Before we buy any ribbon material, let's convert what the sister is asking for into the right unit. Sarah needs \(\displaystyle 5ft\) in order to make the ribbon, so to convert that to \(\displaystyle in\) we need to multiply \(\displaystyle 5\) by \(\displaystyle 12\). We do this because \(\displaystyle 1ft=12in\).

\(\displaystyle 5*12=60\)

So we can see that Sarah needs to buy \(\displaystyle 60in\) of ribbon material in order to make a ribbon that is exactly \(\displaystyle 5ft\) long.

Our answer is \(\displaystyle 60in\).

In order to convert \(\displaystyle yd\) into \(\displaystyle in\), let's first convert our \(\displaystyle yd\) into \(\displaystyle ft\), since \(\displaystyle ft\) is the unit in between the two.

\(\displaystyle 1yd=3ft\), so in order to convert this we need to multiply our number of \(\displaystyle yd\), \(\displaystyle 3\), with the number of \(\displaystyle ft\) it takes to make \(\displaystyle 1yd\), \(\displaystyle 3\).

\(\displaystyle 3*3=9\)

We now have \(\displaystyle 9ft\), so converting this to \(\displaystyle in\) should make it easier. 

\(\displaystyle 1ft=12in\), so in order to convert what we have we need to multiply our \(\displaystyle 9\) by \(\displaystyle 12\) for the same reasons above.

\(\displaystyle 9*12=108\)

We can conclude that \(\displaystyle 3yd=108in\).

Our answer is \(\displaystyle 108in\).

Since the conversion we are asking for is from two different metric systems, the conversion rate will not be a whole number.

While it differs slightly, the conversion we will use for \(\displaystyle in\) to \(\displaystyle cm\) is \(\displaystyle 1in=2.54cm\)

We have \(\displaystyle 10in\), so in order to convert that to \(\displaystyle cm\) we'll have to multiply our number by \(\displaystyle 2.54\).

\(\displaystyle 10*2.54=25.4\)

Our answer is \(\displaystyle 25.4cm\)

While the conversion may vary, the one we will be using for this problem is \(\displaystyle 1ft=30.48cm\).

Since we are at \(\displaystyle 2ft\), we'll need to multiply this by \(\displaystyle 30.48\) in order to convert it to \(\displaystyle cm\).

\(\displaystyle 2*30.48=60.96\)

Our answer is \(\displaystyle 60.96cm\)

For this problem, it's important to know that \(\displaystyle 1 in = 2.54cm\). This conversion factor will allow you to convert twelve inches into centimeters. 

Aside from knowing the conversion factor, it's important to also know how to set up this kind of problem so you can be successful at solving the question. 

Often times, it's easier to solve/set up through the use of dimensional analysis. Begin by drawing a "t". In the top left corner of the t we will write in our original unit (\(\displaystyle 12\) inches). We know that our final answer must me in centimeters - therefore, we need to be able to "cross out" the inches units. This can be done by placing \(\displaystyle 1\) inch (the conversion factor) in the bottom right corner of the t. The inches will cancel out because think of them as being divided out. When you have one thing as the numerator of the fraction and the same thing is the denominator of the fraction, they will cancel out as \(\displaystyle 1\). The same concept goes for dimensional analysis with units. 

In order to complete the t, we need to include the \(\displaystyle 2.54 cm\) in the top right corner to finish the conversion factor. This will leave us with an answer ending in centimeters. 

Now, we must multiply across the top and divide by the numbers on the bottom. 

\(\displaystyle \frac{12 \times 2.54}{1} = \frac{30.48}{1} = 30.48 cm\)

The statement shows that the sum of three numbers yields the same result regardless of the order in which they are added; this is a demonstration of the associative property of addition.

The statemet shows a number being added to its additive inverse to obtain a sum of 0; this is a demonstration of the inverse property of addition.

This statement shows that two numbers can be added in either order to achieve the same result; this is a demonstration of the commutative property of addition.

The friends have the bus from 5:00 PM to 3:00 AM - this is 

\(\displaystyle 3 + 12 - 5 = 15 - 5 = 10\) hours.

The cost of renting the bus will be

\(\displaystyle \$ 320 +\$ 18 \times 10 = \$ 320 +\$ 180 = \$500\).

Forty-two friends paying $9 each will pay a total of

\(\displaystyle 42 \times \$9 = \$378\).

The teacher will pay the difference, or

\(\displaystyle \$500 - \$378 = \$122\).

The initial elevation of the plane is 6,159 feet in elevation. Ascent is an increase in elevation and descent is a decrease, so, to the elevation, in turn, add 17,785 feet,  and subtract \(\displaystyle D\) feet. This is

\(\displaystyle 6,159 + 17,785 - D\)

\(\displaystyle = 23,944- D\)