Answer:
We have to find the z critical value at 100% - 90% = 10% level of significance.
Since the normal distribution has two tails, we therefore, need to divide the significance level into two tails with each tail having area of 5%.
Now using the standard normal table, the z critical is:
Answer:
The perimeter of polygon ABCD, to the nearest thousandth units is
22.227 units
The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units
The area of polygon ABCD' is 19.5 units²
Step-by-step explanation:
The coordinates forming the polygon are
A (-4,-1), B(-2,3), C(2,2), and D(4,-3)
The perimeter then is given by the sum of the length of the sides as follows;
Length of line between two X and Y points distance, xi and yj apart is
length XY =
Therefore, the length between points AB is
length AB =
= = 4.472 units
Similarly, length BC is given by
Length BC = = 4.123 units
Length CD = = 5.385 units
Length DA = = 8.246 units
The perimeter is equal to;
length AB + Length BC + Length CD + Length DA
= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units
If the point D is moved up 2 units and left 1 unit we have
D' = x-1, y+2 where x and y are the coordinates of point D
D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)
The length D'A = =7 units
The perimeter of polygon ABCD'
length AB + Length BC + Length CD + Length D'A
= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.
The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows
=
=
Triangle ABC we have
A(-4,-1)
B(-2,3)
C(2,2)
=
=
Triangle ACD'
A(-4,-1)
C(2,2)
D'(3, -1)
=
= 10.5 units²
Area of polygon = =
+
= (9 + 10.5) units²
Area of polygon ABCD' = 19.5 units².
Answer:
31
Step-by-step explanation:
The series are given as geometric series because these terms have common ratio and not common difference.
Our common ratio is 2 because:
1*2 = 2
2*2 = 4
The summation formula for geometric series (r ≠ 1) is:
or
You may use either one of these formulas but I’ll use the first formula.
We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.
Therefore, the solution is 31.
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Summary
If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.
Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:
Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:
Above should be applied for series that have common ratio not equal to 1.
Above should be applied for series that have common ratio exactly equal to 1.
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Topics
Sequence & Series — Geometric Series
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Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
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