Answer:
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Step-by-step explanation:
Let (a,b) be the coordinates of the foot of the perpendicular from the point (−1,3) to the line 3x−4y−16=0
Slope of the line joining (−1,3) and (a,b), is m
1
=
a+1
b−3
Slope of the line 3x−4y−16=0 or y=
4
3
x−4,m
2
=
4
3
Since these two lines are perpendicular,m
1
m
2
=−1
∴{
a+1
b−3
}⋅{
4
3
}=−1
⇒
4a+4
3b−9
=−1
⇒3b−9=4a−4
⇒4a+3b=5...(1)
Point(a,b) lies on line 3x−4y=16
∴3a−4b=16....(2)
On solving equation (1) and (2) we obtain
a=
25
68
and b=−
25
49
Thus, the required coordinates of the foot of the perpendicular are {
25
68
,
25
49
}
Answer:
The answer is shown in the plotted graph attached with the answer.
Step-by-step explanation:
i) Let y = f(x)
ii) According to the first equation we will consider x = -6, -5, -4, -3, -2, -1, 0, and
1
Therefore x and y = x + 4 for -6 ≤ x < 2
- -6 -2
- -5 -1
- -4 0
- -3 1
- -2 2
- -1 3
- 0 4
- 1 5
iii) y = 6 when x = 2 is the second equation given for the graph
iv) x y = -x + 2 for x > 2 is the third equation given
The scatterplot that shows a negative linear association between the variables is B
Answer:
The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072
Step-by-step explanation:
In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:
p(0) = (1 - 0.312)^(12) = 0.688^(12) = 0.01124
We now need to calculate the probability that one child learns to swim before 6 years of age.
p(1) = 12*0.312*(1 - 0.312)^(11) = 3.744*(0.688)^(11)
p(1) = 3.744*0.01634
p(1) = 0.0612
The probability of 1 or less children from that group to learn how to swim before 6 years of age is:
p = p(0) + p(1) = 0.01124 + 0.0612 = 0.07244
