Basic Math Questions and Answers

We seek the plane passing through the points A 1 2 5 B 3 7 2 C 1 5 6 i Define position vectors a b c to the respective points A B C ii Construct displacement vectors AB b a and BC c b iii Use the cross product to find n the vector normal to the plane containing AB and BC iv What does the result in iii mean In particular what does the result mean in terms of being able to find the plane Find the plane through the pointer 125 12 2 79 1 5 6 and the additional paint 1

Wes wants to treat his friends to some are ames He has 50 ame tokens W three responses show a number of friends Wes could divide his tokens among ly 2 people 3 people 4 people CLEAR

In American foo team s goal posts one way to eare points by kicking the ball between the other 4 This is called a field goal and is worth 3 points During heir game last week Rudo s football team scored 29 points uld they have scored all 29 points by making only field goals Yes because 29 is greater than 3 No because 3 and 29 are not even 7 Yes because 29 is divisible by 3 No because 3 is not a factor of 29 CLEAR CHE

many whole number factors does the number 18 have 18 1 18 18 2 9 18 3 6 18 4 4R2 19 5

Which of the following describe the liberal side of the political spectrum O more use of government to achieve equality government should be involved as little as possible in people s lives Otheir beliefs are in the middle seeking a balance with the role of the government none of these liberalism is not on the political spectrum

candies andies Mrs Gomez is putting together gift bags full of candy for the 12 children who will be at her son s birthday party If each child is to receive the same number of candies and there are to be no remaining candies how many total candies should Mrs Gomez buy 60 candies 100 candies

Restaurants often slip takeout menus under Tim s apartment door So far Tim has collected 5 menus for Italian food and 10 other menus What is the experimental probability that the next menu slipped under Tim s door will be from an Italian restaurant Simplify your answer and write it as a fraction or whole number P Italian

Harry s little siste ed paint on his factor rainbow for the number 42 Which answer oice shows the correct Factors of 42 rainbow for 42 Factors of 42 12 Factors of 42 CLEAR

and 43 4 and 19 Tactor pair of the number 76 3 and 22 8 and 9

Demand is 1 000 units year Placing an order costs 10 K The annual cost to carry h items is 2 each In what quantities should the item be ordered a Find EOQ Optimal b Find the Total Annual Inventory Cost TC c If Lead time is 4 days what is ROP Quantity

O Prove the following statements Use a to prove b to prove c a If a b are relatively prime and a b both divide c then ab c Hint use Q2 of HW2 b For nonzero integers d dn define lcm d dn as the smallest positive integer divisible by each d If d dn are pairwise relatively prime then d dn lcm d dn Hint induction on n may be useful c In the setup of the Chinese Remainder Theorem if x Z is a particular solution then x E Z is also a solution if and only if x x mod M where M d dn Hint Show that d must divide x x for each i

18 5 Points b Use the order of operations to evaluate a 16 32 2 c DETAILS d LARM 11 2 x 32 3 510 5 8 52 8 3 x 2

Few companies take the time to estimate the value of a good customer and often spend little effort to keep one Suppose that a customer at a restaurant spends on average R per visit and comes F times each 1 year for example if a customer purchases once every two years then F 0 5 The restaurant realizes a gross profit margin of M expressed as a fraction on the average bill for food and drinks In addition the fraction of customers defecting not returning each year is D Complete parts a and b 2 a Develop a mathematical model to compute V the gross profit during a customer s lifetime in doing business with the restaurant this is often called the economic value of a customer RFM D Simplify your answer b If the average purchase per visit is 40 the gross profit margin is 0 4 that is 40 customers visit an average of six times each year and 30 of customers defect each year what is the economic value of the customer V The economic value of the customer is Round to the nearest dollar as needed

A company is trying to predict the long run market share of a new men s deodorant Based on initial marketing studies they believe that 40 of new purchasers in this market will ultimately try this brand and of these about 60 will purchase it in the future Preliminary data also suggest that the brand will attract heavier than average buyers such as those who exercise frequently and participate in sports and that they will purchase about 15 more than the average buyer Complete parts a and b a Calculate the long run market share that the company can anticipate under these assumptions The long run market share is Type an integer or a decimal rounded to three decimal places as needed

QUESTION 11 Calculate the probabilities based on the fo Positive Resu 2569 478 Virus Present Virus Not Present Total a What is the probability of having a false SYMBOL

Use the following sample to estimate a population mean 27 9 110 2 70 6 58 6 87 1 94 5 130 1 77 4 34 81 9 73 7 Assuming the population is normally distributed find the 95 confidence interval about the population mean Enter your answer as an open interval i e parentheses accurate to two decimal places 95 C I

Test whether H2 at the a 0 01 level of significance for the sample data shown in the accompanying table Assume that the populations are normally distributed Click the icon to view the data table Determine the null and alternative hypothesis for this test OA Ho H1 H2 H H1 H2 B Ho H1 H2 H H1 H O C Ho H1 H2 H H1 H OD Ho H1 H H H1 H

The sample space includes the spinner below Event A is landing on orange P A P List the following Note Input the probabilities as a percent rounded to 3 significant digits as needed Include the percent sign P A B

9 Interst 5 Use the bar graph below to answer the following questions 3 1000 900 800 700 600 500 400 300 200 100 0 Simple and Compound Interest of 5 5 Annually on a 300 Loan Basic Geometric Con 10 Years 15 20 25 Series A Series B Series A Series B a Which series A or B is for simple interest and which one is for compound interest Justify your answ b Approximately how much more interest is made after 25 years compounded as opposed to simple

Question 1 1 point You want to calculate a 98 confic of n 18 What is the appropriate cri

