Sequences & Series Questions and Answers

A circle has a central angle measuring radians that intersects an arc of length 45 in What is the length of the radius the circle Round your answer to the nearest tenth Use 3 14 for O 2 4 in O 19 1 in 3r 105 6 in O 135 0 in

Lashonda made 25 000 in taxable income last year Suppose the income tax rate is 15 for the first 9000 plus 17 for the amount over 9000 How much must Lashonda pay in income tax for last year

A TV has a listed price of 879 98 before tax If the sales tax rate is 7 75 find the total cost of the TV with sales tax included Round your answer to the nearest cent as necessary

The table below defines a function f x x f x 2 0 1 2 04 28 4 12 What is the value of 4

etermine intervals on which the function is increasing decreasing and constant ing CAP

7 dr for the given F and C 7 x y27 and C is the line from the point 5 4 to the point 7 6 F dr 0 Find X

solve the inequality x 2 x 2 0

4 Solve cos 0 2sin sin 0 0 0 0 Hint put everything in terms of sine 5 marks

19 Given acute angles A and B where m A 4x 31 and m B 2x 4 Find the value of x if sin A cos B

For the table below select the correct scatter plot of the data Choose the correlation depicted by the data You will select TWO answers for this question Average Price Number Sold Number Sold Number Sold PROS ENQUAN 11 112 Average Price 8 Jeans Sales Positive Comeliation RAGHIN Average Price S No Correlation 126 114 Avtar Price 5 Negative Correlation 28 36 83 40 64

he figure shows the flow of traffic in vehicles per hour through a network of streets 400 300 X2 XI X3 X4 b Find the traffic flow when X3 0 and X5 70 X1 X2 X3 X4 X5 c Find the traffic flow when X3 X5 100 x1 x2 X3 X4 X5 600 X5 a Solve this system for x i 1 2 5 If the system has an infinite number of solutions express X1 X2 X3 X4 and x5 in terms of the parameters s an X1 X2 X3 X4 X5 100

Which of the following statements about a vector space V over Ris false Olfe Rand v V with cv 0 then either e 0 or v 0 or both V can be the set 0 v v where v 0 The additive inverse of 0 is 0 If u is the additive inverse of v then v is the additive inverse of u

the results and develops the probability distribution below for a randomly selected student What is the mean of the probability distribution Hours Studied X 0 5 1 1 5 2 2 5 O 0 20 0 46 O 0 85 1 50 Probability Distribution Probability P X 0 07 0 2 0 46 0 2 0 07

Find the sum of the following series 1 e 1 2

9 For f x sin 2x 1 2 a Complete a table of values for the key points c Write a mapping formula e Sketch the new graph Be sure to fill the grid with as many cycles as will fit b e a 2 5 X 0 J 2 K 3 2 2x f x sin x b Sketch the starting function d Determine the translated key points x axis scale 1 square A 4 2

9 Quadrilateral PQRS is a rectangle If mzQRP 2x 1 and RPQ 5x 7 find the value of x x 12 2x 1 5x 7 P

Consider the following integral 50 X COS 10 sin 5 9 5892 10 0 Using an integration step size of 5 and the Trapezoidal method the integral can be found to have an error of 0 0248 per ste Approximately how large would you expect the per step error to be if a step size of 2 5 is used Oa 1 55 10 per step O b 7 75 x 10 4 O c 6 20 10 3 per step per step O d 3 10 x 10 3 per step

6 Cual de estas fracciones es igua a 1 2 O F 2 6 O G 3 6 O H 2 2 O J 2 1

6 Cual de estas fracciones es igu a 1 2 O O O O F 2 6 O G 3 6 O H 2 2 J 2 1

A teacher assigns a score from 1 to 4 to each student project The table below shows the probability distribution of t scores for a randomly selected student Which score is most likely Probability Distribution Score X Probability P X 1 2 3 4 0 1 02 03 04 0 06 0 20 0 48 0 26

Find the remaining sides of a 30 60 90 triangle if the side opposite 60 is 18 20 3 10 3 3 3 022 2 11 2 20 3 10 3

X Select one 1 2 y 3 1 3 Which graph correctly represents the relationship of x and y 2 5 O O 0 y V 1 1 6 5 y y 5 3 5 10

el peso de una caja de macarrones F tazas G pulgadas H onzas J litros

Given P 2 b a bc c a d 1 d b a d d bc a Calculate ph by indretion where a d I 1 b calculate lim ph 8 10 Note In part a it is a d 1 not a d 1 Please show all working step by step

Simplify Answer should be written as an integer or a fraction no decimals Use absolute value signs as if needed 31 12 64

Set up the equation for the following word problem and solve the equation Let y be the unknown number 13 times the difference between a number and 60 is equal to the number plus 59

14 Multiply as indicated 2 1 2x 3y 4x y 91 2 4x 5y 16x 40xy 9 a b a b tdsys 15 1 99 2 3992 1 a 2ab b a 2

Determine the Fourier trigonometric series for y t shown in the figure M 2 01 y t m 2 TT

