Lesson 2 Making More $ Solidify Understanding

Ready

Use the given number line to answer problems 1–8.

1.

Find the distance between point $A$ and each of the points on the number line.

$A F =$

$A C =$

$A G =$

$A B =$

$A D =$

$A E =$

2.

Find the total of all the distances listed for problem 1.

3.

Find the average of the distances that you found in problem 1.

4.

Which point on the number line is located the average distance away from point $A$ ?

5.

Find the distance between point $D$ and each of the points on the number line.

$D F =$

$D C =$

$D G =$

$D A =$

$D B =$

$D E =$

6.

Find the total of all the distances from point $D$ that you found in problem 5.

7.

Find the average of the distances that you found in problem 5.

8.

Is there an integer point on the number line located the average distance away from point $D$ ?

Set

9.

Create a scatterplot for the data in the table. Let “English Scores” be the independent variable and “History Scores” be the dependent variable for your work.

English Scores	History Scores
$60$	$65$
$53$	$59$
$44$	$57$
$61$	$61$
$70$	$67$

10.

Use technology to find the correlation coefficient between the English and History scores. Does your result indicate a strong or weak correlation? Explain.

11.

Would it be correct to claim that a change in one of the scores would cause the other one to change?

12.

Which linear function is the best model for the data? Explain why your choice is the best model for the data.

Use technology to find the correlation coefficient for problems 13–15. Then write the equation for the regression line.

13.

S&P Value	Russell Value
$2,470.5$	$1,071.99$
$2,488.65$	$1,052.05$
$2,789.82$	$1,246.73$
$2,783.36$	$1,183.98$
$2,878.48$	$1,281.88$
$2,912.43$	$1,310.66$
$2,823.16$	$1,213.35$

14.

Elevation (ft.)	Snow Pack (in.)
$8,900$	$26$
$10,349$	$34$
$5,972$	$33$
$10,039$	$40$
$8,766$	$33$
$9,177$	$47$
$6,250$	$38$

15.

Time (days)	Total Number of Infections
$1$	$142$
$2$	$303$
$3$	$459$
$4$	$639$
$5$	$821$
$6$	$929$
$7$	$1,025$
$8$	$1,175$
$9$	$1,353$
$10$	$1,509$

16.

Which of the sets of data in problems 13–15 is the least correlated? Why?

Indicate if you agree or disagree with the statements in problems 17–18, and explain why.

17.

Ice cream sales and tomato production have a strong, positive correlation. Therefore, ice cream must cause tomato growth.

18.

The number of people camping and the number of oranges for sale have a strong, positive correlation. Therefore, when people go camping, it must cause more oranges to be at the store.

Go

Find the solution to each system of linear equations.

19.

${\begin{cases} 3 x - 5 y = 30 \\ 3 x + 2 y = 16 \end{cases}$

20.

${\begin{cases} x = 7 y - 12 \\ 5 x - 30 y = - 35 \end{cases}$

Find the solution to each system of linear inequalities.

21.

${\begin{cases} 8 x - 5 y < 40 \\ 2 x + 3 y \geq 12 \end{cases}$

22.

${\begin{cases} y \leq - \frac{1}{2} x + 4 \\ y > 3 x - 6 \end{cases}$