotating cone II

Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm. - Circle and angle

What is the length of the arc of a circle with radius r = 138 cm with cental angle 2.07 rad? - Hollow sphere

Calculate the weight of a hollow brass sphere (density 8.5 g/cm^{3}), if the outer diameter is 10 cm and wall thickness is 3 mm. - Cube - angles

Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base. - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.

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