Aboy found a bicycle lock for which the combina- tion was unknown. the correct combination is a four-digit number, d1d2d3d4, where di, i = 1, 2, 3, 4, is selected from 1, 2, 3, 4, 5, 6, 7, and 8. how many different lock combinations are possible with such a lock?

4096 possible combinations

Step-by-step explanation:

If a experiment can takes place in forms n1, then a second experiment can takes place in forms n2, ... , then a i-experiment can takes place in ni forms finally the number of possibilities to carry out the entire experiment are :

n1 x n2 x ... x ni

This is call the multiplication principle.

In our experiment (finding a four - digit number)

d1 can be chosen between 1,2,3,4,5,6,7,8

d2 can be chosen between 1,2,3,4,5,6,7,8

.

.

.

d4 can be chosen between 1,2,3,4,5,6,7,8

The lock combinations are d1 x d2 x d3 x d4 = 8 x 8 x 8 x 8 = 8^4 = 4096

38.6°

step-by-step explanation:

resultant is 10 pound

smaller force = 8 pound

angle formed = tan⁻¹(

                        =tan⁻¹(

                          =tan⁻¹(0.8)

                        =38.6°

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).