Sequences & Series Questions and Answers

2x 200 4x 40x 1 7x 21 x 7x 30 6 10 3a a 60b 75b5 5a b 10a

5 In the expavion Coefficient is C 1 of 2x ay 4 Find 64 sum of the the value of a a 3

Find the unknown angles in triangle ABC for the following triangle if it exists A 27 7 b 43 7 ft a 27 7 ft SLEE Select the correct choice below and if necessary fill in the answer boxes to complete your choice Round to the nearest tenth as needed O A There are two possible sets of remaining angles The measurements for when B is smaller are B C OB There is only one possible set of remaining angles The measurements for the remaining angles are B OC No such triangle exists and C The measurements for when B is larger are B and C 0

The credit remaining on a phone card in dollars is a linear function of the total calling time made with the card in minutes The remainin credit after 22 minutes of calls is 26 92 and the remaining credit after 48 minutes of calls is 23 28 What is the remaining credit after 57 minutes of calls

4x 52 5x 3 OA 8 00 4 13 12 OC 4 11 10 6 9 5 100 7 92 9 2 OB 8 13 12 11 OD 4 00 9 8 10 9 6 5 8 7 64 6 2 5

Basics to Multiplying Kat Simplify each expression 1 1 7b 8 9b 9b 3 A 6b C 3 56 81b k 7 5 7k A 5 k 6 C k 5 B b D 36 3b 2 k 2 7k 5 2 k 8 k 2 4 B D k 1 4k k 7 k 8

6 The RED dotted graph represents the parent function of y Determine what transformations were made for the graph in BLUE 4 points DRAG DROP THE ANSWER Vertical compresion by 2 Vertical stretch by 2 Shifted 4 units left Shifted 4 units right Shifted 1 unit down Reflected over x axis Reflected over y axis Shifted 1 unit up Note Use CTRL D to drag the option via keyboard

Question 1 4 Let f x x 4x 1 and g x 2x 3 Determine 2 f x g x 2x 6x 1 O 2x 2x 5 6x 2x 5 2x 3

Question 1 8 Multiply Express your solution with positive exponents 2a 566 7a b 146 a 14 ab 565 85 a ab

Question 1 15 Determine an equivalent form by rationalizing the denominator 6 5 3 6 3 15 3 6 5 5 15 6 3 5 3 3 6 5

Simplify the expression O C 12 13 C 12 1 C6 3 15 13

Receipt Chaos Name Sadaf Amici Use the percent proportion to fill in the missing parts of each receipt 1 Buffalo Wild Wings Receipt Medium wings 15 99 Sodas 3 21 Basket of Fries 3 99 TOTAL 2319 TIP 20 NEW TOTAL 23 19 123 19 2319 X 23 191 20 100 LO 23 19 Per

Simplify the expression Assume all variables are positive 2 3 y 7 7 5

9x 25y 225 The hyperbola 9x 25y 225 has its center at 0 0 Type an ordered pair The hyperbola 9x 25y 225 has vertices at 5 0 5 0 Simplify your answer Type an exact answer using radicals as needed Use a comma to separate answers as needed Type an ordered pair using integers or fraction Give the equations of the asymptotes for the hyperbola 9x 25y 225 Choose the correct answer below 5 A Y 3X 25 OB y gx X 3 O C y 5x 9 OD Y 25x 4

What is the vertex of the following parabola y 4x 24x 23 3 13 3 13 3 24 3 24

3 49 70 8 tayos sat gala a b c The ta y s sat galata y s sat af 2 answer B 1 9 C 6 Jata sat gate D 9 E

P varies inversely with q If P 10 when q 3 find the value of P when q 6 When q 6 P

5 1 The current I in an electrical conductor varies inversely as the resistance R of the conductor The current is ohms ampere when the resistance is 784 ohms What is the current when the resistance is 9604 2 The current is ampere Simplify your answer Type an integer or a fraction

Multiply the radical expression 2 4 11

ck here to watch the video ltiply and simplify the radicals Assume all variables are greater than or equal to zero 18a 3 15a

Simplify the radical expression Assume y 0 12 32y 32112

Suppose you are given a square with an inscribed circle as shown below If the area of the square is 100 m what is the area of the circle Use 3 14159 for T a

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function f has real zero s 8 JA Q S

5 4 J 2 1 Y intercept End Behavior 24 22 20 18 16 14 12 10 0 10 Degree 6 4 2 0 C 2 Zeros and multiplicity 6 Leading coefficient As x g x As x g x 2 g x Equation of g x in intercept form Challenge Equation of g x in standard form

