Answer:
And we can find the individual probabilities using the probability mass function
And replacing we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And for this case we want to find this probability:
And we can find the individual probabilities using the probability mass function
And replacing we got:
Answer:
No solution
Step-by-step explanation:
This is no solution due to the fact that the slope of both of the equation are the same. So they are parallel. If the b value is the same then it is infinitely many solutions. Due to the fact that the b value is not the same they are a set of parallel line. Parallel line do not touch or intersect ever so there for this is a no solution set.
This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where
m=slope of line
(x0,y0) is a point through which the line passes.
We know that the line passes through A(3,-6), B(1,2)
All options have a slope of -4, so that should not be a problem. In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.
So we can check which line passes through which point:
a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3) means that line passes through A(3,-6) => ok
b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
****** this equation is not the line passing through A & B *****
c. y=-4x+6 subtract 2 from both sides (to make the y-coordinate 2)
y-2 = -4x+4, rearrange
y-2 = -4(x-1)
which means that it passes through B(1,2), so ok
d. y-2=-4(x-1)
this is the same as the previous equation, so it passes through B(1,2),
this equation is ok.
Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
Answer:
The percentage increase in bird population in the second years is 4% .
Step-by-step explanation:
Given as :
During two years, the population of birds of an island became 7 times more than before.
The the percentage increase in first year = = =40%
Let The percentage increase in second year = = r%
So, According to question
The initial population of bird = x
The increase population of bird =7 times before = 7 x
Now,
The increase population of bird = initial population of bird × (1+ ) × (1+ )
Or, 7 x = x × (1+ ) × (1+ )
Or, = 1.4 × (1+ )
Or, 7 = 1.4 × (1+ )
Or, = (1+ )
Or, 5 = (1+ )
Or, (1+ ) = 5
Or, = 5 - 1
Or, = 4
∴ r = 4 × 100
I.e r = 400
so, The percentage increase = r% = 4
Hence The percentage increase in bird population in the second years is 4% . Answer
Recall that
where is the angle between the vectors whose magnitudes are , respectively.
We have