The experimental probability is what actually happened in an experiment. In this case, Kelly spun the spinner \(\displaystyle 40\) times, and she landed on yellow \(\displaystyle \frac{14}{40}\) times; thus, our experimental probability is \(\displaystyle \frac{14}{40}=\frac{7}{20}\)

In this problem we have a total of \(\displaystyle 19\) marbles. That means that each marble, regardless of color, has a \(\displaystyle \frac{1}{19}\) chance of being picked, as shown in the images below. This image shows equal probability because each marble has a \(\displaystyle \frac{1}{19}\) chance of being drawn, which is equal to the probability of all of the other marbles.

Samantha wants to know what her probability is of drawing a red marble out of her bag. Remember, probability is the number of favorable outcomes over the total number of outcomes:

\(\displaystyle \textup{P}=\frac{\textup{favorable outcomes}}{\textup{total outcomes}}\)

For this problem there are \(\displaystyle 2\) red marbles; therefore, 

\(\displaystyle \textup{P(red marble)}=\frac{2}{19}\)

The mean absolute deviation is the average distance between each data point and the mean. So the first step to solving for the mean absolute deviation is to solve for the mean.

The mean is the average of a data set. In order to solve for the mean, we add all of our heights together, and divide by the number of people in our data set. 

\(\displaystyle \frac{66+69+70+70+71+72+72+72+73+73+74+75+75+65}{14}=71.9\textup{ in}\)

Next, we subtract to find the distance between each data point and \(\displaystyle 71.9\), which is shown in the following table:

Now that we have all of the distances from the mean, we find the average of those differences to find the mean absolute deviation: 

\(\displaystyle \frac{5.9+2.9+1.9+1.9+0.9+0.1+0.1+0.1+1.1+1.1+2.1+3.1+3.1+3.1}{14}=2.0\)

In order to solve this problem, we need to recall the formula for the area of a circle: 

\(\displaystyle A= r^2\pi\)

The circle in this question provides us with the radius, so we can use the formula to solve:

\(\displaystyle A=32^2\pi\)

Solve:

\(\displaystyle A=1\textup,024\pi\textup{ in}^2\)

Complementary angles are defined as two angles that when added together equal \(\displaystyle 90^\circ\)

From the question, we know that the two angles are complimentary, and thus equal \(\displaystyle 90^\circ\), so we can set up the following equation:

\(\displaystyle x+20=90\)

Next we can solve for \(\displaystyle x\):

\(\displaystyle \frac{\begin{array}[b]{r}x+20=90\\ -20-20\end{array}}{x= 70}\)

In order to solve this problem, we need to recall the volume formula for a cube:

\(\displaystyle V=l\times w\times h\)

Now that we have the correct formula, we can substitute in our known values and solve: 

\(\displaystyle V=6\times6\times6\)

\(\displaystyle V=216\textup{ in}^3\)

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be \(\displaystyle 15\%\) of \(\displaystyle \$57\).  The keyword "of" gives us a clue and indicates that we are going to multiply. 

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

\(\displaystyle 15\%\rightarrow0.15\)

Next, we can perform the multiplication operation and find the tip:

\(\displaystyle \frac{\begin{array}[b]{r}57\\ \times\ .15\end{array}}{ \ \ \space 8.55}\)

The server's tip will be \(\displaystyle \$8.55\)

In order to solve this problem, we need to start at \(\displaystyle -8\) on the number line. 

Next, we have \(\displaystyle +16\) which means we need to move \(\displaystyle 16\) places to the right on the number line. When we have an addition sign  \(\displaystyle (+)\) we move to the right because that is towards the positive side of the number line. When we have a subtraction sign \(\displaystyle (-)\) we move to the left because that is towards the negative side of the number line. 

The orange arrow moved \(\displaystyle 16\) places to the right, and ended at \(\displaystyle 8\); thus,

\(\displaystyle -8+16=8\)

In order to determine whether or not the table shows a direct proportion, we will divide the quantities in the \(\displaystyle X\) coordinate column by the quantities in the \(\displaystyle Y\) coordinate column. In order for the table to show direct proportion, each quotient should be the same value. 

In this example, each quotient is the same value; therefore, this table does show direct proportion.

The proportion is \(\displaystyle 7.\)

We know that Elizabeth is going to pay \(\displaystyle 100\%\) of the \(\displaystyle \$200\) concert because that is the total cost. Plus, she is going to pay \(\displaystyle 10\%\) of the \(\displaystyle \$200\) because that is the sales tax. 

First, we need to convert our percentages into decimals in order to multiply. 

\(\displaystyle 100\%\rightarrow1.00\)

\(\displaystyle 10\%\rightarrow0.10\)

Next, we can write a numeric expression and solve:

\(\displaystyle 1.00(\$200)+0.10(\$200)=1.10(\$200)\)

\(\displaystyle \$200+\$20=\$220\)