Sequences & Series Questions and Answers

The probability that a missile hits a target successfully is 0 75 In order to destroy the least three successful hits are required Then the minimum number of missiles that ha the probability of completely destroying the target is NOT less than 0 95 is

Describe the effect that each change in the equation y log2 x has on the graph for the following transformations 8 y 0 5 log x a b y log x 2 C d y log 2x 6 y log 3x 4

36 Suppose that x y s t is the linear operator on R defined by the equations 2x y S 6x 2y t Find the image of the liner y 1 under this operator

Select one of the patterns below and state what you notice and wonder then share the next number in the pattern 2 8 32 128 512 40 120 360 1080 3240 1000 500 250 125 62 5 256 192 144 1008 81

xx WENDY S Ch T 7 Calculate Is Right Are there really 256 ways to personalize a Wendy s hamburger 1 Is that number to low or too high too TON 2 How many different ways do you think there is to personalize a Wendy s hamburger Exactly 256 pirkti 3 List out the different toppings to put on your hamburger at Wendy s Fresh beef American cheese crisp lettuce tomato Pickie ketchup Hayo and onion bacon 4 To calculate we will use either permutation or combination Which one should we use Why In orger Permutation to calculate Everything 5 What is the formula for combination 900 1 901 9 9c2 36 9c3 84 904 126 9c5 126 906 84 WENDY S 6 What is the formula for permutation 967 36 908 9 9c9 1 There are 512 ways to personalize a Wendy s hamburger 3 The number of ways to personalize that you found is for a single patty burger How could we find the number of ways to personalize for a single double or triple stack Calculate the number of ways to personalize a Wendy s single double and triple tools

The table shows the linear relationship between the elevation in thousands of feet and the standard temperature in degrees Fahrenheit F Elevation thousands of feet 2 8 12 16 Temperature F 04 52 31 17 3 Determine the slope and y intercept of the linear relationship between x the elevation in thousands of feet and y the temperature in degrees Fahrenheit Part A What is the slope 0 4 0 3 5 3 5 Part B What is the y intercept OD 0 52

If there is 5 280 feet in 1 mile and if there is 3600 second in 1 hour what is the closest value for 26 feet per second speed 00 0

1 y x 1 5 4 13 2 d Re X F X 4 0 Y y x 1 1 y

ompute the Fourier series for the function f R given by f x 1 x 0 x 0

What is the aspect ratio of Tire A a O b O c O d Tire A P185 75R14 aspect ratio 75 aspect ratio 14 aspect ratio 185 aspect ratio 75 Tire B P205 75R14

MI 200 1 44 14 El 3 0 9 C 0 3 2

the answer said we should pick 0 in 20 But I think 1 0 2 also could be zero if add itself 4 times I wonder how this 4 ns Group has 12 elements of order Classify Z4 X Z4 X Zg 1 2 4 with the fundamental theorem Ask Questio

taller than their main opponents Listed are heights in centimeters of randomly selected presidents along with the heights of their main opponents Complete parts a and b below Height cm of President 180 182 181 183 192 178 Height cm of Main Opponent 165 179 173 177 190 169 Type integers or decimals Do not round Identify the test statistic t 3 73 Round to two decimal places as needed Identify the P value P value 0 007 Round to three decimal places as needed What is the conclusion based on the hypothesis test Since the P value is less than or equal to the significance level reject the null hypothesis There is sufficient evidence to support the claim that presidents tend to be taller than their opponents b Construct the confidence interval that could be used for the hypothesis test described in part a What feature of the confidence interval leads to the same conclusion reached in part a

Find the sum of the first 6 terms of the arithmetic sequence 4 4 12 14

Which point on the graph is located at coordinates 4 3 Press the hotspot to select the point with the given coordinates Press the answer box after each selection to save your response 1 6 5 4 3 2 1 5 6 3 2 Lagun 1 24 5 7 12 3 4 5 6

5 The co efficient of x in the expansion of 3 x 9 1 1 2x 3x 1 2 a 56 c 154 is b 65 d 62

8 Determine the fourth term in the geometric sequence 16x

The 10 participants in an experiment had the following reaction times in milliseconds 481 483 483 486 489 502 504 507 509 880 Complete the parts below to identify any outliers a Let Q be the lower quartile and Q3 be the upper quartile of the data set Find Q and Q3 for the data set 2 0 23 0 b Find the interquartile range IQR of the data set 1QR 0 Lower boundary Upper boundary X X Outliers c Calculate a lower boundary using Q 1 5 1QR Calculate an upper boundary using Q3 1 5 1QR Note that 1 5 1QR means 1 5 times the IQR X d Any values less than the lower boundary or greater than the upper boundary are considered outliers Identify all the outliers of the data set is more than one outlier separate them with commas If there are no outliers click None 00 5 X None th Sub

Below are the noontime temperatures in degrees Fahrenheit of 20 world cities measured on the same day 88 69 37 49 85 58 Send data to calculator 60 59 70 80 68 66 60 77 43 52 69 67 62 67 Construct a box and whisker plot sometimes called a boxplot by adjusting the Use the to plot outliers if any 35 Continue 40 45 50 55 60 65 FO 70 150 75 80 85 90 D 95 100 X

