Basic Math Questions and Answers

After preparing and posting the closing entries for revenues and expenses the income summary account has a debit balance of 33 000 The entry to close the income summary account will be Multiple Choice Debit Owner Withdrawals 33 000 credit Income Summary 33 000 Debit Income Summary 33 000 credit Owner Withdrawals 33 000 Debit Income Summary 33 000 credit Owner Capital 33 000 Debit Owner Capital 33 000 credit Income Summary 33 000 Debit Owner Withdrawals 33 000 Credit Owner Capital 33 000

Perpetual Inventory Using FIFO Beginning inventory purchases and sales for Item Zeta9 are as follows Oct 1 Inventory 7 15 24 Sale Purchase Sale 58 units 16 43 units 64 units 18 21 units Assuming a perpetual inventory system and using the first in first out FIFO method determine a the cost of the goods sold on October 24 and b the inventory value on October 31 a Cost of the goods sold on October 24 b Inventory value on October 31

12 An encryption program creates the appropriate verification and confirmation code in the following scheme regarding the multipliers of a password entered into the system Password Examples given in accordance with the Schema A 2600 180 350 Verification B 900 Code 32 22 5 2 52 7 According to the password program given above which of the following passwords entered into the system has the largest confirmation code Confirmation code C 480 18 34 D 294

3 The set G 0 2 4 6 is a group with the operation xo y defined as the remainder of dividing the number xy 3x 3y 6 by 8 i In G the element 0 o 0 o 0 is equal to ii The neutral element of o in G is iii The inverse element 0 in G is

215 A 7 246 X 2 a 213 B 8 There are exponent expressions in each of the triangles in the figure below Accordingly what is the value of a in the triangle in the middle of the bottom row The exponent expression in the triangle on the top row is obtained by multiplying the exponent expressions in the two closest triangles on the bottom row C 9 D 10

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by VA t 2t 2 and VB t 5 t respectively Complete parts a through c below 10 0 01 2 3 4 0 1 2 3 4 L hour s 4 hour s while Anna rides 8 miles in hour s while Benny rides 8 miles in V 0 0 1 2 3 4 5 What does this mean geometrically A The area under the line representing Benny s velocity from 0 to 1 is more than the area under the line representing Anna s velocity from 0 to 1 OB The line representing Benny s velocity is decreasing while the line representing Anna s velocity is increasing OC The lines intersect at a t value before the given time indicating that Benny has passed Anna OD The area under each line from 0 to 1 is the same for both riders 4 b If the bikers ride for 1 hour who rides farther Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals A Since Benny rides 4 5 mile s and Anna rides 3 mile s Benny rides farther OB Anna and Benny both ride mile s OC Since Benny rides mile s and Anna rides mile s Anna rides farther hour s hour s 07 13 012 34 c If the bikers ride for 8 miles who wins the race Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals OA They tie in the race because they both ride 8 miles in O B Benny wins the race because she rides 8 miles in OC Anna wins the race because she rides 8 miles in Save

Suppose the following plate is placed on a vertical wall so that the top of the plate is 1 m below the surface of a pool that is filled with water Compute the force on the plate 3 A plate shaped like an isosceles triangle with a height of 3 m and a base of length 2 If a y axis in the vertical direction is drawn on the face of the triangle where the origin is the vertex of the triangle find the width function w y for each value of y on the face of the triangle w y m The force on the plate is N Tupe an integer or decimal rounded to one decimal place as needed eufee

Complete the truth table given below for the conditional statement p a A q p pa q P Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables pq r TIT T TIT F TFT FIF T T F T Click to select F T T F p q T T F F T T T T F T F T The given conditional statement is a tautology Click to select Click to select Tru FIT FF 9 r T Click to select v pg 91 T Click to select F F T F Click to select p r T F T Click to select T T T T T Click to select

Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p V q A pr q n r r p V q p1 9 1 T T F T F F T F T F T F P T T T T F F F F q T T F F T T F F p V q T T T T T T Click to select Click to select The given conditional statement is a tautology Click to select Click to select True False p 1 T Click to select Click to select F T T T T Click to select F Click to select T F F Click to select T T F T T p V q p 9 T F Click to select F Click to select F F F pVg p 1 q r T Click to select T Click to select T Click to select T