Which of the below is the completely factored form of the polynomial show 4a 96 2a 3b 2a 3b 2a 3b 2a 36 4a 9b a b

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function f has real zero s 125 125 T8 O Q

Decide whether the following statement is true or false If false tell why For f x x 5 x 8 5 is a zero of multiplicity 3 Choose the correct answer below A The statement is true OB The statement is false because 5 is not a zero of f x OC The statement is false because 5 is a zero of multiplicity

State the excluded values for each n 4 4n 8 9 11 63 2x x x 2x 35 10 12 10 12 m 17m 72 8m 72m p 12p 27 p 16p 63

Find the value of the property given the following Annual Rent 612Vacancy and collection los 5 Operating expenses 35 of gross income Capitalization rate 9

Consider a retirement savings account where the monthly contribution is 110 for the first 20 years is increased to 215 for the next 25 years and then is increased once again to 425 for the last 10 years The APR is always 6 5 compounded monthly What is the value of the account at the end of 55 years The value of the account at the end of 55 years is Round the final answer to the nearest cent as needed Round all intermediate values to two decimal places as needed

Solve the following system of equations If there is a unique solution enter it as an ordered pair in the form x y If there is no solution enter Inconsistent If there are infinitely many solutions enter your answer as a line in the form y mx b 2x 4y 24 5x 7y 54

els that are the same 6x 2 2 6x 1 a Show that when x 3 Arun s answer is incorrect Explain why his method is incorrect f Discuss your answers to parts a to e with other learners in How will you convince them about your findings if your ans Simplify these expressions Make sure you factorise the numerator before you cancel with the denominator 6x 3 b 5x 10 3 5 Show that 6x 4 20x 25 simplifies to 7x 3 C 6x 9 3 d 8x 20 4

13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation

12 Which equation matches each graph Describe each graph in terms of its slope and y intercept b y 3 x 2 d y 3 x 2 a y 3 2 x 1 c y 3 2 x 1 Graph A Graph B y 4 2 b Graph C 0 2 4 14 Match each graph with its equation Justify your choice a 2 2 0 0 2 0 y f x 6 ly 2 13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation 0 2 Graph D 2 X 0 2 y 1 2 x 2 y 2 2 x 1 y2 2 x 1 y 1 2 x 2 X y g x y 1 x 2 1 y 2 x 1 y 1 3 x 2 2 c a y 4 b y h x 2 0 7 10 b y 3 c y 1 4 d y y 2 3 2 35 2 x 8 15 Use a graphing calculator or a computer with graphing software Graph each equation Sketch or print the graph Write instructions that another student could follow to get the same display x 5 x y 1 x 2 3 y 1 y 1 Volume of Liquid mL 10 20 2 y 2 x x 11 x 2 x 2 0 375 x 4 0 5 x 6 3 16 Chlo conducted a science experiment where she poured liquid into a graduated cylinder then measured the mass of the cylinder and liquid Here are Chlo s data Mass of Cylinder and Liquid g 38 9 51 5 a When these data are graphed what is the slope of the line and what does it represent b Choose variables to represent the volume of the liquid and the mass of the cylinder and liquid Write an equation that relates these variables c Use your equation to determine the mass of the cylinder and liquid when the volume of liquid is 30 mL d Chlo forgot to record the mass of the empty graduated cylinder Determine this mass Explain your strategy

8 Solve each equation below 4 pts each a 0 05 1 15 5 c log 2x 4 2 b log x log x d 4ln 6x 5 15 2

quation 2 pts each log 1 243 x 7 Graph f x log4 x 2 5 pts a What is the y intercept s b What is the x intercept s c What is the domain of f x d What is the range of f x log 49 1 log 0 log 2 0 x

a 3 3 3 3 11 5 7 1 27 13 15 x 8 15 17 19 1 n 11 21 12 b 2 5 x 10 7 x 15 3 k 5 V 5 2 3 2 3 2 x 2 14 9 4 8 10 12 6 2 21 1 14 16 m 12 5 18 x 2 2 3 11 v 4 n 5 6 3 m 14 4 b 8 8 1 P 6 n 3 3 2 2 1 7

