The
chance to land on the number three is only a ¼ or 0.25 chance. Knowing that we
can also understand the law of large numbers. The law of large numbers states
that as the number of spins gets very large, eventually the experimental
probability will reach the theoretical probability. Eight spins of the spinner
is not a large number, so the probabilities will be different. In this case
resulting in zero times landing on three. Therefore, Megan should not be
concerned that the spinner is unfair.
Answer:

Step-by-step explanation:

1. set the equation for the area of each shape equal to each other
2. simplify each side until you get 
3. subtract 16 from both sides which will give you 
4. subtract 3x from both sides which will give you the value of x. 
5. check that
is correct by plugging it into the equations
triangle:

rectangle:

the areas are the same
3/5 I think sorry if I’m wrong
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:
![CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]](https://tex.z-dn.net/?f=CI%20%3D%20%5Coverline%7Bx%7D%20%5Cpm%20Z_%7B%5Calpha%20%2F2%7D%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%5C%5CCI%20%3D%20138%20%5Cpm%201.645%5Ctimes%20%5Cdfrac%7B34%7D%7B%5Csqrt%7B90%7D%7D%5C%5C%5C%5CCI%20%5Capprox%20138%20%5Cpm%205.896%5C%5CCI%20%5Capprox%20%5B138%20-%205.896%2C%20138%20%2B%205.896%5D%5C%5CCI%20%5Capprox%20%5B132.104%2C%20143.896%5D%20%5Capprox%20%5B130.10%2C%20143.90%5D)
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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