Required information NOTE This is a multi part question Once an answer is submitted you will be unabl Fill the provided truth tables and check whether the given conditional statements a contingency pv q Click to select Click to select T Click to select F Click to select The given conditional statement is Click to select Click to select tautology P T T F F 9 T F contingency contradiction p pv q Click to select Click to select Click to select Click to select V

p T T T T F F F F Required information NOTE This is a multi part question Once an answer is submitted you will be unable to rete Complete the truth table given below to verify the associative laws q r T T T F F T T F F F T F T F T F p q T T F F F F F F p q Ar T F F F Click to select Click to select Click to select Click to select qAr T F F F T F F F p q T F F F Click to select Click to select Click to select Click to select

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews From the past records they have found that the length of a first interview is normally distributed with mean 36 minutes and standard deviation 9 minutes Round your answers to four decimal places LUSE SALT a What is the probability that a first interview will last 40 minutes or longer b Eleven first interviews are usually scheduled per day What is the probability that the average length of time for the eleven interviews will be 40 minutes or longer

What is the real size in um of a cell that s 90mm wide on a photograph The scale bar on the photo is 2 7cm long and it represent 5 m Your Answer to

ROBLEM 1 2j 2 j17 Express solution in algebraic and trigonometric forms 9 7j 1 3j 3p Solve z j 3 Express solution in algebraic form 4p Compute 3p Mark on the complex plane solutions of 3 z z 4

5 6 the A Show that the amount of salad is a rational number B Write the amount of salad as a decimal 7 375 C What will Rafael pay for the salad The temperature dropped steadily by 40 F over a 20 hour period Find the quotient 40 20 and explain what it means in this context Mr Nguyen s credit card Find the quotient 2103 and explain what it The balance on Mr Finch s credit card is 210 It is 3 times the balance on means in this context MP Use Repeated Reasoning Use the table shown A Convert each fraction in the table to a pattern in the results decimal Describe a B Does this pattern continue Why or why not Fraction 100 100 m 00 8 8 Michelle has to find the decimal equivalent of 15 yards How can she do this without first writing the mixed number as a fraction Decimal

USE SALT a Use the binomial distribution to find the probability of exactly 10 successes Round your answer to three decimal places b Use the normal distribution to approximate the probability of exactly 10 successes Round your answer to four decimal places X c Compare the results of parts a and b These results are fairly different These results are almost exactly the same

Let x represent the dollar amount spent on supermarket impulse buying in a 10 minute unplanned shopping interval Based on a newspaper article the mean of the x distribution is about 26 and the estimated standard deviation is about 10 USE SALT a Consider a random sample of n 100 customers each of whom has 10 minutes of unplanned shopping time in a supermarket From the central limit theorem what can you say about the probability distribution of x the average amount spent by these customers due to impulse buying What are the mean and standard deviation of the x distribution The sampling distribution of x is not normal The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean 26 and standard error 0 1 26 and standard error 1 26 and standard error o x 10 Is it necessary to make any assumption about the x distribution Explain your answer It is not necessary to make any assumption about the x distribution because n is large It is necessary to assume that x has an approximately normal distribution It is necessary to assume that x has a large distribution It is not necessary to make any assumption about the x distribution because is large b What is the probability that x is between 24 and 28 Round your answer to four decimal places Probabilities should be between 0 and 1 c Let us assume that x has a distribution that is approximately normal What is the probability that x is between 24 and 28 Round your answer to four decimal places 0 1587 d In part b we used x the average amount spent computed for 100 customers In part c we used x the amount spent by only one customer The answers to parts b and c are very different Why would this happen The standard deviation is larger for the x distribution than it is for the x distribution The mean is larger for the x distribution than it is for the x distribution The sample size is smaller for the x distribution than it is for the x distribution The x distribution is approximately normal while the x distribution is not normal The standard deviation is smaller for the x distribution than it is for the x distribution In this example x is a much more predictable or reliable statistic than x Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer How does the central limit theorem tell us that the average customer is much more predictable than the individual customer The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation Thus the average customer is more predictable than the individual customer The central limit theorem tells us that small sample sizes have small standard deviations on average Thus the average customer is more predictable than the individual customer

