Sequences & Series Questions and Answers

I sin cos value of the expression 5T J 5x cos 3 12 12 T sin COS 5T 5T 3 12 12 Simplify your answer including any radicals Use integers or fractions for any numbers T sin cos sin

Sketch the graph of each linear inequality 1 y2 x 3 A B D 44 16 2 2 x 3y 15 A B C D

5 2 Graph the solution to the system y 7 y2 3 Show Your Work

9 9 y Zx 2 V Ia ia y x 2

8 y x 4 2 13 y x 6 6 A B 6 D 17 y AV V x X N

Find the standard deviation for the group of data items 5 1 5 1 5 1 5 1 The standard deviation is Round to two decimal places as needed

Use the display of data to find the mean median mode and midrange The mean of the data is Round to the nearest tenth as needed Frequency 79944 HTT P N9TY 6

work 12 2 Find the mean for the data items in the given frequency distribution Score x Frequency f The mean is 1 2 2 3 32 2 4 6 5 5 Round to 3 decimal places as needed 65 5 7 8 8 6 9 3 10 3

Find the mode for the data items in Score x Frequency f 1 2 2 2 3 1 gr 4 4 5 8 6 7 7 5 8 4 9 5 Use a comma to separate answers as needed 10 2 1 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode s is are OB There is no mode

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the grouped frequency distribution to the right Among the classes with the greatest frequency which class has the least number of social interactions Choose the correct answer below A 65 69 OC 60 64 OE 70 74 G 50 54 OL 55 59 BO B 75 79 OD 45 49 OF 85 89 H 90 94 J 80 84 Number of Social Interactions 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 Frequency 12 18 18 18 9 8 7 7 0 3

Describe what is misleading in the visual display of data below Marijuana Use Among College Students in the Last 30 Days Never Used 29 3 Not in Last 30 Days 10 Used 1 9 Days 5 5 Used 10 29 Days 3 5 Used All 30 Days 1 7 Choose the correct answer below A The chart is too small B The percentages do not add up to 100 C The title does not explain what is being displayed D Colors on the chart are too light and distort the data

12 1 The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph More college graduates had starting salaries in the 61 000 65 000 range than in the 46 000 50 000 range Choose the correct answer below of Graduates Frequency 400 300 200 100 Question 8 12 1 23 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars Q IEEEIN Points A False because the bar for 61 65 has the same height as the bar for 46 50 B False because the bar for 61 65 is shorter than the bar for 46 50 OC True because the bar for 61 65 is taller than the bar for 46 50 D True because the sum of the heights of the first two bars in the graph is greater than the sum of the heights of the last two bars

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution What is the class width The class width is Type a whole number Points 0 of 1 Number of Social Interactions 20 26 27 33 34 40 41 47 48 54 55 61 62 68 69 75 76 82 83 89 Frequencies 15 HARSHST 4 14 17 13 5 7 1 19 11 14

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution How many students had at least 45 social interactions for the week The number of students was Type a whole number Points 0 of 1 Number of Social Interactions 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 Frequency a 12 11 18 20 19 504 9 7

MY NOT An article titled The Discipline of Business Experimentation provides several examples of randomized experiments in the context of making business decisions In one such experiment the retail Kohl s decided to test whether opening stores an hour later would lead to a significant decrease in sales The experiment involved 100 of the company s stores which were divided into two groups One group of stores opened an hour later than usual The other group continued with regular store hours The experiment did not find a meaningful difference in sales between the groups of stores Explain why it is important that the company use random assignment to create the two experimental groups If the groups were not randomly assigned Kohl s employees would be upset that they were not given fair treatment Random assignment allows the researcher to create groups that are equivalent This ensures that the experiment does not favor one experimental condition over another Business decisions should only be made after a randomized experiment has been conducted This is the only way to prove if opening the store earlier will be effective Random assignment allowed the researchers to use blinding and thus the employees were not aware of which experimental condition they were assigned to

The is found by adding all the data values and dividing by the total number of values Fill in the blank below The is found by adding all the data values and dividing by the total number of values

The heights of ten male students in inches in a college biology class are listed below Find the mean 72 72 71 67 67 72 76 72 73 68 72 OA 67 inches OB 68 inches OC 72 inches OD 71 inches

A questionnaire was given to students The first question asked was How stressed have you been in the last week on a scale of 0 to 10 with 0 being not stressed at all and 10 being as stressed as possible The responses are shown in the table CCEED a Which stress rating describes the greatest number of students out of 10 Type a whole number Part 1 of 2 O Points 0 of 1 Stress Rating Frequency e 6 4 0 1 2 3 4 5 6 7 8 9 10 5 17 11 10 11 26 35 18 16

Compute the range for the set of data 15 15 15 20 26 26 26 OA 20 4 OB 20 OC 11 OD 30 3

The February utility bills in dollars for ten residents of a large city are listed below Find the mode amount 71 67 67 72 76 72 73 68 72 72 OA 67 OB 72 OC 76 OD 73

12 HW If the maximum and minimum values in a data set are averaged the result is the Fill in the blank below If the maximum and minimum values in a data set are averaged the result is the median mode mean

me graph shows the percentage change in a price index over 17 years In what year s of the years displayed was the change in the price index the greatest In what year s was the change in ice index the least How do actual prices in 1991 compare to those in 1990 Based on this graph what can you conclude about changes in prices during the period shown Click the icon to view the graph what year s of the years displayed was the change in the price index the greatest A 1992 B 1990 OC 2000 and 2005 OD 2002 Graph chart Percent change from previous year N WA i I I 2000 2002 2004 2006 U X

