Objective 9 TEKS Tracker

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TAKS Objective 9

TEKS Tracker

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TAKS Objectives Review and Practice

Grade 11 (Exit Level) TAKS Test

TAKS

TEKS Tracker

As you complete the review and practice pages for TAKS Objective 9, check off the boxes next to the TEKS you have covered below.

Objective 9

The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

Pages Tracker TEKS

8.3 _{Patterns, relationships, and algebraic thinking. The student identiﬁes}

proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:

126–127

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8.3.B estimate and ﬁnd solutions to application problems involving percents and other proportional relationships such as similarity and rates

8.11 _{Probability and statistics. The student applies concepts of theoretical}

and experimental probability to make predictions. The student is expected to:

128–129

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8.11.A ﬁnd the probabilities of dependent and independent events 130–131

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8.11.B use theoretical probabilities and experimental results to make

predictions and decisions

8.12 _{Probability and statistics. The student uses statistical procedures to}

describe data. The student is expected to:

132–133

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8.12.A select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation

134–135

h

8.12.C select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology

8.13 Probability and statistics. The student evaluates predictions and

conclusions based on statistical data. The student is expected to: 136–137

h

8.13.B recognize misuses of graphical or numerical information and

evaluate predictions and conclusions based on data analysis 138

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Objective 9 Mixed Review

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TEKS 8.3.B Review

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TEKS 8.3.B Review

8.3.B Estimate and ﬁnd solutions to application problems involving percents and other proportional relationships such as similarity and rates.

You can use proportions to solve percent equations. A proportion is an equation in which two ratios are set equal to each other. To use proportions for solving problems, be sure that the values in the ratios on each side of the equation correspond to each other in the same order.

A waiter receives a tip of $13.65 on a bill of $65. What tip would the waiter receive on a bill of $40, assuming the tipping rate is always the same?

tip 1

}

bill 15

tip 2 }

bill 2 Be sure the values in the ratios correspond.

13.65 } 65 5 x }

40 Substitute the three values that are known.

13.65(40)5 65x Cross products property

546 }

65 5 x Simplify and solve for x.

8.45 x

The waiter would receive a tip of $8.40 on a bill of $40.

EXAMPLE

On Monday, a cosmetologist earned an $18 commission for selling $150 in salon products. If the cosmetologist earns a $42 commission on Tuesday, what is the value of the salon products she sold that day?

Write a proportion.

18

}

1505 }

Solve the proportion. 150+ 5 18 +

5 5 x

The cosmetologist sold in salon products.

YOU DO IT T A K S O b je c ti v e 9 TE K S 8. 3 .B Re view

42 x

6300

18x

350 $350

42 x

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TEKS 8.3.B Practice

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TAKS

h8.3.B When you ﬁnish this page, you can check off a box on your TEKS Tracker, page 125.

1. Andre drove 155 miles in 2 hours 30 minutes. Assuming he will continue to travel at the same speed, how long will it take him to travel 263.5 miles?

A 4 h 25 min

B 4 h 20 min

C 4 h 15 min

D 4 h 10 min

2. Cassandra would like to buy a digital camera. She found the one she wants available at an online store and at an electronics store. The online store is offering the camera for $224 with free shipping. The electronics store usually sells it for $260, but it is on sale this week at a 10% discount. Which store offers the better deal and how much will she save buying it from this store?

F The electronics store has the better deal and she will save $26 by buying it there.

G The electronics store has the better deal and she will save $10 by buying it there.

H The online store has the better deal and she will save $26 by buying it there.

J The online store has the better deal and she will save $10 by buying it there.

3. Emily is typing a 500-word research paper for her science class. She has been typing for 20 minutes and has completed 300 words of her report. How much longer will it take her to ﬁnish typing the paper?

A 13 min 20 sec

B 13 min 33 sec

C 33 min 20 sec

D 33 min 33 sec

4. The average grade on a geometry test for 18 of the students in class was 86.4%. There was one student absent the day of the test and after this student took the test the class average was 86.8%. What was this ﬁnal student’s score on the test?

