Answer:
option B
![\frac{31}{50}-\frac{4}{25} i](https://tex.z-dn.net/?f=%5Cfrac%7B31%7D%7B50%7D-%5Cfrac%7B4%7D%7B25%7D%20i)
Step-by-step explanation:
Given in the question a complex fraction
<h3>Step1</h3>
To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.
![\frac{5+4i}{6+8i}(\frac{6-8i}{6-8i})](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B4i%7D%7B6%2B8i%7D%28%5Cfrac%7B6-8i%7D%7B6-8i%7D%29)
<h3>Step2</h3>
Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
![\frac{30+24i-40i-32i²}{36-64i^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B30%2B24i-40i-32i%C2%B2%7D%7B36-64i%5E%7B2%7D%20%7D)
<h3>Step3</h3>
Simplify the powers of i, specifically remember that i² = –1.
![\frac{62-16i}{36+64}](https://tex.z-dn.net/?f=%5Cfrac%7B62-16i%7D%7B36%2B64%7D)
<h3>Step4</h3>
![\frac{62}{100}-\frac{16i}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B62%7D%7B100%7D-%5Cfrac%7B16i%7D%7B100%7D)
<h3>Step5</h3>
simply
![\frac{31}{50}-\frac{4}{25}i](https://tex.z-dn.net/?f=%5Cfrac%7B31%7D%7B50%7D-%5Cfrac%7B4%7D%7B25%7Di)
Answer:
0.7486 = 74.86% observations would be less than 5.79
Step-by-step explanation:
I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)
Problems of normally distributed samples can be solved using 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.
The general format of the normal distribution is:
N(mean, standard deviation)
Which means that:
![\mu = 5.43, \sigma = 0.54](https://tex.z-dn.net/?f=%5Cmu%20%3D%205.43%2C%20%5Csigma%20%3D%200.54)
What proportion of observations would be less than 5.79?
This is the pvalue of Z when X = 5.79. 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{5.79 - 5.43}{0.54}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B5.79%20-%205.43%7D%7B0.54%7D)
![Z = 0.67](https://tex.z-dn.net/?f=Z%20%3D%200.67)
has a pvalue of 0.7486
0.7486 = 74.86% observations would be less than 5.79
Mary = (1/3)x
Erin = x - 8
John = x
Here is your equation:
(1/3)x + (x - 8) + x = 267
Take it from here.
5^2 = 25
3^0 = 1 (anything that is exponented by 0 is 1)
25 - 1 = 24
24 is your answer
hope this helps
Answer:
x + 6
Step-by-step explanation:
If you dont know the value of x you cant solve the problem fully