Sequences & Series Questions and Answers

What is the measure in radians of the angle A 120 Select one O a 2 3 O b 2 7 O C 4 d 3 4

Use the given sets below to find the new set Enter each number separated by a comma If there are no numbers in the resulting set leave the answer blank A 4 6 7 9 and B 8 3 5 An B

Sergio invests 4900 in two different accounts The first account paid 12 the second account paid 3 in interest At the end of the first year he had earned 471 in interest How much was in each account at 12 o at 3

Solve the system of equations using the elimination method I 4y 8 5 5x y 21 If there is a unique solution write the solution as an Ordered Pair One solution O No solution Infinite number of solutions

Solve the system of equations using substitution method 10 Y Y 3 x 11 38 If there is a unique solution write the solution as an Ordered Pair ordered One solution O No solution Infinite number of solutions

There are 60 students in a class 40 of them know how to swim 44 know how to play chess and 48 know how to speak another language At least how many students can do all three swim play chess and speak another language

Solve the compound inequality 3x 4 4 or 4x 626 Graph the solution on the number line 10 11 C

Write a system of equations to describe the situation below solve using any method and fill in the blanks The freshman and sophomore classes at Springfield High School are decorating floats for homecoming The freshmen have already spent 210 on their float plus they need to buy floral sheeting that costs 97 per roll The sophomores who have spent 219 so far on theirs still need to purchase vinyl grass at 88 per roll Both classes plan to buy the same number of rolls since they have the same area to cover By coincidence the two floats will have the same total cost in the end How many rolls will each class be buying How much will each class spend in total By buying rolls the two classes will each spend in total

Homework 2 EAS 305 section A Spring 2023 WebAssign plant at site is completed by the contract date Use the operations of union intersection and complementation to describe each of the following events in terms of A A2 and A3 draw a Venn diagram and shade the region corresponding to each one a At least one plant is completed by the contract date A A n A U A n A A U A n A n A3 A U A A3 OA UA UA A A A3 A A A3 A Subscript Subscript 2 A Subscript 3 A Subscript Subscript 2 A Subscript 3 A Subscript1 A Subscript 3 A Subscript1 Subscript 2 Subscript 2 A Subscript 3

18 58 100 17 19 21 23 Complete the following tables Measured Value s d 18 58 1500 C 25 0 5306 m 4 Subtract 0 0062 L 0 0128 km 136 g 3 49 R 132 519 133 9 54 B 6 578 g 10 02 g 26 1387 26 19 Significant Digits and Sl 4 2 24 Perform the indicated operations Give the answer to the correct number of significant digits 1 Add 2 Add 3 Add 8 55 mL 11 6 mL 20 0 ml Calculated Value Rounded off 6 249 mm 6 3 10 98 g 11 0 0 0573 mol 69 95 km h 296 038 cm 6 15mL 49129 5 Subtract 0 057 70 0 296 0 480 km 24 07 km 504 07km 504 6 Subtract C s d 51 08 mol 9 9 mol 41 10 mol 2 3 2 3 4 26 i 24 TO 16 56 mL 6 3 mL 1026m2 10 18 4 g mL x 5 5 mL 101 2mL 18 1 0058 t x 1000 kg t L005 120 358 6 g 2 02 mol 71529715 56 9 g 2 000453 g mol 28 44 52 3 004 mol x 4 3 g mol 12 91 729 456 7 L x 7 8 mol L 362126m2 7 9 g 3 456 g mol 212859 moz 411 21 4 g x 1 kg 1000 g 21 400 kg 6 0 g 24 3 g mol 324 69 moz 2 64 g 5 38 g mL 0 4907 mL

Solve the triangle LL F mZF mZG mZHz 9 47 G 4 5 12 H

A 12 ft Select all the correct expressions for BC C Select one or more AC tan27 b 12tan63 a C d 12cot 27 12 sin27 27 B

Given a right triangle ABC if angle A is 45 and side a is 4 m what is the length of side b Hint Angle C is the right angle Select one a 12 m b 8 m O c 4m Od 2 8 m

Given the right triangle below if AB 9 and BC 14 find AC round to nearest whole number A B Select one O a 13 Ob 28 C 277 d 17 C

From the figure given below given that B is a right angle the value of sin C is C b A Select one a a b O b b a Oc a c d c b C a B

Synthetic Division 500 Question Use synthetic division to evaluate f x 4x 3 27x 2 3x 64 when x 7

Find lim x y 0 0 esin 2x 4x e sin 2x 4x lim x y 0 0 L Type an integer or a simplified fraction

What is the graph of the rational function y a b TO 10 Select one COA a OB b OCC OD d S 10 33 10 10x 10 x C 2x 4 x 1 Im O my ES 10 46 10 1 10 x 10 x

hal expr X GGoogle prattempt 2922918 cmid 409937 1 A out of Simplify the rational expression State any re

