The correct answer is the choice that you have selected, the third choice.
When, we are looking at the residuals for a regression line, we always want to see the points balance like in the third choice. This means that the equation that we found is right in the middle of the points.
The probability of picking a green marble the first time is 3/20 and the probability of picking a yellow marble the second time is 8/20.
probabilities are heavily related to percents so it would make sense that the probability of picking a color would be the number of that color divided by the total number.
note that it is really important that the problem said that the marble was replaced. If the marble was not replaced, the probability of picking a yellow marble the second time would be 8/19 if the first marble picked was not a yellow one.
I hope this helps.
Answer:
<u><em></em></u>
- <u><em>Event A: 1/35</em></u>
- <u><em>Event B: 1/840</em></u>
<u><em></em></u>
Explanation:
<u>Event A</u>
For the event A, the order of the first 4 acts does not matter.
The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.
Thus, the number of ways that the first <em>four acts</em> can be scheduled is:


And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).
Therefore the<em> probability of Event A</em> is:

Event B
Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.
The number of ways in which <em>four acts </em>can be scheculed when the order matters is:


The number of ways <em>the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth</em> is 1: P(4,4)
Therefore, <em>the probability of Event B</em> is:

Its probably a fraction.
You would know the answer if you researched what your question was on google
(t^2+1)^100
USE CHAIN RULE
Outside first (using power rule)
100*(t^2+1)^99 * derivative of the inside
100(t^2+1)^99 * d(t^2+1)
100(t^2+1)^99 * 2t
200t(t^2+1)^99