<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
Answer:
80 movies must be streamed.
Step-by-step explanation:
To find the average cost, you must divide the total cost by the number of movies watched.
When you watch 1 movie, you pay the initial fee of $80 plus a $4 purchase of the film.
The equation is shown as such:
average cost = (total cost)/(number of movies)
Your total cost can be represented as 
, while the number of movies is represented as 
.
You want the average to equal 5, so your equation is shown as follows:
simplifying this, we get
which can then be simplified to
X = 80 movies.
Not sure but I think it's (3)
Answer:
25% decreased by 60% is 10
Step-by-step explanation:
New value =
25 - Percentage decrease =
25 - (60% × 25) =
25 - 60% × 25 =
(1 - 60%) × 25 =
(100% - 60%) × 25 =
40% × 25 =
40 ÷ 100 × 25 =
40 × 25 ÷ 100 =
1,000 ÷ 100 = 10
hope this helps :)
Answer:
B) Scalene Triangle
Step-by-step explanation:
This must be a scalene triangle because:
If it were a right triangle, there would be a right angle so A is out
If it were an equilateral triangle, all 3 angles would be equal to each other so C is out
If it were an isosceles triangle, 2 angles would be equal to each other so D is out
A scalene triangle consists of angles that add up to 180 degrees, but none of them are equal to each other. Therefore B is right.
