8.11A the Student Is Expected to Find the Probabilities of Dependent and Independent Events

Objective 9: The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.

8.1B The student is expected to select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships. 1. (8.1B, 08-1, 9) On a weekly basis Miley Cyrus sets aside 5. (8.1B, 08-1, 9) On a weekly basis Miley Cyrus sets aside 1 1 1 1 of her weekly salary for rent, for credit card of her weekly salary for rent, for credit card 2 5 5 4 1 1 payments, for groceries and utilities, and the rest, payments, for groceries and utilities, and the rest, for 4 2 approximately $15, for entertainment. Which of the entertainment. If Miley’s weekly salary is $325, which of following is closest to Miley’s weekly salary? the following is closest to Miley’s entertainment budget?

A $75 A $75 B $300  B $40  C $379 C $25 D $158 D $15 2. (8.1B) Ted noticed that 62.5% of the coins he had were 2 6. (8.1B) A store advertised a ladies’ clothing sale as “ minted before the year 2000. What fraction of his coins 5 were minted before the year 2000? off”. What was the percentage discount? 1 1 A C A 15% C 30% 6 2 2 3 5 B 16 % D 40%  B D  3 8 8 3. (8.1B) In her last basketball season, Marci made 40% of 7. (8.1B) A shirt was originally priced at $19.95 is on sale 55 field goal attempts. To find the number of goals Marci for 20% off. One way to calculate the savings is to made, you can multiply 55 by ____. multiply $19.95 by ____.

A 0.04 1 1 A  C B 0.4 5 20 C 4 1 D 40 B D 20 4 4. (8.1B) Two-fifths of 425 people interviewed declared 8. (8.1B) A chair originally priced at $270.00 is marked that steak was their favorite meat. To find the number of “50 percent off”. One way to find the savings when the set people who chose steak as their favorite meat, you can is bought at the sale price is to divide $300.00 by ___. multiply 425 by ____. A 50 A 0.04 B 150 B 0.4 C 0.5 C 0.25 D 2 D 2.5

73 8.3B The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. 1. (8.3B, 09-38, 9) George Lopez bought gardening 6. (8.3B, 08-2, 9) During a softball game Shakira threw 85 supplies for $79.75, not including tax. If the tax rate was pitches, 34 of which the umpire called strikes. What 8%, what was the total cost of these gardening supplies, percent of Shakira’s pitches did the umpire not call strikes? including tax? A 51% C 25% A $86.13  C $87.75 B 40% D 60%  B $73.37 D Not here 2. (8.3B, 09-39, 10) Thalía bought an alarm clock that was 7. (8.3B, 08-1, 10) Patricia Navidad of Mujeres Asesinas 2 on sale for 25% off the regular price of $24.99. She paid an is making a sugar solution to pour into her hummingbird 8% sales tax on the sale price. Which of the following is feeders. The solution is to be 4 parts to 1 part sugar. If closest to the amount Thalía paid for the alarm clock, Patricia uses a gallon of water, how many cups of sugar will including sales tax? she need?

A $18.74 C $17.24 A 16 cups C 2 cups B $22.99 D $20.24  B 1 cup D 4 cups  3. (8.3B, 06-21, 10) Bruce went to a barbershop for a 8. (8.3B, 08-1, 11) The drawing below shows three gears. haircut. The price for a haircut at this barbershop is $15, tax included. If Bruce tipped the barber 15% of the cost of the haircut and the tax, how much change in dollars and cents should he have received if he paid with a $20 bill.

Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

The ratio of the rotation rate of Gear A to Gear B is 3:1, which is equal to the rotation rate of Gear B to Gear C. If Gear A rotates at a rate of 270 cycles per minute, what is the rotation rate of Gear C?