Question 10 1 point A random sample of 25 observations population with a population variand confidence interval for population m

tion 3 1 point pose a 95 confidence interval for p 0 0 To make more useful inferences f th of the confidence intepal Which

estion 7 1 point n economist is interested in stu country The population standard

Question 4 1 point If you were constructing a 999

Find the equilibrium price and quantity producers surplus for P D x 71 1 p S x 35 2x 20 OP 47 q 288 P 47 q 180 OP 47 9 240 p 50 1 Tox and 10 9 240

A fair 2 sided coin is tossed 3 times What is the probability that the coin lands on tails once Note Input the probability as a percent rounded to three significant digits as needed Include the percent

r 6 12 sin What shape does the polar equation form when graphed OA Limacon without an inner loop Cardioid that is symmetric to line 0 Which graph represents the equation OA C 2 OB Limacon with an inner loop OD Cardioid that is symmetric to the polar axis OC OD

Find the producer s surplus for the following supply function at the given point S x x 2 x 1 2 0 67 2 0 67

If mRJX 213 and mSV 53 find m RUX R J V U S X

Match the notation on the left with its meaning on the right n A P A n S P ANB P A XP BIA P AUB P A P B P ANB 0 P AUB P A P B P ANB P ANB P B P AIB 1 The Probability of A and B occurring together for non mutually exclusive events 2 The Addition Rule for non mutually exclusive events 3 The Theoretical Probability of the event A occurring 4 The probability of A or B occurring for mutually exclusive events 5 This statement is true for all mutually exclusive events 6 The Conditional Probability for an event A knowing that another event B has already occurred

QUESTION 1 The sample space includes a deck of 52 playing cards Event A is all the red face cards in the sample space List the following Note Input the probabilities as a percenf rounded to 3 significant digits as needed Include the percent sign n A P A n A P A

Three cards are drawn from a standard deck of 52 cards without replacement What s the probability that all three cards are fac cards Note Input the probability as a percent rounded to three significant digits as needed Include the percent sign

Two events exist such that P A 0 8 P A U B 0 2 and P An B 0 16 Select ALL the properties of probability that are violated here a P All outcomes 1 b 0 P B 1 C c None of the above d 0 P A 1

ey Graco plans to conduct book signin ent ways can she visit each of these c

determine whether u v and w lie in the same plane when positioned so that their initial points coincide 19 u 1 2 1 v 3 0 2 w 5 4 0

A publisher reports that 43 of their read percentage is actually over the reported pe the O

Consider the function f x x x 2 For each part if there are multiple answers separate them with a comma If there is no real answer input DNE If necessary you may round to 2 decimal places a State the vertex of the graph of the function Be sure to simplify b State the y intercept s of the graph of the function c State the x intercept s of the graph of the function d Graph the function 10 8 6 4 O

Assume that it costs a company approximately C x 400 000 140x 0 002x dollars to manufacture x smartphones in an hour a Find the marginal cost function Use it to estimate how fast the cost is increasing when x 10 000 per smartphone Compare this with the exact cost of producing the 10 001st smartphone The cost is increasing at a rate of per smartphone The exact cost of producing the 10 001st smartphone is b Find the average cost function C and the average cost to produce the first 10 000 smartphones C x 10 000 c Using your answers to parts a and b determine whether the average cost is rising or falling at a production level of 10 000 smartphones The marginal cost from a Select than the average cost from b This means that the average cost is Select higher lower Thus there is a difference of at a production level of 10 000 smartphones

4 A bag contains 40 marbles 12 of the marbles are red What is the percent of red marbles in the bag

Suppose the probability of an event is 0 40 What are the odds in favor of this event

Find the range and the standard deviation correct to two decimal places 82 93 100 100 100 range standard deviation

The weekly sales of Honolulu Red Oranges is given by q 990 22p Calculate the price elasticity of demand when the price is 30 per orange yes 30 per orange Interpret your answer The demand is going Also calculate the price that gives a maximum weekly revenue Find this maximum revenue by per 1 increase in price at that price level

ts DETAILS LA mean the median and the mode of the following sa SMITHNM13 14 2 033 Salary 21 000 20 000 Frequency 4

In how many ways can a president vice president secretary and treasurer be elected from a group of seven pec ways

10 6 Points DETAILS SMITHNM13 13 Suppose that you toss a coin and roll a die The sa P

The number or Factors may belong to more than one number All factors will be used at least once one factor humbers to show all the factors of each product 1 7 21 and 25 each product has is shown in parentheses 3 5 7 21 25 CLEAF

Introduce slack variables as necessary and then write the initial simplex Maximize z x 6x2 tableau for the given linear programming problem subject to Complete the initial simplex tableau X1 X 1 52 53 1 0 9 2 1 0 0 0 1 0 0 0 0 N 0 0 0 9 with X1 2x2 10 9x1 x2 9 3x1 2x 6 X1 0 X 0

A data set includes the age at marriage for 100 randomly selected married couples Choose the correct answer below OA The samples are independent because there is a natural pairing between the two samples B The samples are independent because there is not a natural pairing between the two samples OC The samples are dependent because there is a natural pairing between the two samples OD The samples are dependent because there is not a natural pairing between the two samples

Complete thee by placing each fact The first fast should be less than the second actor Not a factor 30 15 First factor of 30 correct pair to equal the product 30 6 2 Possible Factor Pairs of 30 Second factor First factor 1 3 4 5 Second factor of 30 DROP 10

Leo multip two whole number factors together to equal a product of 17 Then hen broke and spilled ink on his work of these must be one of the factors Leo multiplied