# Algebra 2 and Trigonometry

## Educators

Problem 1

In a controlled experiment, two groups are formed to determine the effectiveness of a new cold remedy. One group takes the medicine and one does not. Explain why the two groups are necessary.

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Problem 2

In the experiment described in Exercise 1, explain why it is necessary that a participant does not know to which group he or she belongs.

Luca A.

Problem 3

Organize the data in a stem-and-leaf diagram.
The grades on a chemistry test:
$\begin{array}{llllllllll}{95} & {90} & {84} & {85} & {74} & {67} & {78} & {86} & {54} & {82} \\ {75} & {67} & {92} & {66} & {90} & {68} & {88} & {85} & {76} & {87}\end{array}$

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Problem 4

Organize the data in a stem-and-leaf diagram.
The weights of people starting a weight-loss program:
$\begin{array}{lllllllllll}{173} & {210} & {182} & {190} & {175} & {169} & {236} & {192} & {203} & {196} & {201} \\ {187} & {205} & {195} & {224} & {177} & {195} & {207} & {188} & {184} & {196} & {155}\end{array}$

Luca A.

Problem 5

Organize the data in a stem-and-leaf diagram.
The heights, in centimeters, of 25 ten-year-old children:
$\begin{array}{llllllllllll}{137} & {134} & {130} & {144} & {131} & {141} & {136} & {140} & {137} & {129} & {139} & {137} & {144} \\ {127} & {147} & {143} & {132} & {132} & {142} & {142} & {131} & {129} & {138} & {151} & {137}\end{array}$

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Problem 6

Organize the data in a frequency distribution table.
The numbers of books read during the summer months by each of 25 students:
$\begin{array}{lllllllllllll}{2} & {2} & {5} & {1} & {3} & {0} & {7} & {2} & {4} & {3} & {3} & {1} & {8} \\ {5} & {7} & {3} & {4} & {1} & {0} & {6} & {3} & {4} & {1} & {1} & {2}\end{array}$

Luca A.

Problem 7

Organize the data in a frequency distribution table.
The sizes of 26 pairs of jeans sold during a recent sale:
$\begin{array}{llllllllllllll}{8} & {12} & {14} & {10} & {12} & {16} & {14} & {6} & {10} & {9} & {8} & {13} & {12} \\ {8} & {12} & {10} & {12} & {14} & {10} & {12} & {16} & {10} & {11} & {15} & {8} & {14}\end{array}$

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Problem 8

Organize the data in a frequency distribution table.
The number of siblings of each of 30 students in a class:
$\begin{array}{lllllllllllllll}{2} & {1} & {1} & {5} & {1} & {0} & {2} & {2} & {1} & {3} & {4} & {0} & {6} & {2} & {0} \\ {3} & {1} & {2} & {2} & {1} & {1} & {1} & {0} & {2} & {1} & {0} & {1} & {1} & {2} & {3}\end{array}$

Luca A.

Problem 9

Graph the histogram of each set of data.
$\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 35-39 & {13} \\ \hline 30-34 & {19} \\ \hline 25-29 & {10} \\ \hline 20-24 & {13} \\ \hline 20-1 & {8} \\ \hline 15-14 & {8} \\ \hline 10-14 & {19} \\ \hline 5-9 & {15} \\ \hline\end{array}$

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Problem 10

Graph the histogram of each set of data.
$\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 101-110 & {3} \\ \hline 91-100 & {6} \\ \hline 81-90 & {10} \\ \hline 71-80 & {13} \\ \hline 61-70 & {14} \\ \hline 51-60 & {2} \\ \hline 41-50 & {2} \\ \hline\end{array}$

Luca A.

Problem 11

Graph the histogram of each set of data.
$\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline \$ 55-\$59 & {20} \\ \hline \$ 50-\$54 & {15} \\ \hline \$ 45-\$49 & {12} \\ \hline \$ 40-\$4 & {5} \\ \hline \$ 35-\$4 & {10} \\ \hline \$ 30-\$34 & {12} \\ \hline \$ 25-\$29 & {16} \\ \hline\end{array}$

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Problem 12

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Average temperature for each month for a given city

Luca A.

Problem 13

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Customer satisfaction at a restaurant

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Problem 14

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Temperature of a patient in a hospital over a period of time

Luca A.

Problem 15

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Grades for students on a test

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Problem 16

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Population of each of the states of the United States

Luca A.

Problem 17

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Heights of children entering kindergarten

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Problem 18

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample.
Popularity of a new movie

Luca A.

Problem 19

The grades on a math test of 25 students are listed below.
$$\begin{array}{llllllllllll}{86} & {92} & {77} & {84} & {75} & {95} & {66} & {88} & {84} & {53} & {98} & {87} & {83} \\ {74} & {61} & {82} & {93} & {98} & {87} & {77} & {86} & {58} & {72} & {76} & {89}\end{array}$$
a. Organize the data in a stem-and-leaf diagram.
b. Organize the data in a frequency distribution table.
c. How many students scored 70 or above on the test?
d. How many students scored 60 or below on the test?

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Problem 20

The stem-and-leaf diagram at the right shows the ages of 30 people in an exercise class. Use the diagram to answer the following questions.
a. How many people are 45 years old?
b. How many people are older than 60?
c. How many people are younger than 30?
d. What is the age of the oldest person in the class?
e. What is the age of the youngest person in the class?

Luca A.