Simple Algebraic Relationship Between FKM(t) and FNA(t)

Using the approximation e^x=1+x for small x, find a simple algebraic relationship between FKM(t) and FNA(t) .
Comment briefly on the relationship you have found.

Find a simplealgebraicrelationshipbetween the negative binomial probability
P(x) = ((x-1)!/(n-1)!(x-n))*(P^n)(1-p)^x-n for x = n, n + 1, .. and the binomial probability for the probability of n successes in x trials.

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K.
Let S be the subspace of F.
Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

Show that any algebraic extension of a perfect field is perfect (using the below hint only).
Hint: Let K be a perfect field and F an algebraic extension of K. If F is not perfect, then there is a polynomial f(x) an element of F[x] that has an irreducible factor p(x) with a repeated root u. Here u is algebraic over K; let g(x)

Suppose that L has transcendence degree n over K and that L is algebraic over K(α1, . . . , αn). Show that α1, . . . , αn is a transcendence basis for L over K.
Might help:
Theorem - Definition: Let L be an extension of K, A a subset of L. The following are equivalent:
(1) A is a maximal algebraically

1.) Write the following as an algebraic expression using x as the variable : the sum of a number and -8
2.) Write the following as an algebraic expression using x as the variable: Five more than the product of 7 and a number.
3.) Solve -3 ( -19+4 )/-5

Please see the attachment to see these questions properly.
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Question 1
If [K:F] is finite and u is algebraic over K ,prove that [F(u):F] divides [K(u):F]
Hint:[F(u):F] and [K(u):F(u)] are finite by Theorems 10.4,10.7 and 10.9
Apply Theorem 10.4 to
Theorem 10.4
Le

A car has a tank that holds 12 3/8 gallons of gasoline. Mr. Brown fills his tank and drives along the highway until he runs out of gas. If his car averages 19 2/5 mpg, how far has he traveled?

1. Three prizes are to be distributed in a Creative Design Talent Search Contest. The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize.
a. Express the total value of the three prizes as an algebraic expression.
b. Comment on the ki