A jeweler is dividing
3
8

of a pound of rubies among 4 lots. What part of a pound will each lot weigh?

A)
1
4
B)
1
8
C)
1
16
D)
3
32

Question:

A jeweler is dividing 3/8 of a pound of rubies among 4 lots. What part of a pound will each lot weigh? A.1/4 B.1/8 C.1/16 D.3/32

Option D

Each lot weight part of pound

Solution:

Given that,

A jeweler is dividing 3/8 of a pound of rubies among 4 lots

To find: part of a pound each lot weigh

From given,

Let "x" be the part of a pound each lot weigh

Therefore,

This forms a proportion and solve by cross multiplying

Thus, each lot weight part of pound

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

20

step-by-step explanation: