The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.
<h3>What is the nth term of an arithmetic series?</h3>
The nth term of an arithmetic sequence is calculated by the formula
aₙ = a + (n - 1) · d
Here the first term is 'a' and the common difference is 'd'.
<h3>Calculation:</h3>
The given sequence is an arithmetic sequence.
3, 7, 11, 15, 19, ....
So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.
Thus, the required 21st term in the sequence is
a₂₁ = 3 + (21 - 1) × 4
⇒ a₂₁ = 3 + 20 × 4
⇒ a₂₁ = 3 + 80
∴ a₂₁ = 83
So, the 21st term in the given arithmetic sequence is 83.
Learn more about the arithmetic sequence here:
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Answer:
The confidence interval for 90% confidence would be narrower than the 95% confidence
Step-by-step explanation:
From the question we are told that
The sample size is n = 41
For a 95% confidence the level of significance is ![\alpha = [100 - 95]\% = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%5B100%20-%2095%5D%5C%25%20%3D%20%200.05)
and
the critical value of 
is 
For a 90% confidence the level of significance is ![\alpha = [100 - 90]\% = 0.10](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%5B100%20-%2090%5D%5C%25%20%3D%20%200.10)
and
the critical value of is 
So we see with decreasing confidence level the critical value decrease
Now the margin of error is mathematically represented as
given that other values are constant and only 
is varying we have that
Hence for reducing confidence level the margin of error will be reducing
The confidence interval is mathematically represented as
Now looking at the above formula and information that we have deduced so far we can infer that as the confidence level reduces , the critical value reduces, the margin of error reduces and the confidence interval becomes narrower
Just multiply 1000 jumps by 3 to get your answer.
Answer:
9
Step-by-step explanation:
3 3/4= 3.75.
3.75-2=1.75
1.75+5.5=7.25 or 7 1/4
7.25+1.75=9
Answer:
c = -6
Step-by-step explanation:
To find the value of c to make the line pass through the point K = (2, -3), we just need to use the values of x = 2 and y = -3 in the equation, then we find the value of c.
So, we have that:
y - 1.5*x = c
(-3) - 1.5 * (2) = c
-3 - 3 = c
c = -6
So the value of c is -6
To check if the value is correct, we can use the value x = 2 and see if the value of y is -3:
y - 1.5*x = -6
y - 1.5*2 = -6
y - 3 = -6
y = -6 + 3 = -3
So it's correct.
