Your class is learning to tie knots. each student needs a piece of rope that is 3/8 yard long. how many yards of rope are needed for the 16 students in your class?

6 yards

Step-by-step explanation:

Given that one class is learning to tie knots

There are 16 students in the class.

Each student has to have a separate piece of rope to learn to tie knots.

Length of the piece of rope needed for each child = 3/8 yars

Hence total length required for all the  16 students would be

a direction variation question

So we multiply 16 by 3/8 to get

answer.

Answer = 16(3/8) = 6 yards

think about it deeply and passionately about this property

i am sorry

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