2. (10 points) Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for discoloration, and 27 were found to be discolored. A total of 562 stones were neither cracked nor discolored. One of the 600 stones is selected at random. For each of the following events, draw the event space for the scenario described above and shade in the area representing the event. Use it to calculate the probability of the event. a. The block is cracked, discolored, or both. b. The block is both cracked and discolored. c. The block is cracked but not discolored.

the answer is that it is true

answers

\3. yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. for example,  57=112−82=292−28257=112−82=292−282.

\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.

can i get some in proving questions 1 and 2?

the diagram shows you   triangle def with de=4, df=9 and de≠df≠ef.

the sum of the lengths of two triangles' sides are always greater than the length of the third side:

substitute sides lengths:

then 5< ef< 13 (option 3 is true).

def is a scalene triangle with all sides of different lengths (option 5 is true, option 2 is false).

answer: correct choices are 1, 3 and 5