The intersection point of the two lines is (2,1,0).
The respective direction vectors are
L1: <1,2,4>
L2: <4,1,15>
Since the normal vector of the required plane is perpendicular to both direction vectors, the normal vector of the plane is obtained by the cross product of L1 and L2.
i j k
1 2 4
4 1 15
=<30-4, 16-15, 1-8>
=<26, 1, -7>
We know that the plane must pass through (2,1,0), the equation of the plane is
26(x-2)+1(y-1)-7(z-0)=0
simplifying,
26x+y-7z=52+1+0=53
or
26x+y-7z=53
Check:
Put points on L1 in the plane
26(t+2)+(2t+1)-7(4t+0)=53 ok
For L2,
26(4t+2)+(t+1)-7(15t+0)=53 ok
Answer:
1.50 I think
Step-by-step explanation:
51.50-50 equals 1.50
the sales tax is close to 217.94
Answer:
0.505 = 50.7% probability of a negative test.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
142 + 6 = 148 people tested positive. Of those, 142 had the disease and 6 did not.
7 + 145 = 152 people tested negative. Of those, 7 had the disease and 145 did not.
Find the probability of getting someone who tests negative, given that he or she did not have the disease.
This is the probability of a negative test.
152 negative tests out of 148 + 152 = 300
152/300 = 0.507
0.505 = 50.7% probability of a negative test.