Answer:
B. weight of a bag of apples
Step-by-step explanation:
A continuous random variable is a variable that is measured not counted. It can be any number between integers in decimal form.
So from the options given above, only the weight of bag of apples is a continuous variable as it will be measured.
While the others cannot be expressed in the form of decimals.
So the correct answer is:
B. weight of a bag of apples ..
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:
Step-by-step explanation:
Given that points scored is the dependent variable Y and Number of people attending the game is the independent variable is independent variable x
The correlation coefficient, slope and intercept are calculated as shown below:
x y
378 54
350 57
320 59
478 80
451 82
250 75
489 73
451 53
410 67
215 78
113 67
250 56
450 85
489 101
472 99
Mean 371.0666667 72.4
std dev 117.5138087 15.42632259
covariance 667.5733333
r 0.394558035
Slope 3.005642934
Intercept 153.4581182
y = 3.006x+153.46 is the regression line.
Corre = 0.3945 (weak positive)
