How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … (a) There are no other restrictions. (b) xi ≥ 3 for i = 1, 2, 3, 4, 5, 6 (c) 3 ≤ x1 ≤ 10 (d) 3 ≤ x1 ≤ 10 and 2 ≤ x2 ≤ 7

The equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … Will have:

(a) 6 solutions where there are no other restrictions.

(b) 4 Solutions for xi ≥ 3 for i = 1, 2, 3, 4, 5, 6(x3 + x4 +x5 + x6 = 25)

(c) 4 Solutions for 3 ≤ x1 ≤ 10

( x3 + x4 + x5 + x6 = 25)

(d) 5 Solutions for 2 ≤ x2 ≤ 7

Step-by-step explanation:

The equation have 6 unknown variables . This means it will have 6 solutions when no condition is imposed as in (a) above. The number of unknown variables in the equation will give the numbers of solutions

When the conditions are imposed, the numbers of unknown variables will give the number of solutions.

In (b) and (c), the equation will reduce to x3 + x4 +x5 + x6 = 25) and the unknown variables are 4, giving 4 solutions

In (d), the equation will reduce be 5 unknown variables(x2 + x3 + x4 +x5 + x6 = 25) and the solution is 5

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.