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
128 ounces or divided by 16 equaling 8 ounces of liquid
Step-by-step explanation:
the mean value is the sum of all values divided by how many values there are.
so,
(3 + -5 + 70 + -90 + -13) / 5 = -35/5 = -7
-7° F is the mean temperature of the 5 cities.
Answer:
0.5
Step-by-step explanation:
There are 15 pieces of the same size candy in the bag. Two are orange flavored, six cherry flavored. So the probability of picking an orange or a cherry flavored candy is 6/15+2/15=8/15≈0.5
Answer:
3
Step-by-step explanation:
24x (1/8) = 3
hope this helps
