Answer:
Step-by-step explanation:
![\frac{10}{1 + 2i} \\ \\ = \frac{10}{1 + 2i} \times \frac{1 - 2i}{1 - 2i} \\ \\ = \frac{10(1 - 2i)}{ {1}^{2} - {(2i)}^{2} } \\ \\ = \frac{10 - 20i}{ {1} - {4i}^{2} } \\ \\ = \frac{10 - 20i}{ {1} - {4( - 1)} } \\ ( \because \: {i}^{2} = - 1) \\ \\ = \frac{10 - 20i}{1 + 4} \\ \\ = \frac{5(2 - 4i)}{5} \\ \\ = 2 - 4i](https://tex.z-dn.net/?f=%20%5Cfrac%7B10%7D%7B1%20%2B%202i%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%7D%7B1%20%2B%202i%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%20%20-%20%202i%7D%7B1%20%20-%20%202i%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%281%20-%202i%29%7D%7B%20%7B1%7D%5E%7B2%7D%20-%20%20%7B%282i%29%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B%20%7B1%7D%20-%20%20%7B4i%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B%20%7B1%7D%20-%20%20%7B4%28%20-%201%29%7D%20%7D%20%20%5C%5C%20%28%20%5Cbecause%20%5C%3A%20%20%7Bi%7D%5E%7B2%7D%20%3D%20%20-%201%29%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B10%20-%2020i%7D%7B1%20%2B%204%7D%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%282%20-%204i%29%7D%7B5%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%202%20-%204i)
They should ideally be the same. However, the difference is that the theoretical probability is what is expected to happen while the experimental probability is what happens in the actual scenario. The computation for both would be the same, and they should ideally be the same, unless other factors in an experiment would confound it.
3. primal. 4. venture. 5. venture
The values on the number line are between 0 and 1. There are 8 points from 0. The distance between two consecutive points would be
1/8 = 0.125
Since the given point is on the second point after 0, the equivalent value would be
2 * 1/8 = 2/8
Dividing the numerator and denominator of 2/8 by 2, we have 1/4
Thus, the two equivalent fractions for the point on number line are
2/8 and 1/4