Given that the complex Fourier integral representation of f x is 1 2a etwx dw 8 2 0 a w what is the Fourier transform of f x Select one O A OB O C C D 2a a w 8 a S a w 8 an a w eiwx dw None of the above

1 point Let W be the set 1 3 Let W be the set 2 9 2 3 Determine if W is a basis for R and check the correct answer s below A W is a basis B W is not a basis because it does not span R C W is not a basis because it is linearly dependent 6 1 0 0 5 0 3 Determine if W is a basis for R and check the correct answer s below A W is a basis B W is not a basis because it is linearly dependent C W is not a basis because it does not span R

Let 2i C 112 1 3 4i 3 i A where c 0 is a constant If c 6 then A 1

Figure 1 As shown in Figure 1 BD bisects ABC which is inscribe in circle O The line EC is tangent to circle O at point C Prove that ABD DBC 7 marks

Use the graph to find the following a the domain off Q b the range of f c the x intercepts d the y intercept e intervals on which f is increasing f intervals on which f is decreasing g intervals on which f is constant h the number at which f has a relative minimum i the relative minimum of f j f 5 k The values of x for which f x 3 1 Is f even odd or neither a What is the domain off 0 00 Type your answer in interval notation b What is the range of f 4 00 Type your answer in interval notation c What are the zeros of the function The left zero of the function is 3 and the right zero is 7 d What is the y intercept The y intercept of the function is 21 e Over what interval is f increasing 5 00 Type your answer in interval notation f Over what interval is f decreasing 0 5 Type your answer in interval notation g Over what interval is f constant Type your answer in interval notation

Find an equation for the graph sketched below 4 m f x 7 3 5 4 3 1 i hey 2016 16 N 1 i ti Lin

Graph the linear equation y 6 Use the graphing tool to graph the linear equation Click to enlarge graph Ay 10 8 6 4 2

Fill in each blank so that the resulting statement is true Consider the line whose equation is 6x y 3 0 The slope of any line that is parallel The slope of any line that is parallel to this line is Type an integer or a simplified fraction The slope of any line that is perpendicular to this line is Type an integer or a simplified fraction Use the graph of y f x to graph the function g x f x 2 y f x Q DI 6 4 a 2 4 Q 4 this line is GOOD The slope of any line that is perpendicular to this line is Choose the correct graph of g below OA 1119 Q a Q Q OB OD a Q G

4 9 3 11 7 B 3 5 7 9 11 13 C 3 5 9 D 13 11 Select all of the following that is false OB CA D C B OD C A AND m

ou are going on a vacation that will cost 8 000 You plan to pay for it using an installment plan but only want to finance 2 600 What percent of the total cost should the down payment be

Write the following function in terms of its cofunction 3n 10 Write your angle in radians and make sure to use parentheses For example your answer might take the form cos Brouide cot

Perform the division 15x 60x5 12x5 15x4 60x5 5 12x nial 41 2012 BEN Simplify your answer

3 f x 4x 4 Find f 4 5 w t 3 2t Find w 0 7 f x x 2 Find 7 9 k t t 4t Find k 8 4 h n n n Find h 6 6 p t 1 2t Find p 5 8 h t 3t 4 Find h 9 10 h x x 5x Find h 4

Which of the following graphs represents the inequality 42b O 2 N 3 3 5 5 55 6 9 9 6 7 188 B 00

Simplify Assume no division by zero See Example 8 Objective 4 442 514 3

Write a function for the sinusoid 9 6 5 3 y 2 5 1 1 2

1 Solve a log x 3 log x 2 log 3x 2 b 2x 2 2x 96

The functions f x 2 8x 286 and g x 0 01x 4 9x 370 model the chance as a percent that a 60 year old will survive to age x The bar graph to the right shows the chances of 60 year olds surviving to various ages a Find and interpret f 70 b Find and interpret g 70 c Which function serves as a better model for the chance of surviving to age 70 Chance of survival Chances of 60 Year Olds Surviving to Various Ages 93 90 75 60 45 30 15 70 63 25 80 90 Age 2 7 100 e 2 a Select the correct choice below and fill in the answer box es to complete your choice Simplify your answers is 70 OA f 70 which means that the chance of a 60 year old surviving to the age of B f 70 which means that the chance of a 60 year old surviving to the age of 70 is

Se de quality Graph the solution set and write it in internal notation SUBMI

Match the number line with its equivalent interval notation 10 Choose the correct answer below OA 0 2 OC 0 00 OE 2 U 2 00 OG 0 2 OI 2 00 2 0 2 OB 2 2 O D 2 OF 0 2 OH 9 2 O J 2 00

You flip 3 coins 20 times and record the number of heads The results are listed below 2 1 0 2 2 0 2 2 3 2 1 2 1 2 1 1 2 1 3 1 Complete the frequency table c a d DONE b Number of Heads 0 1 2 3 Frequency a b C d

Suppose the data below show the number of televisions by brand sold by a particular Walmart store last month Brand Sony Number Sold 20 Panasonic 10 Samsung 19 Sharp 12 Toshiba 19 12 Vizio