Answer: 1/3 (x + 6)
Explanation: given f(x) = 3x - 6.
Let y = f(x) and so y = 3x - 6.
Trade places between x and y.
x = 3y - 6
Solve for y
x + 6 = 3y
y = x + 6/3
Now the new y is the inverse and so y = f-1(x)
f-1(x) = 1/3(x + 6)
Answer:
0.6517
Step-by-step explanation:
Given that in a certain game of chance, your chances of winning are 0.3.
We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)
Also there are only two outcomes
Let X be the number of games you win when you play 4 times
Then X is binomial with p = 0.3 and n =4
Required probability
= Probability that you win at most once
= 
We have as per binomial theorem
P(X=r) = 
Using the above the required prob
= 0.6517
Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.
2 standard deviations = 2 × 0.5 = 1
63 - 1 = 62 seconds
63 + 1 = 64 seconds
Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.