F 98% G 94%

H 90.4% J 87.2%

5. At a public high school, 40% of the students in the tenth grade are taking a music class this semester. How many of the 75 tenth graders at the school are taking a music class?

A 45 students

B 30 students

C 28 students

D 25 students

6. On a map, the scale reads 3 cm 5 90 km. If the distance between two cities is 240 kilometers, how far apart are they located on this map?

F 8 cm G 9.2 cm

H 10 cm J 11.25 cm

7. Mark manages a retail clothing store. The store just received a shipment of jeans from a local distributor. If Mark wants to sell the jeans in the store for $86 a pair and the cost to purchase them was $33 a pair, what is the percent mark-up on each pair of jeans? Round your answer to the nearest tenth, if necessary. A 38% B 138% C 160.6% D 260.6%

TEKS 8.3.B Practice

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TEKS 8.11.A Review

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TEKS 8.11.A Review

8.11.A Find the probabilities of dependent and independent events.

You can use probabilities to make predictions about the likelihood of the occurrence of an event. Probabilities always range in value from 0 to 1, with a probability of 0 meaning that the event will never occur and a probability of 1 meaning that the event will always occur.

Independent events are those where the outcome of the ﬁrst event does not affect the

outcome of the second event. Dependent events are those where the outcome of the first event affects the outcome of the second event. That is, the occurrence of the first of two dependent events impacts the probability that the second event will occur. The probability of two dependent events occurring and the probability of two independent events occurring are both found by multiplying the probability of the first event times the probability of the second event, given that the first event occurred.

A laundry basket contains several colored socks. There are 4 red socks, 6 blue socks, 4 black socks, and 10 white socks in the basket. Two socks are randomly selected from the basket, one at a time without replacement. What is the probability that both socks are blue?

There are 6 blue socks and 24 total socks. So, the probability of the first sock being a blue one is }₂₄6, or }1₄. After the first sock is pulled out, there are 5 blue socks among the 23 socks that remain. So the probability of the second sock being blue is }₂₃5. Notice that this probability is not the same as for the first selection. These are dependent events.

The probability that both socks are blue is the product of these probabilities: 1 } 4+ 5 } 23, or 5 } 92. EXAMPLE

Brynn bought a package of pens in a variety of colors. There are 5 blue pens, 4 red pens, 6 black pens, and 3 green pens. If she randomly picks two of the pens, one at a time without replacement, what is the probability that she chooses 2 red pens?

FIRST PICK: Number of red pens: Total number of pens: SECOND PICK: Number of red pens: Total number of pens:

Probability5 }+ }5 YOU DO IT T A K S O b je c ti v e 9 TE K S 8. 1 1 .A Re vie w

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18

3

17

4

18

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17

2

}

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TEKS 8.11.A Practice

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h8.11.A When you ﬁnish this page, you can check off a box on your TEKS Tracker, page 125.

1. Victoria is taking a history test that has 30 true/false questions and 15 multiple choice questions with four answer choices for each question. If she guesses on 4 true/false questions and also guesses on 3 multiple choice questions, what is the probability that she will get every question that she guessed on correct?

A }₁₂₉₆1 B }₁₀₂₄1

C }₉₆1 D }1₇

2. Blake and Nick are playing a game where they take turns rolling two number cubes. They both have one more roll remaining in the game. The winner of the game will be the player who has the greatest sum for the two numbers showing on the top faces of the number cubes in their ﬁnal turn. Suppose Blake has just rolled a sum of 9. What is the probability that Nick will win the game by rolling a sum greater than 9?

F 1}₃ G }₁₀3

H }₁₈5 J }1₆

3. From a standard deck of 52 playing cards, Kelly randomly picks a card, replaces it, and then selects another card. What is the probability that the two cards she chooses are both hearts?

A 1}₂ B }1

4 C 1}₈ D }1

16

4. In a bag there are 15 watermelon seeds that Andrew is going to plant. All of the 15 seeds look the same, but 3 of the seeds will produce seedless watermelons and the remaining 12 seeds will produce watermelons that have seeds in them. What is the probability that when Andy picks the ﬁrst two seeds out of the bag, one at a time without replacement, that the ﬁrst one he chooses will produce a watermelon with seeds and the second one he chooses will produce a seedless watermelon?

F }₃₅6 G }₂₅4

H 22}₃₅ J 1}₃

5. Zach is playing a board game with his sister. The game is played using a spinner like the one shown below. In order to win the game on his next turn, Zach needs to spin at least a 6. What is the probability that Zach will spin a number greater than or equal to 6 and win the game? 2 8 4 7 5 3 6 1 A 3}₄ B 3}₅ C 3}₈ D 1}₃

TEKS 8.11.A Practice

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TEKS 8.11.B Review

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TEKS 8.11.B Review

8.11.B Use theoretical probabilities and experimental results to make predictions and decisions.

You can use experiments to predict probabilities. When you do an experiment using repeated trials of an event to ﬁnd the likelihood of an event occurring, it is known as an experimental probability. Another type of probability is known as theoretical

probability, which is the ratio of the number of favorable outcomes to the number of

all possible outcomes for an event.

As the number of trials increases when conducting an experiment, the experimental probability of an event will become closer and closer to the theoretical probability for that event.

Sean tosses a coin 50 times and records the results. He ﬁnds that the coin landed tails 28 times and heads 22 times. How does the experimental probability of the coin landing heads compare to the theoretical probability of the coin landing heads? The experimental probability of the coin landing heads is

number of heads

}}

total number of tosses5

22 }

50, or 0.44.

The theoretical probability is }}} _{number of all possible outcomes}number of favorable outcomes . When a coin is tossed, there is one favorable outcome (landing heads) and two possible outcomes (landing heads and landing tails), so the theoretical probability is 1}₂, or 0.5.

The experimental probability of 0.44 is slightly less than the theoretical probability of 0.5.

EXAMPLE

A number cube is rolled 90 times and the results are recorded. The number 4 was rolled 18 times. How does the experimental probability of rolling a 4 compare to the theoretical probability of rolling a 4?

Experimental probability 5 Theoretical probability 5 Comparison: YOU DO IT T A K S O b je c ti v e 9 TE K S 8. 1 1 .B Re vie w

18

}

90

, or 0.2

1

}

6

, or 0.1

}

6 The experimental probability of 0.2 is slightly greater

than the theoretical probability of 0.1

}

6.

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TEKS 8.11.B Practice

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TAKS

1. Abby is conducting a survey of people living in her city. One of the questions asks for the respondent’s month of birth. Of the 225 people who have responded so far, the results show that 25 people have birthdays in March and 17 people have birthdays in April. What is the experimental probability that the next person she surveys was born in either March or April?

A }₂₀₂₅17 B }17

225 C 1}₉ D }14₇₅

2. Steven kept a record of the number and type of shots he made and attempted during the ﬁrst 6 games of his junior year in basketball. The results are shown in the table below. In his next game, what is the experimental probability that the ﬁrst shot he attempts will be a three pointer and that he will make the shot? Made Attempted Two pointers 49 78 Three pointers 3 8 Free throws 12 15 F }₁₀₁3 G }₁₀₁11 H 3} 8 J 367 } 808

3. Philip is randomly drawing a card from a standard deck of 52 playing cards. What is the probability that he will draw either a 7 or a club? A }₅₂1 B }₁₃4 C 17} 52 D 9 } 26

4. Hope is planning an experiment where she will roll a number cube and toss a coin. What is the theoretical probability that in her ﬁrst two attempts she rolls a 3 and tosses heads both times? Round your answer to the nearest thousandth.

Record your answer and ﬁll in the bubbles in the grid below. Be sure to use the correct place value. 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8 0 9 1 2 3 4 5 6 7 8

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5. Lane has a marble collection that he keeps in a cloth bag. The number of each color of marble is shown in the table below. Every color he has is listed. If he randomly selects two marbles from the bag, one at a time without replacement, what is the probability that both marbles are green?

Color Number Red 13 Blue 14 Green 24 Yellow 23 A }₁₃₆₉144 B }₂₇₀₁276 C 12}₃₇ D 1727}₂₇₀₁

TEKS 8.11.B Practice

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TEKS 8.12.A Review

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TEKS 8.12.A Review

8.12.A Select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation.

You can use different measures of central tendency (often called averages) to describe a set of data. The three types of averages are mean, median, and mode.

Mean – the sum of the data values divided by the number of data values

Median – the middle number when the values in the data set are ordered numerically

(When a data set contains an even number of data values, the median is the mean of the two middle numbers.)

Mode – the number(s) in the data set that occurs most frequently (There can be more

than one mode and there can be no mode.)

To determine which type of average most accurately describes a set of data, calculate the mean, median, and mode, and compare each one to the complete set of data values. The range is the difference between the greatest value and the least value in a set of data. The range of a set of data can also be used to describe the set of data.

The line plot below shows the number of siblings that students in an English class have. What measure of central tendency best describes the data?

1 2 3 4 0

Meanø 1.7 Median5 1 Mode5 0

The measure that best represents the data is the median. There is a large cluster of data around 0, 1, and 2, so the median is the best representation.

EXAMPLE

Grant has kept a record of his scores in math this semester. 74, 87, 72, 98, 85, 74, 78, 73, 74, 91

What measure of central tendency best represents the data? Meanø

Median5 Mode5

The measure that best represents the data is the .

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80.6

76

74 mean

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TEKS 8.12.A Practice

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TAKS

h8.12.A When you ﬁnish this page, you can check off a box on your TEKS Tracker, page 125.

1. The salaries of several people in a company are listed. Which measure will best represent this data? President $234,560 Vice President $156,090 Manager $95,000 Clerk $30,000 Clerk $27,000 Warehouse clerk $22,000 Warehouse clerk $21,500 Secretary $18,000 Customer Service $17,500 Customer Service $17,500 A Mean B Median C Mode D Range

2. The times for the 8 girls in the ﬁnal of the 100-meter hurdle race at a track meet are listed below according to the lane the girls ran in. Is the mean a good representation of the data? Why or why not?

Lane #1 – 16.33 sec Lane #2 – 16.38 sec Lane #3 – 15.88 sec Lane #4 – 15.59 sec Lane #5 – 21.45 sec Lane #6 – 16.47 sec Lane #7 – 16.72 sec Lane #8 – 16.74 sec

F Yes, it represents the data well.

G No, it is too high to represent the data.

H No, it is too low to represent the data.

J No, it is the same as one data point.

3. During the ﬁrst week of February in a northern city, the daily high temperatures were 328F, 108F, 48F, 188F, 298F, 108F, and 308F. Which two measures of central tendency give the best representation of the data?

A Mean and range

B Mean and median

C Median and mode

D Mode and range

4. Visitor counts for a small museum during the ﬁrst 7 days of last month are shown below. The museum is open 7 days per week. A staff member analyzing attendance records states that the median number of daily visitors was 35. Does this accurately represent the data?

Day Visitors Wednesday 22 Thursday 31 Friday 40 Saturday 262 Sunday 170 Monday 12 Tuesday 35

F Yes, the median accurately represents the data.

G No, the range would best represent the data.

H No, the mean would best represent the data.

J No, the mode would best represent the data.

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TEKS 8.12.C Review

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TEKS 8.12.C Review

8.12.C Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.

You can use data displays to represent data pictorially. The best method to display the data depends on what you want to show. Listed below are some general guidelines about when to use different displays.

Line graph – used to display continuous data over time Bar graph – used to show data that are in different categories Stem and leaf plot – used to group data into ordered lists Circle graph – used to compare one piece of data to the whole

Histogram – used to show frequencies of data displayed in equal intervals

Erica kept track of her money allocations for the month of October. Out of the $300 she earned at her weekend job, she spent $100 on her car payment, $100 on clothing/entertainment, $60 on gas, and she put $40 into her savings account. She would like to compare what percent of her earnings she spent in each area. Create the data display that would best show the data, and explain why it is the best choice. Car payment Savings Gas Clothing/ entertainment

Since Erica would like to look at her money allocations in different areas and compare them to each other and to the entire amount, the data are best displayed in a circle graph.

EXAMPLE

Trevor recorded the temperature at the beginning of each hour one morning. At 6A.M. it was 578F, at 7 A.M. it was 598F, at 8 A.M. it was 638F, at 9 A.M. it was 648F, at 10 A.M. it was 668F, and at 11 A.M. it was 708F. Create the data display that best shows the data, and explain why it is the best choice.

Reason: YOU DO IT T A K S O b je c ti v e 9 TEK S 8. 1 2 .C Re view T emperature (8 F) 0 7 8 9 10 11 6 80 60 40 20 Time (A.M.)

Temperature Readings

The temperature slowly

increased throughout the

morning, so a line graph gives

the best representation of

the data.

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TEKS 8.12.C Practice

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TAKS

h8.12.C When you ﬁnish this page, you can check off a box on your TEKS Tracker, page 125.

1. Rob has a list of ages of the 52 people at his family reunion. He would like to create a data display that will allow him to easily ﬁnd the median. Which data display would be most appropriate for this?

A Histogram B Stem and leaf plot

C Circle graph D Line graph

2. Desiree jogs for 10 minutes, walks for 10 minutes, runs for 5 minutes, jogs for 10 minutes, rests for 5 minutes, and then jogs for 10 minutes. Which line graph represents her workout?

F 0 0 Distance Time G 0 0 Distance Time H 0 0 Distance Time J 0 0 Distance Time

3. In the junior class, there are 92 students involved in at least one of three organizations. There are 51 juniors in the band, 42 juniors in the drama club, and 57 juniors in athletics. There are 13 juniors in both band and drama club, 5 juniors in both drama club and

athletics, 24 juniors in both band and athletics, and 8 juniors in all three activities. Which diagram correctly represents this situation?

A B and A thletics Dram a C lu b 13 8 57 51 42 24 5 B Band Athletics Drama Club 42 57 51 42 C Band Athletics Drama Club 13 8 8 8 24 5 D Band Athletics Drama Club 13 20 6 16 24 8 5

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TEKS 8.13.B Review

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TEKS 8.13.B Review

8.13.B Recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

You can look at a data display to determine if it may mislead a viewer and cause them to draw an erroneous conclusion. Some of the most common ways that graphs can be misleading involve the scale used on one of the axes. Check to make sure the intervals are appropriate for the data and that they are all the same size. Also check to see if there are any breaks in the axes, or if a scale does not start at zero.

The graph below shows the sales for a company over a two-month period. Why might this graph be misleading?

Monthly Sales 6.03 6.01 6.07 6.05 6.09 Sales (thousands of dollars) June July Month

The graph may be misleading because the scale on the vertical axis does not start at 0. The graph makes the sales for June, $6080, appear to be almost twice those of the sales in July, $6050, because the bar for June is nearly twice as tall as the bar for July. In fact, the June sales were just $30 more than the July sales.

EXAMPLE

The graph below shows the average gas mileage for three different car models. Why might the graph be misleading?

G

as Mileage for 3 Cars

0 10 30 20 50 40

Miles per gallon

A B C

Model

The graph is misleading because:

YOU DO IT T A K S O b je c ti v e 9 TE K S 8. 1 3 .B Re view

the width

of each of the bars in the graph is not

the same, giving the impression that

Model C has a much greater average

than either of the other models. The

width of the bars should be the same,

and since the vertical scale is

continuous, the heights of the bars

would then provide a better visual

comparison of the actual data.

