Sequences & Series Questions and Answers

1 10 Janelle wants to challenge you to Toothpick and Tiles game described in problem 1 7 Using exactly four tiles solve her challenges below Justify your answers with pictures and labels 3 Create a tile pattern where the number of toothpicks is exactly double he number of tiles Create a tile pattern where the number of toothpicks is more than ouble the number of tiles HINT Drag the four tiles to the right

se the Distributive Property to remove the parentheses in the following expression 7 m 5 m 5 Simplify your answer Goods

doso wor 1000 101 aquis2 siulquos wod2 sanojensvoo c 3 3 exact x 36 97 15dmonton 0 00359

Solve and graph the solution set 8x 3 5x 9 The solution set is x

1 5 1 point Solve the equation 7 9 10r r 9 07 r 9 or r 10 r 9 or 1 r 5 14 or r 5 14 r 1

10 1 point Factor completely 49 2 7 x 7 x 7 x x x 7 prime

Americans trust in government and the media has generally been on a downward trend since pollsters first asked questions on these topics in the second half of the twentieth century Trust in government hit an all time low of 14 in 2014 while trust in the media bottomed out at 32 in 2016 The bar graph shows the percentage of Americans trusting in the government and the media for five selected years Use this information to answer parts a c SILE a Use the information in the graph to estimate the yearly loss in the percentage of people trusting in government The yearly loss in the percentage of people trusting in government is Round to the nearest tenth as needed The model predicts the percentage of people trusting in government will be in 2024 Type an integer or decimal rounded to the nearest tenth as needed Percentage 70 60 50 40 30 20 10 b Write a mathematical model that estimates the percentage P of people trusting in government x years after 2003 The mathematical model P estimates the percentage P of people trusting in government x years after 2003 Use integers or decimals for any numbers in the expression Use the answer from part a to answer this part c If the trend shown by the data continues use the mathematical model from part b to project the percentage of people trusting in government in 2024 Trust in media Trust in Goverment 55 35 31 47 44 19 18 40 41 16 2003 2007 2011 2015 2019 Q Q 5

You may wish to write code to answer these questions If p is a prime and g is an integer from the set 1 2 p 1 we say that g is a companion of p when ga mod pa e Z and 1 a p 1 2 p 1 1 Find all of the companions of 11 Justify your answer 2 Describe how you would go about proving or disproving the following statement 104651 is prime and 24578 is a companion of 104651 3 Let s be an integer such that 1 s 104651 and 24578 mod 104651 3190

Identify the type of fallacy in this statement The game has not even started and I already know our team will lose Select the correct answer below O ad hominem O genetic fallacy hasty generalization

x 3 3 for x 1 for for f x x 3 4 Find f 3 1 x 2 x 2

Answer the following a The diameter of Mercury at its equator is approximately 4 88 10 kilometers Write this number in standard notation b An astronomer s infrared telescope is able to detect radiation with a wavelength of 0 0000196 meters Write this number in scientific notation a kilometers b meters X

2 Let U Names of the states in the United States A States that begin with the letter A AK AL AZ AR B States that border Mexico AZ CA NM TX C States on the Pacific coast AK CA OR WA a 2 pts Find BUC Answer 1 pt Reasoning Explanation 1 pt b 1 pts Find n BNC Answer 0 5 pt Reasoning Explanation 0 5 pt

10 The first term in an arithmetic sequence is 2 The third term in the sequence is 6 The eighth term in the sequence is 26 Create a table for the sequence 11 Write an explicit and recursive function for the sequence 12 A high school club is researching a tour package offered by the Island Kayak Company e company charges 35 per person and 245 for the tour guide Complete the table using the information The Number of People Price of Tour Package 1 2 3 4 5 a Write an explicit function that represents the total cost C x of this kayak tour package for x club members b How much would the package cost for 20 people

10 9 11 2 8 7 5 F C 32 C K C 273 Directions Use the formulas to convert between each temperature scale 1 2 3 4 Name Period Surface temperature of the sun Average temperature of a human Temperature of Lava Temperature of dry ice frozen CO Average yearly temperature of Antarctica Temperature of a hot bath Temperature of outer space Hottest temperature recorded on Earth Death Valley in the United States Temperature of the moon Temperature Conversions Average winter temperature in Siberia Temperature that water freezes Kelvin 5778 K 329 7 K Date 30 K F 32 Celsius 1 170 C 57 C 45 C 0 C Fahrenheit 98 6 F 109 3 F 455 F 50

Tell if the terms are like or unlike 6v 2 Are the terms like or unlike Like Unlike

7 Person time A sample of 100 healthy men was followed for the development of prostate cancer They were followed for different amounts of time 20 men were followed for 5 years and then developed prostate cancer 10 men were followed for 1 year and then were lost to follow up The remaining men were followed for 10 years and never developed prostate cancer Calculate the number of person years of observation accrued by this population 8 The incidence rate of a non fatal disease is 400 100 000 person years People usually have the disease for an average of 3 years at which time the disease resolves spontaneously Think about which pieces of information you have about this disease and any equations we might have learned that link these pieces of information hint see

K Question 4 1 1 11 The next number is Identify a pattern in the given list of numbers Then use this pattern to find the next number More than one pattern might exist so it is possible that there is more than one correct answer 37 31 25 19 13 HW Score 0 0 of 11 points O Points 0 of 1 C Sav

1 1 point Based on the table below Taxi Cab B has the greater rate of change Taxi Cab Taxi Cab Miles Driven 10 15 20 25 True False A 25 35 45 55 B 15 27 39 51

1 point Which situation below would represent a negative rate of change John s parents put 40 on his school account for lunch Each day he pays 3 for lunch Let y represent the amount of money John has after x days in his school account Judy is babysitting after school and charges 20 a day Each day she gets paid she puts half of what she earns in a savings account Let y represent the amount of money Judy has in her bank account after x days John s situation would have a negative rate of change Both situations would have a negative rate of change Judy s situation would have a negative rate of change Not enough information 0000

