Mathematical Induction Questions and Answers

2 1 5 8 1 3 1 1 61 9 11 12 Question 1 8 34 points Basic Trigonometry Which expression represent tan for the triangle shown 19 0 g C OF 1 4 OF YIN bo

Two planes are circling an airport awaiting their landing clearance If the following measures in the diagram below are correct how far are the two planes away from each other Find the distance from point D to point C C 1800ft B 2800 feet 4557 feet 5796 feet 7200ft

Amy scheduled herself from 8 00 AM 1 00 PM Sunday through Wednesday On Wednesday she needed to release her intervals from 11 00 AM 1 00 PM at the last minute She serviced all of the other time for which she posted What was her overall Commitment Adherence percentage Enter whole numbers no decimals only 20 11

The Richter scale measures the intensity or magnitude of an earthquake The formula for the magnitude R of an earthquake is R log B where a is the amplitude in micrometers of the vertical motion of the ground at the recording station T is the number of seconds between successive seismic waves and B is an adjustment factor that takes into account the weakening of the seismic wave as the distance increases from the epicenter of the earthquake Use the Richter scale formula to find the magnitude R of the earthquake given that the amplitude is 220 micrometers the time between waves is 1 2 seconds and B is 2 1

What fundamental assumption underlies the concept of an ocean commons

ite the given numeral as numerals in the Hindu Arabic Roman traditional Chinese and Greek systems of numeration 99111 moose the correct equivalent Greek numeral below A Spf B Spe DC fwe D L 1 aay 1111 11

y y 931 1534 2330 3648 5541 8852 Use linear regression to find the equation for the linear function that best fits this data Round parameters to two decimal places

Find tan 8 where is the angle shown Give an exact value not a decimal approximation 0 5 4 tan 0

At the end of each month Bryan deposits 200 into an account that pays 4 per year compounded monthly How much will the annuity be worth at the end of 5 years OA 1083 26 B 2189 94 OC 26 519 60 D 12 750 80

16 Which of the following sentences shows correct subject verb agreement OA Either John or Sue are traveling to the show OB Either John or Sue are travelled to the show OC Either John or Sue is traveling to the show OD Either John or Sue is travelled to the show 17 Which of the following is the best way to find credible resources OA Search for publications that are at least 15 years old OB Use a database of peer reviewed articles OC Check your local library OD Use an Internet search engine

Evaluate using exponent laws show all work leave answers in fraction form if necessary 29 b 5 16 81 d 2 4

The table shows the number of video games sold worldwide for the five highest selling video games in 2010 Assuming this trend continues and that the total sales of all other video games is negligible if a person chooses to purchase one of these video games determine the empirical probability that the person will purchase a Game 2 b Game 5 c Game 1 a P Game 2 b P Game 5 c P Game 1 Type an integer or a simplified fraction Type an integer or a simplified fraction Type an integer or a simplified fraction Game Game 1 Game 2 Game 3 Game 4 Game 5 Total Games Sold 18 170 000 17 390 000 11 810 00 11 000 0 8 990 0 67 360

Laura and Martin obtain a 30 year 150 000 conventional mortgage at 9 0 on a house selling for 180 000 Their monthly mortgage payment including principal and interest is 1207 50 a Determine the total amount they will pay for their house b How much of the cost will be interest c How much of the first payment on the mortgage is applied to the principal a The total amount that Laura and Martin will pay for their house is Round to the nearest dollar as needed b They will pay a total of Sin interest Round to the nearest dollar as needed c of the first mortgage payment is applied to the principal Round to the nearest cent as needed

Plot the points with polar coordinates 2 7 with es 2 34 and 5 75 6 SIN KIM 214 KE6 X using the pencil

Find a basis for the row space of A 1 1 36 0 1 2 3 1 1 Find a basis for the null space of A Verify that every vector in row A is orthogonal to every vector in

