Answer:
No. of times Ellen draws a blue marble = 120
Step-by-step explanation:
No. of red marbles = 3
No. of blue marbles = 2
So, the required probability is 120.
Answer:
638 in.²
Step-by-step explanation:
Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.
SA = PH + 2LW
where
P = perimeter of base = 2(L + W),
H = height of prism
L = length of base
W = width of base
SA = 2(16 + 7)(9) + 2(16)(7)
SA = 638
Perimeter = (x+2) + x + (x+2) + x
Perimeter = 4x + 4
Area = x(x+2)
Area = x^2 + 2x
8.9
The equation for the grain size is expressed as the equality:
Nm(M/100)^2 = 2^(n-1)
where
Nm = number of grains per square inch at magnification M.
M = Magnification
n = ASTM grain size number
Let's solve for n, then substitute the known values and calculate.
Nm(M/100)^2 = 2^(n-1)
log(Nm(M/100)^2) = log(2^(n-1))
log(Nm) + 2*log(M/100) = (n-1) * log(2)
(log(Nm) + 2*log(M/100))/log(2) = n-1
(log(Nm) + 2*log(M/100))/log(2) + 1 = n
(log(33) + 2*log(270/100))/log(2) + 1 = n
(1.51851394 + 2*0.431363764)/0.301029996 + 1 = n
(1.51851394 + 0.862727528)/0.301029996 + 1 = n
2.381241468/0.301029996 + 1 = n
7.910312934 + 1 = n
8.910312934 = n
So the ASTM grain size number is 8.9
If you want to calculate the number of grains per square inch, you'd use the
same formula with M equal to 1. So:
Nm(M/100)^2 = 2^(n-1)
Nm(1/100)^2 = 2^(8.9-1)
Nm(1/10000) = 2^7.9
Nm(1/10000) = 238.8564458
Nm = 2388564.458
Or about 2,400,000 grains per square inch.
Answer: x = 13/5
Explanation:
(x+4)/(3x+1) = 3/4
Cross multiply:
4(x+4) = 3(3x+1)
4x + 16 = 9x + 3
4x - 9x = 3 - 16
-5x = -13
x = -13/-5
x = 13/5