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TEKS 8.13.B Practice

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TAKS

1. A newspaper included the following graph in an article which concluded that the value of this collectable tin has increased dramatically since it was released in 1960. Is this an accurate statement? V alue (dollars) 0 2.70 2.60 2.50 Year

Value of Collectable Tin

1960 1970 1980 1990 2000

A No; the small increments used for the vertical scale make the graph appear to be steep, implying that the value has increased quickly.

B No; the years on the horizontal axis are too spread out.

C No; the value of the collectible tin has actually decreased over time.

D Yes, it is an accurate statement.

2. Why might this graph be misleading?

Number sold (thousnds)

0 1200 800 Year Shoe Sales 1990 1994 1998 2002 2006

F The years on the horizontal axis do not cover enough of a time span.

G The shoe sales are increasing recently, so the graph will continue to rise.

H The large increments on the vertical axis compress the graph and make it appear that there was little change.

J The data should not be displayed in a line graph; the sales are not continuous.

3. The histogram below shows the test scores of the students in an accounting class. Which conclusion about the graph is true?

Accounting Test Scores

Score 0 1 2 3 4 71–75 76–80 81–85 86–9 0 91–9 5 Students

A Half of the students scored below 83.

B Two students had a score of 100.

C A total of 14 students took the test.

D The mode of the test scores occurs in the interval 86–90.

4. The box and whisker plot below shows the ages of the employees working at a new restaurant. Which statement is true?

Ages of Employees

28 21

16 37 52

10 20 30 40 50

F Of the restaurant’s employees, 25% are between the ages of 16 and 28.

G The median age of the restaurant’s employees is 32.5 years.

H Of the restaurant’s employees, 50% are between the ages of 28 and 52.

J The range of the employees’ ages is 52 years.

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Mixed Review

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Mixed Review

h_{When you ﬁnish this page, you can check off} a box on your TEKS Tracker, page 125.

1. Julie is doing an experiment to see how many times she can drop a marble into a jar from a height of 10 feet above the jar. After attempting to do this 36 times, she was successful 15 times. What is the probability that her next attempt will not be successful, and is this an example of experimental

probability or theoretical probability? (8.11.B)

A }₁₂5; experimental probability

B }₁₂7; experimental probability

C }₁₂5; theoretical probability

D }₁₂7; theoretical probability

2. Kendra is mowing the lawn for her parents. The area of the lawn is 1500 square yards. She has mowed 660 square yards so far. What percent of the lawn does she have left to mow? (8.3.B)

F 56% G 51%

H 48% J 44%

3. Leslie has been keeping a record of the number of aces she serves in her tennis matches. She would like to order these numbers from least to greatest using a data display so she can easily calculate the different types of averages. Which data display is best for this situation? (8.12.C) A Line graph

B Stem and leaf plot

C Box and whisker plot

D Bar graph

4. Mallory is running a relay at a track meet. She needs a pair of colored markers to place in two different locations on the track for the handoff she will be receiving. The markers are in a bag that contains 4 red, 3 yellow, and 5 orange markers. If she randomly picks 2 markers, one at a time without replacement, what is the probability that she picks 2 orange markers? (8.11.A) F }₃₆5 G }5

33 H }₁₂5 J }25

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5. Luke knows his scores on the 4 history tests he has taken this quarter. He has displayed these data in the box and whisker plot shown below. He showed his mother the graph and told her that 50% of his history test scores have been between 86% and 92%. Why might this statement be misleading to his mother?(8.13.B)

History Test Scores

86 79.5

75 90 92

74 78 82 86 90 94

A According to the display, 50% of his tests are not in the 86–92% range.

B His mother does not know how to read a box and whisker plot.

C Luke did not interpret the box and whisker plot accurately.

D This is not an appropriate display since he has only 4 test scores to use.

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