TheXSquaredFactor

Oh, I am realizing that there are duplicates... nvm

Of course, a dice has 6 faces that are all equally likely to occur.

A) Let's make a table that illustrates the probability of just one 6 showing up on one roll:
 

As you can see from this table, there is only a 1/6 probability of getting a 6 the first time. What about three times in a row? Multiply the probabilities of all independent events together. Each event has a 1/6 chance. 

\(P=(\frac{1}{6})^3=\frac{1}{6}*\frac{1}{6}*\frac{1}{6}=\frac{1}{216}\approx0.46\%\)

Therefore, there is a 1/216 chance in rolling a 6 three times in a row. 

B)

We'll use the same method as above. However, these events aren't all the same, so we'll have to calculate the events independently. 

Let's do it for rolling a 5

The probability of rolling a five is alos 1/6. Let's try the next event for seeing the chances of rolling a 1:

Here, too, there is a 1/6 probability of rolling a 1. Let's find the possibility of rolling an even number:

Now that we have determined the probability of each event occurring. Multiply the probabilities of each event together to get the total probability:

\(\frac{1}{6}*\frac{1}{6}*\frac{1}{2}=\frac{1}{72}\approx1.39\%\)

Therefore, there is a 1/72 chance of rolling a 5, then a 1, and then an even number.

C)

Use the same method as illustrated above.

Let's first find the probability of getting an odd number:

Now, let's find the probability of a number greater than 2:

Finally, the last one, which is rolling a 5:

Multiply the probabilities

\(\frac{1}{2}*\frac{2}{3}*\frac{1}{6}=\frac{2}{36}=\frac{1}{18}\approx5.56\%\)

YOu're done now!

Here is the original expression:
 

\(\frac{14}{1}*\frac{7}{12}\)

To multiply this, just multiply the numerator and the denominator. Calculate the numerator by doing \(14*7=98\) and calculate the denominator by doing \(1*12=12\).

Therefore, you answer becomes

\(\frac{98}{12}\)

But wait! You are not done yet! You must reduce the fraction to its simplest terms. To do this, calculate the GCF of the numerator and denominator. The GCF happens to be 2. Take that factor out of both the numerator and denominator. 

\(\frac{98}{12}\div\frac{2}{2}=\frac{49}{6}=8.1\overline{66666}\)

I think you meant y=mx+b.

This is the standard equation of a straigth line where m is the slope, and b is the y-intercept. 

SImplifying this should be relatively simple. 

In this equation, your eventual goal is to isolate y. Let's see how to do this:
 

If you are ever pondering about whether or not this answer is correct, plug the answer you got into your equation and see if the statement is true. :

Therefore, \(y=2\) is the correct and only correct solution for the given equation

Here another one, if you want to play along!
 

Change one letter in "tower" to make something that wipes things dry.

Use the trigonometric ratios to find the height of the building:

 

One last note before you go!

Be sure that your calculator is in degree mode when doing this calculation!