Answer:
![\dfrac{38}{3}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B38%7D%7B3%7D%20)
Step-by-step explanation:
![12\dfrac{2}{3} =](https://tex.z-dn.net/?f=%2012%5Cdfrac%7B2%7D%7B3%7D%20%3D%20)
![= 12 + \dfrac{2}{3}](https://tex.z-dn.net/?f=%20%3D%2012%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20)
![= \dfrac{12}{1} + \dfrac{2}{3}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B12%7D%7B1%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20)
![= \dfrac{12}{1} \times \dfrac{3}{3} + \dfrac{2}{3}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B12%7D%7B1%7D%20%5Ctimes%20%5Cdfrac%7B3%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20)
![= \dfrac{36}{3} + \dfrac{2}{3}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B36%7D%7B3%7D%20%2B%20%5Cdfrac%7B2%7D%7B3%7D%20)
![= \dfrac{38}{3}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B38%7D%7B3%7D%20)
Answer:
0.0062 = 0.62% probability of this occurring
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
![\mu = 2000, \sigma = 20](https://tex.z-dn.net/?f=%5Cmu%20%3D%202000%2C%20%5Csigma%20%3D%2020)
a. If the process overfills the bottle by more than 50 milliliters, the overflow will cause a machine malfunction. What is the probability of this occurring
Probability of filling the bottle with more than 2000 + 50 = 2050 milliliters, which is 1 subtracted by the pvalue of Z when X = 2050. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{2050 - 2000}{20}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B2050%20-%202000%7D%7B20%7D)
![Z = 2.5](https://tex.z-dn.net/?f=Z%20%3D%202.5)
has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability of this occurring
Ugh, I hate FLVS. I'm not exactly sure, but i know that 2 to the 12 power is 24, and 2 to the fourth power is 8. Sorry I'm not being very helpful.
We know that point M is a midpoint of segment RS, and line l passes through segment RS. Since l passes through RS at its midpoint, M, then we can declare that l is the bisector of RS. Your best answer is A since the above is the basic definition of a bisector.