A bacterial culture triples in population every 10 minutes If the population initially is 500 1 Determine the population after 20 minutes y 2 When will the population reach 70 000 t 44 9 minutes Round your answer to 1 decimal pla

Question 22 of 25 On a piece of paper draw a box plot to represent the data Then determine which answer choice matches the box plot you drew 12 18 20 23 25 28 32 36 37 40 41 O A OB C 12 20 12 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 17 28 26 30 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 37 34 30 38 41

1 Simplify the expressions 2a 32a 2a 16a 32a b C 4yz 15x y 3xy z 8x yz 2c 5c 3 c 4c 21 2c 1

T Sin U Select one a 0 64 Ob 1 57 C 0 82 11 S 7 U

Find the exact value of csc 240 sec 330 Select one a 4 3 3 OO Ob 0 C 3 2 3 6 d 3

In the triangle shown below the length of AB is 8 inches and angle A measures 60 What is the distance of BC Please round to two decimals Select one a 17 inches Ob 6 93 inches OC 4 80 inches Od 4 61 inches 8 60 B C

If angle A is 30 and side AB 100 m find the length of the side BC B 30 Select one a 75 O b 100 3 O c 200 m O d 50 m

Use Taylor s formula for f x y at the origin to find quadratic and cubic approximations of f near the origin f x y 4 cos x y

Use your calculator to find the measure of each angle to the nearest degree sin 0 85

Which of the following accurately shows the range of the function defined below 3 x 0 f x x 2 0 x 2 2x 5 X22 X O 3 00 O 2 00 O 3 6 O 0 00

The graph of a for the function that best describes this graph piecewise defined function is given Write a definition 0 0 13

A rectangie nas width 2x 3 and length 2x 4 What is the perimeter of the rectangle 8x 2 4x 12 4x 2 2x 12

The daily cost to a manufacturing company is modeled by the function C x 4x 1600 where C x is the total daily cost and x is the number of items manufactured Find C 1000 and interpret its meaning C 1000 This value represents The product of the daily cost and the number of items The number of items manufactured when the daily cost is 1000 The daily cost when 1000 items are manufactured

Problem 8 Let P be the statement If n is an even number greater than 2 then n is a sum of two prime numbers Write down the converse P of the statement P Determine the logical value of P

Which graph best represents a function with a range of all real numbers greater than or equal

1 Write the domain and range for each relation a 5 3 K 2 1 2 1 123 5 6 7 8 76X 7 W b ences 10 CSATS53N4 9 8 7 6 5 4 3 2 1 2 3 2 3 4

3 For each set of data identify the relation as linear quadratic or neither Calculate the first differences and second differences if necessary a X 0 1234 3 4 4 Identif y 2 13 28 43 58 1st Diff 2nd Diff b X 2 1 4 7 10 y 6 0 12 42 90 1st Diff 2nd Diff

3 The sum of a number and 10 increased by 3

Please work the following two problems on this sheet Clearly indicate your final solutions 5 points Find the volume of the region that lies inside the sphere x y z 2 and outside the cylinder x y 1 Clearly show how you calculate bounds for each variable Use whichever coordinate system see most appropriate 15 6 56

a The domn and range domain 04 range 4 decreasing testimate the flowing Enter your ansung terse A b The nervas on which is men and on which decen increasing

Find the coefficients that must be placed in each shaded area so that the function s graph will be a line satisfying the specified conditions y 63 0 x intercept 21 y intercept 9 m The coefficient for the x term is and the coefficient for the y term is

A football coach orders one hoodie or one long sleeve performance shirt for each of his 45 players Each hoodie costs 60 and each long sleeve performance shirt costs 45 The entire order totaled 2 400

A boat travels 101km from the port on a bearing of 136 degrees and then 24km on a bearing of 255 degrees it then anchors in that position another vessel plans to leave the same port and joins the first boat by traveling in a straight line a How far must the second vessel travel in km b On what bearing must the second vessel travel

10 Find the exact value of csc cos co 1 7 25

You sell T shirts for a fundraiser For each T shirt you sell the company that makes th shirts receives x dollars and you receive the remaining amount You sell 12 T shirts for a total of 12x 72 dollars How much money do you receive for each T shirt that you sell

Vithout using induction prove that for all non negative integers n n n k n2n 1

We want to solve the equation 10x 11x6 0 First factor 10x 11x 6 By the zero product property we know 0 OR 0 And therefore we know that 83 OR OR X Do not use decimal approximations in your answer Use fractions instead

1 8 pts AXYZ is given Prove without using any triangle congruences XY YZ XZ if and only if ZX Y Z Note this is an if and only if statement so there are TWO things to prove he right

A children s inflatable pool takes 24 minutes to fill with an electric air pump It takes 49 minutes to let the air out of the pool If the pool s valve is accidentally left open how long will it take to fill the pool It will take minutes Simplify your answer Type an integer or decimal rounded to two decimal places as needed

e the reflexive property of 40

Find the greatest common factor of x 1 2 x 1 2 x 1 x 1 x 1 x 1 7