Larry made 5 batches of punch. Each batch ises 24 fluid ounces of lemon juice and 5 pints of orange juice. If each serving is 1 cup, how many servings did he make all together?

65 servings

Step-by-step explanation:

Larry made 5 batches of punch.

In each batch, she uses the amount of lemon juice = 24 fluid ounces

and the amount she uses of orange juice = 5 pints

Since 1 pint = 16 fluid ounces

∴ 5 pints = 16 × 5 = 80 fluid ounces

Total quantity of punch in each batch = 24 + 80

                                                              = 104 fluid ounces

Total quantity of punch in 5 batches = 104 × 5

                                                             = 520 fluid ounces

If each serving is 1 cup.

and 1 cup = 8 ounces

He made the number of servings all together =

                                                                           = 65 cups

He made 65 servings all together.

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}