Answer:
D
Step-by-step explanation:
you take away 12 from the total and you'll find how many Zach read (20) then 12+20=32
Answer:
75, 105
Step-by-step explanation:
12. 180-105 = 75
13. 105
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
Answer:
0.1575
Step-by-step explanation:
Probability of picking a girl is 0.45 and probability of a girl scoring A is 0.35.
Therefore probability of a girl scoring A is 0.45*0.35=0.1575
7272=2(length+width)
Length =6 + 2 width
7272=2( 6+2width +width)
3636= 6+ 3width
3630=3 width
Width= 1210
Length = 6+2(1210)=2426
