Mathematical Induction Questions and Answers

H The design of boats is based on Archimedes Principle which states that the buoyant force on an object in water is equal to the weight of the water displaced Suppose you want to build a sailboat whose hull is parabolic with cross section y 6x Your boat will have length I in meters and its maximum draft the maximum vertical depth of any point of the boat beneath the water line will be H in meters Every cubic meter of water weighs 10000 newtons What is the maximum possible weight for your boat and cargo weight newtons Select a blank to input an answer

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7 erences TB MC Qu 03 52 Static Why are adjusting e Why are adjusting entries recorded at the end of the accou Multiple Choice The company s accounts must be adjusted to ens

Theorem The number of partitions of r into parts 1 or 2 equals a Prove this theorem using generating functions b Prove this theorem again using Ferrers diagrams

FICO Score APR 30 Year Term 20 Year Term 15 Year Term 770 789 5 5 5 68 6 88 8 17 750 769 6 0 6 00 7 16 8 44 730 749 6 5 6 32 7 46 8 71 710 729 7 0 6 65 7 75 8 99 690 709 7 5 6 99 8 06 9 27 Calculate the monthly payment for a 20 year term mortgage after a 20 down payment on a 281 700 00 purchas for a household with a 731 credit score Show your work 10 points

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A manufacturer produces two mo hours of painting time and Mode maximum total weekly hours ava hours and 108 hours respectively of each type should be produced bikes of Model A bikes of Model B What is the maximum profit Question Help Message instr

If your miles per gallon is 32 with your old factory tires What will your new MPG be with new tires The circumference of the old factory installed tires were 82 inches while your new tires are 102 inches around O 30 mpg O 35 mpg O 40 mpg O45 mpg

4 Points DETAILS amplitude Find the amplitude period and phase shift of the function y sin x 4x period Trigonometry Spring 20 X phase shift O webassign net web Student Assignment Responses last d Graph one complete period T 4 7 8 y 1 0 5 0 5 1 Assignment 4 Trig Fu X 8 614 X O 1 744 15 18 y 1 0 5 0 5

1 Calculate the mean and standard deviation of the following sets of numbers 2 points each a 1 7 8 9 11 13 15 16 22 b 4 5 6 6 6 7 7 8 c 1 1 1 1 0 8 0 5 0 2 0 1 0 2 0 5 0 5 2 Using the student s t distribution and assuming a 95 confidence interval what is the statistical uncertainty in the mean value calculated for set a 2 points 3 Using Gaussian statistics and assuming a 95 confidence interval what is the statistical uncertainty in the mean value calculated for set a 2 points 4 You need to measure power across a resistor and have chosen to calculate the power using the measured resistance of your resistor and the measured voltage across said resistor If you measure the voltage as 5 3 V 0 15 V and the resistance of the resistor is measured with a Wheatstone bridge as 1 4 km2 0 3 k2 what is the resulting uncertainty in power Could you decrease your uncertainty if you instead measured the current through the resistor with an uncertainty of 25 A Justify your answers 8 points

The image below shows a letterboxed image with an aspect ratio of 16 9 displayed on a screen with an aspect ratio of 4 3 It is a 60 inch screen Answer the following questions Width of TV Height of TV Height of image d Percent of the screen s area occupied by the image a b PGP C

A cylinder is placed within a cube The diameter of the cylinder is equal to the length of each side of the cube What is the volume of the space outside the cylinder and inside the cube if the side of the cube measures 10 inches 10 10 10 607 cubic inches 200 cubic inches O 215 cubic inches

6 Suppose you have a clothes dryer that uses 4000 watts of power and you run it for an average of 1 hour each day If you pay the utility company 14c per kilowatt hour of electricity what is the average daily cost to run your dryer How much would you save in a year if you replaced it with a more efficient model that uses only 2000 watts I watt 1 joule sec 1 kilowatt hour 3 6 x 10 joules

After retirement you want to live on a retirement account which earns 5 9 annual interest compounded monthly from which you can make monthly withdrawals of 5000 Which finance formula would you use to determine how much money needs to be in your retirement account upon retirement Annuity with Payments In Compound Interest Annuity with Payments out Continuous Compound Interest Simple Interest

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5 Find the Taylor series expansion for f x 216 15 2 about 2 1 up to and including the 2 term f x BA

Please verify 40d using a conversion of 2 s and decimal numbers

4 Perform the following conversions a 42 2 in cm b c d e f 0 64 min 2 2 2 00 in cm 42 8 kg lb 3 5 qt mL 20 0 L gal

Exercise 3 6 1 In this exercise you will explore the ideas of orthogonal vectors orthogonal matrices and why these ideas are useful a Plot the vectors v 2 1 b Compute v v and 22 The fact that you get an answer of 1 for both is due to the length of the vectors being equal to 1 Now compute v v2 and v2 v1 The fact that you get an answer of 0 for both of these answers is due to the fact that these two vectors are perpendicular or orthogonal to one another c Now consider the matrix A v v2 2 11 whose columns are v and v respectively and the matrix AT V A AT and AT A What does this tell you in terms of inverse matrices V 2 1 in the zy plane 1 2 11 whose rows are v and v2 transposed i e turned sideways respectively Compute d What do you think is the general fact one can say about how to construct these nice orthogonal matrices like A in general How would you go about it in words don t actually come up with an example for a 3 x 3 matrix