PAGE 13 OF 13 A APPLICANCE WARRANTY THE WARRANTY ON THE MOTOR OF A DISHWASHER IS 8 YEARS IF THE BREAKDOWN TIMES OF THIS MOTOR ARE NORMALLY DISTRIBUTED WITH A MEAN OF 10 2 YEARS AND A STANDARD DEVIAITON OF 1 8 YEARS FIND THE PERCENT OF MOTORS THAT CAN BE EXPECTED TO REQUIRE REPAIR OR REPLACEMENT UNDER WARRANTY 5 POINTS 29 B GRADING ON A NORMAL CURVE MR SANDERSON MARKS HIS CLASS ON A NORMAL CURVE THOSE WITH Z SCORES ABOVE 1 8 WILL RECEIVE AN A THOSE BETWEEN 1 8 AND 1 1 WILL RECEIVE A B THOSE BETWEEN 1 1 AND 1 2 WILL RECEIVE A C THOSE BETWEEN 1 2 AND 1 9 WILL RECEIVE A D AND THOSE UNDER 1 9 WILL RECEIVE AN F FIND THE PERCENT OF GRADES THAT WILL BE A B C D AND F C EXPECTED ATTENDANCE IF THE DAY IS SUNNY 1000 PEOPLE WILL ATTEND THE BASEBALL GAME IF THE DAY IS CLOUDY ONLY 500 PEOPLE WILL ATTEND IF IT RAINS ONLY 100 PEOPLE WILL ATTEND THE LOCAL METEOROLOGIST STATES THAT THE PROBABILITY OF A SUNNY DAY IS 0 4 OF A CLOUDY DAY IS 0 5 AND OF A RAINY DAY IS 0 1 FIND THE NUMBER OF PEOPLE THAT ARE EXPECTED TO ATTEND D CONSTRUCTING A TEST A TEACHER IS CONSTRUCTING A MATHEMATICS TEST CONSISTING OF 10 QUESTIONS SHE HAS A POOL OF 28 QUESTIONS WHICH ARE CLASSIFIED BY LEVEL OF DIFFICULTY AS FOLLOWS 6 DIFFICULT QUESTIONS 10 AVERAGE QUESTIONS AND 12 EASY QUESTIONS HOW MANY DIFFERENT 10 QUESTION TESTS CAN SHE CONSTRUCT FROM THE POOL OF 28 QUESTIONS IF HER TEST IS TO HAVE 3 DIFFICULT 4 AVERAGE AND 3 EASY QUESTIONS E HOW MANY DIFFERENT ARRANGEMENTS CAN BE MADE WITH THE NUMBERS 28535852

Show that is an eigenvalue of A and find one eigenvector v corresponding to this eigenvalue 5 1 1 1 3 42 A 1 4 2

7 A bookstore classifies its books by reader group type of book and cost What is the probability that a book selected at random is a child s book given that it costs 15 Child Adult Fiction Nonfiction Fiction Nonfiction 10 10 120 255 60 110 150 35 200 75

Tara is registering for a physics class The morning classes are 1st 2nd and 3rd periods and the afternoon classes are 4th 5th and 6th periods Below is a table of teachers and the periods they teach the math class If Tara requests an afternoon class what is the probability that she will be assigned Mrs David for 5th period 4th 6th Williams Brown Davis mu 1st X Y 2nd X X X 3rd X X X X X 5th X X X X X

You can choose whether you are provided the equation of a quadratic function in standard form factored form or vertex form If you needed to know the information listed which form would you choose and why a the vertex b c d e the y intercept the zeros the axis of symmetry the domain and range

5 Which model is best for making predictions about this data set 1 point Variable 1 Variable 5 49 11 12 8 75 6 25 4 25 3 17 1 57 9 58 11 72 10 99 8 41 2 34 6 09 7 62 3 21 20 01 23 85 22 32 17 23 5 51 12 42 15 48 Oy 2 0259x 0 167763 y 0 00319504x 1 98351x 0 273178 y 0 00329151x 0 0689209x 1 60841x 0 831659 Oy 474127 1 15404

Exercise 12 Find all solutions to the equation 2 tan 4nt 1 3 11 in radians Round your answers to the nearest hundredth Exercise 13 Solve the equation 4 sin x 2 3 6 for x if 0 x 2 Round your answer to the nearest hundredth

a Find the percentage of the are b Find the percentage of the 20 67 c Find the percentage of the 1 23

