A)
First note that the plates can have between 4 and 6 symbols so we will need to find the number of plates with 4 symbols, 5 symbols and 6 symbols. We add these to get the total. In this part repetition of symbols is allowed. Since there are 26 + 10 =36 possible symbols we look at each position on the plate and think of how many choices there are. We multiply the number f choices using the counting principal since the choices are each independent -- one symbol does not affect another. There are 36 choices for the first symbol, 35 for the second and so on. The number of plates is:
4-symbols = (36)(36)(36)(36)=36^4
5 symbols = (36)^5
6 symbols = 36^6
So the total here is: 36^4+36^5+36^6
B) Here we do not repeat symbols so there are 36 choices for the first symbol but only 35 for the next and 34 for the one after and so on.
4-symbols = (36)(35)(34)(33)
5 symbols = (36)(35)(34)(33)(32)
6 symbols = (36)(35)(34)(33)(32)(31)
So the total here is: (36)(35)(34)(33)+(36)(35)(34)(33)(32)+(36)(35)(34)(33)(32)(31)
c)
In order for there to be a repeated symbol we have 36 choices for the first symbol, 36 for the next and so on. However, for the last symbol we have to pick from one of the ones already selected so there are 3, 4 or 5 choices respectively.
4-symbols = (36)(36)(36)(3)
5 symbols = (36)(36)(36)(36)(4)
6 symbols = (36)(36)(36)(36)(36)(5)
So the total here is: (36^3)(3)+(36^4)(4)+(36^5)(5)
D)
The probability is given by (the number of plates with at least one repeated symbol)/(the total number of plates if repetitions are allowed) = (the answer to c) / (the answer to a)
Answer:
percentage he will select the blue rubber duck over the green ruber duck is (blue duck 1.25) (green duck 0.25)
Step-by-step explanation:
your person without a brain
Answer:
Step-by-step explanation:
The volume of a cylinder is given by :
.....(1)
Where
r and h are the radius and the height of the cylinder.
We need to solve the equation of r. Cross multiplying both sides in equation (1).
Dividing both sides by 
. So,
So, the radius of the cylinder is equal to 
.
Answer:
<em>7.2 miles</em>
Step-by-step explanation:
Janet hikes a trail 3.6 miles long each day. Considering the forth and back path, she trails 2*3.6= 7.2 miles.
Since she has hiked 5 days in the past week, she has hiked 5*7.2 = 36 miles.
The question does not specify if the path back is to be considered. If not, then the total distance traveled is 3.6*5 = 18 miles.
Answer:
3600 hours
Step-by-step explanation:
let total life time of t four transistors T = X1 + X2 + X3 + X4 (where X1,X2,X3 and X4 are life time of individual transistors
mean of the length of time that four transistors will last =E(T)=E(X1 + X2 + X3 + X4)
=E(x1) + E(x2) + E(x3) + E(x4) =900+900+900+900 =3600
and standard deviation of total time =SD(T)=sqrt(Var(T)) = sqrt(Var(X1) + Var(x2) + Var(x3) + Var(x4))
where sqrt means the square root
=sqrt(302+302+302+302) =sqrt(3600) =60
