Math - Others Questions

5 Determine if S x 1 x2 is linearly independent or dependent

Problem 4 Two fire towers Gold Tower and Tower B are 70 miles apart with Tower B due east of Gold Tower A fire is spotted from the towers Gold Towe eports the fire at a bearing of N 70 E and Tower B reports the fire at a bearing of N 60 W How far is the fire from Gold Tower How far is the fire from Tower B

Determine if S 4t t 5 t3 5 3t 3t 2t3 is a basis for P3

Find the distance between u 1 2 5 and v VE 3 0 1

3 Determine if W the set of all odd functions is a subspace HERENTH

11 Find a basis for the subspace of R spanned by S 2 3 1 1 3 9 0 1 5

9 Find the dimension for M3 2

4 Determine if S 1 1 1 2 2 2 3 3 3 is linearly independent or dependent

2 10 Find the basis for the row space and the dimension for M 5 8 3 1 10 6 7 5

5 Determine if S 1 2 1 1 is a basis for R

14 Given u 0 1 1 2 and v 1 1 3 0 find u v

15 Find the vector with the given length v 3 and in the direction of u 0 2 1 1

Determine if W the set of all vectors in R whose components are integers is a subspace

Find the angle between u 2 3 1 and v 3 2 0

19 Determine if u 0 3 4 and v 1 8 6 are orthogonal parallel or neit

12 Find the Wronskian for x sinx cos x

18 Determine if u 4 3 and v are orthogonal parallel or neither

3 Find the Wronskian for x ex x ex

Determine if W the set of all vectors in R2 whose second component is the square of the first is a subspac

Devon invested 7500 in three different mutual funds A fund containing large cap stocks made a 7 5 return in 1 yr A real estate fund lost 10 4 in 1 yr a a bond fund made 3 5 in 1 yr The amount invested in the large cap stock fund was three times the amount invested in the real estate fund If Devon had a net return of 234 across all investments how much did he invest in each fund Devon invested S in the large cap fund in the real estate fund and S in the bond fund X

21 You check the patient s IV and find that there is 200 mL of fluid remaining in the bag If you are to hang a new bag by the time there are 50 ml remaining how soon should you return The drop factor is 15 and the drop rate is 25 gtt min

Consider a directed graph G with N nodes and M directed edges Each node has an associated integer weight Your task is to find the maximum weight of any simple cycle a cycle with no repeated nodes in the graph Design an algorithm to solve this problem efficiently

d 3 points What is the inverse of 19281207 in mod 19381 You may leave your final answer with an exponent

The propeller of a small plane at full speed rotates exactly 7500 revolutions per min Find the angular speed of the propeller in degrees per second

33 Which two instructional strategies can a teacher use to create a community of leamers that demonstrates respect for all students Choose 2 answers Work with students individually to address academic needs Provide cooperative learning activities that involve the entire class Incorporate a variety of text and print materials to facilitate individual learning activities Provide access to materials so that students have access to multiple perspectives on the content

Problem 1 A simply supported beam AB is loaded by a vertical force of 20kN as shown below Assume EI is constant SFD BMD conjugate beam A 5 0m 20 kN C 5 0m B 1 Draw SFD and BMD and sketch conjugate beam of the simply supported beam with the appropriate loadings of the conjugate beam in the space above 10

evenues osts Sales Cost of goods sold Gross profit Selling and administrative expenses Operating sticome boss Rhinebeck Company Product Line Income Statement For the Month Ended October 31 Mariable Hats 71 000 32 600 38 400 27 400 11 000 Variable cost of goods sold Gloves 105 700 42 300 63 400 42 800 20 600 Fix costsar 20s of the cost of goods sold and 30 of the selling and administrative expenses Rhinebeck that fixed coars would not be materially affected if the Gloves line were discontinued terential analysis deted October 11 to determine if Mutfers should be continued Altematree 2 It an amount is cers wnter 0 If required ua minus sign ta indicate a nud LA Differential Analysis Continue Alt 53 or Discontinus Alt 2 Mufflers Differential Analysis Continue Alt 1 or Discontinue Alt 2 Mufflers October 31 21 600 Mufflers 45 000 27 000 18 000 25 000 7 000 Continue Discontinue Differential Effects Mufflers Mufflers Alternative 1 Alternative 2 Alternative 2 45 000 0 45 000 0 21 600 Nem

Make or buy A company manufactures various sized plastic bottles for its medicinal product The manufacturing cost for small bottles is 55 per unit 100 bottles including fixed costs of 12 per unit A proposal is offered to purchase small bottles from an outside source for 36 per unit plus 3 per unit for freight a Prepare a differential analysis dated January 25 to determine whether the company should make Alternative 1 or buy Alternative 2 the bottles assuming fixed costs are unaffected by the decision If an amount is zero enter 0 Unit costs Differential Analysis Make Bottles Alt 1 or Buy Bottles Alt 2 January 25 Purchase price Freight Variable costs Fixed factory overhead Total unit costs Make Buy Differential Effects Bottles Bottles Alternative 1 Alternative 2 Alternative 2 X QOOQ

Product J19 is produced for 11 per gallon Product J19 can be sold without additional processing for 18 p gallon or processed further into Product R33 at an additional cost of 7 per gallon Product R33 can be sold 24 per gallon a Prepare a differential analysis dated April 30 on whether to sell Product J19 Alternative 1 or process further into Product R33 Alternative 2 If required use a minus sign to indicate a loss Differential Analysis Sell Product J19 Alt 1 or Process Further into Product R33 Alt 2 April 30 Revenues per unit Costs per unit Profit Closs ne Sell Product J19 Alternative 1 18 11 Process Further into Product R33 Alternative 2 24 18 Differential Effects Alternative 2 X X