A European growth mutual fund specializes in stocks from the British Isles continental Europe and Scandinavia The fund has over 121 stocks Let x be a random variable that represents the monthly percentage return for this fund Suppose x has mean 1 7 and standard deviation 0 6 LAUSE SALT a Let s consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks Is it reasonable to assume that x the average monthly return on the 121 stocks in the fund has a distribution that is approximately normal Explain Yes is x is a mean of a sample of n 121 stocks By the central limit theorem approximately normal b After 9 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places 0 9330 c After 18 months what is the probability that the average monthly percentage return x will be between 1 and 2 Round your answer to four decimal places X the x distribution d Compare your answers to parts b and c Did the probability increase as n number of months increased Why would this happen Yes probability increases as the standard deviation increases No the probability stayed the same Yes probability increases as the standard deviation decreases Yes probability increases as the mean increases e If after 18 months the average monthly percentage return x is more than 2 would that tend to shake your confidence in the statement that 1 7 If this happened do you think the European stock market might be heating up Round your answer to four decimal places x This would be very unlikely The probability that x was greater than 2 is than 5 of all such samples have means more than 2 One would suspect because less that the European stock market

Which of the following expressions is equivalen to x x A x10 B x 5 C X25 D X 30

The mayor of a town believes that over 47 of the residents favor annexation of a new bridge Is there sufficient evidence at the 0 01 level to support the mayor s claim State the null and alternative hypotheses for the above scenario Answer Ho Keyp Keyboard Short Tables

Let f x x a Simplify f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations 1 13 h 13 b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE dne X c Determine the equation of the line tangent to y f x at x 13 y 1307

The graph of y f x is shown below 3 X 2 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes ONO b Is f x continuous at x 3 Yes No c Is f x differentiable at x 3 Yes No d Does lim f x exist X 1 CYes No e Is f x continuous at x 1 Yes No 2 f Is f x differentiable at x 1

Determine whether each statement is true or false You have one submission for each statement a For every function f x if f x is continuous at x a then f x is also differentiable at x a True False b For every function f x if f x is differentiable at x a then f x is also continuous at x a True False

The graph of y f x is shown below 3 2 b Is f x continuous at x 3 OYes No d Does lim f x exist X 1 OYes No The graph of the function decreases linearly with a slope of 1 to the point 1 1 and then increases linearly with a slope of 1 from the point 1 1 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes No c Is f x differentiable at x 3 Yes No e Is f x continuous at x 1 Yes No 1 f Is f x differentiable at x 1 Yes No 2 3

Let f x x a Simplify Computing derivatives using the limit definition f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE y c Determine the equation of the line tangent to y f x at x 13

A website has 400 000 members The number y of members increases by 9 each year a Write an exponential function that represents the website membership after t years b How many members will there be after 3 years Round your answer to the nearest ten thousand a y b about memboro

Use the definition of an exponent to write the given product in exponential form Answer 3 5 5 5 5 5 7 7 Enter one base and one exponent in each box going from left to right All of the boxes may not be used 3 5 5 5 5 5 7 7

4 4 0 4 y 0x00 X

4 0 0004 OC

4 t 0 4 y X 00

40 30 20 10 60 50 40 10 20 30 40 D 40 30 20 10 60 50 40 e 0 10 20 30

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that which the following is are true Select all that apply Each subset of the population has an equal chance of being included in the sample The simplest method of selection is used to create a representative sample Every sample of size n from the population has an equal chance of being selected Every sample of size n from the population has a proportionally weighted chance of being selected Every member of the population has an equal chance of being included in the sample

Assume that x has a normal distribution with the specified mean and standard deviation Find the indicated probability Round your answer to four decimal places USE SALT 28 0 3 8 P x 30 x You may have computed the probability between two values Consider which area of the distribution is appropriate

