Let us say T= probability of head turning up = 1/2 in one toss
H = probability of a tail turning up = 1/2 in one toss
Then P (56 heads or more) =
1/2^100 [ C(100,56) + C(100,57) + C(100,58) + ....
C(100,98) + C(100,99) + C(100,100) ]
where C(N, R) = N ! / [ (N - R)! R! ] number of occurrances of R formed from
N tosses.
Answer:
15 ounces per box
Step-by-step explanation:
The rate StartFraction 165 ounces Over 11 boxes EndFraction describes the relationship between the number of boxes and the weight of the crackers in the boxes. What is the weight, in ounces, of one box?
Total weight of crackers in the boxes = 165 ounces
Total number of boxes = 11 boxes
What is the weight, in ounces, of one box?
Weight per box of crackers =
Total weight of crackers in the boxes / Total number of boxes
= 165 ounces / 11 boxes
= 15 ounces per box
The weight, in ounces, of one box is 15 ounces
Answer:
D. a shape with six faces where all six faces are identical
Taking
and differentiating both sides with respect to
yields
![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
Solving for the first derivative, we have
Differentiating again gives
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
Solving for the second derivative, we have
Now, when
and
, we have
Answer:
A.)130 80
Step-by-step explanation:
1y/3x
-8x/1xy
answer:130 80
