Sequences & Series Questions and Answers

er of elements in the set is hole number C

K Identity any relative maxima or minima and intervals on which the function is decreasing and increasing

12 A sine function has an amplitude of 5 a period of 4T and range ye R 2 y 12 Identify the correct equation of this function A y 5sin 20 7 C y 5sin 0 50 7 13 The arc length along a circle of radius 5 cm that corresponds to a rotational angle ofis 4 47 5 A ST 4 B 14 Simplify coscos 117 A cos B sin 30 117 30 C coscos sinsin 5 4 B y 5sin 20 7 D y 5sin0 50 7 T 30 C cos D 45 4 D sin 30

Martha is comparing the following two functions f x log x g x log z She determines that g r has a vertical stretch In at least one complete sentence determine if Martha is correct by explaining how to determine if a function has a vertical stretch or vertical compression as a result of the constant a given that g x af x

Consider the following finite arithmetic sequence 14 13 8 13 6 2 2 a Write the recursive formula for this sequence Enter a n 1 to representa 1 o a o an an Preview Preview b Write the explicit formula for this sequence Preview c How many terms are in this arithmetic sequence

A supporting girder structure is shown to the right Find the length x 6 16 m 40 5 28 5 x 4 50

Consider an experiment where a pair of dice one red one green is thrown and the number facing up on each die is noted Q Let A be the event that neither number exceeds three The event A is the event that A B C D both numbers exceed three at least one number is three or more both numbers are at least three at least one number exceeds three Q Let E be the event that the sum of the numbers is four The event E is A 1 3 2 2 3 1 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 B D 1 1 1 2 1 1 1 2 2 1 1 4 1 5 1 6 2 3 2 4 2 5 2 6 3 3 3 4 3 5 3 6 4 4 4 5 4 6 5 5 5 6 6 6 1 4 1 5 1 6 2 3 2 4 2 5 2 6 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6

Question 9 Simplify the expression log5 75 O2 logs 0 3 O The expression cannot be simplifie O 15log 5 2

QTwo dice one red one green are thrown and the numbers facing up are noted The event that neither number exceeds two is A 2 3 4 B The set of all pairs of distinguishable integers that do not exceed two C The set of pairs of integers that do not exceed two D None of these E 1 1 1 2 2 1 2 2 F 1 1 1 2 2 2 2 A coin is tossed three times and the sequence of heads and or tails is noted The event that heads comes up at most twice is A HHT HTH THH HTT THT TTH TTT B HHT HTT TTT C 3 8 7 8 1 4 None of these G HHT HHH DE F Hint

Question 3 The pH of an acidic solution is a measure of the concen the solution with smaller values of the pH indicating hig lab experiment the pH of a certain acid solution is chan counter antacid tablets into the solution In this experim to the equation X pH 5 13 log 0 5 x where x is the number of grams of antacid added to the logarithms to write the formula involving sums and or c x

Thirsty after exercising in the gym you are thinking of buying a fruit smoothie or a protein shake The smoothies come in 9 flavors and 5 sizes while the protein shakes come in only 3 flavors and 3 sizes Let us formulate a procedure for deciding which drink you will choose QA valid procedure for choosing a drink is A B C D E Step 1 Choose a flavor for the smoothie 9 choices Step 2 Choose a size for the smoothie 5 choices Step 3 Choose a flavor for the shake 3 choices Step 4 Choose a size for the shake 3 choices Alternative 1 Choose a smoothie Step 1 Choose a flavor for the smoothie 9 choices Step 2 Choose a size for the smoothie 5 choices Alternative 2 Choose a protein shake Step 1 Choose a flavor for the shake 3 choices Step 2 Choose a size for the shake 3 choices Step 1 Choose a type of drink 2 choices Step 2 Choose a flavor 12 choices Step 3 Choose a size 6 choices Alternative 1 Choose a flavor for the smoothie 9 choices Alternative 2 Choose a size for the smoothie 5 choices Alternative 3 Choose a flavor for the shake 3 choices Alternative 4 Choose a size for the shake 3 choices Step 1 Choose a smoothie Alternative 1 Choose a flavor for the smoothie 9 choices Alternative 2 Choose a size for the smoothie 5 choices Step 2 Choose a protein shake Alternative 1 Choose a flavor for the shake 3 choices Alternative 2 Choose a size for the shake 3 choices The number of possible drinks is If you want both a smoothie and a shake the number would be Check Clear Help Check Clear Free Hint