3 6 6 Read section 3 4 and then try the following a Find the matrix E which swaps the first and second rows of a 4 x 7 matrix Then show this matrix is invertible by multiplying it by itself Why does this make sense b Find the matrix E which scaled the fourth row of a 4 x 7 matrix by a 10 What about by a factor of a 10 Then show these matrices are invertible by multiplying them c Find the matrix E which performs row2 row2 7row What new row operation undoes this operation What is the corresponding matrix Show me that these two matrices are inverse to one another d Show me the two ways that you can perform the three elementary row operations I asked you you to consider in each part above swap first and second scale the fourth row by a factor and then the first combination both by actually performing the operations by hand and then by multiplying the corresponding matrices E E E A e Now since E E E A is the resulting matrix from the reduction algorithm it is some upper triangular matrix U so we have A E E E A U Find the inverse for E and multiple both sides on the left order matters to obtain E E E E A E E A E U Now repeat the same for E and E and finally multiply these inverse matrices together to find L such that A LU Congratulations you have worked out how row reduction is also a matrix factoring algorith

Write the augmented matrix as a system 4 3001 350 250 0 7 0 3 I Z Y 2 Semen Question Help Video Message ins

9 Using a table of signs determine in which intervals the function f x x 1 5 x is positive or negative

etermine the horsepower developed by a passenger car traveling at a speed of 70 mi h on an upgrade of 9 percent with a mooth pavement The weight of the car is 4 500 lb and the cross sectional area of the car is 35 ft Assume the density of air is 0766 lb ft and the aerodynamic drag coefficient is 0 4 Use the following equation for the rolling resistance R in lb R Crs 2 15C W or which C 0 012 C 0 650 x 10 6 sec ft2 u is the vehicle speed in mi h and W is the weight of the vehicle in lb

e Baker makes floral arrangements She has 17 nt cut flowers and plans to use 5 of them How different selections of the 5 flowers are possible How

Each successive figure below is made of small triangles like the first one in the sequence Conjecture the numbe small triangles needed to make a the 100th figure b the nth figure A A www a How many small triangles are needed to make the 100th figure It would require small triangles

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1 2 3 What differentiates an argument from an opinion Are arguments always biased How could a writer craft an unbiased argument Thinking ahead How do you think the audience context and purpose can affect the parts of an argume

For this picnic you need to feed at least 300 people If you want to feed everyone but still have equal numbers of buns and hot dogs what is the minimum number of packages of buns and hot dogs you need respectively Express your answer as two integers separated by a comma

The gap between two consecutive automobiles distance between the back of a vehicle and the front of the following vehicle is 95 ft At a certain time the front vehicle is traveling at 50 mi h and the following vehicle at 45 mi h If both vehicles start accelerating at the same time determine the gap in ft between the two vehicles after 11 sec if the acceleration of the vehicles can be assumed to take the following forms 3 6 3 6 du 3 4 0 07u leading vehicle 3 3 0 065u following vehicle where u is the vehicle speed in ft sec ft dt du dt

Figure is not drawn to scale 6 m 11 m 3 m What is the surface area of the aquarium Note TH top of the aquarium is open m

The length of a rectangular garden is 3 feet longer than its width If the garden s perimeter is 182 feet what are the dimensions of the garden The width of the garden is The length of the garden is feet feet

2 A record club has found that the marginal profit P x in cents is given by P x 0 0007x 0 31x 50 7x for x 400 where x is the number of members currently enrolled in the club Approximate the total profit when 240 6 members are enrolled by computing the sum P x Ax with Ax 40 i 1 The total profit when 240 members are enrolled is approximately Round to the nearest cent as needed CON 3 Marginal profit in cents 26 000 20 800 15 600 AP x 0 0007x 0 31x 50 7x 10 400 5 200 XIUM IV V VI 100 3 104 0 200 Number of members 300 A

10 Write the following numbers in the correct scientific notations use correct sig figs 3 points a 0 0000111345 b 14584 c 678

How old is the oldest oceanic crust How do we know this Explai where you would find the youngest sea floor crust and why

KABMQ34 Select all items equivalent to 24 2019 Illustrative Mathematics All Rights Reserved Select all that apply CA the area of a square with side length 24 units OB the side length of a square with area 24 square units Oc the positive number x where x x 24 OD the positive number y where y 24 24 DE the edge length of a cube with volume 24 cubic units OF the volume of a cube with edge length 24 units Submit Answer

Jose and Jorge sell mango and guavas at their fruit stand One day they ask if you can run the stand so they can visit their grandmother at the hospital You agree but when you arrive you realize that they never told you what the prices were and there is no sign The only thing you have is a list of orders and total cost to use to figure it out You see two orders that you can use to figure out the two unknown prices 1 mango and three guavas cost 12 and 2 mangos and 1 guava cost 5 That led to the following system x 3y 12 2x y 5 Where x represents the price of mangoes and y represents the price of guavas Solve this system of equations using each of the three methods Show your work Substitution Graphing 1 How much do the mangoes and guavas cost Elimination

