Math - Others Questions

Solve a Consumers or Producers Surplus Problem The supplier of a popular board game called Who Dunnit has a price supply equation given by p S x 20 2 6x dollars which gives the price per game when z games are supplied If market equilibrium is reached when 22 games are sold at a price of 77 2 eac find the producers surplus The surplus is Your answer must begin with

The flight of a cannonball toward a hill is described by the parabola y 2 0 12x 0 002x where x is time in terms of seconds and y is the distance in terms of miles The hill slopes upward along a path given by y 0 15x Where on the hill does the cannonball land

Use the change of base formula to compute log 5 Round your answer to the nearest thousandth

Use the properties of logarithms to evaluate each of the following expressions a log 48 2log 4 b 7 Ine Ine

Determine whether or not the sentence is a statement You will find the store at the first set of lights Is the given sentence a statement O No because it could be labeled as true or false O No because it is a command It cannot be determined with further information OYes because it could be labeled as true or false

5 Use Divergence Theorem to compute the net outward flux for F x y z where S is the cylinder x y z x y 4 0 z 8 10 points

The plane s elevation relative to the ground in meters as a function of time in seconds is graphed Elevation meters 8 000 7 000 6 000 5 000 4 000 3 000 2 000 1 000 400 800 1 200 1 600 Time seconds How long did it take the plane to land seconds

5 Use Stokes Theorem to evaluate F dr where F y xz y and C is the ellipse x x 10 1 in the plane z 1 8 points

3 Use Green s Theorem to evaluate the line integral of F x y 4x y on C the boundary of x y 0 y sinx 0 x oriented counterclockwise 8 points

Solve the following second order determinant 4 6 3 17 A 50 B 50 C 86 D 86 Jy

Evaluate the surface integral f S xyz ds where S is the part of the plane z 6 y that lies in the cylinder x y 4 8 points

Solve the following determinant 20 110 U 70 80 A 9300 B 8800 9700 8500 2

2 For what values of a b and c is F ax2 by2 cxy conservative 8 points

We can lease a computer for 1 000 per month or we can purchase one for 15 000 The purchased computer will also cost 40 per month for a maintenance cost At an interest rate of 5 per month how many months would I need the computer for for the purchased system to break ev Note you will need to use a 1 2 tabulated table to solve Between 14 and 15 months Between 15 16 months O Between 16 17 months More then 18 months

Yellow Pages Directory company must decide whether to compose their own ads or pay an outside firm to do them They can buy them outside for 21 00 per ad If they choose to do them insidethey will have to do the following two things 1 Buy computer hardware for 12 000 This Quipment will last 3 years and have a salvage value of 2 000 2 Hire an employee at an annual cost of 45 000 per year In addition to the two new fixed costs there will also be a 4 00 per ad variable cost if they choose to prepare their own ads At 10 interest rate how many ads do they need do annually to break even they decide to prepare the ads themselvces O 1 895 ads per year O2 895 ads per year

1 Given the graph of f x complete the following table by indicating whether each value is zero positive or negative Point A B C LL F f x f x f x y f x VA E B

1 Given the following consolidation test results a Plot the e log o curve b Using Casagrande s method determine the preconsolidation pressure c Calculate the compression index Cc from the lab e log o curve e 1 21 1 195 1 15 1 06 0 98 0 925 Pressure o kN m 25 50 100 200 400 500 NOTE Show all the calculation steps

21 29 Is job satisfaction going down In the last 10 years several authors have stated that people are miserable in their jobs and have become increasingly unhappy over time Job satisfaction scores from participants in the General Social Survey GSS in 1975 and 2006 were studied Higher scores indicate greater satisfaction with 2 5 being a neutral score Here are summaries of scores for 1975 and 2006 16 Sample Size 1165 2177 Year 1975 2006 Mean 3 37 3 32 Standard Deviation 0 81 0 80 a Is there a significant decrease in mean scores from 1975 2006 What do these data show about job satisfaction in 1975 compared to 2006 b The paper from which the data came includes several years from 1972 2006 1975 was the year with the highest mean score What if any effect does this information have on your assessment of

A4 A 44 24 45 29 27 f t 34 of of fo 34 34 EN 2 32 3 44 4 30 of of 44 15 4 44 54 44 a The card drawn is a 2 55 of 4 4 54 d The card drawn a diamond 54 e The card drawn is not a club 54 A card is drawn randomly from a standard 52 card deck Find the probabilities of the given events f The card drawn is a 2 or 5 69 c The card drawn is not a face card b The card drawn is a face card Jack Queen or King 60 69 g The card drawn is between and including 2 through 5

People walking into a soccer match were asked if they had eaten at a Chipotle in the past month The number of people who responded yes was 276 and no was 103 Find the probability that if a person is chosen at random they have eaten at Chipotle in the past month Round your answer to one decimal place

