Describe fully the single transformation which takes shape A to shape B.
2 answers:
Answer:
Clockwise rotation 90° about the center of (4,3)
Step-by-step explanation:
A, B, C: (1,6) (3,8) (5,6) -> A'B'C' (7,6) (9,4) (7,2)
clockwise 90° rotation formula:
x' = (y - y₀) + x₀ x: original x₀: center
y' = - (x - x₀) + y₀
For A (1,6) -> A' (7 , 6)
7 = (6 - y₀) + x₀ x₀ - y₀ = 1 ... (1)
6 = - (1 - x₀) + y₀ x₀ + y₀ = 7 ... (2)
(1) + (2): 2 x₀ = 8 x₀ = 4
(2)-(1): 2 y₀ = 6 y₀ = 3
Rotation center: (4 , 3)
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The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
<h3>How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>
Suppose that we have:
- Sample size n > 30
- Sample mean =
- Sample standard deviation = s
- Population standard deviation =
- Level of significance =
Then the confidence interval is obtained as
- Case 1: Population standard deviation is known
- Case 2: Population standard deviation is unknown.
For this case, we're given that:
- Sample size n = 90 > 30
- Sample mean =
= 138
- Sample standard deviation = s = 34
- Level of significance =
= 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).
At this level of significance, the critical value of Z is: = ±1.645
Thus, we get:
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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