USE SALT A report set a goal of 0 541 for the proportion of babies still being breastfed one year after birth The organization also used the survey data to estimate the proportion who were still being breastfed one year after birth to be 0 351 for babies born in a particular year Suppose that the survey used a random sample of 1 000 parents and that you want to use the survey data to decide if there is evidence that the goal is not being met Let p denote the population proportion of all babies born in that particular year who were still breastfeeding at 12 months Hint See Example 10 10 Hp The shape of the sampling distribution is approximately normal The sampling distribution is centered at 0 0224 x a Describe the shape center and variability of the sampling distribution of p for random samples of size 1 000 if the null hypothesis Ho p 0 541 is true Round your standard deviation to four decimal places 0 541 MY NOTES PRACTICE ANOTHER b Would you be surprised to observe a sample proportion as small as p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 Since the probability of a sample proportion this small or smaller is 0 met The standard deviation of the sampling distribution is We would not B be surprised to observe a sample proportion of p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 is true The probability of a sample proportion this small or smaller is 0 0132 X which is greater than 0 05 c Would you be surprised to observe a sample proportion as small as p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 0 05 there is 0 We would B be surprised to observe a sample proportion of p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 is true The probability of a sample proportion this small or smaller is 0 05 which is less than d The actual sample proportion observed in the study was p 0 351 Based on this sample proportion is there convincing evidence that the goal is not being met or is the observed sample proportion consistent with what you would expect to see when the null hypothesis is true Round your answer to four decimal places Consider the evidence that the goal is not being met convincing if the probability the event occurs when Ho P 0 541 is true is less than 0 05 which is less than O convincing evidence that the goal is not being

a Assuming that L 3 in the figure below sketch the function to which the Fourier e series converges for 0 x 3 g x 3 if 0 x 1 0 if 1 x 2 1 if 2 x 3

3N a101 b 22 c 34 Submit Answer 3 57 Points DETAILS STITZTRIG3 2 3 006 ASK YOUR TEACHER Use the Law of Cosines to find the angles if possible Round your answers to two decimal places If an answer does not exist enter ONE MY NOTES PRACTICE ANOTHER

You may need to use the appropriate appendix table or technology to answer this question The average U S daily internet use at home is two hours and twenty minutes A sample of 81 homes in a certain city showed an average usage of one hour and 40 minutes with a standard deviation of 90 minutes We are interested in determining whether or not the average usage in that city is significantly different from the U S average a State the null and alternative hypotheses in minutes to be tested Enter for as needed 1 00 Your answer cannot be understood or graded More Information Ho H 1 00 X X b Compute the test statistic 0 65 X Your answer cannot be understood or graded More Information c The null hypothesis is to be tested using a 0 05 Determine the critical value s for this test Round your answer s to two decimal places If the test is one tailed enter NONE for the unused tail test statistic 2 58 test statistic 2 2 58 X X d What do you conclude O Reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average Reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average X

5 Solve the following exponential equation 1 25 55 6

Find the unknown angles in triangle ABC for the following triangle if it exists A 29 1 b 44 1 ft a 26 9 ft Select the correct choice below and if necessary fill in the answer boxes to complete your choice Round to the nearest tenth as needed A There is only one possible set of remaining angles The measurements for the remaining angles are B and C B There are two possible sets of remaining angles The measurements for when B is smaller are B 52 9 and C 98 The measurements for when B is larger are C 23 8 C No such triangle exists

3 Solve the following exponential equation 64 1024

1 Solve the following exponential equation 1 625 54 3

6 Rewrite the given expression using natural logarithms only Ing 17

If in air at 30 C will cool from 100 C to 70 C in 1 minute find its temperature at the end of 2 minutes

4 Find the exact value of the following logarithmic expression logi 81

Use the parent function f n log and transformation techniques to graph A z log x 7 Als indicate which transformation s is are applied Determine the domain range and vertical asymptote of Select all transformations that apply DReflect the graph of f about the n axis Horizontally stretch the graph off by a factor of 7 O Horizontally compress the graph of f by a factor of 7 Dvertically compress the graph of f by a factor of 7 Shift the graph of f 7 units down Oshift the graph of f 7 units to the left Vertically stretch the graph of f by a factor of 7 Reflect the graph of about the y axis shift the graph of f 7 units up shift the graph of f 7 units to the right

Julio deposits 1500 in a savings account that pays 2 4 interest per year compounded monthly The amount in the account after n months is given by An 1500 1 0 024 0 024 12 a Find the first six terms of the sequence Round your answers to the nearest cent A A A3 A4 A5 A6 S b Find the amount in the account after 5 years Round your answers to the nearest cent Aso