In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes. Make a list of all the different possible outcomes when two number cubes are rolled. What fraction of the possible outcomes is favorable? Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain.

Hey there!

You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.

6/21 outcomes will be favorable.

Here is a list of all possible out comes:

1 - 1

1 - 2

1 - 3

1 - 4

1 - 5

1 - 6

2 - 2

2 - 3

2 - 4

2 - 5

2 - 6

3 - 3

3 - 4

3 - 5

3 - 6

4 - 4

4 - 5

4 - 6

5 - 5

5 - 6

6 - 6

The underlined ones have one or two 3's in their outcome. There are 21 outcomes total, and 6 of them have 3's in them. We will find the percentage by doing 6/21 = .286, or 28.6%. This means that for every 100 outcomes, you should expect about 29 of them to be favorable.

I hope it helps and have an amazing day! You've got this!

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im not sure

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°