A 30 cycles per minute  B 90 cycles per minute 2.75  C 810 cycles per minute D 2430 cycles per minute 4. (8.3B, 04-29, 10) Of the 32 students in Ms Zane’s class, 9. (8.3B, 09-48, 11) 48. Dora the Explorer can solve a set 25% have brown hair. Of the remaining students, 12.5% of 5 math problems in 12 minutes. At this rate, how long have red hair. How many students in Ms. Zane’s class have will it take her to solve 20 sets of 7 math problems? red hair? A 58 minutes A 3  B 5 hours 16 minutes B 4 C 48 minutes C 21 D 5 hours 36 minutes  D Not here 5. (8.3B, 04-11, 9) Antonio works 40 hours per week at 10. (8.3B, 04-39, 11) Amber is making a patchwork quilt Electronics Warehouse. He earns $6.50 per hour plus a 3% using 3 different types of fabric. Each type of fabric is cut commission on the total dollar value of the service into rectangles. The first fabric is cut into pieces measuring contracts he sells. If Antonio’s hourly rate were increased 3 inches by 5 inches. The dimensions of the rectangles of by $0.15 and his commission were raised to 5%, how much the second type of fabric are 125% of those of the first type, would he earn if he sold $4000 worth of service contracts and the dimensions of the third type of fabric are 125% for the week? those of the second. What are the approximate dimensions of the third type of fabric? A $126.50. C $466.00 B $206.65 D $580.00 A 3.75 in. by 6.25 in. C 5.50 in. by 7.50 in. B 4.69 in. by 7.81 in.  D 4.25 in. by 6.25 in.

74 8.11A The student is expected to find the probabilities of dependent and independent events. 1. (8.11A, 09-15, 10) Selena Gomez has a bag of 5 marbles 5. (8.11A, 04-14, 11) Jamal has a game with 2 groups of that are identical in size. The bag contains 4 blue marbles tiles. The first group of 26 tiles is labeled with all the letters and 1 red marble. If Selena randomly draws a marble from of the alphabet. The second group of 10 tiles is numbered 0 the bag, replaces it, and then draws another marble, what is through 9. If Jamal draws 1 letter tile and 1 number tile as the probability that she will first draw a blue marble and random. What is the probability that he will draw a letter in then a red marble? his name and an odd number? 4 4 1 1 A  C A  C 25 5 13 4 1 1 5 7 B D B D 5 4 52 26 2. (8.11A, 09-32, 11) At an ice-cream shop, customers can 6. (8.11A, 06-25, 11) Winners from the math club’s fund- order a sundae with 1 type of ice cream, 1 type of sauce, raiser randomly select a gift certificate from Box A and from and 1 type of topping. The types of ice cream, sauces, and Box B. The contents of each box are shown below. toppings offered are shown below.

What is the probability that the first winner will randomly If each type of ice cream, sauce, and topping is likely to be select a DVD certificate and an amusement park certificate? selected, what is the probability that a customer will order a sundae with vanilla ice cream, caramel sauce, and 20 9 A  C walnuts? 289 289 1 1 A  C 9 1 B D 60 11 17 19 1 1 B D 4 12 3. (8.11A, 06-45, 9) A jar contains 6 red marbles and 10 7. (8.11A, 06-17, 10) Jerry has a CD case that contains 4 blue marbles, all of equal size. If Dominic were to cumbia music CDs, 1 rock-and-roll CD, 2 rap CDs, and 3 randomly select 1 marble without replacement and then duranguense CDs. What is the probability of Jerry select another marble from the jar, what would be the randomly selecting a duranguense and then, without probability of selecting 2 red marbles from the jar? replacing it, randomly selecting a rap CD from his case? 9 3 1 3 A C A C 64 5 2 50 1 3 1 1 B  D B  D 8 8 15 20 4. (8.11A, 08-2, 10) Maria José of Sortilegio knitting 8. (8.11A, 08-2, 11) Tony Hawk has a jar filled with 120 basket contains 3 balls of blue yarn, 2 balls of white yarn, marbles. He has 72 red marbles, 17 blue marbles, 13 green and 3 balls of red yarn. One evening Maria José randomly marbles, and 18 purple marbles. What is the probability that selected a ball of yarn from her basket and replaced it after he will randomly select a blue marble, without replacement, she finished knitting. The next evening she randomly and then a purple marble from the jar? selected another ball of yarn from the basket. What is the probability that on the first evening the selected ball of 7 17 A C yarn was white and that on the second evening the selected 24 800 ball of yarn was red? 3 13 9 3 B  D A C  140 840 64 32 5 3 B D 8 28

75 8.11B The student is expected to use theoretical probabilities and experimental results to make predictions and decisions. 1. (8.11B, 09-3, 9) Miley Cyrus won 9 of 15 tennis games 5. (8.11B, 09-18, 10) At an automobile dealership, 2 out of she played. At this rate, which of the following is the best every 12 cars sold are red. Which is the best prediction of prediction of the number of tennis games she will win out the number of red cars sold when the automobile dealer of her next 12 games? sells 150 cars?

