Mathematical Induction Questions and Answers

a What is 10 of 50 b What number is 10 more than 50

fried 6 There is an annual squid eating contest happening where contestants eat as many squids as they can in 15 minutes This year we have a strong participant Joey whose squid eating speed is given by the function y 10e x x x 2x 1 squids minute a What is Joey s average eating speed over the 15 minute period Round your answers to two decimal places

Find the eigenvalues and bases for the eigenspaces of the linear opera T M M 2 defined by 22 22 T a b b 2c a c C d d 14 points

1 2 0 3 4 Write an equation in slope intercept form for the line with y intercept 3 and slope 0 0 5 X 8 08 6 S

5 Using the chromatic recursive formula count the number of different k colorings of the following graph

Practice 4 Determine the measure of each ZA to the nearest degree a C b c 5 1 cm A 4 cm 5 cm B A 12 3 cm B B 6 8 cm C 9 2 cm

Read the list of verbs foretold overtook will inflict will petition A writer would most likely use these verbs in an essay that includes O the present and past tenses O the future and present tenses the future and past tenses

5200 Monthly Furniture Sales IL 201 5400 401 5600 601 5800 801 1000 Price Range xpand image Question 8 of 8 The graph provided shows the monthly total sales of furniture items categorized by five different ranges of price Determine the percentage of sales of furniture items less than or equal to 400 Select a Choice Below A B C D Approximately 40 5 Approximately 34 1 Approximately 2 7 Skip Approximately 23 6

TEA 178 17 0 362 154 248 118 110 Average price of super in US cities V Sep 12 D 12 New 12 De 12 36 13 Feb 11 Mar 13 Apr 13 ck to expand image May 13 An 11 M 11 Aug 11 Sep 13 Question 2 of 8 Skip The average price in cents per pound of sugar observed during the period of September 2012 to September 2013 in most U S cities is displayed in the line graph provided What was the approximate percentage increase in the price in cents per pound of sugar from November 2012 to March 2013 Select a Choice Below A B C About 15 54 About 25 32 About 22 54

Classic Trailers job cost records yielded the following information Click the icon to view the job cost information Use the dates above to identify the status of each job Compute the following balances for Classic a Work in Process Inventory at August 31 D Finished Goods Inventory at August 31 C Cost of Goods Sold for August Begin by identifying the status of each job Job No 1 2 3 4 Started July 21 July 29 August 3 August 7 Date Finished Sold August 17 August 26 September 11 September 13 August 29 September 1 Job No 1 Job No 2 Job No 3 Job No 4 August 16 August 21 Data table Job No Started July 21 July 29 August 3 August 7 Date Finished August 16 August 21 Total Cost of Job at August 31 Sold August 17 August 26 September 11 September 13 August 29 September 1 Status of Job at August 31 3 500 13 500 6 100 4 400 Finished goods Sold Work in process Total Cost of Job at August 31 3 500 13 500 6 100 4 400

Find all values of x where the function is discontinuous k x e x 4 Select the correct choice below and if necessary fill in the answer box to complete your choi OA The function is discontinuous when x OB The function is discontinuous when xs OC The function is discontinuous when x2 O D The function is discontinuous when O E The function is discontinuous when x Use a comma to separate answers as needed OF The function is continuous for all x values

to Find f 2 if f x 8 10x f 2 Simplify your answer Type an integer or a fracti

Find the derivative of the function 4 8 y 6 X co x

Find the cost of each item in 10 years assuming an inflation rate of 7 compounded continuously Round your answers to the nearest cent a movie admission 8 00 b CD 14 95 c textbook 110 00 d electric bill 105

Use Boolean Identities to simplify the following Boolean functions 1 xyz xy z x yz x y z xyz 2 wxy z wxyz wxy z wx yz wx y z wx y z w xy z w x yz w x yz 3 w x y w xz wxz wx y z

Ms Lee visited London while on vacation and rode The London Eye Ferris wheel After 15 minutes she hit a maximum height of 136 meters and then a minimum height of 1 meter after 30 minutes a Write a sinusoidal function to model this situation where h is the height in metres above the ground and t represents the time in minutes from when Ms Carone boarded the ride b What is the radius of The London Eye c At what time s to the nearest minute is Ms Carone 99 meters above the ground during the first rotation d How long does it take to go around The London Eye once

Chapter 9 There is a misconception that centerlines or the tolerance block control the location size limits coaxiality alignment between two cylinders

16 11 Why is the drying step which is so important in the processing of traditional ceramics usually not required in the processing of new ceramics 16 15 Liquid phase sintering is used for WC Co compacts even though the sintering temperatures are below the melting points of either WC or Co How is this possible

Determine the center and radius x y 14x 2y 1 A center 7 2 radius 3 B center 4 1 radius 5 00 A B C C center 7 1 radius 7

choice that completes the seMBRICO DOID validity of an argument with two premises construct a truth table for a conditional statement of the form premise 1 A prem