At an international conference flags from 8 different countries will be displayed Of these flags 4 are from the continent of Africa and 4 flags are from the continent of Europe The flags will be displayed in a row alternating between continents A flag from Africa will be in the first position In how many ways can the flags be displayed 0 X

3 If mA 20 1 a 14 9 ft and b 29 8 ft there are two possible solutions to the triangle Find both solutions m B m C C m B in

Use the Valid Argument table below or a Truth Table to determine if the following symbolic form of an argument is valid or invalid p q and p therefore q Valid Arguments Direct Reasoning p q P 9 Invalid Arguments Fallacy of the Converse p q 9 Contrapositive Reasoning p q 9 P Fallacy of the Inverse p q P Disjunctive Reasoning pva pva Misuse of Disjunctive Reasoning pvq P Pv4 Transitive Reasoning p 9 P 4117 Misuse of Transitive Reasoning P 4 1 P 7111

Six people from different positions at a company were interviewed for a survey Their number of years at the company and annual salaries are as shown in the table below What is the MODE number of years at the company for these employees Look carefully at the values because they may not be the same as in the previous question Position Administrative Assistant Sales CEO Years at Company 6 7 8 Project Management 3 IT 7 Salary 29 000 38 600 140 000 53 500 77 400

3 6 9 2 5 B The price of a home is 290 000 The bank requires a 10 down payment at the time of closing The mortgage on the house is a 20 year fixed rate mortgage at 7 Use this information to find the amount of the monthly payment Round your answer to the nearest cent Use the formula below to solve the problem P Payment 1 2 248 2 2 124 3 2 012

an ace or a 6 Probability of Compound Events Mutually Exclusive P A or B P A P B Not Mutually Exclusive P A or B P A P B P A and B Independent Events P A and B P A x P B Dependent Events P A and B P A x P B P BIA 1 7 26 2 2 13 3 1 169 lity of selecti

6 9 12 5 a 6 or a red card Probability of Compound Events Mutually Exclusive P A or B P A P B Not Mutually Exclusive P A or B P A P B P A and B Independent Events P A and B P A x P B Dependent Events P A and B P A x P B P BIA 1 15 26 probability of select O2 18 26

The bar graph below represents various colors of cars sold Use the graph to answe the question Approximately how many more black cars than tan cars were sold Cars Sold in Thousands 882882 50 40 30 10 White Yellow Tan Red Black Silver 1 30 000 2 10 000

The table shows the results of a study done to determine whether or not a certain drug improves the symptoms for patients with a particular condition Based on this information what is the probability that a patient shows no improvement if the patient was given the drug Drug No Drug Total 1 0 338 2 0 675 3 0 442 Improvement 270 120 390 No Improvement 530 280 810 Total 800 400 1200

You want to have 200 000 in an account after 30 years for your retirement Your investment counselor suggests that you make regular quarterly deposits into an annuity that pays 5 interest compounded quarterly Find the amount that must be deposited quarterly rounded to the nearest cent P 1 418 64 2 155 16

A single six sided die is rolled twice The 36 equally likely outcomes are shown below Find the probability of getting two numbers whose sum is 4 Second Roll First Roll 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6

9 2 Two coins are flipped If H represents the coin landing on heads and T represents the coin landing on tails then the set of equally likely outcomes for the combinations are TT TH HT HH What is the probability of an outcome of exactly two tails 1 3 4 O2 1 4 03 1

6 9 12 15 18 Let p and q represent the following statements p He sets the alarm q He does not get up on time Write the following statement using symbols only If he sets the alarm then he will get up on time 1 p q 021 9 3 pa 4 p g

3 01 9 12 15 18 Make a scatter plot of the points in the table and then select the type of function from those below that would best represent the data X 0 2 7 10 11 13 15 y 6 2 1 238 2 3 8 1 The data is best represented by a quadratic function 2 The data is best represented by a linear function 3 The data is best represented by an exponential function

Listen A tree casts a shadow 8 feet long At the same time a person who is 5 feet tall casts a shadow that is 2 feet long How tall is the tree 1 20 feet 2 11 feet 3 17 feet 4 3 2 feet

A TI 84 calculator costs 110 18 Find the total cost of the calculator if sales tax is 8 Round to the nearest cent 1 118 99 2 117 71 3 100 27

Suppose 8500 is deposited into a savings account earning 5 interest compounded quarterly Find the balance in the account in 5 years rounded to the nearest cent Use one of the formulas below to solve the problem Future Value A P 1 1 Present Value P 1 10 897 32 2 9 044 70 3 13 845 60 A 1 5

Last year Andrew s salary went from 30 000 to 35 000 Calculate the percent increase and round to the nearest tenth 1 14 3 2 8 7 3 16 7 4 52

A couch sells for 810 Instead of paying the total amount at the time of purchase the same couch can be bought by paying 400 down and 55 per month for 12 months How much is saved by paying the total amount at the time of purchase 1 280 2 250 3 400 4 260

2 A family plan for a cell phone has a monthly base price of 99 plus 12 99 for each additional family member added beyond the primary account holder Write a linear function to model the monthly cost C x in dollars of a family plan for x additional family members added 01 C x 12 99x 99 2 C x 12 99x 99 3 C x 99x 12 99 C x 99x 12 99

The price of a cell phone dropped from 800 to 750 Calculate the percent decrease and round to the nearest tenth 1 6 3 2 63 3 67