It is true that the product of two consecutive even integers are always one less than the square of their average.
<u>Step-by-step explanation</u>:
Let the two consecutive odd integers be 1 and 3.
- The product of 1 and 3 is (1
3)=3 - The average of 1 and 3 is (1+3)/2 =4/2 = 2
- The square of their average is (2)² = 4
∴ The product 3 is one less than the square of their average 4.
Let the two consecutive even integers be 2 and 4.
- The product of 2 and 4 is (24)=8
- The average of 2 and 4 is (2+4)/2 =6/2 = 3
- The square of their average is (3)² = 9
∴ The product 8 is one less than the square of their average 9.
Thus, It is true that the product of two consecutive even integers are always one less than the square of their average.
Given:
First term of an arithmetic sequence = 5
Second term = 3
To find:
The explicit formula for the given arithmetic sequence.
Solution:
We have,
First term: 
Second term: 
Common difference is
Now, the explicit formula for an arithmetic sequence is
where, a is first term and d is common difference.
Putting a=5 and d=-2, we get
It can also be written as
Here, n is an integer greater than or equal to 1.
Domain is the set of input values.
Therefore, the explicit equation is or and domain is all interest greater than or equal to 1.
I thinks it C, this a difficult question but idk, that my closest guess...
Answer:
Th computed value of the test statistic is 3.597
Step-by-step explanation:
The null and the alternative hypothesis is as follows:
Null Hypothesis:
the population correlation coefficient is equal to zero
the population correlation coefficient is not equal to zero
The test statistics for Pearson correlation coefficient is thus computed as :
where;
r = correlation coefficient = 0.60
n = sample size = 25
So;
t = 3.597
Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069
Decision Rule:
Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.
Conclusion:
We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.