Nicole deposited 4400 in a savings account earning 6 compounded monthly If she makes no other deposits or withdrawals how much will she have in her account in two years 4959 50 4928 00 9342 76 9328 00

Arithmetic Series Find the sum of the finite arithmetic series 28 50 4m 1 046 62 O 224 432

In the following A is the set of outcomes when a coin is flipped A H T B is the set of outcomes when a die is rolled B 1 2 3 4 5 6 C is the set of outcomes when a tetrahedral die is rolled C 1 2 3 4 D is a set of colors D red green blue white E is a set of flavors E vanilla chocolate strawberry moca lemon lime F is a set of sizes F small medium large and G is a set of types G diet creamy dangerously rich Identify the set of outcomes and also its cardinality in each experiment Note When entering the set of outcomes use times for cartesian product use cap for intersection an cup for union U I Experiment Choose a size or type then a flavor Set of outcomes

Rewrite the repeating number as a fraction 18 181818 Of 0 0 0 0 1836 101 181 9 200 11 P

Find the sum of the first 18 terms for the arithmetic series S18 5 8 11 14 17 53 56 522 549 1044 1098

Given the sequence What term n in the sequence is 106 On 32 On 33 n 34 4 7 10 13 16 19 35

Geometric Sequence Consider the first six terms of a sequence shown in the graph Which equation below explicitly defines the sequence a 6 2 4 32 16m Oa 16 Oa a 32 17 16 15 14 13

A culture of bacteria triples by the end of each hour If there were initially 40 bacteria in a culture how many bacteria should there be after 3 hours 1 728 000 bacteria 1080 bacteria 120 bacteria 320 bacteria

Use the graph to estimate the slope of the line tangent to the given graph at 2 2 O 6 a 1 b 1 6 6 5 4 3 2 y 6 5 4 3 0 T 1 2 3 4 5 6 2 3 4 ST 5

Let S Cyberdine InGen LexCorp Omni Tyrell Umbrella Weyland Yutani A Then A Cyberdine InGen LexCorp Omni Tyrell Umbrella Weyland Yutani Enter the elements separated by commas If the set is empty enter empty set Explain it Practice Let S be the set of all integers and let N r ES r 0 Then mark all that are correct A pp is an a positive integer C SESS 0 X N E B pp is an a negative integer D F s ES s 0 None of the above

3 2 1 0 f x Check x 3 2 x 3x 1 3 x 6x 6 Clear Check Clear Help Check Clear Help Check Clear Help Do it if 4 x 1 if 1 x 1 if 1 x 4 Do it Do it Help Do it 4 3 2 1 First piece 3 0 2 3 4 O 2 Second piece Whole graph 3 X 4 Third piece

The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30 Find the score that is 2 standard deviations above the mean A score of is 2 standard deviations above the mean

Let ABCD be a square with side length 24 Let P be the point on side AB with AP 8 and let AC and DP intersect at Q Determine the area of triangle CQD

The graph of the equation below is a conic section Complete parts a through d below 9x 24xy 16y 20x 15y 175 0 a Identify the type of conic section Choose the correct answer below OA Parabola B Ellipse OC Hyperbola b Use axis rotation formulas for x and y to transform the quadratic equation to an equation in u v coordinates with no cross term Type an equation Simplify your answer Use integers or fractions for any numbers in the equation c Find the vertex or vertices in the u v system The vertex vertices in the u v system is are Type an ordered pair using integers or decimals Use a comma to separate answers as needed d Write the vertex or vertices in the x y system The vertex vertices in the x y system is are Type an ordered pair using integers or decimals Use a comma to separate answers as needed

THIS ASSIGNMENT WILL COUNT AS 2 DAILY GRADES YOU HAVE 2 WEEKS TO COMPLETE IT AND WILL GIVE YOU AS MUCH IN CLASS TIME AS POSSIBLE BUT THAT WILL BE LIMITED 0 9 0 8 0 7 0 6 0 5 0 4 03 0 2 a 03 0 3 0 4 0 6 0 B

The soup pot is 8 5 inches tall with a radius of 4 inches What is the volume of the soup pot Answer choices are rounded to the nearest whole cubic inch

