1) In a college, each student ID card is linked with a unique
5-digit pin from...
1) In a college, each student ID card is linked with a unique
5-digit pin from the set {0,1,2,3,4,5,6,7,8,9}. A) Find the number
of ID cards possible. B) Find the number of ID cards possible if
the 5-digit number is an odd number? C) Recalculate A&B if the
digits are not allowed to be repeated.
2) A license plate has 3 letters followed by 4 digits. How many
different license plate numbers can be formed if the letters cannot
be...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?
Imagine I chose 10-digit prime numbers p,q and r, such that
n=pqr happened to be a...
Imagine I chose 10-digit prime numbers p,q and r, such that
n=pqr happened to be a Carmichael number. Write down an exact
formula for the probability that a random a∈ {0,1, . . . , n−1}
detects the compositeness of n when used in Fermat’s compositeness
test. That is, how many of these a fail to satisfy a^(n−1)≡1 modn.
Show that the probability that a random a will detect the
compositeness of n is less than 1 in a billion
Give direct and indirect proofs of:
(a) a → b, c → b, d → (a...
Give direct and indirect proofs of:
(a) a → b, c → b, d → (a ∨ c), d ⇒ b.
(b) (p → q) ∧ (r → s),(q → t) ∧ (s → u), ¬(t ∧ u), p → r ⇒
¬p.
(c) p → (q → r), ¬s\/p, q ⇒ s → r.
(d) p → q, q → r, ¬(p ∧ r), p ∨ r ⇒ r.
(e) ¬q, p → q, p ∨ t ⇒ t...
Let E be a field of characteristic p, where p is a prime number.
Show that...
Let E be a field of characteristic p, where p is a prime number.
Show that for all x, y that are elements of E, we have (x + y)^p
=x^p + y^p, and hence by induction, (x + y)^p^n = x^p^n + y^p^n
.
The demand for bicycles is:
Q = 4000 – 20P + 0.04Y
Where Q is number...
The demand for bicycles is:
Q = 4000 – 20P + 0.04Y
Where Q is number of bicycles, P is the Price, and Y is
income.
a. Calculate the price elasticity of demand (arc
elasticity) from P = $80 and Y = $50,000 to P = $84 and Y =
$50,000.
b. Calculate the point elasticity of demand
for P = $80 and Y = $50,000.
c. What happened to Total Revenue when P increased
from $80 to $84?
d. Given your answers in...