The sale tax on an item is %6. Express the total cost, C, in terms of the price of the item, P. Can someone help me with how to resolve this problem.

Explanation:

The sales tax is 6% of the price P

6% of P = 0.06P

Add on the original cost P to get P+0.06P = (1+0.06)P = 1.06P

The 1.06 indicates the final after tax cost is 106% of the original price.

You can think of it like 100% + 6% = 106% = 1.06

So that's how we end up with C = 1.06P

An example using actual numbers:

Let P = $100 be the initial cost before tax

6% of P = 0.06*P = 0.06*100 = 6 dollars is the tax

100+6 = 106 is the final cost

Note how C = 1.06P = 1.06*100 = 106

step-by-step explanation:

sry but any answer choices

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