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3 years ago

The sums that appear when two fair? four-sided dice? (tetrahedrons) with sides 1?, 2?, 3?, and 4 are tossed

Mathematics

1 answer:

Karolina [17]3 years ago

5 0

Answer:

The possible sums are 2, 3, 4, 5, 6, 7 & 8 (but they're not all equally likely)

Step-by-step explanation:

For example, the only way to get a sum of 2 is to roll a 1 and then a 1

And the only way to get a sum of 8 is to roll a 4 and then a 4 (imagine you don't roll the two dice simultaneously; this will help you to see the "other possibilities" that aren't obvious at first)

The probability of rolling a sum of 2 = probability of rolling sum of 8 (1/16 probability for each)

If you roll a 1 then a 2, or a 2 then a 1, there are 2 ways to get a sum of 3

If you roll a 3 then a 1, a 2 then a 2, or a 1 then a 3, there are 3 ways to get a sum of 4

If you roll a 4 then a 1, a 3 then a 2, a 2 then a 3, or a 1 then a 4, there are 4 ways to get a sum of 5 (5 is the most likely sum)

If you roll a 4 then a 2, a 3 then a 3, or a 2 then a 4, there are 3 ways to get a sum of 6

If you roll a 4 then a 3, or a 3 then a 4, there are 2 ways to get a sum of 7

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Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day

AfilCa [17]

Answer:

Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = $5\frac34 \ hrs.$

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

$5\frac34 \ hrs.$ can be Rewritten as $\frac{23}{4}\ hrs$

Number of hours rode on first day = $\frac{23}{4}\ hrs$

Also Given:

Number of hours rode on second day = $6\frac45 \ hrs$

$6\frac45 \ hrs$ can be Rewritten as $\frac{34}{5}\ hrs.$

Number of hours rode on second day = $\frac{34}{5}\ hrs.$

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = $20-\frac{23}{4}-\frac{34}{5}$

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = $\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}$

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day = $\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.$

Hence Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

3 0

3 years ago

an equilateral triangle and a regular pentagon have the same perimeter. Each side of the pentagon is 3 inches shorter than each

klemol [59]

The answer is 4.5 for the side length of the pentagon and 7.5 is the side length for the triangle because 7.5*3(3 sides) = 22.5 and 4.5*5(5 sides)= 22.5. The perimeter is 22.5

6 0

3 years ago

2.75 + .003 + .158 =

Alecsey [184]

2.75 Answer is 2.911

0.003 Make sure you line up the decimal points like shown in example

0.158

_________

2.911

6 0

3 years ago

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