Answer:
The probability that the ball drawn from the second box is red is 40/99
Step-by-step explanation:
We can divide the event that the second ball drawn is red into 2 disjoint events, and obtain its probability by summing both probabilities for the disjoint cases.
- Case 1: The ball drawn from the first box is red and the ball drawn for the second box is also red
- Case 2: The ball drawn from the first box is green but the ball drawn from the second box is red
For the first case, we have 11 balls in the first box, 7 of them being red. Thus, the probability of drawing a red ball is 7/11. After that, we will put the red ball drawn in the second box, so that it will have 9 balls in total, 4 of them being red. As a consecuence, the probability of drawing a red ball in this instance is 4/9. We need to multiply that probability by the probability that a red ball was drawn first, so we have a probability of 7/11 * 4/9 = 28/99 that the balls drawn are both red.
Now, lets go to the second case. The probability of drawing a green ball from the first box is 4/11, and after placing that ball in the second box, the probability that the new ball drawn is red is 3/9 = 1/3; this is because we will have 3 red balls out of a total of 9 (6 are green). Thus, the probability of this second event is 4/11 * 1/3 = 4/33.
Combining both probabilities, the probability that the ball drawn in the second box is red is 28/99 +4/33 = 40/99 = 0.40404040404...
This is the theory of exponential growth. Given that the an athlete is training to run marathon and she plans to run 2 miles in the first week and increase the distance by 8%. The function modeling how far she will run the nth week will be given by
nth=ae^(bx)
nth=2e^(0.08x)
where x is the nth time.
Answer:
28?
Step-by-step explanation:
Answer:
X = 3/2
Step-by-step explanation:
2(4X - 3) + 2 = 8
8X - 6 + 2 = 8
8X - 4 = 8
8X = 12
X = 3/2
Answer:
-16/65
Step-by-step explanation:
Given sinα = 3/5 in quadrant 1;
Since sinα = opp/hyp
opp = 3
hyp = 5
adj^2 = hyp^2 - opp^2
adj^2 = 5^2 = 3^2
adj^2 = 25-9
adj^2 = 16
adj = 4
Since all the trig identity are positive in Quadrant 1, hence;
cosα = adj/hyp = 4/5
Similarly, if tanβ = 5/12 in Quadrant III,
According to trig identity
tan theta = opp/adj
opp = 5
adj = 12
hyp^2 = opp^2+adj^2
hyp^2 = 5^2+12^2
hyp^2 = 25+144
hyp^2 = 169
hyp = 13
Since only tan is positive in Quadrant III, then;
sinβ = -5/13
cosβ = -12/13
Get the required expression;
sin(α - β) = sinαcosβ - cosαsinβ
Substitute the given values
sin(α - β) = 3/5(-12/13) - 4/5(-5/13)
sin(α - β)= -36/65 + 20/65
sin(α - β) = -16/65
Hence the value of sin(α - β) is -16/65