A 4 C 11 A 75 C 15 B 7  D 6 B 25  D 12 2. (8.11B, 09-57, 11) Francis, Leon, and Shelby are running 6. (8.11B, 08-3, 11) Thalia is on the varsity softball team. for president for their school’s student council. A random So far this season she has 55 hits in 82 times at bat. Based survey of 60 students was taken to determine whom they on this information, which is most likely to be the total planned to vote for in the election. The results are shown in number of hits Thalia will have for the season if she bats 15 the table below. more times?

A 10 B 22 C 65  D 70

Based on the data in the table, which of the following is the best prediction of the number of students who will vote for Leon if 2500 students vote?

A 1208 C 916  B 292 D 550 3. (8.11B, 06-44, 10) The table below shows the results of 7. (8.11B, 04-43, 10) The table below shows the results of a rolling a fair number cube 50 times during a classroom number cube being rolled. activity.

Based on these results, what is the experimental probability of rolling a 1? What is the difference between the theoretical probability of rolling a number less than 4 and the experimental results 2 A 2.5% C  recorded in the table above? 5 1 A 8% C 58% B D 0.6 B 79% D 29% 6 4. (8.11B, 04-32, 9) A spinner was spun 20 times. The results are shown in the table below.

Which color on the spinner has the same experimental probability as theoretical probability? A Red C Blue B White D Yellow

76 8.12A The student is expected to select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation. 1. (8.12A, 09-5, 9) Jenni Rivera entered her dog in a dog 5. (8.12A, 06-29, 9) Ms Díaz asked each of her 27 statistics show. Her dog got a score of 64. Which measure of data students to write down an integer from 1 to 10. To can Jenni use to determine whether her dog’s score was in determine that most common number the students picked, the top half of all scores at the show? which measure of central tendency should Ms Díaz use?

A. Median  A. Mode  B. Mode B. Mean C. Mean C. Median D. Range D. Range

2. (8.12A, 04-34, 10) Nicholas earned the following grades 6. (8.12A, 06-23, 11) Last Friday a used-car dealer had cars on his science exams: 83, 88, 87, and 83. If Nicholas for sale for $600, $690, $695, $710, $725, $750, $850, scores a 90 on his last exam, which measure of central $995, $995, $995, and $1495. Select the most effective tendency will give him the highest score? measure to use to convince potential customers that the dealer’s prices are very low. A. Mode B. Median A. Mean C. Range B. Median D. Mean C. Mode D. Range 3. (8.12A, 03-18, 10) Given the set of data 7. (8.12A, 0540, 11) The table shows Cain’s 7 quiz scores {20, 15, 10, 20, 15, 10, 20, 20, 50}, which statement best for the first 6-week period. Each score is based on a 50- interprets the data? point scale.

A. Only the mean is 20 B. The range of the set of data is 20 C. The mean, median, and mode are all 20  D. The mode and median are not the same

4. (8.12A, 03-8, 11) An automobile dealer is analyzing a frequency table identifying the number of vehicles of each color sold during the last 6 months. Which measure of data describes the most popular color of vehicle sold? Which of the following gives the highest value for Cain’s A. Mean quiz scores for the first 6-week period? B. Median

C. Mode  A. Mode  D. Range B. Mean C. Range D. Median

77 8.12C The student is expected to 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 or without the use of technology. 1. (8.12C, 09-18, 9) President Obama surveyed the farmers 3. (8.12C, 09-37, 10) Tyra Banks practiced gymnastics for in his country about the crops they grow. The results of the 50 minutes. The time she spent on each activity is recorded survey are shown below. in the table below.

• A total of 13 farmers grow cotton. Gymnastics Practice • A total of 14 farmers grow wheat. • A total of 20 farmers grow corn.

