MAP 7th Grade Math

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Questions 1 - 10

A university wanted to compare the heights of women on the basketball team and women on the swim team. The data is in the dot plots provided.

Basketball players

Swimmers

Using the dot plots provided, what is the mean absolute deviation of the height of basketball players, rounded to the nearest tenth?

Explanation

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.

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

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

Screen shot 2016 03 01 at 1.23.05 pm

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

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

A university wanted to compare the heights of women on the basketball team and women on the swim team. The data is in the dot plots provided.

Basketball players

Swimmers

Using the dot plots provided, what is the mean absolute deviation of the height of basketball players, rounded to the nearest tenth?

Explanation

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.

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

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

Screen shot 2016 03 01 at 1.23.05 pm

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

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

If a server at a restaurant gets a tip on a bill of $\$57$ , then what will be the amount of the tip?

$\$8.55$

$\$8.50$

$\$8.60$

$\$8.45$

Explanation

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 of $\$57$ . 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:

$15%\rightarrow0.15$

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

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

The server's tip will be $\$8.55$

If a server at a restaurant gets a tip on a bill of $\$57$ , then what will be the amount of the tip?

$\$8.55$

$\$8.50$

$\$8.60$

$\$8.45$

Explanation

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 of $\$57$ . 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:

$15%\rightarrow0.15$

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

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

The server's tip will be $\$8.55$

Calculate the volume of the provided figure.

$216\textup{ in}^3$

$215\textup{ in}^3$

$214\textup{ in}^3$

$213\textup{ in}^3$

Explanation

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

$V=l\times w\times h$

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

$V=6\times6\times6$

$V=216\textup{ in}^3$

Calculate the volume of the provided figure.

$216\textup{ in}^3$

$215\textup{ in}^3$

$214\textup{ in}^3$

$213\textup{ in}^3$

Explanation

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

$V=l\times w\times h$

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

$V=6\times6\times6$

$V=216\textup{ in}^3$

Samantha has a bag of marbles containing pink marbles, orange marble, red marbles, purple marbles, white marbles, black marble, green marbles, and yellow marble. What is the probability that Samantha will pick a red marble out of the bag?

$\frac{2}{19}$

$\frac{1}{19}$

$\frac{3}{19}$

$\frac{2}{18}$

Explanation

In this problem we have a total of marbles. That means that each marble, regardless of color, has a $\frac{1}{19}$ chance of being picked, as shown in the images below. This image shows equal probability because each marble has a $\frac{1}{19}$ 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:

$\textup{P}=\frac{\textup{favorable outcomes}}{\textup{total outcomes}}$

For this problem there are red marbles; therefore,

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

$\frac{2}{19}$

$\frac{1}{19}$

$\frac{3}{19}$

$\frac{2}{18}$

Explanation

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:

$\textup{P}=\frac{\textup{favorable outcomes}}{\textup{total outcomes}}$

For this problem there are red marbles; therefore,

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

Solve:

Explanation

In order to solve this problem, we need to start at on the number line.

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