G2023 fter a genetics experiment on 49 pea p haracteristics was tallied with the resu

ANC UB the the number of elements in the following set The number of elements in the set is Type a whole number PIS A S 32 8 6 5 B

8 05 PM Fri Apr 21 n Use a calculator to appr

A shipping crate holds 20 shoeboxes The dimensions of a shoebox are 6 inches by 4 inches by 12 inches For 10a 10b select True or False for each statement

For the following geometric sequence find the common ratio r and then write an expression for the general or nth term a 5 5 2 5 5 4 8 Type an integer or a simplified fraction Use integers or fractions for any numbers in the expression

Source SC Inc FF LLC GIT CE CO Face Value of Bond 10 000 1 000 10 000 5 000 Quoted Cost of Price Bond 70 25 96 00 104 00 104 375 a a a a Interest Rate 3 00 2 50 5 25 4 75 Annual Interest b b b b Annual Yield C C C C

9 Sandy and Morry Doran purchase a NYC Municipal 50 000 bond at a quoted price of 94 375 The bond pays annual interest at a rate of 3 10 Barry Severes purchased a 25 000 Baltic Ridge School District bond at

Find the sample standard deviation of the data Round two decimal places 64 6 28 36 4 8 8 15 49 2 63 6 57 4 20 2

possible 2 5 0 85 1 n 1 O 50 3 48 7 32 9 O Not possible Question 34 Find the sum of the infinite geometric series if possible If not possible enter the words not possible 100 100 1 n 1 1 pts

n 5k k 1 diverge O neither O converge Question 36 1 pts Find the sum of the infinite geometric series if possible If not possible enter the words not possible 8 1 1 1 n 1

1 2 4 8 arithmetic Question 23 1 pts Find the 9th term of the arithmetic sequence an 25 6 3n 1 ag Question 24 1 pts Write the nth term rule for the arithmetic sequence with the given term and common difference Fill in the formula 0 0 n 1 below

from 33 to 65 The percent of data within the given interval is 87 95 O93 O92 Question 17 Find the sixth term of the sequence 4 12 36 a6 O 1026 1 pts O 900

Find the recursive formula of the geometric sequence 3 12 48 192 anan 1 a1 Question 32 1 pts Find the sum of the infinite geometric series if possible If not possible enter the words not possible 15 14 1 11 n 1 12

Question 28 Determine if the sequence is geometric by typing yes or no in the box in all lowercase 156 1565 15655 156555 Question 29 1 pts Write the explicit formula of the geometric 1 pts

O an O O an O an O an an an an Question 19 II Write an expression for the nth term of this sequence 5 11 29 83 245 3 7 11 15 19 1 3n 4 n 3 1 13n 4 n 3 4 3n n 3 n n 3 37 1 2 n 1 2n 1 3n 2 5n 2 1 1 pts

less than 40 The percent of data within the given interval is O 21 20 16 O 15 Question 15 O A normal distribution has a mean of 4 and standard deviation of 1 What percent of values are from 2 to 6 of the values are from 2 to 6 1 pts 95

Match the correct equation with the graph A 10 86 2 2 x y 6 9 Select 10 6 10 1 x8 y 2 4 Select B 3 x 2 y 3 36 Select 4 x 4 y 4 25 Select D C

A recently married couple ran up a 6 944 credit card balance for wedding expenses Their credit card charges interest with a 13 99 annual percentage rate What monthly payment is required if the couple wants to pay off this debt with 7 monthly payments over the next 7 months Use two decimal place accuracy Hint Y 7 12

A C 11 Find AB A 30 72 40 in 19 B 88 17 km C B

Use the figure to find GBA n AC Which of the following is GBAN AC BA 4GBC A D F

3 fluid has density 4 kg m and flows in a velocity field v yi xj 2z k where x y and z are measured in meters and the components of v in meters per second ind the rate of flow outward through the sphere x y 4

Use the basic probability principle to solve the following problem Express each probability as a fraction reduced to lowest terms A 12 sided die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 7 8 9 10 11 12 Find the probability of rolling a 1 or a 5 The probability of rolling a 1 or a 5 is Type an integer or a simplified fraction

A single fair die is tossed Find the probability of rolling a number greater than 4 What is the probability of rolling a number greater than 4 Simplify your answer Type a fraction C