Standard form of a point that goes through-2,4 and the slope is -1/7
1 answer:
<u>Answer:</u>
Standard form of a line passing through (-2, 4) and having slope of -1/7 is x + 7y = 26
<u>Solution:</u>
Given that we need to determine standard form of a line that goes through (-2 , 4) and slope of the line is -1/7
Standard form of line passing through point ( a , b ) and having slope m is given by
(y – b) = m ( x – a) --------(1)
In our case given point is ( -2 , 4 ) and slope is -1/7 that means
a = -2 , b = 4 , m = -(1/7)
On substituting given value of a , b and m is equation (1) we get
=> 7( y - 4 ) = -x – 2
=> 7y + x = -2 + 28
=> x + 7y = 26
Hence standard form of a line passing through (-2,4) and having slope of –(1/7) is x + 7y = 26
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Answer:
(a) The histogram is shown below.
(b) E (X) = 4.2
(c) SD (X) = 2.73
Step-by-step explanation:
Let <em>X</em> = <em>r</em><em> </em>= a driver will tailgate the car in front of him before passing.
The probability that a driver will tailgate the car in front of him before passing is, P (X) = <em>p</em> = 0.35.
The sample selected is of size <em>n</em> = 12.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 12 and <em>p</em> = 0.35.
The probability function of a binomial random variable is:
(a)
For <em>X</em> = 0 the probability is:
For <em>X</em> = 1 the probability is:
For <em>X</em> = 2 the probability is:
Similarly the remaining probabilities will be computed.
The probability distribution table is shown below.
The histogram is also shown below.
(b)
The expected value of a Binomial distribution is:
The expected number of vehicles out of 12 that will tailgate is:
Thus, the expected number of vehicles out of 12 that will tailgate is 4.2.
(c)
The standard deviation of a Binomial distribution is:
The standard deviation of vehicles out of 12 that will tailgate is:
Thus, the standard deviation of vehicles out of 12 that will tailgate is 2.73.