Which of the following formulas generate the sequence first few terms of which are 5 8 11 14 17 20 23 26 O a5 3n n 0 R O a 5n n20 7 O a 3 5 n20 76 O a 3n 5 n20 n

Let sin x cos x cotx cscx Verify the identity by transforming the left hand side into the right hand side

1 point Convert the following integers from binary notation to decimal notation a 10112 b 10111002 c 10001010112

ve the given initial value problem y y 36y 36y 0 y 0 6 y 0 23 y 0 461

Question 27 3 Select the correct inequality to make a true statement 1 v 0 333

Round the following to the nearest hundredth 0 061 0 005 0 096

1 Statistical Inferences Question 10 Which distribution shown here has the LARGEST standard deviation Select one The purple distribution The red distribution The standard deviation of all three is equal The green distribution 12

The trunk of a leaning tree makes an angle of 12 with the vertical To prevent the tree from falling over a 35 0 m rope is attached to the top of the tree and is pegged into level ground some distance away If the tree is 20 0 m from its base to its top calculate the angle the rope makes with the ground to the nearest degree

The Birch and Swinnerton Dyer Conjecture The Birch and Swinnerton Dyer conjecture is a conjecture about the relationship between the zeta function of an elliptic curve and the behavior of the points on that curve An elliptic curve is a type of curve that has many interesting mathematical properties The Birch and Swinnerton Dyer conjecture states that if the zeta function of an elliptic curve has a zero at a particular point then there are infinitely many points on that curve that have that same number as their x coordinate

s tAu in the blanks for the missing values in the table S T t T n T S nvi s tAu

in the blank with an appropriate word phrase or symbol ne biconditional statement p q is ne biconditional statement pq is only when p and q have the same truth value CARR only when p and q have the same truth value

If f x x 8 g x x 8 and h x then f g h x 8x4 X The number of bacteria in a refrigerated food product is given by N T 27T2 127T 36 5 T 35 where T is the temperature of the food When the food is removed from the refrigerator the temperature is given by T t 6t 1 2 where t is the time in hours Find the composite function N T t N T t Find the number of bacteria after 2 3 hours Give your answer accurate to the nearest whole value hartoria

In Exercises 8 find the perimeter of the region 8 4 mm

Fv P 1 r 1 r Fv 501 1 0 08 40 0 08

2 1 10 2 A 3 B 232 4 1 a A 2B and A 2B T b A 2B v and A 2B v T and 1 2 5

Find a value of s in the interval 0 the given statement csc s 1 5421 that satisfies S Round to eight decimal places as needed

13 The Xs show the positions of two basketball teammates relative to the circular key on a basketball court The player outside the key passes the ball to the player on the key What is the length of the pass 5 ft 16 ft 12 ft

In circle E EF 9 and the area of shaded sector 187 Find the length of the arc highlighted below Express your answer as a fraction times 7 F H K E

The figure below shows a circle with center IV diameter IH secant HX and tangent MC Which of the angles must be right angles Select all that apply M ZNML ZIPH ZNHX ZHNM NID H N I S P

Consider the expression where x 1 and x 1 00 00 1 If the expression is simplified what is the result 2 4 1 1 2x 4z 1 1 x 1 x 1 x 1

Consider the equation Which statement is true The equation has one solution x 1 2 The equation has two solutions x 2 and x 4 The equation has no solution because x 1 2 is extraneous The equation has two solutions x 2 and x 4 3 3x 6 x 4 6x 8 2x 4

Which of the following statements you will prove using Mathematical Induction Select ALL that applies On n is divisible by 3 n is a positive integer 1 2 2 2 2 2 1 for all nonnegative integers n The reciprocal of any non zero rational number is also rational The sum of two rational numbers is rational

Consider the polynomial function T x 2x x 3 x 1 What are the zeros of T x x 3 x 0 and x 1 x 1 x 0 and x 3 x 2 x 1 and x 3 x 3 x 1 and x 2

Suppose you have to prove that P n is true for all positive integers using the method of Mathematical induction Arrange the steps of your proof Assume that statement is true for n k Verify that the statement is true for n 1 Conclusion Prove that the statement is true for n k 1

Question 10 Members of the Board of Governors of the Federal Reserve serve a 04 O 14 Points 2 2 year appointment

Are the triangles similar If yes by which postulate 4 in Z 5 in 2 in Yes by SSS Yes by AA Yes by SAS Yes by AAS Not similar 10 in

Which checking account requires a higher balance and has a higher interest O NOW account O No frills account Money market account

What is the best way on writing the formula for the volume of cone Assuming float pi 3 14159 A B vol 3 14 r r h 0 33 vol 0 33 3 14 r r h C vol pi r r h 3 D vol 0 33 pi r r h

Prove using Mathematical induction that for any non negative integer 5 7 9 2n 3 n n 4

1 23 P L LLL Let an be a bounded sequence of complex numbers Show that for each 0 the series 1 ann converges uniformly for Rez 1 Here we choose the principal branch of n 00 K Solution ann an C Rez 1 Apply Weierstrass M test ann Cn Rez n 1 Mn Mn an converges uniformly for Rez 1 E