14) Find the infinite sum of the geometric sequence given: 2 3, 1 2, 3 8, 9. ( 1 8 )n. 15) Find the following sums. A) 10

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1 Honors Algebra Trigonometry Spring Final Review Sheet III NON-TRIGONOMETRY PORTION Directions: Show all work on a separate sheet of paper. ) Simplify. A) (+5)!! B) (+)! ( )! ) Epand. (a b) 5 ) Find the term. (5 + y) ) Find the standard deviation of the population data:,,, 8, 9,, 8 5) How many outfits can be created from 6 tops and 5 pairs of pants? 6) A local buffet offers salads, appetizers, 7 entrees, and desserts. Assuming you select one of each option, how many unique meals can be created? 7) A group consists of 6 men and 7 women. people are chosen to form a committee. A) How many ways can the people be chosen to form a committee? B) How many ways can a President, Vice-President, Secretary, and Treasurer be chosen to form the committee? C) How many ways can men and women be chosen to form a committee? 8) There are red, blue, green marbles in a bag. Three marbles are chosen at random without replacement. A) What is the probability that all three marbles are blue? B) What is the probability of selecting green, blue, and red marbles? C) What is the probability of selecting blue and red marbles? 9) Two cards are selected from a standard deck of cards without replacement. A) What is the probability of selecting a face card and then a non-face card? B) What is the probability of selecting clubs? C) What is the probability of selecting two Queens? D) What is the probability of selecting a 5 and then a 0? 0) One card is chosen from a standard deck. A) What is the probability it is a spade or a diamond? B) What is the probability it is a spade or a King? C) What is the probability it is a spade or a face card? D) What is the probability it is a red card or a Queen? ) Answer the following questions for the arithmetic sequence given:, 7,, 5, B) Find the sum of the first 0 terms. ) Answer the following questions for the arithmetic sequence given: a = 8 and a 8 =. B) Find the sum of the first 50 terms. ) Answer the following questions for the geometric sequence given: 8, -7, 9, -, B) Find the sum of the first 6 terms (using the S n formula). ) Find the infinite sum of the geometric sequence given:,, 8, 9, 5) Find the following sums. A) 0 n= 5n 7 B) ()n 5 n= C) ( 8 )n n=

2 #6-9: Solve the following equations. 6) ln(+5)=ln(-)-ln(+) 7) log (-) = log (+) 8) 5log( ) = 9) log (+) + log (+) = log (+5) #0-: Round answers to the nearest hundredth. 0) If $500 is invested at a rate of.5%, how long will it take to triple if compounded a) semi-annually b) quarterly c) continuously ) Radioactive iodine is a by-product of some types of nuclear reactors. Its half-life is 60 days. That is, after 60 days, a given amount of radioactive iodine will have decayed to half the original amount. Suppose a contained nuclear accident occurs and gives off an initial amount of C of radioactive iodine. How long will it take for the radioactive iodine to decay to a level of 0% of the original amount? #-6: Simplify. ) e ln0 ) log (/7) ) log 9 log 5) log 5 6) log7 log6 9 #7-8: Epand. y 7) log 5 z 8) log 5 6 #9-0: Condense. 9) log log( ) log 0) log0 log0 log 0( ) #-5: Solve the following equations. ) 7 (+) = 9 ) 6 ( + ) + = 6 ) e ( + ) = 6 ) 0 log(+) = 5) + = 5 6) Consider the following set of homerun distances (in feet) to center field in ballparks: {87, 00, 00, 0, 0, 0,, 5, 0,, 57, 6}. a. Find the mean, median, and standard deviation. b. Draw a dot plot of the data. c. Describe the shape of the distribution. d. Is the mean or median a better measure of center for this distribution? Why? 7) Based solely on the mean and median given, decide on the shape of the distribution (a) Mean = 00 (b) Mean = 5 (c) Mean = 95 Median = 00 Median = 9 Median = 05

