# Examples for 8th grade - page 119

1. Find midpoint FM=5y+13, MG=5-3y, FG=? M is the midpoint of FG. Use the given information to find the missing measure or value.
2. A kite ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
3. Days2minutes Write a formula that converts x days to y minutes. The formula is:
4. Proportion 3 For every 8 mango trees in the orchard, there are 4 star apple trees. If there are 1320 trees, how many trees of each kind are there?
5. A sculptor A sculptor is duplicating a statue based on an original statue. If the scale factor of the replication is 3.2, will the new statue be larger or smaller than the original statue (enter 1 = larger, 0= smaller)
6. The devils The devils weighed in hell with Dorota. They found that Dorota and the two devils weigh 250 kg together and Dorota and the four devils weigh 426 kg. All the devils weigh the same. How Much Does Dorota Weigh?
7. Balls From the bag with numbered balls (numbers 1,2,3,. ..20) we pick one ball. What is the probability of choosing a number containing 1?
8. Average speed The truck drove 1/2 of the way on the highway at 80km/h. The other half of the way 20km/h. Calculate the average speed
9. Bag of peanuts Joe eat 1/3 of a bag of peanuts, mark eat 1/4 of the remaining in the bag of peanuts, Alvin eat 1/2 of the remaining bag of peanuts, peter eat 10 peanuts, there are 71 peanuts left. Hon many peanuts were in the bags?
10. Positive integers Several positive integers are written on the paper. Michaella only remembered that each number was half the sum of all the other numbers. How many numbers could be written on paper?
11. Dice and coin A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
12. Divide Divide the number 72 in the ratio 7: 2 and calculate the ratio of the numbers found in this order and write down as decimal.
13. Pebble The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
14. RPM An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
15. Drive to NJ Ed drove to New Jersey at 30mph. He drove back home in 3 hours at 50 mph. How many hours did it take Ed to drive to New Jersey?
16. Working alone Tom and Chandri are doing household chores. Chandri can do the work twice as fast as Tom. If they work together, they can finish the work in 5 hours. How long does it take Tom working alone to do the same work?
17. Tree trunk What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
18. Three pumps together One pump fills the tank in 1.5 hours, the second in 2 hours, and the third in 3 hours 20 minutes. How many minutes will the tank fill with three pumps if they work simultaneously?
19. The second The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
20. Pine's forest There were so many pines in the forest that if they were sequentially numbered 1, 2, 3,. .. , would use three times more digits than the pine trees alone. How many pine trees were there in the forest?

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