Basic Math Questions and Answers

all in the blank with an appropriate word phrase or symbol compound statement that is always false is known as a compound statement that is always false is known as a

ect the correct choice that completes the sentence compound statement that is always true is known as

Hints for the problems Problem 1 26 The reaction at A has two components A and Ay You will use the two components to calculate the reaction at C When using Sum of moments about one the load force is divided into two components The Distance is also divided into two components The reaction at C has two components Cx and Cy Find both of them through equilibrium equations and Free Body Diagram FBD When calculating the average shearing stress and bearing stress the resultant Problem 1 29 Remember Normal Stress Axial Stress is perpendicular to the surface and Shear stress is parallel to the surface P will be divided into two components What is the surface area A 2 2 force C should be used C C C

How many distinguishable permutations are there for the letters in the word TENNESSEE

POSSIBLE POINTS 1 In the original plan for area codes in 1945 the first digit could be any number from 2 to 9 the second digit was either 0 or 1 and the third digit could be any number except 0 With this plan how many area codes were possible O 180 O 1000 144 O 729

POSSIBLE POINTS 1 9 To win a certain state lottery you must correctly choose 6 numbers out of a possible 59 numbers The order which the selections are made does not matter How many different selections are possible

POSSIBLE POINTS 1 9 A club with ten members is to choose three officers president vice president and treasurer If each office is to be held by one person and no one can hold more than office in how many ways can those offices be filled

POSSIBLE POINTS 1 9 You are taking a multiple choice test that has 5 questions Each question has 3 answer choices with one correct answer per question If you select one of these three answers for each question and leave nothing blank in how many ways can you answer the test O 120 O 6 125 243

PO In a race in which 7 cars are entered and there are no ties in how many ways can the first four finishers come in

The number 863 068 is between what two numbers in the tens Enter the smaller number in the first box and the larger number in the second Smaller Number in the tens

The number 1 026 045 600 is between what two numbers in the billions Enter the smaller number in the first box and the larger number in the second I Smaller Number in the billions Larger Number in the billions

20 This graph shows the population P in millions of a small country where t is the number of years since 2000 Researchers are using this data to predict future populations 10 45 30 100 15 55 Calculate the average rate of change from t 10 to t 15 Include units in your final answer

The graph shown represents which of the following polar equations Ba 2 OA r 3 3sing OB r 4 2sing 1 2 3 4 5 6 7

On the table rest 8 dominoes as shown below A Suppose you were to line them up in a single row so that any two sides touching had matching numbers Draw a graph that would represent the dominoes B What kind of path is appropriate for this situation Explain your response C What would the sum of the two end numbers be

For each of the following draw the graph on a separate sheet of paper then answer the questions ABCDE A 011007 B 0010 0001 000 00100 C D E 0 Is it connected Yes is it complete No 2 ABCDE A00100 B 00011 608 C D 10000 01001 1010 0 Is it connected Yes Is it complete No 3 A B C D E ABCDE 1 1 17 101 11 1 Is it connected Yes Is it complete Yes 11 01

Miguel a scheduler at Mangel Wurzel Transport gets a call from a regular customer needing to move 42 6 m of rock and soil which Miguel knows from previous experience has an average density of 250 kg m Miguel has available a dump truck with a capacity of 11 m and a maximum safe load of 5600 kg Calculate the number of trips the dump truck will have to make to haul the customer s load away

14 Prime factorization 16 Convert decimal to 20 30 40 83 17 0 1 54 7 4 18 0 97 Convert fraction to decimal 19 5 15 72 71 6 112 ab 30 n x x fraction

The figure shows a medicine wheel which is a Native American structure This circular structure is perhaps 2500 yr old There are 27 aboriginal spokes in the wheel all equally spaced Type an integer or a simplified fraction CXID 2x The central angle in radians is approximately 27 Simplify your answer Type an exact answer in terms of x Use integers or fractions for any numbers in the expression b If the radius of the wheel is 71 0 ft find the circumference 446 1 ft Round to the nearest tenth as needed c Find the length of each arc intercepted by consecutive pairs of spokes 16 52 ft Do not round until the final answer Then round to the nearest hundredth as needed d Find the area of each sector formed by consecutive spokes