A scientist conducts an experiment with mice Mice entered a room and had to choose between going through a red door and going through a blue door 7 of the mice went through the red door and 6 went through the blue door A mouse enters the room What is the probability that it goes through the red door Write your answer as a percent rounded to two decimal places You need not enter the symbol prob

A fair die is rolled once Find the probabilities of the given events Leave your answer as a fraction in the simplest form a The number rolled is a 3 b The number rolled is odd c The number rolled is at least 3

A bag of Skittles has 8 red 5 orange 4 yellow and 3 green Skittles What is the probability of randomly picking each of the following Write your answer as a fraction in the simplest form If the answer is 0 or 1 you must enter 0 or 1 a An orange Skittle b A purple Skittle c An orange or yellow Skittle

16 58 If the block at C is moving downward at 4 ft s determine the angular velocity of bar AB at the instant shown AR 2 ft B 3 ft 30 Prob 16 58 vc 4 ft s

16 1 The angular velocity of the disk is defined by w 5r 2 rad s where is in seconds Determine the magnitudes of the velocity and acceleration of point A on the disk when t 0 5 s 0 8 m Prob 16 1

B 2 5 in Prob 16 5 16 6 A wheel has an initial clockwise angular velocity of 10 rad s and a constant angular acceleration of 3 rad s Determine the number of revolutions it must undergo to acquire a clockwise angular velocity of 15 rad s What time is required 16

16 20 The operation of reverse for a three speed utomotive transmission is illustrated schematically in the gure If the crank shaft G is turning with an angular speed f 60 rad s determine the angular speed of the drive shaft H Each of the gears rotates about a fixed axis Note that gears A nd B C and D E and F are in mesh The radii of each of hese gears are reported in the figure TA 90 mm Trc 30 mm TD 50 mm TE 70 mm TF 60 mm Prob 16 20 B G 60 rad s G 16

16 65 The pinion gear rolls on the gear racks If B is moving to the right at 8 ft s and C is moving to the left at 4 ft s determine the angular velocity of the pinion gear and the velocity of its center A www 4 ww Lanfing B A Probs 16 64 65 0 3 ft

7 1 Given that u 7 2 Calculate i u Ans i 3 3 a Given that C ii 2u iii 4u 3v 3 9 3 c Given that AB iii J and BA Find CB b Express in column notation the unit vectors parallel to BA and CE in a above BC and determine the components of AD Comment on the position of points A and D

Name Date Period Westover is hosting a fund raising carnival You are going to make a themed game with prizes to raise money Follow the steps below and let s design our game THEME AND GAME 10 Points We are going to have a theme for our game You can use whatever you want The prizes will be based on this theme You can use the same theme from past projects if you want The theme for our game is What kind of game do you want to do The only requirement is that you need a repeatable trial that only has two possible outcomes success or failure This can be anything for example hit or miss guess right or wrong knock down all the bottles or don t etc It also needs to be repeatable 10 times like shooting 10 shots guessing 10 times or knocking down the bottles 10 times Really any game can be thought of as success or failure so be creative Write what kind of game you want to do below don t worry about the details right now for example shooting a basketball 10 times or guessing something 10 times or knocking down all the pins targets 10 times You can use games from the fair as an example if you want For our game we will PRIZES 10 Points Now we need some prizes for people to win We need to know how much our prizes are worth as well For our game we will use the following prize structure O successes no prize 1 2 or 3 successes pencil with fancy eraser fitting our theme 4 5 6 or 7 successes small prize fitting our theme 8 or 9 successes large prize fitting our theme 10 successes mega prize fitting our theme The prizes for our game will be General Prize Pencil with Fancy Eraser Small Prize Specific Theme Prize made up How Much It Is Worth made up

1 State the transformations and then graph the function a y 3x 12 b y 2 x 3 4 8 8 6 6 A 4 4 2 2 18 16 14 12 10 8 6 4 2 ON 199 6 8 10 12 14 16 18 18 16 14 2 12 10 8 6 4 2 0 2 4 6 8 10 12 24 11 14 16 2 2 4

Find the inverse of each matrix if it exists 6 3 5 7 3 32 2 G 34 6 3 8 Use a matrix equation to solve each system of equations 9 2x y 9 x y 3 10 4x 2y 22 6x 9y 3 2 1 2 0 K 3 L 21 0 4 01 1 11 12 MONEY Kevin had 29 quarters and dimes The total value of all the coins was 4 70 How many quarters and dimes did Kevin have Problem Solving xhium instilleos termine whether each pair of matrices are inverses of each other 14 M 11 2x y 4 3x y 1 16 R boss 1 3 N 11 0 2 4 5 0 Extra P s 4 2 2 S 4 2

xi yi 1 14 2 4 3 2 Find the natural cubic spline to interpolate the three points given Do it by your hand

