Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
Answer:
4.5 hours
Step-by-step explanation:
distance equals rate times time, a relationship that can be solved for time:
time = distance / rate
Here the time is (135 miles) / (30 mph) = 4.5 hours
The bus requires 4.5 hours to get to the museum.
quotient is 6 and the remainder is 23
Answer is $330.63 because 15% of 287.5 is 43.125 then you add 47.125 to 287.5 and get 330.63
So decrease is 375-250=75
so convert 75/375 to percent
percent means part out of 100 so
x/100=x%
divide 125/375=0.3333/1
multiply by 100/100=33/100=33%
the answer is 33% or B