In Exercises 5 8 find the areas of the sectors formed by ZJLK J 6 7 5 M L 50 7 ft K 13 in 125 L M J M 140 L 1 m K 8 M 8 cm 45

If mHV 38 and mID 120 find m A D I H A

At a college financial aid office students who applied for a scholarship were classified according to their class rank Fr freshman Sosophomore Jr junior Se senior Construct a frequency distribution for the data Fr Fr So Jr Se Se Fr Jr Fr Fr Fr Fr So So Fr 3r Se Se Se Jr Jr So Fr So Jr Fr So Jr Se Se Rank Frequency Fr So Jr 7

II Engineering students obtained the following data during a lecture of Design of Experiments The process s inputs are and w whereas y is the output From previous knowledge on the process the following ARX model structure i proposed y k ay k 1 Bx2 k 1 yw k 2 k y k x k w k 0 3 6 0 1 0 3 1 4 4 0 2 0 5 2 3 8 0 1 0 1 3 4 8 0 5 0 8 4 5 4 0 2 0 1 5 4 3 0 2 0 3 a Define all required vectors and matrices to estimate a y y through least squares 20pts b Calculate e 10pts 6 2 8 0 6 0 5

3 List 3 factors Don might consider when deciding which mode of transportation to use Explain why he should consider each factor a cost of transportat b

Diagrams are not to scale Find the m ABC if mLADC 2x 25 and m AC 7x 4 a 122 b 37 C61 74 9 Mo Tonic O B D A C Tact Reviem

According to a recent survey six of every 8 dentists interviewed recommend Yukky Gum A Amnong those interviewed what is the ratio of those who recommned Yukky Gum those who do not B Among those interviewed there are times as many dentists who do not recommend Yukky Gum as dentists who do C What fraction of the dentists interviewed recommend Yukky Gum

Which of the following is closest to the volume of the pyramid 1 12 1 spinning the spinner one time 4 6 12 A D B 0 D C A D

14 a Diagrams are not to scale If AB 60 and DE 48 find AF b C 12 24 18 36 E A F B D

is are education funds awarded to students who demonstrate or show potential fo xcellence in a certain area Grants O Scholarships O Financial aid

Given NP 18 3 and OQ 36 5 find the area of rhombus NOPQ Round your answer to the nearest tenth if necessary P 20 4 in 20 4 in 0 20 4 in 20 4 in N

In Exercises 11 13 find the area of the shaded region 11 12 17 ft 8 ft 3 mm T 17 mm 13 10 cm 10 cm

Classify the sample as random systematic stratified or clustered Every seventh customer entering a shopping mall is asked to select his or her favorite store This is a Choose one sample stratified random clustered systematic X

periodic function Model the height of the minute hand as a sinusoidal function Then determine the peak and Trough of your model Determin the period of your model Determine the Equation of the Axis of your model Determine the Amplitude of your model Create a sinusoidal equation using both Sine and Cosine to model your scenario Ans Given wall clock Consider 25 2 264 240 727 171 Consider k h t Z 60 min 360 6 60 N Axis 252 Amplitude a 12 phase ghift 30 ar sint Model is h t 12 sin6t 252 This is sinuscidal function Consider bct t 0 time 1 45pm Nov time time 3pm t 45min

each question set S is linearly dependent Determine a set of a linearly independent vectors that spans the same space as Span S Place zeros in any vector that you do not need i e if you nly need 2 vectors then write all zeros for the last two vectors S contains only the vectors 1 2 1 4 2 2 1 4 0 he new linearly independent set with the same span would be

Factor the polynomial f x 3x 12x 3x of f x 3x 12x 3x 18 given that x 3 is a zero O f x x 2 x 1 x 3 O f x 3 x 2 x 1 x 3 O f x 3 x 2 x 1 x 3 O f x x 2 x 1 x 3

Use the graph of y secx to find all values of x 0 sxs 2r for which the following is true Enter your answers as a comma separated list sec x 1 rad

