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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The solutions to the questions are given below
a)
sample(n) word length sample mean
1 5,4,4,2 3.75
2 3,2,3,6 3.5
3 5,6,3,3 4.25
b)R =0.75
c)
- The mean of the sample means will tend to be a better estimate than a single sample mean.
- The closer the range of the sample means is to 0, the more confident they can be in their estimate.
<h3>What is the students are going to use the sample means to estimate the mean word length in the book.?</h3>
The table below shows sample means in the table.
sample(n) word length sample mean
1 5,4,4,2 3.75
2 3,2,3,6 3.5
3 5,6,3,3 4.25
b)
Generally, the equation for is mathematically given as
variation in the sample means
R =maximum -minimum
R=4.25-3.5
R =0.75
c)
In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.
They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.
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Answer:
52degrees
Step-by-step explanation:
Let the measure of the largest angle be x
middle angle be y
smallest angle be z
Since the sum of angle in a triangle is 180 degrees, hence;
x + y + z = 180 .... 1
If the measure of the largest angle is 32 less than 3 times the smallest angle, then;
x = 3z - 32
3z = x+ 32
z = x+32/3 ..... 2
If he measure of the middle angle is 8 more than half the measure of the largest angle, then;
y = x/2 + 8 .... 3
Substitute 2 and 3 into 1;
x + x/2 + 8 + (x+32)/3 = 180
multiply through by 6
6x + 3x + 48 + 2(x+32) = 1080
9x + 48 + 2x + 64 = 1080
11x + 112 = 1080
11x = 1080-112
11x = 968
x = 968/11
x = 88 degrees
Get the middle angle y;
Since y = x/2 + 8
y = 88/2 + 8
y = 44 + 8
y = 52 degrees
Hence the measure of the middle angle is 52degrees
The footage is 1000 square footage
Answer:
The slope of the line is -5