18 The growth model A 112 5e0 012t describes Mexico s population in millions t years after 2010 How long will it take Mexico to double its population Round your answer to the nearest whole number 424

a spreadsh to calculate the following function its derivative and its definite integral from x O to x 4 calculations x 3 1 2 f x Use dx 0 01 and display your results as three traces on a single graph Save your work in Microsoft Excel standard format xls xlsx and submit the file Be sure to submit the actual file and not just a link to the file somewhere in the cloud CO4 W14 4 W14 5

Find all zeros and periods of cosh z and sinh z Solution We have that cosh z cos iz thus the zeros of cosh z are at z in 2 imn m 0 11 12 and the periods of cosh z are 2 mi m 0 1 12 We have that sinh z i sin iz thus the zeros of sinh z are at z m 0 1 2 and the periods of cosh z are 27mi m 0 1 12 mai

4 The vertical position h in metres of a Ferris wheel is modeled using the function h t 6 sin t 5 7 where t is the time in seconds and h is the height in metres a Determine the period and amplitude of this function Explain the meaning of these quantities within the context of the question b Calculate the height at t 20 seconds c Determine the first time that the height is 11 m d When is the next time that this height is reached again

Find the measure in degrees of the central angle The area of a sector is 6x sq units The measure is Type an integer or a simplified fraction 6 Picture is not drawn to scale

Find the area of the sector shown in the figure 5x 8 Ly G The area is Simplify your answer Type an exact answer in terms of t Use integers or fractions for any numbers in the expressi

Use the following sample to estimate a population mean 16 8 19 8 18 5 14 1 35 1 3 3 29 6 35 1 2 9 9 15 4 16 30 4 30 6 2 12 3 4 3 13 7 20 9 29 9 41 3 23 9 13 2 30 1 4 3 16 9 32 4 23 9 29 8 19 3 26 6 16 7 23 5 22 2 14 4 20 4 19 10 4 22 6 14 7 11 7 Download CSV 19 4 36 9 21 2 24 1 19 12 5 22 1 36 2 3 16 Find the 98 confidence interval about the population mean Enter your answer as a tri linear inequality accurate to two decimal place

3 Show that y eat cos t is a solution of the differential equation y e at a cos t sin t Is this differential equation pure time autonomous or nonautonomous

If I toss a fair coin seven times and the ou on the next toss is a 0 5 b less than 0 5

Chapter Homework t K The Berkner Company is prepa Click the icon to view the Requirement Prepare a cash payments bud

A student has a current grade of 75 percent in a class The first test was worth 20 percent and the second test is worth 25 percent The student got 61 percent on the first test What grade does the student need on the second test in order to get a passing TEST average

entrance exam company determined that a score of 20 on the mathematics portion of the exam suggests that a student is ready for college level mathematics To achieve this goal the company recommends that students take a care curriculum of math courses in high school Suppose a random sample of 200 students who completed this care set of courses results in a mean math score of 20 4 on the college entrance exam with a standard deviation of 3 8 Do these results suggest that students who complete the core curriculum are ready for college level mathematics That is are they scoring above 20 on the mathematics portion of the exam Complete parts a through c below b verty that the requirements to penorm me test using me osmounon are satsmed uneck all mat apply A The sample data come from a population that is approximately normal B The students test scores were independent of one another C The students were randomly sampled D The sample size is larger than 30 E Aboxplot of the sample data shows no outliers OF None of the requirements are satisfied

Assume A is a 3 x 3 matrix and A 2 0 L 2 Then an eigenvalue for A is 0 6

Excerpt by Shane Burcaw My little brother leans over the bed and slides his arms under my knees and behind my shoulders lifting and carrying me to my wheelchair He sits me down gingerly almost getting me in the perfect position a nearly impossible task He unplugs my phone from the charger and sets it on my lap walks to the kitchen to pour a cup of coffee which he leaves on the edge of the dining room table for me then comes back into my room I m going back to bed Are you good he asks I thank him and drive to the dining room to find the coffee that will inject me with the energy to make it through the day My laptop is sitting next to the cup of steaming coffee more like coffee flavored milk Andrew made it very sweet Part of Dad s morning routine after getting me up at 6 a m for a shower and putting me back in bed afterward is to open my laptop on the edge of the table so I have something to do when Andrew goes back to sleep I can t physically type on a keyboard or lift the cup of coffee to my lips but like all daily tasks I ve found ways to improvise I have an app for my iPhone that transforms it into a wireless mouse pad and keyboard I love you Apple Sticking out of my coffee is a super long bendy straw that I ordered off the Internet It is long enough so that the straw reaches my mouth when the coffee is sitting on the table Little adaptations like these are what allow me to thrive 25 What is the main idea of the excerpt Shane needs his brother to get out of bed 8 Shane depends on his family for all daily tasks Shane has learned to improvise in spite of his disability Shane has used technology to cope with his challenges 26 Which word best describes Shane in the excerpt A Resilient B Helpless Optimistic

