on the average 5 oranges will give 3 cupful of juice. if 2 cupfuls make a pint, how many oranges must be used to make 3 gallons of juice.

90 oranges

Step-by-step explanation:

First, find out how many cupfuls are in 3 gallons of juice.

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

16 cups = 1 gallon

48 cups = 3 gallons

For every 5 oranges, you get 3 cupfuls of juice.  This gives you the ratio of 5/3.  Multiply 48 cups, which is 3 gallons, by the ratio to find out how many oranges you will need.

48 × 5/3 = 90

You will need 90 oranges for 3 gallons of juice.

80 oranges are used to make 3 gallons of juice

Step-by-step explanation:

1 gallon = 8 pint

3 gallons  = 3 * 8 = 24 pint

1 pint = 2 cup full of juice

24 pint = 24 * 2 = 48 cups

Now, we have to find how many 3 cups are in 48. So, 48 ÷ 3 = 16

3 cup of juice is taken form 5 oranges.

Therefore, 16 groups of 3 cups of juice will be taken from 5 *16 = 80 oranges

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:

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