Sequences & Series Questions and Answers

Use the laws of exponents to simplify 3 3 3 1 10 3 1 35 3 10 Simplify your answer Type exponential notation with positive

In triangle ABC sin 4 0 05 A 12 C OA 66 13 OB 23 87 OC 36 87 n O What is the approximate measure of angle B 52 199 C B

Given that g x a g 8 X 7 X 6 find each of the following O A b g 7 c g 6 d g 18 75 A g 7 0 Simplify your answer OB g 7 does not exist O c g 7 is not a real number c Select the correct choice below and if necessary fill in the answer box to complete your choice OA 9 6 Simplify your answer B 9 6 does not exist Oc g 6 is not a real number d Select the correct choice below and if necessary fill in the answer box to complete your choice OB g 18 75 does not exist e g x h g 18 75 Type an integer or decimal rounded to three decimal places as needed

The points 5 3 and 3 8 are endpoints of the diameter of a circle Determine the center of the circle C The center of the circle is Simplify your answer Type an ordered pair Use integers or fractions for any numbers in the expression Type an exact answer for each coordinate using radicals as needed

1 In a study of fatal car accidents some accidents were attributed to high speed or drunk driving a The probability that the fatality was attributed to high speeds was 0 57 b The probability that the fatality was attributed to drunk driving was 0 62 c The probability that high speed and drunk driving caused the accident was 0 41 a 1 pt What is the probability that a fatal accident will be attributed to high speeds or drunk driving X Work 0 25 pts Replace these words with a cropped picture of your work for question 1a only Answer 0 25 pt Reasoning Explanation 0 5 pt b 2 pts What is the probability that a fatal accident will be attributed to neither cause

Solve each inequality 1 x 3 5 A No solution B x22 or x 8 C x2 16 or x 6 D All real numbers 2 m 3 1 A m 4 or m 2 B All real numbers C m 3 or m 3 3 cm 3

7 0 2k 1 2 2 6 4 28 A 1 5 k 1 B 4 9 k 1 4 C k 0 8 or k 2 1 D All real numbers 9 3 5 1 8v 5 42 11 97 A No solution B 4 2 v 4 7 C 4 9 v 1 1 D v 4 2 or v 24 7 8 8 3 9 5 9 2n 11 31 A 1 5 n 4 4 B n 2 8 or n 0 2 C 4 n 1 5 D n 0 2 or n 2 8

x 2 4 A x 2 or x 1 B x 4 or x 2 C x 2 or x 10 D 2 x 6 4 n 4 2 1 3 A 1 n 2 B 3 n 3 C n 1 or n 2 D n 3 or n 3

Find the product Write the result as a polynomial in standard form 30 x y 30 x y 30 x y 30 x y

Suppose during a 5 year period the profit P in billions of dollars for a large corporation was given by P 7 2Y where Y represents the year a Fill in the chart b What are the units of P Y d What was the initial profit 0 1 2 3 P c What does the 2 in the equation represent and what are its units

Perform the indicated operation 4p p 3 31 7

Multiply using the rule for finding the product of the y 1 y 1 1 1

Find the product b 1 b 2 b 4 b 1 b 2 b 4

1 point Charlotte is driving at 59 1 mi h and receives a text message She looks down at her phone and takes her eyes off the road for 3 60 s How far has Charlotte traveled in feet during this time Helpful information 1 min 60 s 1 h 60 min 1 mi 5280 ft 74 3 ft 312 ft 59 1 ft O2 45 ft

Avicenna an insurance company offers five year commercial property insurance policies to small businesses If the holder of one of these policies experience property damage in the next five years the company must pay out 24 100 to the policy holder Executives at Avicenna are considering offering these policie for 916 each Suppose that for each holder of a policy there is a 4 chance they will experience property damage in the next five years and a 96 chance they will not If the executives at Avicenna know that they will sell many of these policies should they expect to make or lose money from offering them How much To answer take into account the price of the policy and the expected value of the amount paid out to the holder Avicenna can expect to make money from offering these policies In the long run they should expect to make dollars on each policy sold Avicenna can expect to lose money from offering these policies In the long run they should expect to lose dollars on each policy sold Avicenna should expect to neither make nor lose money from offering these policies

K Complete the sentence below Suppose that the graph of a function f is known Then the graph of y f x 2 may be obtained by a the graph of f a distance of 2 units Suppose that the graph of a function f is known Then the graph of y f x 2 may be obtained by a of the graph of f a distance of 2 units shift of

f x 4x 2 x 5 ifx 1 if 1 x 2 if x 2

Simplify the expression 5 6c 5d4 6 5 6c 5d4

Multiply the monomials 4 3 5 4 6 X 6 15 5 2 X 15 5 X

2 Observational Studies 2 1 In the following descriptions of a study confounding is present Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study Furthermore suggest how you would change the study to eliminate the effect of the confounding variable a A prospective study is conducted to study the relationship between incidence of lung cancer and level of alcohol drinking The drinking status of 5 000 subjects is determined and the health of the subjects is then followed for 10 years The results are given below Drinking Status Heavy drinker Light drinker Total Lung Cancer Yes No 50 30 80 Total 2 150 2 200 2 770 2 800 4 920 5 000 b A study was conducted to examine the possible relationship between coronary disease and obesity The study found that the proportion of obese persons having developed coronary disease was much higher than the proportion of nonobese persons A medical researcher states that the population of obese persons generally has higher incidences of hypertension and diabetes than the population of nonobese persons

