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Answer:
Step-by-step explanation:
The conjugate is found by changing the sign of the square root term.‡ (For this purpose, i = √-1.)
a) the sign of 3i is changed: 2 + 3i
b) the sign of sqrt(-5) is changed: 8 -sqrt(-5) = 8 -i√5
c) the sign of 2i is changed: 7 +2i
d) the sign of sqrt(7) is changed: 4 +√7
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‡ Actually, the conjugate of a binomial is formed by changing the sign <em>between</em> terms. The purpose is to allow the product of the binomial and its conjugate to be the difference of squares.
Conventionally, the conjugate of a complex number is the value with the sign of the imaginary part reversed. That is why (-2i+7)* = 7+2i.
1. The probability that we select a red marble is 1/3.
We found this out by taking the amount of red marbles there are and the total amount of marbles. The total amount of marbles is 18 and there are red marbles. So, it would become 6 out of 18 or 6/18. Then, we simplify 6/18 to the simplest form. The greatest common factor of both of those numbers is 6. Lastly, we divide each of them by 6 to get the simplest form.
6/18 = (6/6)/(18/6)
(6/6)/(18/6) = 1/3
So, therefore, the theoretical probability of picking a red marble is 1/3.
2. The probability that we select a blue marble is 2/3.
We can find this out by taking the amount of blue marbles there are and the total amount of marbles. We know that the total amount of marble is 18 and there are 12 blue marbles. So, we simply get the GCF (greatest common factor) and divide them by it.
Greatest Common Factor of 12 and 18 = 6
12/18 = (12/6)/(18/6)
(12/6)/(18/6) = 2/3
Thus, the theoretical probability of picking a blue marble is 2/3.
Answer:
90
Step-by-step explanation:
