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:
Company B
Step-by-step explanation:
Company A charges 25 per window, company b charges 40 per window, and company c charges 35 per window so company b has the highest rate
So the change in between terms is 5 so you would put 5x, then for the first term, which is 2, 5*1(x)(because it's first term) then the difference between 5-2(because it's the 2nd term) So you would plug 100 in for x so 5(100)-3=497. Hope this helped!
Answer:
c. Cluster sampling
Step-by-step explanation:
Taking into account that the exercise researcher is looking with limited resources to study a population that is divided, her best option is cluster sampling, which is a method applicable to this type of population, we could select in each group randomly her sample, the observational study is discarded because she does not have much availability of time or resources, nor would the stratified study be useful because she should select subgroups and create them to take samples and this would take more time and resources and sampling systematic is not adequate because it must have all the individuals and after having the list select the sample, but as we know, it is a process that will study the number of individuals so this option is not feasible.
Answer:
c = <u>0.5 cm</u>
Step-by-step explanation:
Using the Sine rule in the triangle, then
= ( cross- multiply )
c × sin105° = 2 × sin15° ( divide both sides by sin105°
c = ≈ 0.5 cm ( to the nearest tenth )