by Eric Sheninger This morning I read a great article on PBS Media Shift by Audrey Watters entitled Why Schools Should Stop Banning Cell Phones and Use Them For Learning Up until this past year the rule of thumb was that students could bring their phones to my school but they could not be on seen or heard This rule applied throughout the school day on or at any school sponsored functions and was strictly enforced I cannot begin to explain all of the battles with students and parents that my administrative team and I had to deal with because of the established policy Fortunately for me I have already begun to work with my staff and students to transform the teaching and learning culture at New Milford HS as it pertains to cell phones as mobile learning devices As a principal it took me a while to accept the fact that these small but powerful computing devices could play an important role in the classroom This shift in mindset can be directly attributed to what I have learned from innovative educators in the social media spaces that I now delve into on a routine basis The knowledge that I have acquired from my Personal Learning Network PLN provided me with the ideas and strategies to utilize student cell phones as mobile learning devices 17 Which sentence best expresses the controlling idea of the article Up until this past year the rule of thumb was that students could bring their phones to my school but they could not be on seen or heard BI cannot begin to explain all of the battles with students and parents that my administrative team and I had to deal with because of the established policy As a principal it took me a while to accept the fact that these small but powerful computing devices could play an important role in the classroom This shift in mindset can be directly attributed to what I have learned from innovative educators in the social media spaces that I now delve into on a routine basis 18 What kind of argument is the author making A Logical

The null and alternative hypotheses are given Determine whether the hypothesis test is left tailed right tailed or two tailed What parameter is being tested Ho H P 0 1 p 0 1 What type of test is being conducted in this problem Right tailed test Left tailed test Two tailed test What parameter is being tested Population proportion Population standard deviation Population mean CHCECIE

Consider the following A 1 0 0 1 1 0 0 3 0014 0 0 1 1 a Compute the characteristic polynomial of A det A 2

Consider the following A 1 1 0 0 4 1 0 05 a Compute the characteristic polynomial of A det A 1 23 2 112 20

Prove 7 6n 1 is divisible by 36 for every n E N

2 Prove 1 2 3 n n n 1 2n 1 for all natural numbers n N 3 Prove 7 6n 1 is divisible by 36 for every n N

e M R For questions 11 15 the child frombirth to age tv two year old children an

MATH 1530 Chapter 8 Practice Worksheet 3

For questions 16 20 an employment information service time workers over the age of 25 and without high school random sampleof 10 full time workers without high scho test the claim that the mean salary is 24 600 22 954 23 438 19 212 21 456 24 655 25 493 16 List the null and alternative hypotheses Label the cla 17 State the level of significance

Use a graph of the function f x x 6x 15x 20 to estimate the local extrema of the function Use these to determine the intervals on which the function is increasing and decreasing 40 20 1 A 20 40 60 80 local maximum co local minimum 4 An online service can give you a more accurate answer Give the coordinates x y of the 6 7 8 Use interval notation to answer these The function is increasing on The function is decreasing on

The quadratic function g x if represented by the table below g x 8 X 1 0 1 2 3 5 4 5 8 What is the distance between the maximum y value of g x and f x x 6x 9

Let Q x be the statement x 1 2x If the domain consists of all integers what are these truth values Enter T for the truth and F for the false a Q 0 b Q 1 c 3XQ x d vxQ x e 3x Q x f vx Q x

A census of labor force in a large metropolitan area found that the t people to commute to work has a mean of 20 5 minutes and a stan 15 4 minutes What is the probability that a random sample of 40 p mean commute time that is greater than 25 minutes OP Z 20 5 25 z Pz P 2 O 25 20 5 15 4 39 20 5 25 15 4 40 25 20 5