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sertanlavr [38]
3 years ago
12

What is the answer for this?

Mathematics
1 answer:
ra1l [238]3 years ago
3 0

Answer:

Proved

Step-by-step explanation:

Given

(2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7

Required

Prove

On the right hand side, we have:

2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7

Rewrite:

2 * 3* 10^2  * 10^5 = 3.5 * 10^7 + 2.5 * 10^7

6* 10^2  * 10^5 = 3.5 * 10^7 + 2.5 * 10^7

Apply law of indices

6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7

6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7

Express 6 as 3.5 + 2.5

(3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7

Open bracket

3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7

Proved

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This is a case of joint probability: you want to know what the odds are of this event AND that event occurring. For a joint probability, the formula is usually given as:

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where P(A) is the probability of event A happening, P(B) is the probability of event B happening, and P(A and B) is the probability of both happening.

For this problem, let's say that event A is the probability that the spinner stops at the green color. Since the spinner has 3 colors and they have equal area (sector) occupied in the circle, each color has the same chance, 1/3 chance of being picked. Thus, there's a 1/3 chance of the spinner stopping at the green color so P(A)=1/3.

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Using the formula, we can then calculate P(A and B), the probability that the spinner stops at green and a yellow card is selected:

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