Question

Find the number of 5-lists of the form (x1, x2, x3, x4, x5), where each xi is a nonnegative integer and x1 + x2 + x3 + x4 + 3x5 = 12.

Does this have to be answered by cases or is there a systematic way to determine all of the possibilities?

Answer #1

2. Find the number of integer solutions to x1 + x2 + x3 + x4 +
x5 = 50, x1 ≥ −3, x2 ≥ 0, x3 ≥ 4, x4 ≥ 2, x5 ≥ 12.

How many solutions are there to equation x1 + x2 + x3 + x4 = 15
where xi , for i = 1, 2, 3, 4, is a nonnegative integer and
(a) x1 > 1?
(b) xi ≥ i, for i = 1, 2, 3, 4?
(c) x1 ≤ 13?

How many non-negative integer solutions are there to
x1+x2+x3+x4+x5 = 60
(a) where x1 <= 17 and x2 <= 17
(b) where x1 <= 17 and x2 <= 17 and x3 <= 17 and x4 <=
17
Side question: is there any reason why, for (a), that we can't just
give x1 and x2 both 18 "stars" (from the sticks and stars
representation of the problem) and then calculate the number of
ways to distribute the remaining 60 - (18...

What is the generating function for the number of non-negative
integer solutions to
x1 + x2 + x3 + x4 + x5 = 50
if:
1.) There are no restrictions
2.) xi >= 2 for all i
3.) x1 <= 10
4.) xi <= 12 for all i
5.) if x1 is even

Find the number of solutions to
x1+x2+x3+x4=16 with
integers x1 ,x2, x3, x4
satisfying
(a) xj ≥ 0, j = 1, 2, 3, 4;
(b) x1 ≥ 2, x2 ≥ 3, x3 ≥ −3,
and x4 ≥ 1;
(c) 0 ≤ xj ≤ 6, j = 1, 2, 3, 4

n = 5, x1 = 10, x2 = 3, x3 = 7 and x4 = 8
if standard deviation = 5, obtain x5.

Find the number of integer solutions to x1+x2+x3=20 given the
following restrictions:
(A) x1>=3, x2>=2,x3>=5
(B) x1>=0, x2>=0, x3<=6

Find the number of distinct solutions for x1 + x2 + x3 = 100
given that x1, x2, x3 are nonnegative integers with at least one
of them being more than 40.
use

Give augmented matrix for this system. Find all solutions to
this system. Indicate all parameters.
x1-x2+x3+x4=1
2x2+3x3+4x4=2
x1-x2+2x3+3x4=3
x1=? x2=? x3=? x4=?

A man has four (4) stock investments that have values: X1, X2,
X3 and X4 where Xi ∼ N($5000, 2500) for i = 1, 2, 3, 4. Determine
the probability that he sells all four investments on a given day
if he has given an order to sell all four investments when: a.at
least one of the four investments exceeds $5022 in value, b.all of
the four investments exceeds $5022 in value, c.the average of all
four of the investments...

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