3 Name: Hour: Date: _ 8) The mean length of a python is m with a standard deviation of 0.m. The mean width of the same species of python is 5kg with a standard deviation of 5.kg. A.m python weighing 5 kg is captured in a state park. Which characteristic of the snake is more unusual? Eplain your answer. Algebra Practice with Standardized Values workshe Adult height and shoulder width 9) Height and shoulder width follow a normal distribution Male Female Height (in.) Mean Std. Dev a) How tall is a male with a z-score of -0.8? Shoulder width (in.) Mean b) What is the shoulder width of a woman with a z-score of.? Std. Dev c) A woman is 5 6. What is her z-score? Interpret the z-score. d) A woman is 5 7 and her husband is 6. Who. How is relatively tall is a taller? male with a z score of.6? e) What percent of women are taller than 5 9? f) If Cheryl s shoulder width is in the top 0% for women, what is the smallest her shoulder width could be? g) What percent of men are between 5 and. 5 6? If a female is 5 5 tall and a male has a z score of 0., who is relatively taller? Wh actually taller? 0) Emily earned a 7% on her AP Biology test and an 9% on her Honors Algebra II/Trig test. The mean for the biology test was 60 with a standard deviation of 7.. The mean for the HAT test was 85 with a standard deviation of.8. On which test did she do relatively better? Justify your answer.. Jimbo (a male) has a standardized value of. for shoulder width. Can he walk b two poles that are set 6.5 inches apart without turning sideways? ) Suppose the distribution of GPAs at Jefferson High School has a mean of. and a standard deviation of The GPAs at Washington High School has a mean of.0 and a standard deviation of What percent of women are taller than 66. inches? a. Ted, a student at Jefferson High School, has a GPA of., and Frank, at Washinton High School, has a GPA of.5. Calculate the z-score for Ted and Frank and comment on which of them has the higher GPA relative to his peers. b. What GPA would Ted need to have the same z-score as Frank? c. What GPA would you need to have to 5. be How in the tall top is 0% a male of the with class a standardized at each high value school? of.? ) Suppose the average height of women collegiate volleyball players is 5 9, with a standard deviation of.. Assume that heights among these players follow a mound-shaped distribution. 6. What range of heights represents approimately 68% of all men? a. According to the empirical rule, about 68% of women collegiate volleyball players have heights between what two values? b. What does the empirical rule say about 7. the How proportion tall is Jenny of players if.5% who of women are between are shorter 6.7 inches than her? and 7. inches? ) Data from the National Vital Statistics Report reveal that the distribution of the duration of human pregnancies (i.e., the number of days between conception and birth) is approimately 8. normal 95% with of male mean badminton μ = 70 and players standard are in deviation the top 6% σ = of 5. height.* Use this normal This means that 95 badminton players are at least how tall? model to determine the probability that a given pregnancy comes to term in: a. less than 5 days b. more than 7 days c. over 0 days. d. * between I completely 60 and made 80 this days. up. Please don t report me to the International Badminton P Confederation.** ) Suppose that the wrapper of a certain candy bar lists ** its I also weight made as. this up. ounces. Please Naturally, forgive the me. weights of individual bars vary somewhat. Suppose that the weights of these candy bars vary according to a normal distribution with mean μ =. ounces and standard deviation = 0.05 ounces. a. What proportion of candy bars weigh less than the advertised weight? b. What proportion of candy bars weigh more than.5 ounces? c. What proportion of candy bars weigh between. and. ounces? d. If the manufacturer wants to adjust the production process so that only candy bar in 000 weighs less than the advertised weight, what should the mean of the actual weights be (assuming that the standard deviation of the weights remains 0.05 ounces)?

4 5) Identify the sampling technique used in each scenario. a. Every 5 th person boarding a plane is searched thoroughly. b. At a local community College, five math classes are randomly selected out of 0 and all of the students from each class are interviewed. c. A researcher randomly selects and interviews fifty male and fifty female teachers. d. A researcher for an airline interviews all of the passengers on five randomly selected flights. e. Based on,500 responses from,000 surveys sent to its alumni, a major university estimated that the annual salary of its alumni was $9,500. f. A community college student interviews everyone in a biology class to determine the percentage of community college students that own a car. g. A market researcher randomly selects 00 drivers under 5 years of age and 00 drivers over 5 years of age. h. A local politician uses a random number generator to select the names of 50 people off of a numbered list to interview. i. All of the teachers from 85 randomly selected nation s middle schools were interviewed. j. To avoid working late, the quality control manager inspects the last 0 items produced that day. k. The names of 70 contestants are written on 70 cards, The cards are placed in a bag, and three names are randomly picked from the bag. 6) SAT math scores in recent years at East Ranch High School have varied normally with a mean of 58 and a standard deviation of. They randomly selected One hundred samples among the students who went through a rigorous training program designed to raise their SAT math scores and also randomly selected One hundred sample among the student who did not take any training program. The average SAT math score of the student who went through a rigorous training was 00 point higher than the student who didn t go through any training. Is this an eample of an eperiment or an observational study? 7) Researchers wish to investigate the efficacy of a new blood pressure medication. A sample of 00 volunteers with high blood pressure is chosen. Half of them are assigned to the treatment group. The other half are assigned to the placebo group. In the treatment group subjects show improved blood pressure after 6 weeks. In the control group, 0 people show an improvement. a) Is this an observational study or an eperiment? Why? b) What sampling method was used? 8) According to the National Center for Health Statistics,.% of all births in the US were to teenagers in 999. To see if this percentage has changed since then, a random sample of 000 births was investigated and were to teenage mothers. The sample was chosen by using a random number generator to pick birth mother names from a list of all teenage US births. What sampling method was used?

5 SOLUTIONS A) ( + 5)( + )( + ) B) ) a 5 80a b + 080a b 70a b + 0ab b 5 ) 50 y ) σ.96 5) 0 outfits 6) 68 meals 7A) 75 B) 7,60 C) 5 8A) 9A) 0 B) 7 C) D) 66 B) 7 0A) C) 7 B) A) a n = n B) 80 A) a n = 6n + 6 B) -650 C) 6 D) 7 A) a n = 8 ( )n B) 8 ) 8 5A) 0 B) 6) No solution 7) X=7 8) = ) = C) 7 0 A).69 yrs B).55 yrs C). yrs ) t 9 days ) 0 ) - ) 5) -5 6) 7) log5 log5 y log5 log5 z 8) log5 log5 log 5( 6) 9) log ( ) ( ) log0 0) ) =-9 ) =(ln/ln6) -, or =-.6 ) =ln8 -, or.079 ) = 5) =.65 6 A) 7.08, med =, s.7 C) skewed right D) median 7 A) symmetric B) skewed right C) skewed left 8) length; z-score is further from 0 9 A) B) 7.89 C) z=0.96; her height is 0.96 standard deviations above the mean. D) The husband; z-score is larger E) % F) 7.09 G).7% 0) AP Bio; her z-score is larger A) z T =.8; z F =.7; Frank B). C) Jeff:.9; Wash:.86 A) in B) 8.85% A).0098 B).7 C).09 D).97 A).059 B).7 C).6006 D).85 5) a. systematic b. cluster c. stratified d. cluster e. convenience f. convenience g. stratified h. SRS i. cluster j. convenience k. SRS 6) observational study 7) a) eperiment b) voluntary sample 8) SRS