The graph shows the height of a ball in relation to the number of seconds since the ball was thrown Which point represents the height of the ball at the time that it was thrown Click on the graph to plot a point Height of the Ball feet 0 Height of a Ball 1 2 3 Time Since the Ball Was Thrown seconds B Altintos

The right circular conical tank shown in the figure below loses water out of a circular hole of area A at its bottom dh 8 ft dt Aw h When water leaks through a hole friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA 2gh where c 0 c 1 is an em constant Determine a differential equation for the height of the water h at time t 0 The radius of the hole is 3 in g 32 ft s2 and the friction contraction factor is c 0 6 Assume t apex of the cone is of negligible height and volume 20 ft circular hole ft s

For high speed motion through the air such as the skydiver shown in the figure below falling before the parachute is opened air resistance is closer to a power of the instantaneous velocity v t kv2 dv dt mg Determine a differential equation for the velocity v t of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity Assume the downward direction is positive Use k 0 for the constant of proportionality g 0 for acceleration due to gravity and v for v t

1 Determine the empirical formula of a compound that contains 28 4 Copper and 71 6 Bromine feme 2 Determine the empirical formula of a compound that contains 528g of Tin and 3 37g of Fluorine xoom 26000 bro sporby to calon 00500 no 3 What is the empirical formula for a sample that is found to be 36 2 Aluminum and 63 8 Sulfur bransporby te pod nohto proprio bes prepelin 500g of Ru 4 Determine the empirical formula for a compound that contains 72 2 Magnesium and 27 8 Nitrogen

Suppose you invest 7 000 in a stock with beta of 0 5 and 3 000 in another stock with a beta of 1 4 What s the beta of the resulting portfolio Round to two decimal places

Use the compound interest formulas A P1 and A Pe to solve the problem given Round answers to the nearest cent Find the accumulated value of an investment of 25 000 for 7 years at an interest rate of 5 5 if the money is a compounded semiannually b compounded quarterly c compounded monthly d compounded continuously a What is the accumulated value if the money is compounded semiannually Round your answer to the nearest cent Do not include the symbol in your answer b What is the accumulated value if the money is compounded quarterly Round your answer to the nearest cent Do not include the symbol in your answer c What is the accumulated value if the money is compounded monthly Dune in the net ont in the in

of the annuity account necessary to fund the withdrawal given Assume end of period withdrwwals and compounding at the seme intervals as withdrawals Pound your answor to the newrest cent 5400 per month foe 10 years If the account earns inh per year and if there is to be 10 000 left in the aneuty at the end of the 10 years M V 5

onerges uniformly to 0 f D R If and only if lim n rightarrow infty sup lf x f x x in D 0

30 left in solution in solution duringon process is gebound where in is the P X 800 number of filtering steps Find the n 16 and n 5 whole number recrest amants left forr CRand to the 201 SA 800 B 26 C800 80072 200 purkculate maks during a Fittering by the equation O tering d 3200 01 201

From April 7 12 2020 the Pew Research Center surveyed Americans about the likelihood of coronavirus significantly disrupting their ability to vote in the November presidential election Of the 4 917 polled 3 294 answered Very Likely or Somewhat Likely Construct a 95 confidence interval for the population proportion of Americans who would answer this question with Very Likely or Somewhat Likely Lower bound 0 657 Upper bound 0 683 Lower bound 0 669 Upper bound 0 681 Lower bound 0 652 Upper bound 0 687 rhound 0 643 muer

efendants in federal criminal cases Of thes only 1879 went to trial and 320 resulted in acquittals Construct a 99 confidence interval for the true proportion of federal cases that go to trial that result in acquittals Lower bound 0 148 Upper bound 0 193 Lower bound 0 153 Upper bound 0 187 Lower bound 0 159 Upper bound 0 181 Lower bound 0 156

Determine whether the given matrices are inverses of each other by computing their product 231 0 B A 5 2 1 1 2 2 3 Select the correct choice below and fill in the answer box to complete your choice Type an integer or simplified fraction for each matrix element O A The given matrices are inverses of each other because their product is the matrix B The given matrices are not inverses of each other because their product is the matrix

Solve the system of equations x y z 2 1 2x 4y 2z 8 2 x 8y 3z 60 3 Select the correct choice below and if necessary fill in the answer boxes to complete your choi O A There is one solution The solution set is Simplify your answer OB There are infinitely many solutions The solution set is z z is any real numbe Type expressions using z as the variable Simplify your answer OC The solution set is the empty set

Assume season ticket prices in the lower bowl for the Buffalo Bills will rise from 403 for a 10 game package to 569 Fans sitting in the best seats in the upper deck will pay an increase from 368 to 710 Don Manning plans to purchase two season tickets for either lower bowl or upper deck a How much more will two tickets cost for lower bowl