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BlackZzzverrR [31]
3 years ago
5

An ordinary (fair) die is a cube with the numbers 

Mathematics
1 answer:
sammy [17]3 years ago
3 0

There are a few ways to look at this. If you wanted to look at all the events, you could draw a 6 x 6 grid and label the left side from 1 to 6 and the bottom from 1 to 6. The intersection of a row and a column would be a possible sum. You can check to see if the event you want to occur occurs on a cell by cell basis. Like if you wanted to see how many possibilities are there to get a sum of 12. We know there is only one way, that is to roll a 6 and a 6. Then you would shade the top right corner cell of the grid and check the other ones (for more complicated events). Then the probability is just the number of shaded cells divided by the total number of cells.

But, since you can probably just count the events, how many ways are there to roll any two numbers, if the order matters, there are 36 possibilities (6 x 6 grid). You could roll 4 then 6, 6 then 4, 5 then 5, 5 then 6, 6 then 5, and 6 then 6. There are 6 possibilities with a sum more than 9 and 36 total, so the probability of that one event is 6/36 or 1/6. Try out the last one ;)





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Answer:

Second : 1/6 x + 47

Third : 1 2/3 x + 35 - 1 1/2 x + 12

Fourth : 5 (1/3x) + (5) (7) - (3) (1/2x) + (3) (4)

Step-by-step explanation:

I would start by expanding the expression, showing each step. Then, simplify by collecting like terms.

To expand, you multiply the term outside of the brackets by each term inside the brackets.

5(1/3x + 7) - 3(1/2x - 4)

= 5(1/3x) + (5)(7) - (3)(1/2x) + (3)(4)       Showing how to expand

= 5/3x + 35 - 3/2x + 12           Simplified above step by multiplying

= 5/3x - 3/2x + 47            Collected like terms (35 + 12 = 47)

= 10/6x - 9/6x + 47          Change fractions to the common denominator 6

= \frac{10-9}{6}x + 47   Combine fractions with common denominator

= 1/6x + 47              Fully expanded

See which options match the steps I took to expand the original expression.

The second step is the same as option 4.

The last step is the same as option 2.

I bolded those steps that are the same.

Some options use mixed fractions (whole numbers and fractions).

From the third step, I will convert the improper fractions to mixed fractions.

5/3x + 35 - 3/2x + 12

= 1 2/3x + 35 - 1 1/2x + 12

This is the same as option 3.

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\frac{3}{2}x = 1\frac{1}{2}x   On the left side, 3 goes into 2 ONE time. The ONE becomes the whole number. The remainder is 1, which becomes the numerator.

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