The function f x x is one to one a Find an equation for f x the inverse function b Verify that the equation is correct by showing that f f x x and 1 f x x a Select the correct choice below and if necessary fill in the answer box to complete your choice A 1 x x for x 0 B 1 x for all x O c 1 x for x 0 b Verify that the equation is correct 1 1 x f x and X and The equation is not verified Part 3 of 3 verified 1 1 x 1 x X Substitute Simplify Y

mg The prescribed dosage of a drug is 12 daily meaning that 12 milligrams of the drug should be administered daily for each kilogram of a patient s weight How many 200 milligram tablets shou kg be given each day to a patient who weighs 164 pounds Use the fact that 1 lb 0 45 kg The patient should receive 200tabilligsarach day Round to the nearest whole number as needed

Lena 2735 miles Mekong 4328 kilometers Click the icon to view a table of English and Metric Equivalents Select the correct choice below and if necessary fill in the answer box to complete your choice OA Mekong is the longer river by approximately km Round to the nearest whole number as needed B Lena is the longer river by approximately km Round to the nearest whole number as needed OC Both rivers are the same length rounded the nearest km English and Metric Equivalents English and Metric Equivalents 1 in 2 54 cm 1 ft 30 48 cm

Express 80 kilometers per hour in miles per hour mi hr Round to the nearest hundredth as needed

Construct an inconsistent system of equations whose first equation is 0 5x1 0 3x2 x3 0 8 7

The function f is defined as follows f x 3 int x a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range A The intercept is 1 0 B The intercepts are x 0 for 0 x 1 C There are no intercepts c Choose the correct graph below A o Ly O B 37 O C 5 Q N O D

An automobile manufacturing plant produced 38 vehicles today 15 were vans 11 were sedans and 12 were trucks Each vehicle falls into only one of these categories Plant managers are going to select two of these vehicles for a thorough inspection The first vehicle will be selected at random and then the second vehicle will be selected at random from the remaining vehicles What is the probability that two sedans will be selected Do not round your intermediate computations Round your final answer to three decimal places

Complete the sentence below When functions are defined by more than one equation they are called When functions are defined by more than one equation they are called functions functions

10 Solve the equation by completing the square x 13x 30 0 To complete the square what number should be added to both sides of the equation 169 4 Question 3 1 5 55 Setup Solve Part 2 of 2 Type an integer or a simplified fraction The solution set is Type an integer or a simplified fraction Use a comma to separate answers as needed www

5 Solve each question Round your answer to the nearest hundredth 6 Asanji can wax a floor in 9 minutes One day his friend Maria helped him and it only took 5 63 minutes How long would it take Maria to do it alone A 10 91 minutes C 12 82 minutes 8 Darryl can wax a floor in 10 minutes Asanji can wax the same floor in 15 minutes How long would it take them if they worked together A 6 19 minutes C 5 41 minutes B 15 04 minutes D 12 18 minutes A 4 24 hours C 3 7 hours B 7 14 minutes D 6 minutes 10 Working alone it takes Abhasra eight hours to mop a warehouse Jack can mop the same warehouse in nine hours If they worked together how long would it take them B 3 17 hours D 3 13 hours 7 9 7 Working alone it takes Julio 12 hours to pick forty bushels of apples Molly can pick the same amount in 9 hours Find how long it would take them if they worked together A 6 29 hours C 4 23 hours A 16 42 minutes C 14 58 minutes B 6 51 hours D 5 14 hours 91 Working together Norachai and Scott can sweep a porch in 7 24 minutes Had he done it alone it would have taken Scott 14 minutes Find how long it would take Norachai to do it alone B 14 99 minutes D 11 45 minutes

4 06 05 06 06 HC Students were asked to prove the identity cot x cos x csc x sinx Two students work is given Student A Step 1 Step 2 COS X sinx Step 3 cos x sinx COS X CSCX sinx Step 4 1 1 sin x sinx sinx CsCx sinx eex sinx sin x sinx Student B Step 5 csc x sinx cscx sinx Step 1 cotxcos X Step 2 cotx cosx W cscx sinx Step 4 cotx cos x sin sin Step 5 cotx cos x 1 sinx sinx sinx Step 3 cotxcos x 1 sin x sinx cos x sinx COSX sinx COSX Step 6 cotx cosx cot x cos x Part A Did either student verify the identity properly Explain why or why not 10 points Dart B Name two identities that were used in Student A s verification and the steps they appear in 5 points