Some farmers in the list above grow more than 1 crop. Exactly 3 of the farmers in the list above said that they grow all 3 crops. Which of the following Venn diagrams could not represent this situation? Which of the following graphs best represents the percent of time Tyra spent on each activity during her gymnastics A C practice? A C Gymnastics Practice Gymnastics Practice

B D 

B D  Gymnastics Practice Gymnastics Practice

2. (8.12C, 09-1, 11) Ms Butterworth has an 80-acre farm.

• 38 acres are used for planting corn. • 18 acres are used for planting soybeans. • 10 acres are used for planting wheat.

The remaining acres are used for planting oats. Which of the following graphs best represents these data?

A B C D 

78 8.12C The student is expected to 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 or without the use of technology. 4. (8.12C, 04-40, 9) Students in two honors history classes 5. (8.12C, 06-50, 9) The table below shows the number of student took their first test. Of 40 students taking the test, 12 absences for the school year in Mr Cruz’s math classes. received an A, 16 received a B, 8 received a C, 2 received a D, and the remaining received an F. Which circle graph best represents these data? A C 

Which of the following graphs best represents the data shown in the table?

B D 

8.13B The student is expected to recognize misuses of graphical or numerical information and evaluation predictions and conclusions based on data analysis. 1. (8.13B, 08-3, 10) The graph below shows the total fat 2. (8.13B, 08-3, 9) The table below shows the highest and content of a 3-ounce boneless serving of four types of food. lowest points in elevation for 5 of the 7 continents.

Based on the information in the table, which of the following statements is true? Which conclusion can be drawn from the graph? A Asia’s lowest point is more than 3 times lower than Africa’s lowest point. A The lamb chop has 2 more calories than beef sirloin steak. B North America’s highest point is more than 2,000 feet higher B The foods that were baked each seem to have more grams of than South America’s highest point. total fat than the food that was roasted. C Asia’s highest point is more than 1.5 times as high as Europe’s C The salmon and chicken have the same number of calories. highest point.  D The food that was broiled seems to have fewer grams of total D Europe has the lowest point of all 5 continents fat than the food that was roasted. 

79 8.13B The student is expected to recognize misuses of graphical or numerical information and evaluation predictions and conclusions based on data analysis. 3. (8.13B, 09-52, 9) The graph below shows the 2004 5. (8.13B, 09-4, 10) WWE’s the Undertaker owns a store average yearly earnings of people at least 18 years old that sells auto parts. He budgeted $24,000 for the store’s according to the highest degree they have earned. expenses last month. The graph below shows the percentage of the budget he reserved for each type of expense.

The Undertaker’s Monthly Budget

Which statement is best supported by the data in the graph?

According to the graph, which of the following statements is A The Undertaker budgeted $15, 500 for labor, utilities, and rent. true? B More than 50% of the Undertaker’s budget was reserved for rent and utilities. A In 2004 a person with an associate’s degree earned more than C The Undertake budgeted $16,800 for labor, insurance, and twice as much as a person with a high school diploma. inventory.  B In 2004 a person with a high school diploma earned about D Less than 50% of the Undertaker’s budget was reserved for $9,000 more than a person with only some high school.  labor and inventory. C In 2004 a person with a doctoral degree earned less than 3 times as much as a person with a high school diploma. D In 2004 a person with a high school diploma earned about $100,000 less than a person with a professional degree. 4. (8.13B, 09-9, 11) A total of 1755 customers at an 6. (8.13B, 06-28, 9) When Memorial Elementary held its electronics store were asked to identify which item they annual spring festival, Benjamin surveyed 100 students to planned to purchase in the next month. The table below see which activity they preferred. The graph below shows shows the results of the survey. the results of Benjamin’s survey.

According to the information above, which of the following statements is true? 3 A About of the customers planned to purchase a DVD player. 20  1 Which of the following statements is supported by these B About of the customers planned to purchase a television. 19 data? A Close to half the students surveyed preferred either the moon 2 C About of the customers planned to purchase a laptop walk or the dunking booth.  3 B More than 25% of the students surveyed preferred the pony computer. rides or the pie toss. 1 C The ratio of students who preferred musical chairs to the pie D More than of the customers planned to purchase either a toss was 1:3. 2 D More students preferred musical chairs than preferred all the computer or a DVD player. other activities combined.