There are 10 kids that want ice cream. Each one can choose between chocolate, vanilla or strawberry. You'll collect their choices and make one order, something like: 5 chocolate, 3 vanilla and 2 strawberry. How many possible orders can you make

There are 30 possible orders that can be made.

Step-by-step explanation:

Given : Number of kids that want ice cream= 10

Choices for flavors : chocolate, vanilla or strawberry.

i.e. Number of choices for flavors = 3

Then by Fundamental principle of counting , the number of possible orders can be =(Number of kids ) x (Choices for flavors)

Therefore , the total number of possible orders that can be made = 30.

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step-by-step explanation:

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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}