Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to wi
1 answer:
Answer:
0.46 (46%)
Step-by-step explanation:
The following data is available:
- The probability of player V achieving victory in the first set:
(as indicated, both players are equally able to win the first set)
- The chance of player V winning the 2nd set provided success in the 1st set:
Thus, the probability of player V winning the first 2 sets is:
(1)
Conversely, the possibility of player V losing the 2nd set after winning the 1st set is 0.40 (=1-0.60), leading to
Hence, the probability that player V wins the 1st set yet loses the 2nd set is
(2)
Also, it is noted that:
- The likelihood that player V loses the 1st set:
- The probability of her losing the 2nd set in this situation amounts to 0.70, implying the chance of winning the 2nd set after losing the 1st is 0.30, hence:
Thus, the probability that she loses the 1st set but wins the 2nd set is:
(3)
Combining (2) and (3) results in the probability that player V wins exactly 1 set from the first two is:
(4)
At this stage, the likelihood that she wins the 3rd set is
Thus, the total probability that she wins the 3rd set after winning only 1 of the first 2 sets is:
(5)
Ultimately, the overall chance that player V triumphs against player M can be expressed as the sum of (1) and (5):
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During an archaeological excavation, an ancient campfire is uncovered. The charcoal is determined to have significantly less than 1/1000 of the standard amount of . Calculate the minimal age of the charcoal, taking into account that
Response:
57300 years
Step-by-step breakdown:
Using the relationship of half-life time against fraction, which can be expressed as:
In this context,
N indicates the current atom
represents the initial atom
denotes the half-life
Thus;
However; the objective is to estimate the minimum age of the charcoal while noting
this means , then:
If
Then
Consequently, it can be estimated that the minimum time elapsed is 10 half-lives.
For , the standard half-life time is 5730 years
Thus, the estimation of the minimum age of the charcoal is 5730 years × 10
= 57300 years
Answer:
The scale factor is measured to be 2.5.
Step-by-step explanation:
The triangles are depicted below.
In triangle ΔABC,
the side lengths are AB = 2 units, BC = 2 units
In triangle ΔA'B'C',
the side lengths are A'B' = 5 units, B'C' = 5 units.
The formula for the scale factor in a dilation is given by:
Scale factor =
Thus, the scale factor is 2.5.
