This is rationalising the denominator of an imaginary fraction. We want to remove all i's from the denominator.
To do this, we multiply the fraction by 1. However 1 can be expressed in an infinite number of ways. For example, 1 = 2/2 = 3/3 = 4n^2 / 4n^2 (assuming n is not zero!). Let's express 1 as the complex conjugate of the denominator, divided by the complex conjugate of the denominator.
The complex conjugate of (3 - 2i) is (3 + 2i). Then do what I just said:
4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13
This is the answer you are looking for. I hope this helps :)
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Note: Question does not indicate if probability required is for weight to exceed or below 3000 lbs. So choose appropriate answer accordingly (near the end)
Using the usual notations and formulas,
mean, mu = 3550
standard deviation, sigma = 870
Observed value, X = 3000
We calculate
Z = (X-mu)/sigma = (3000-3550)/870 = -0.6321839
Probability of weight below 3000 lbs
= P(X<3000) = P(z<Z) = P(z<-0.6321839) = 0.2636334
Answer:
Probability that a car randomly selected is less than 3000
= P(X<3000) = 0.2636 (to 4 decimals)
Probability that a car randomly selected is greater than 3000
= 1 - P(X<3000) = 1 - 0.2636 (to 4 decimals) = 0.7364 (to 4 decimals)
The solution will be (7,-5), so the y-value is -5
