Answer with Step-by-step explanation:
We have to prove that
is true for all sets A and B
Let 
Then
or 
and
or 
Hence,
Conversely ,Let 
Then x belongs to A and x does not belongs to B then
x belongs to A- B
Or x belongs to A and x belongs to B then x belongs to 
Hence, 
Therefore, 
a.
b.
The metal obey this law for values of strain until 0.05, where we have a linear relationship (each increase of 0.01 in the strain causes an increase of 100 in the stress). After this point, we don't have a linear relationship anymore.
c. Since an increase of 0.01 in the strain causes an increase of 100 in the stress, the slope is:

Now, calculating the coefficient b (y-intercept), we have:

So the equation is:

d.
The maximum value of stress is 560, and occurs at strain = 0.07.
Answer: 1.091 which is approximately 1 word per second
Step-by-step explanation:
Jack can text 180 words in 2 minutes and 45 seconds. We would convert 2 minutes to seconds
60 seconds = 1 minute
x seconds = 2 minutes
x = 2×60 = 120 seconds
2 minutes 45seconds = 120+45 = 165 seconds
This means Jack can text 180 words in 165 seconds
Let's find his unit rate in texts per second
if jack texts 180 words in 165 seconds
Then jack texts y words in 1 second
165y = 180
y = 180/165= 1.091 words per second
This is approximately 1 word per second
Answer:
<3, <2 or <6
Step-by-step explanation:
<h3>
Answer: 31 games</h3>
======================================================
Explanation:
- 32/2 = 16 games will happen in round 1. Afterward, 16 teams are left.
- 16/2 = 8 games will happen in round 2. Afterward, 8 teams are left.
- 8/2 = 4 games happen in round 3.
- 4/2 = 2 games in round 4.
- 2/2 = 1 game as the final championship.
Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.
To get the total number of games played, we add up the quotients
16+8+4+2+1 = 31
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Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1
We can write that rule as

which is equivalent to
