Lesson 7 Bridging the Gap Solidify Understanding

Ready

Students were surveyed and asked if they have a curfew or not. As part of the survey, they were also asked if they have chores assigned to them. The results are in the table, which you should use to answer problems 1–4.

1.

How many students were surveyed?

2.

How many students said that they have chores?

3.

How many students said that they don’t have a curfew?

4.

Explain any patterns in the data.

Students were surveyed and asked if they prefer swimming or hiking, and if they prefer fruit or vegetables. The results are in the table below, which you should use to answer problems 5–8

	Swimming	Hiking
Fruit	$62$	$54$
Vegetables	$20$	$14$

5.

How many students were surveyed?

6.

How many students said that they prefer swimming?

7.

How many students said that they prefer vegetables?

8.

Explain any patterns in the data.

Set

9.

If your math class had a greater standard deviation for the first quiz of the unit than they did for the second quiz of the unit, what would this tell you?

10.

The table shows some air quality data in the United States for the time period from 1990 to 2000 (See https://openup.org/QAoguR). The study measured two pollutants in the air, lead and ozone. The units are ppm, parts per million.

Year	$1990$	$1991$	$1992$	$1993$	$1994$	$1995$	$1996$	$1997$	$1998$	$1999$	$2000$
Lead	$1.813$	$1.752$	$1.775$	$2.327$	$1.911$	$1.249$	$1.156$	$0.576$	$0.426$	$0.491$	$0.54$
Ozone	$0.090$	$0.091$	$0.085$	$0.087$	$0.086$	$0.091$	$0.086$	$0.086$	$0.091$	$0.088$	$0.082$

Represent the data for each pollutant with a graph and statistical measures.

a.

Lead

Mean:

Median:

Standard Deviation:

b.

Ozone

Mean:

Median:

Standard Deviation:

11.

Which data has greater spread? Explain.

12.

Interpret the relationship between the mean and standard deviation of lead in this context.

13.

What changes in the data for ozone would increase the standard deviation during the period studied?

Go

Find the inverse function for each of the given functions.

14.

$f (x) = \frac{x + 7}{3}$

15.

$g (x) = x^{3} - 7$

16.

$h (x) = - 2 x + 25$

17.

$p (x) = x^{2} + 32$

18.

$k (x) = 43 x - 56$

19.

$j (x) = {(x - 8)}^{2} + 17$

Find the explicit equation for the exponential function.

20.

$x$	$f (x)$
$1$	$6$
$2$	$12$
$3$	$24$
$4$	$48$

21.

$x$	$f (x)$
$3$	$243$
$4$	$81$
$5$	$27$
$6$	$9$