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31. choose a strategy sarah had

$1.19 in coins. jeff asked her for change

for a dollar, but she did not have the

correct change. what coins did she have?

She had 4 pennies 4 dimes 1 quarter and one 50 cent.

Step-by-step explanation:

Consider the provided information.

Sarah had  $1.19 in coins. Jeff asked her for change  for a dollar, but she did not have the  correct change.

We need to find What coins did she have?

She don;t have exact change of $1 that means she don't have two 50 cents, or one 50 cent and 2 quarters or 4 quarters.

So the possible order for sum up of $1.19 is:

$0.01+$0.01+$0.01+$0.01+$0.1+$0.1+$0.1+$0.1+$0.25+$0.5 = $1.19

That means she had 4 pennies 4 dimes 1 quarter and one 50 cent.

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}

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step-by-step explanation: