Answer:
The equation is:
![409 = T - 223](https://tex.z-dn.net/?f=409%20%3D%20T%20-%20223)
And the solution is:
![T = 632](https://tex.z-dn.net/?f=T%20%3D%20632)
Step-by-step explanation:
Given
Represent Kiran with K and Tyler with T
Kiran score is represented as:
![K = 409](https://tex.z-dn.net/?f=K%20%3D%20409)
Also, Kiran scored 223 less than Tyler.
This is represented as:
![K = T - 223](https://tex.z-dn.net/?f=K%20%3D%20T%20-%20223)
Substitute 409 for K
![409 = T - 223](https://tex.z-dn.net/?f=409%20%3D%20T%20-%20223)
Make T the subject
![T = 409 +223](https://tex.z-dn.net/?f=T%20%3D%20409%20%2B223)
![T = 632](https://tex.z-dn.net/?f=T%20%3D%20632)
Answer:
The triangles are not similar
Step-by-step explanation:
In scientific notation :
32 million miles is 3.2 x 10 ^7 miles.
Using the z-distribution, it is found that the lower limit of the 95% confidence interval is of $99,002.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
The other parameters are given as follows:
![\overline{x} = 111000, \sigma = 36730, n = 36](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%3D%20111000%2C%20%5Csigma%20%3D%2036730%2C%20n%20%3D%2036)
Hence, the lower bound of the interval is:
![\overline{x} - z\frac{\sigma}{\sqrt{n}} = 111000 - 1.96\frac{36730}{\sqrt{36}} = 99002](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20111000%20-%201.96%5Cfrac%7B36730%7D%7B%5Csqrt%7B36%7D%7D%20%3D%2099002)
The lower limit of the 95% confidence interval is of $99,002.
More can be learned about the z-distribution at brainly.com/question/25890103
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