Next question Fill in the blank so that the resulting statement is true A sample obtained in such a way that every element in the population has an equal chance of being selected is called a an A sample obtained in such a way that every element in the population has an equal chance of being selected is called a an sample sample

For the functions f x x 3 and g x 5x find the following a fog x and its domain b gof x and its domain a fog x 5x 3 Simplify your answer The domain is Type your answer in interval notation

Let f x 7x 5 and g x 2x 7 Find f g x f g x fg x and 1 f g x Simplify your answer x Give the domain of each

Use the intermediate value theorem to show that the polynomial function has a real zero between the numbers given f x 4x 2x 6 1 and 2 What is f 1 Simplify your answer Type an integer or a fraction

ex 4 A geometric Series has first term 0 and common ratio Ferm of the series is 4 and the Sum r The Second of infinity of the series is 25 al Show that 25r 25 r 4 0 two possible vales b Find the the two Find the corresponding two possible values of a of the first in terms of the d Show that the Bush T Sories given by Sn 25 1 r

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f 240 7 a The slope is Type an integer or a simplified fraction The y intercept is 0 240 Type an ordered pair Type an integer or a simplified fraction The x intercept is 7 0 Type an ordered pair Type an integer or a simplified fraction b Write an equation that defines f f x Simplify your answer Use integers or fractions for any numbers in the expression 280 240 200 169 120 80 40 240 120 160 200 240 280

2 5 Sketch two triangles ADEF AGHF If DE 72 when GH 60 and EF 54 what is the length of side of HF Remember to draw two triangles and label their vertices correctly with corresponding parts labeled

24 Analyze the following graph of a system of two equations Determine the x and y values of the solution of the system State your answers as decimals not fractions y 1

5 Use the following scenario and frequency table to answer the question A classroom of 15 students polled to see who had studied for a quiz that morning The results were as follows No Boys Girls Total Yes 3 4 7 CT 5 3 38 8 Total 8 7 15 Which of the following describes a joint relative frequency O Among the 7 girls 4 studied for the quiz O Of the 15 students surveyed 7 were girls Of the 15 students 5 were boys who did not study for the quiz Of the 15 students surveyed 8 people neglected to study

23 Observe the following graph y H L If 8 is the x intercept of line L what is the slope and y intercept of line L slope y intercept H K

T a f x 2x 3 x 1 Given f x a find f b describe domain and range of f c Show that f f x x and f f x x y 2x 3 x 1 x 2 2x 3 x 1 Domain off x 1 Range y 2

6 Solve the following equation for x The domain of both fand its inverse is the set of all real numbers and f 5 3 7 3f 2x 1 12 f 2x 1 5 f f 2x 1 f 5 Given f 5 3

Which graph best represents the solution set of y 4x B D 6 5 4 3 TETE DE ASS PA

A linear function is shown in the graph below What is the rate of change of this function record your answer as a decimal 8 3 3 4 5

Example 3 If an astronaut visited Jupiter he would weigh about 140 more on Jupiter than on Earth due wity If the astronaut weighs 160 pounds on Earth how much would he

8 Jim and Joe are brothers Joe is 30 older than Jim If Joe is 39 how many years older is he than Jim

Express f x in the form f x x k q x r for the given value of k f x 2x x x 8 k 1 f x

6 Kristen is solving a radical equation and determines that the equation has no solution Which equation is Kristen attempting to solve 0 6 2

If Cierra invests 5 000 into a fund that earns 6 5 interest compounded annually how long will it take for her investment to grow into 200 000 Use A p 1 r O About 59 years O About 28 years

11 log 16z x 27 6

Use the given graph of the function y f x to find the indicated values Click on the graph to see the coordinates of its points a f 4 b f 3 c f 0 d 1 5 0 5 1 1 W

Use the parent function f x b and transformation techniques to graph g x 42 5 2 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of g Select all transformations that apply Horizontally stretch the graph of f by a factor of 2 Reflect the graph of f about the y axis Shift the graph of f 5 units to the left Horizontally compress the graph of f by a factor of 5 Shift the graph of f 5 units to the right Shift the graph of f 2 units up Shift the graph of f 2 units down Vertically compress the graph of f by a factor of 5 Vertically stretch the graph of f by a factor of 2 Reflect the graph of f about the z axis

Find a formula for the inverse of the following function if possible F x 2 x 2

md and interpret the average rate of change illustrated in the lowing graph Value of Machine in thousands of dollars 15 124 Year Q Find the average rate of change Select the correct choice below and fill in the answer box to complete your choice Type a whole number OA The average rate of change is OB The average rate of change is per year per year

Let g v g 4 9 1 immun Evaluate the following expressions Use a calculator when necessary Round solutions to four decimal places if necessary g 2 g 0 5e 2

Let f x Evaluate the following expressions Answers should be exact Do not round DAN 3 f 1 f 4 7 f 0

The Richter scale is used for measuring the magnitude of an earthquake The Richter magnitude M is given by the model M 0 67log 0 37E 1 46 where E is the energy in kilowatt hours released by the earthquake Suppose an earthquake releases 18 500 000 000 kilowatt hours of energy What is the earthquake s magnitude to the nearest tenth a 7 4 b 7 5 C 8 1 d 8 05 OOOO

Match the exponential expression with its simplified form 2 x 7 x x4 x x 2 x 1 X 5 X x 4 X 1 x 8 1 88 x 2 X 1 x