Examples for 9th grade - page 49
- The ship
The ship went upstream speed of 20 km/h in relation to water. River flows at speed 10 km/h. After half an hour, he stopped and returned downstream to the starting point. How long it took way back when even if downstream speed of ship is 20 km/h in relation
We burned two unequally thick and long candles. Longer burnt for three and a half hours and shorter for five hours. After two hours of burning it was identical. How many times was longer candle longer then shorter?
- 3 days
Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day.
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
- Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
Base of perpendicular triangular prism is a right triangle with cathetuses 4.5 cm and 6 cm. What is the surface of the prism, if its volume of 54 cubic centimeters.
- V - slope
The slope of the line whose equation is 8x +8 = 0 is
- Garden pond
Concrete garden pond has bottom shape of a semicircle with a diameter 1.1 m and is 47 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 22 cm?
- Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
- Quadratic function
It is given a quadratic function y = -5x2+12x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
The sum of all deviations from the arithmetic mean of the numerical sequence 1, 7, 7, 26, 43, 47, 80, 96, 113, 120 is:
Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load?
- Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
The speedometer of a car reads 78 km/h. It's accurate to within 4.2% What is the maximum possible error?
- Middle segment
In a triangle ABC with the side /AB/ = 24 cm is constructed middle segment /DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
6 m long reservoir has a diameter of 2.2 m. What is its surface area in square meters?
Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
Three siblings had saved up a total of 1,274 CZK. Peter had saved up to 15% more than Jirka and Hanka 10% less than Peter. How much money they saved each one of them?
- Copy typist
Typist for 12 hours rewritten 15% of the manuscript. After how many hours he will done 35% of the manuscript?
The square of the first number is equal to three-fifths of the second number. Determine both numbers if you know that the second number is 5 times greater than the first, and neither of numbers is not equal to zero.