Match the function with the correct domain a f x x b f x x c f x x d f x x e f x x f f x 10 9 f x log x h f x Domain 1 00 Domain 2 0 U 0 Domain 3 0 Domain 4 0 Function a Function b Function c Function d Function e Function f Function g Function h Choose Choose Choose Choose Choose Choose Choose Choose

1 Describe each transformation as it relates to the parent graph a y x 3 b y x 5 c y 4lx d y 2x e y 2 x 1 4 2 Use the graph of each translated parent function to write its equation na 10 O IN dhy

11 Perry can mop a warehouse in 10 9 hours Ming can mop the same warehouse in 8 3 hours How long would it take them if they worked together A 5 1 hours C 5 18 hours B 3 98 hours D 4 71 hours

Solve each question Round your answer to two d 9 Working together DeShawn and Sarawong can pick forty bushels of apples in 5 62 hours Had he done it alone it would have taken Sarawong 9 1 hours How long would it take DeShawn to do it alone A 11 38 hours C 14 7 hours B 13 47 hours D 17 07 hours

point s possible Submit quiz The number of tropical fish that an aquarium can hold depends on the volume of the fish tank The interior dimensions of the fish tank below are 40 cm 30 cm and 40 cm Each fish requires 10 000 cubic centimeters of water How many tropical fish will this fish tank hold

Which system of inequalities is represented by the graph O O O O y x 2 y 2x 1 y 4 y 2x 2 y x 1 y 4 y x 2 y 2x 1 y 4 y 2x 2 y x 1 y 4 10 10 8 6 4 2 8 6 2 2 4 6 8 10 4 6 8 10

Which inequality is represented by the graph Oy x 2 0y x 2 0 y 3x 2 Oy x 2 4 3 2 1 2 3 4 5

e point P 1 0 lies on the curve y sin 147 If Q is the point x sin 4 f find the slope of the secant line PQ correct to four decimal places for the following valu 1 2 ii 1 5 iii 1 4 iv 1 3 v 1 2 vi 1 1 vii 0 5 viii 0 6 ix 0 7 x 0 8 xi 0 9

Find the distance between the points on a number line 5 80 A T Ft BI E WNM III GO U

14 1 point Write an explicit rule to represent the sequence 20 24 28 32 36 Of n 4n 12 Of n 4n 20 O f n 4n 16 Of n 4n 24 Previous

The area of a parallelogram is 28cm 2 One base of the parallelogram is 14cm long The other base is 7cm long Which of the following are heiahts of the naralleloaram

Question 6 of 10 Academic Total Number of Year End Computers 1985 2005 2006 630 000 13 600 000 14 165 000 Students per Computer 84 1 1 The number of computers being used 4 0 Enter the exact answers for a and b a Find the average rate of change from 1985 to 2005 in 3 9 computers per year il The number of students per computer students per computer per year b Find the average rate of change from 2005 to 2006 in i The number of computers being used ii The number of students per computer computers per year students per computer per year c Using the annual average rate of change between 2005 and 2006 find the number of years after 2005 in which there wa projection of two students per computer Round the answer to the nearest integer

Let A be the set of integers that are multiples of 3 between 2 and 15 inclusive and B be the set of even natural numbers up to and including 20 Find An B

Round your answers to two decimal places a In 1990 a prominent industry showed a net loss negative profit of 1 23 billion In 1999 the industry had a net profit of 8 06 billion Find the average annual rate of change in net profits from 1990 to 1999 The average annual rate of change in net profits from 1990 to 1999 was b In 2008 the industry s net profits were 16 6 billion i Find the average rate of change in net profits from 1990 to 2008 The average rate of change in net profits from 1990 to 2008 was Si II Find the average rate of change in net profits from 1999 to 2008 The average rate of change in net profits from 1999 to 2008 was billion per year billion per year billion per year

View Policies Current Attempt in Progress The African elephant is an endangered species largely because poachers people who illegally hunt elephants kill elephants to sell the ivory from their tusks In the African country of Kenya in the last 10 years the elephant population has dropped from 150 000 to 30 000 Calculate the average rate of change Average rate of change is i eTextbook and Media elephants per year

According to the U S Bureau of the Census workers compensation payments in Florida rose from 362 million in 1980 1 976 billion in 1990 Find the average annual rate of change in payments Average annual rate of change in payments is i million per year

Factor out the greatest common factor 7a 5 a 6 14a 12 a 6 7a 5 a 6 14a 12a 6 Factor completely

buying new truck is my major life decision Post at least 2 paragraphs in response to the following prompts Describe a major life decision you have made or plan to make Explain each of the five steps as it applies to your situation Write a minimum of 3 sentences for each step You can use the transcript for the video to reference specifics without rewatching the whole video

1 For i 1 2 3 4 and 5 let A i i 3 So for example A is the closed interval 1 4 Using either interval or set notation write down each of the following sets 3 a U Ai i 1 b Ai i 2 2 Use The Division Algorithm on the following pairs of numbers In each case you should be able to find a unique q and r subject to the constraints in the algorithm such that a qb r a a 71 b 6 h a 22 b 5