Given A 2 3 and B a 4 if B is the midpoint of AC then find the x coordinates of C 3 5 1

lly the expression 2x 3x 9 2x 3x5 Simplify your answer Use positive exponents only

Simplify the expression 900 256 900 256 30 Simplify your answer Type an exact answer using radicals as needed

There are 4 consecutive integers with a sum of 46 What is the value of the greatest integer

Reading Hour 0 Reading 2 4 1 2 3 2 2 9 3 2 3 4 2 1 Median Reading 2 3 5 2 0 6 2 11 1 2 1 2 3 2 3 2 4 2 3

Curt can be paid in one of two ways for the furniture he sells Plan A Salary of 800 per month plus a commission of 10 of sales Plan B Salary of 900 per month plus a commission of 15 of sales in excess of 6000 For what amount of monthly sales is plan B better than plan A assuming Curt s sales are always more than 6000 Plan B is better than Plan A when Curt s sales are more than

point The table below shows Karen s distance during the marathon What is Brianna s rate of change for the first 2 hours of the race 28 28 24 22 20 lad 18 STOR 10 M 12 10 tance in Miles M M 2 O 0 1 2 3 4 5 Time In Hours 6 miles per hour 2 miles per hour 12 miles per hour 3 miles per hour 6 7 8 9 10

1 1 point Kevin s savings account balance changed from 1140 in January to 1450 in April Find the average rate of change per month Round your answer to the nearest dollar 310 per month 50 per month 103 per month 78 per month DO

Ozark Utica Belen Flint Salem Provo Arbor Clay Huron Dover b Write the set in roster form 0 In a certain county there is a passenger train service Let U be the set of train stations in the county The train stations in the county are along several train lines Let B be the set of stations that are along the Bronze Line Let P be the set of stations that are along the Purple Line Let Y be the set of stations that are along the Yellow Line Use the Venn diagram to get your answers below Consider this set which is written in descriptive form The set of stations that are not along the Bronze Line but are along the Purple Line or the Yellow Line a Which of these is a correct way to write the set OB n PNY OB U PNY OB n PUY OB U PUY Arbor Dover Ozark Utica 0 0 Belen Flint Provo Clay Huron Salem

2 05 01 5 04 5 05 HC Part A Given cos 8 3 determine three possible angles 8 on the domain 0 00 5 points Part B Given 8 495 convert the value of 8 to radians and find sec 9 5 points B i U Font Famil

25 1 point Write an explicit rule to represent the sequence 4 10 16 22 f n 4n 6 f n 6n f n 6n 10 f n 6n 2 Previous

4 1 point Rearrange the equation to isolate h A bh O4 h 2A b h 0 24 h b Ab h

b 10f 15ef 18f 27e

Find the slope intercept form of the line passing through 5 25 and 0 5 www The slope intercept form of the line is y Simplify your answer Use integers or fractions for any numbers in the equation Do not factor

Write an equation for the line shown on the right The equation of the line is y Type an expression using x as the variable Simplify your answer Use integers or fractions for any numbers in the expression

1 1 point 3 4 is one of many solutions to the inequality 2x y 2 2 True False

Ontent Time s The table shows the height in centimeters that a weight bouncing from a spring would achieve if there were no friction for a given number of seconds 0 0 75 1 5 2 25 3 3 75 4 5 5 25 121 le enhancedSequenceViewer 2414283 uri https 3A 2F 2Ff59af8a9 9515 4190 8486 aee0599ad9a3 sequences api brightspace com 6 1 09 Quiz Interpret Trigonometric Models Height cm 0 15 0 15 0 0 15 0 15 From its resting position how long does it take the weight to bounce one direction then the other and then back to its resting position

After making several scale drawings Joseph decides on the best placement for a new grill on mis deck He uses a scale of 2 cm for every 5 in What is the actual area of the space for Joseph s new grill in square inches GPA 10 cm Grill 18 cm Table

Evaluate the following expression 12 20 2 2 12 20 2 2 Simplify your answer

Evaluate the following expression 11 1 9 12 3 7 6 13 5 2 Type an integer or a simpl 1 5 6 6 12

Evaluate the following expression 2 33 2 3

Name Multiply Show or explain your strategy 1 3 times as much as 536 536 X 3 1 608 2 8 times as long as 2 403 meters

Discussion Prompt 2 Write an equation of a vertical line Can you write the equation in slope intercept form Why or why not

Evaluate the expression 3 25 5 3 3 25 0 Simplify your answer Type an integer or a fraction

Evaluate the following exponential expression 4 4 2 11 2 Type an integer or a simplified fraction

Evaluate the following expression 2 4 5 9 7 2 4 5 9 7 Simplify your answer

Evaluate the following expression 3 14 27 9 8 15 8 1 3 4 27 9 8 15 8 Simplify your answer

Evaluate the following expression 14 16 4 15 2 15 3 14 16 4 15 2 15 3 Type an integer or a simplified fraction

No Time Lim Xander who lives in Spain is reading a letter from his pen pal in the United States His pen pal says that the temperature in his city was 37 4 Fahrenheit one day so it was too cold to play soccer outside Xander doesn t know how cold this is because he is used to temperatures in Celsius Help Xander solve the following equation to determine the temperature in degrees Celsius 1 8C 32 37 4 Round your answer to the nearest tenth of a degree

Use an associative property to evaluate the expression 49 4 17 7 7 7 49 4 17 7 7 7 Simplify your answer

Use the properties of addition to find the sum of the real numbers 19 4 34 64 19 4 19 4 34 64 19 4 Simplify your answer