To receive full credit you should show all your work 5 points total 1 Compute A 2B and A2B by using A 2 15 3 and B 0 2 23

Savings Register DATE DESCRIPTION 10 01 10 02 10 15 10 31 10 03 10 04 Cash Babysitting money Rebate check ATM deposit ATM withdrawal WITHDRAWAL DEPOSIT BALANCE 112 74 O 45 00 27 82 25 00 20 00 15 50 2 32 10 00 25 00 87 74 15 50 103 24 2 32 105 56 How much money was deposited in the account between 10 1 and 11 4 10 00 115 56 20 00 95 56

In each of the following statements the people named shared a large candy bar Make a drawing and give your reasoning in finding the fraction of the bar each person ate A Carrie ate 3 5 of the bar and Derek ate the rest Carrie ate of the candy bar Derek ate of the candy bar B Misha ate a quarter as much as Nadira and Oscar ate 3 4 of the bar Misha ate of the candy bar Nadira ate of the candy bar Oscar ate of the candy bar

Find the unknown side in the triangle below 5 m 43 12 m

Suppose that 25 of registered voters in North Carolina are registered Republican 55 are registered Democrat and 20 are registered as Independent A local paper wants to collect a sample to help predict the next election They want to take a sample of 1 500 voters They randomly select 500 Republicans 500 Democrats and 500 Independents Using the information given was this a simple random sample of registered voters in North Carolina O No not all registered voters had an equal chance of being selected O No each group had the same number of voters This would be impossible with a simple random sample O Yes each registered voter had an equal chance of being selected O Yes since there are equal numbers in each of the three categories then it is a simple random sample

Soiden Dragon Restaurant obtained a 9000 loan at 9 compounded annually to replace some kitchen equipment What is the size of the final payment if payments of S1800 are made semiannually 1900 1800 1304 30 1567 76

If mXV 30 and mDI 98 find m H D I X H

Suppose that in a senior college class of 500 students it is found that 200 smoke 241 drink alcoholic beverages 207 eat between meals 113 smoke am drink alcoholic beverages 83 eat between meats and drink alcoholic beverages 90 smoke and eat between meals and 49 engage in all three of these bad health practices If a member of this senior class is selected at random find the probability that the student a smokes but does not drink alcoholic beverages b eats between meals and drinks alcoholic beverages but does not smoke c neither smokes nor eats between meats a P smokes but does not drink alcoholic beverages 0 174 Type an integer or a decimal Do not round COD b P eats between meals and drinks alcoholic beverages but does not smoke Type an integer or a decimal Do not round

9 3 18 solve using the 7y x 4x 7 1 N m tj 4 vertex formula 8 x2 x 4x

IN COD LIBERTY TRUST 2010 COB LIBERTY WE TRUST 2010 IN GOD LIBERTY WE 2010 GELING OF AMERICA E PLURIBUS ONE CENT

A 35 year old married woman who drives a sedan and has never been in an accident OI A 22 year old man who drives a sports car and has been involved in Who would have the highest premium O III two car accidents An 18 year old woman who has a 3 8 GPA is on her parents multi car policy and has a 1 000 deductible IV A56 year old man who has a new car with an anti theft system and has used the same insurance company for twenty years

5 A recent survey asked high school girls to name the sport they like to watch the most The results are shown in the circle graph Find each indicated measure a mFG 32 b MEGB c mDB d mACE Favorite Sport to Watch Tennis 28 Baseball 32 F G Track 40 E Skating 47 D Football 108 C B Gymnastic Basketball 51

Points 2 Question 5 What life insurance can also be used as an investment tool and is regulated by the Securities and Exchange Commission O Universal life insurance O Term life insurance O Variable life insurance

Diagrams are not to scale 15 G D and F are the points of tangency for circle E If mLB 76 mzC x 1 and m2DEF 10x 28 then find m2A 2 91 b C 86 74 83 B G F LL E D C

5 Simplify each of the following expressions x 4 x 1 a 50 points x 3x 2 2x 3 b 50 points x 2 c 50 points d 50 points x 4 5x x x 6 2 x 4 3 5 r 2 r X x 3x x 2