Answer:
0.89736
Step-by-step explanation:
We solve this question using z score formula
Z score = x - μ/σ
x = raw score
μ = population mean
σ = population standard deviation
Hence,
x = 258, μ = 220, σ = 30
Z = 258 - 220/30
=1.26667
Probability value from Z-Table:
P(x<258) = 0.89736
Therefore, the probability that his weights is less than 258 kg is 0.89736
Answer:
Doman is the x intercpet range
Step-by-step explanation:
all real numbers is the domain since the function goes on and on forever and will at one point get to 1 billion or trillion or just on and on forever.
Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)
We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>
The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>
Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>
The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).
The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24
Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.
Answer:
(x-2)^2 + (y-3)^2 = 4
Step-by-step explanation:
Use the equation (x-h)^2 + (y-k)^2 = r^2 where the center of the circle is (h,k) and the radius is r.
