<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.
The difference between these temperatures for the sunset is found as 11 degrees.
<h3>What is temperature difference?</h3>
In science, the term Delta T (ΔT) refers to the temperature between two measuring points. The temperature varies according to time and/or location.
Some key features regarding the temperature difference are-
- Merus, for example, uses it to assess the effectiveness of such a heat exchanger.
- Or to evaluate the effectiveness of a heating or cooling system.
- A fourth letter of a Greek alphabet is, (Δ). Whereas is the capital letter symbol and the lower case letter.
- The sign is also used in mathematics. Describes the "difference" between any two changeable quantities. T is a value in a process that represents a difference between two observed temperatures.
Now, according to the question;
Let the initial temperature be 'T' = 4 degrees.
Let the final temperature be 't' = -7 degrees.
Therefore, the temperature difference is;
ΔT = T - t
= 4 - (-7)
= 4 + 7
ΔT = 11
Therefore, the difference between these temperatures is 11 degrees.
To know more about the temperature difference, here
brainly.com/question/24746268
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Answer:
84%
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
So for 190000 we have:
z = (190000 - 200000) / (10000)
z = -1
and this value represents 0.1587
for 230000 we have:
z = (230000 - 200000) / (10000)
z = 3
and this value represents 0.9987
we subtract:
0.9987 - 0.1587 = 0.84
Which means that it represents 84% of the houses
The answer is 0.04444... or 2/45. Whichever is more useful to you.
You would have to divide $16.76 by 4 to find out how much 1 gallon costs and after that multiply the amount a gallon costs by 7 to get your answer
