Answer:
- If a group of 9 kids have won a total of 100 trophies, then at least one of the 9 kids has won at least 12 trophies.
- If a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee.
- The average of three real numbers is greater than or equal to at least one of the numbers.
Explanation:
1)
Suppose that each kid has less than 12 trophies
Total trophies = 100
Maximum trophies won by one kid = 11
total kids = 9
total number of trophies = 9 * 11 = 99 which contradicts the fact the total number of trophies are 100
2)
Suppose that person has less than 2 cups of coffee a day
Total cups of coffee = 400
he has bought at least one cup of coffee each day
which means
total number of cups of coffee = 1* 366 = 366 which contradicts the fact the person buys at least 400 cups of coffee in a year
3)
Average of three number = (a+ b+ c)/3
suppose that there are real numbers a, b, and c such that all three numbers are less than the average of the three numbers.
Let m be the average (a+b+c
)/3 = m. Then our assumption states that (a < m) and (b < m) and (c < m). By adding all the inequalities we get a + b + c < 3m. But m is defined to be (a+b+c)
/3 , so a + b + c = 3m. But now we have that 3m = a + b + c < 3m. So 3m < 3m which is an obvious contradiction. Thus our claim is true
211x=6A•16
211x=96A
211x=96A
___. ___
211. 211
x=96A
___
211
It's hard to show fractions on here :•)
Answer:
He can use following computer program to make the class room more interesting and effective:-
- 1. <u>Reference software</u> : This software help students to access the atlases and dictionaries.Teacher can include this software in research projects .
- 2. <u>Educational Games</u>: This types of software is very effective for younger children because it motivates them to learn.This software companies have combined gaming and education into one .
- 3. <u>Graphical software</u> : Student can use this software to create and changes images available on the internet itselfs .
Answer:
Microsoft Word can dohjr iiejdnff jfujd and
They are versatile because they can be used for all sorts of tasks. They can also do many of the same tasks in different ways. They are diligent because they will do a task thoroughly until it is finished.
They work at a constant speed to do the task. Unlike a human, they will not slow down or get bored or start making mistakes that they were not doing earlier. So once they are programmed correctly to do a task, they will do it diligently.