F1 2 55 3 4 60 5 70 65 75 Temperature in degrees Fahrenheit 6 Using the tool provided construct a box and whisker plot sometimes called a boxplot for the data 80 7 The following data are the maximum temperatures in degrees Fahrenheit of 16 cities in the United States measured on the same day 78 68 62 60 67 78 71 81 82 57 58 59 68 64 72 73 Send data to calculator HTD 85 00 X 9 5 10 11 12

The cost of holding a party at a rollerskating rink is a function of n the number of people in the party The cost function C can be represented with this set of rules C n 150 0 n 12 260 12 n 20 400 20 n 30 The cost of a party with 9 people is A The cost of a party with 20 people is

describes the graph shown below Press to hear the question read out loud A 3 10 8 6 X 3 B x2 3 C 0 00 0 04 4 e 2 0 2 Speed 1x 4 6 8 10

ind the shortest distance from the point P 7 5 7 to a point on the line given by 1 x y z 2t 7t 1t he distance is

The series k 1 is p k a Converges absolutely Conditionally convergent c Diverges b d None of the above Answer O A OB C

14 02 59 01 Time Remaining 1 point Given the following f x 3x 7 g x 13 2x and h x 6x Complete the following f h x 2 108x 7 187x 54x 252x 294 216 2

d f x y z log 1 x y z 0 1 0 Let xy sin x f x y x y 0 x y 0 0 x y 0 0 and let 1 2 be a unit vector Find af 0 0 3

LA306 Suppose V R x n Prove that linear functions Po Q n on V given by Pk p p 0 form a basis of V

1 point a Evaluate tan z if z 63 degrees tan z b Evaluate arctan y if y 63 arctan y degrees c Evaluate tanc if c 63 tan c degrees d Evaluate tan if 63 degrees tan d

The first two terms of an infinite geometric series are 4 and 3 Which of these could be used to find the sum of the series

A sound is four times louder than a second sound of 225 decibels What decibel level would this louder sound have a 285 b 825 c 231 d 450

Question 17 1 point 4 Listen A bacterial population doubles every 4 months If there were originally 2000 cells in the sample how many will there be in 2 months a 2828 b 8000 c 512 000 Saved d 2519 Question 18 1 point 4 Listen The profits for a company can be modeled by the logarithmic function tantaneous increase in

To three decimal places the slope of the tangent to the curve f x 2log x 10 at x 4 is a 0 217 b 9 660 c 8 800 0317

For each of the functions below state the domain and range the restrictions the intervals of increasing and decreasing the roots y intercepts and vertices a f x 2x 8 b f x x 2 c f x x 1

7 Pitt lake is a freshwater lake in southern British Columbia with the highest tidal change of any freshwater lake in the world In a daily 24 hour period the highest tide is traditionally at 11 00 am reaching 5 8 m and the lowest tide is traditionally at 11 00 pm reaching only 0 4 m These are seasonal times and heights a Determine a function that gives the total height of the lake h in terms of the hours after midnight b Create a sketch of this function Don t forget to label sketch c What is the tidal height at 1 30 pm

Let f x 4x5 20x 68 284x 64x 264 a Use the rational zeros theorem to identify the rational zeros of f x b Identify the linear factors of f x that correspond to the rational zeros This part is not c Use long division of polynomials to factor f x completely This part is not graded d Identify all of the real zeros of f x

6 Solve the matrix equation 1 1 2 3 0 2 1 2 1 578 0X40 3 0 1 3 5 7 2 1 using the inverse matrix method 1

Which linear function has the greates rate of change A The Equation B The Table OC The graph Comparing rates of change Which function has the greatest rate of change 17 A y 3x 5 B X y 2 8 0 2 2 12 4 22 44 C Ay

Which of the following points lies on the line y 2 3 x 4 A 4 2 B 4 2 C 4 2 D 6 2

The sum of a geometric series is 2912 If r 3 and n 6 find the first three terms of the sequence

he sum of a geometric series is 2912 If r 3 and n 6 find the first three terms of the sequence 2912 2906 2900 72 24 8 0 3

An auditorium has 20 rows The first row has 11 sets the second row has 13 seats and the third row has 15 seats Assuming the pattern continues how many seats are in the auditorium Write the answer in the space below

uan was gifted a piggy back for his birthday on January 2nd He saved 15 from his allowance in January he saved another 18 in February 21 in March and so on If this pattern continues much will Juan s piggy bank contain after 12 months O 378 O 48 O 247 109

Which is the common ratio of the indicated geometric sequenc 01 a 30 a 3 75 n 4 03 10 23 01 0 O O 13 04 10

Which is the sum of the following series 7 3 2 1 O 755 O 381 O 335915 O 741

Fill in the blank In the sequence 5 10 15 20 25 30 84 O 25 O 15 O 20 O 10

ompare column A and column B then choose the statement that is true about the given quantitie Column A The tenth term of the sequence a 2n 5 Column B IM k The quantity in column A is greater The relationship cannot be determined from the given information The two quantities are equal O The quantity in column B is greater

Fill in the blank 263 is the O 42nd 43rd 044th O 45th term of 5 11 17 23

Check all of the following that are arithmetic sequence 1 3 9 27 51 2 5 9 14 20 3 4 5 6 7 5 2 1 4 7

What is Sn for the arithmetic series described a 91 d 4 an 15 1060 945 116 106

Which is the nth term of the indicated sequence a 7 d 2 n 25 55 55 04 O 41