Use the digits 1,2,3,4,5 and the following clues to find the 5-digit number. Clue 1: The number is less than 30 000
Clue 2: The 3 is next to the 2
Clue 3: The 2 is NOT next to the 1 or 4
Clue 4: The 5 is NOT next to the 1 or 4
Clue 5: The 3 is next to the 4 or 5

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

we can set up an equation to find the girls' ages. the equation is         28=0.5x-5+x. (comment if you need me to explain how i got this equation.) so, you add x and 0.5x to get 1.5x and add 5 to each side. your new equation is 33=1.5x. now divide both sides of the equation by 1.5 to get 22=x. because x is mary's age, to find jasmine's age we subtract mary's age from 28. we find that mary is 22 years old and jasmine is 6 years old.