# Examples for 9th grade - page 13

- Madams

During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe - Diofant equation

In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58° - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Octahedron - sum

On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also. - Cubes

Cube, which consists of 27 small cubes with edge 4 dm has volume: - Freedom

In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number. - Map

On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes. - Phone numbers

How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - Clocks

How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand? - Triangle ABC

Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle h_{AB}to the side AB. - Building

How high is the building that throws horizontal shadow 95.4 m long at angle 50°? - Square diagonal

Calculate the length of diagonal of the square with side a = 4 cm. - 4side pyramid

Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees. - Trains

From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. - Wire

One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls? - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - Prism

Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5. - Two doctors

Doctor A will determine the correct diagnosis with a probability 86% and doctor B with a probability 87%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors.

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