4 3 2 3 st q The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 1 12 10 9 7 6 2 6 7 J

This survey records how many times a group of people visited a supermarket in January 22 23 20 1 19 19 16 23 12 9 18 14 22 6 15 12 7 11 3 4 15 9 16 15 Score 1 5 6 10 11 15 16 20 21 25 How many people were surveyed altogether How many people visited fewer than 6 times How many people visited more than 10 times Click the tally column to tally off the data and complete the frequency table You can click the numbers above as you tally them to cross them off Tally Frequency 000 1 1 1

The envelopes of letters received by an office one morning were measured The widths in centimetres were as follows 23 8 15 3 20 5 15 4 19 2 20 0 24 7 12 8 9 7 18 9 24 4 13 1 15 9 12 2 20 6 6 9 20 0 11 3 10 0 16 1 Width 5 w 10 10 w 15 15 w 20 20 w 25 Click the tally column to tally off the data and complete the frequency table You can click the numbers above as you tally them to cross them off How many envelopes were measured altogether How many envelopes measured less than 20 cm How many envelopes measured 20 cm or more Tally Frequency 000 1 1 2

62 GRIDDABLE A family of 9 people is planning a trip to the movies The table shows different ticket prices at two nearby theaters Theater Central Cinemas Midway Theater Prices of Movie Tickets Adult Child 10 50 12 00 8 00 7 50 Senior 9 00 7 50 If they see a movie at Central Cinemas the total cost of their tickets will be 84 00 If they go to Midway Theater they will spend 85 50 How m many family members need an adult ticket or lo TEKS A2 3 B MP AZ A21 C

Residential staircases are usually built with a slope of 70 If the vertical distance between the first floor and the second floor is 10 feet how much horizontal space does the staircase require

A woman with her employer s matching program contributes 300 at the end of each month to her retirement account which earns 7 interest compounded monthly When she retires after 4 years she plans to make monthly withdrawals for 26 years If her account earns 5 interest compounded monthly then when she retires what is her maximum possible monthly withdrawal without running out of money The maximum possible monthly withdrawal is approximately Simplify your answer Round to the nearest cent as needed

Use the amortization table to determine how much of the 2nd payment is interest Click the icon to view the amortization table The interest amount of the 2nd payment is Type an integer or a decimal

A new employee charged 8040 on his credit card to relocate for his first job After noticing that the interest rate for his balance was 27 compounded monthly he stopped charging on that account He wishes to pay off his balance in 3 years using automatic payments sent at the end of each month a What monthly payment must he make to pay off the account at the end of 3 years b How much total interest will he have paid a What monthly payment must he make to pay off the account at the end of 3 years S Round to the nearest cent as needed b How much total interest will he have paid S Round to the nearest cent as needed

Dex plans to create a rectangular raised garden bed Soil costs 5 per cubic foot and the 2 by 12 wood boards to create the walls of the bed costs on average 2 30 per linear foot If Dex has a 100 budget to create and fill the garden bed what is the largest bed that Dex can create

Which value would you have to eliminate if it appeared as a possible solution to the equation below 17 2 11 I 16 14 014 011 10 10

Find the unknown lengths for the similar triangles below 3f 19 in 3 ft 4 2 ft ft If needed round to 2 decimal place ft If needed round to 2 decimal place Question Help Video Message instructor D Post to forum

Solve 4 c 4 CI 4 c 2 1 Enter your answer s as a reduced fraction separated by commas

Suppose you work in a call center You call people up and offer to sell them an upgrade to their 13 mobile phone plan You have a success rate of 15 or 0 15 or That means that you sell 100 the product to 15 of the people you call Use the binomial distribution spreadsheet or do calculations by hand if you d rather to answer the following questions Question 1 Find the probability that no sales are made after you make 10 calls 2 Find the probability that you make 3 or more sales after you make 20 calls 3 Suppose your manager wants you to average 5 sales per day What is the minimum number of calls that you should make to ensure that you meet that goal 4 How many calls should you plan to make each day if you want to have a 95 chance of making at least Type answers below T

There is about 50 x 109 of gold atoms in one drop of a sea water How many grams of gold can be obtained from 1 tonne of sea water if we know that the mass of 1 drop is 33 mg 4 9x10 g

Find the equation C 4 3 and of the hine which passes through Line 1 2x 5 Parallel to

During an experiment the following times in seconds were recorded Find the mean 6 8 5 9 6 5 3 7 5 9 6 The mean is Round to one decimal place as needed TEE

Find the mean height of the six tallest buildings If necessary round results to one decimal place Building Building 1 Building 2 Building 3 Building 4 Height ft 1483 1483 1450 1381 Building Height ft 1283 1260 1250 1227 Building 5 Building 6 Building 7 Building 8 The mean is ft Round to one decimal place as needed