Answer:
a) Var[z] = 1600
D[z] = 40
b) Var[z] = 2304
D[z] = 48
c) Var[z] = 80
D[z] = 8.94
d) Var[z] = 80
D[z] = 8.94
e) Var[z] = 320
D[z] = 17.88
Step-by-step explanation:
In general
V([x+y] = V[x] + V[y] +2Cov[xy]
how in this problem Cov[XY] = 0, then
V[x+y] = V[x] + V[y]
Also we must use this properti of the variance
V[ax+b] = 
V[x]
and remember that
standard desviation = ![\sqrt{Var[x]}](https://tex.z-dn.net/?f=%5Csqrt%7BVar%5Bx%5D%7D)
a) z = 35-10x
Var[z] = 
Var[x] = 100*16 = 1600
D[z] = 
= 40
b) z = 12x -5
Var[z] = 
Var[x] = 144*16 = 2304
D[z] = 
= 48
c) z = x + y
Var[z] = Var[x+y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] = 
= 8.94
d) z = x - y
Var[z] = Var[x-y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] = = 8.94
e) z = -2x + 2y
Var[z] = 4Var[x] + 4Var[y] = 4*16 + 4*64 = 320
D[z] = 
= 17.88
Step-by-step explanation:
the volume of a box (or prism) is always
length × width × height
so, box A
13 × 12 × 16 = 2,496 in³
box B
18 × 25 × 16 = 7,200 in³
box C
12 × 14 × 22 = 3,696 in³
box D
20 × 22 × 17 = 7,480 in³
so, she can use B or D.
Answer:
Solution:
the boat's speed in still water: x
The speed with current: (x+3)
The speed against current: (x-3)
The equation is
3(x+3) = 4(x-3)
x = 21 mph
The distance = 3*(21+3)= 72 miles
I choose (A)
Step-by-step explanation:
Answer:
15:17
Step-by-step explanation:
Since the triangle has a right angle, we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where
SOA stands for
Sin Ф = opposite side/hypotenuses side
Cosine Ф = adjacent side/hypotenuses side
Tangent Ф = opposite side/adjacent side
With respect to ∠B given that ∠D=90°,
BD is the adjacent side
CB is the hypotenuse side
and DC is the opposite side
Hence Sin B = 15/17
we are given points as
(-2,-4)
(0,2)
(1,5)
we can points
and then we can join them
After that we can get idea about it's shape
we can see that
this is straight line
so, this is linear model
Hence, option-C................Answer
