At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only $3. the sandwiches are made with either turkey or ham. the fruit is either an apple or an orange. the drink is either bottled water or juice. the number of boxes they make for every possible combination is the same. if you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get an orange and not get juice in your box?

Answer is 0.25

Step-by-step explanation:

Given that sandwiches are made with either turkey or ham.

Probability for turkey or ham = 1/2

Also given that the fruit can be either apple or orange.

So, probability for apple or orange is also = 1/2

Also, the drinks can be either bottled water or juice

Same probability will be = 1/2

The given options of sandwiches, fruits, and drinks are mutually independent of each other.

Hence, the probability that you will get an orange and not get juice in your box

= or 0.25

Therefore, the answer is 0.25.

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}