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3 1 months When this computer relay microchip malfunctions the entire satellite is useless A large London insurance company is going to insure the satellite for 50 million dollars Assume that the only part of the satellite in question is the microchip All other components will work indefinitely LUSE SALT a For how many months should the satellite be insured to be 98 confident that it will last beyond the insurance date Round your answer to the nearest tenth of a month x months b If the satellite is insured for 84 months what is the probability that it will malfunction before the insurance coverage ends Round your answer to four decimal places c If the satellite is insured for 84 months what is the expected loss to the insurance company in dollars Round your answer to the nearest dollar x d If the insurance company charges 3 million for 84 months of insurance how much profit does the company expect to make in dollars Round your answer to the nearest dollar

Use the given nth term formula to compute the firs n 4n 3 2 a1 22 33 34 25 an

Consider the following probability P Z 2 14 LUSE SALT Let z be a random variable with a standard normal distribution Find the indicated probability Round your answer to four places P Z 2 14

with a mean of 7 6 ounces and standard deviation of 0 4 ounce Examine the figure below and answer the following questions Area Under a Normal Curve 0 15 2 35 13 5 H 30 20 0 34 H 68 95 99 7 34 13 5 2 35 0 15 H o 20 H 30 a Estimate the probability that the machine will overflow an 8 ounce cup b Estimate the probability that the machine will not overflow an 8 ounce cup c The machine has just been loaded with 800 cups How many of these cups do you expect will overflow when served

ights of female college stu normall istributed with ssuming inches answer the following questions Hint Use the figure below with mean and standard deviation o Area Under a Normal Curve 0 15 2 35 13 5 H 30 H 20 0 34 l 68 95 99 7 34 13 5 H o H 20 30 a What percentage of female college students are taller than 67 inches 2 35 0 15 b What percentage of female college students are shorter than 67 inches c What percentage of female college students are between 64 6 inches and 69 4 inches d What percentage of female college students are between 62 2 and 71 8 inches and standard deviation

Consider the following normal curve 17 Look at the normal curve above and find 19 Look at the normal curve above and find o Look at the normal curve above and find o 21 23

Find the area of the shaded region in square units y 9 8 7 6 10 5 4 3 2 1 square units 1 f x 8 2x 2 3 4 5

c In light of their ability to buy and sell in world markets at the stated prices on the same graph as their PPC show all of the combinations of the two goods it would be possible for them to consume This is also known as their consumption possibilities curve or CPC Instructions Use the tool provided to draw all combinations of coffee beans and nuts it would be possible for them to consume Plot only the endpoints of this curve 56 52 48 Coffee Beans pounds day ANTENNA BA 44 36 32 28 24 20 16 4 Krisha Tom s PPC PPC 7 38 34 Tools CPC

pose that mean retail price per gallon of regular grade gasoline is 3 49 with a standard deviation of 0 10 and that the retail price per gallon has a bell ed distribution E Please use empirical rule approximations for this problem hat percentage of regular grade gasoline sells for between 3 29 and 3 69 per gallon to 1 decimal What percentage of regular grade gasoline sells for between 3 29 and 3 59 per gallon to 1 decimal What per regular and

tive 597 514 1563 648 1708 1727 1776 793 1810 2005 2015 2025 2053 2173 2204 2244 2355 2514 2543 2890 B Department Store 454 471 476 570 576 595 598 618 633 661 706 714 746 765 782 826 836 854 943 1009 Part a Mean to 2 decimals Part b Standard Deviation to 2 decimals Part c Maximum Minimum Range to 1 decimal Part d First Quartile to 2 decimals Third Quartile to 2 decimals Interquartile Range to 2 decimals Automotive Department Store Formula N A N A N A N A N A N A N A N A N A N A N A N A N A N A N A N A

Find the equation of the parabola having the following properties vertical stretch by factor of 6 opening up horizontal translation 6 units to the right vertical translation 3 units up i ii iii iv

b X Y x During a figure skating routine Jackie and Peter skate apart with an angle of 15 between them Jackie skates for 5 meters and Peter skates for 7 meters a Draw a diagram of this situation and clearly label all measurements How far apart are the skaters to the nearest meter at that point C 2 marks C 1 mark A 2 marks

4 3 A Find the value of the indicated variable 5 47 Find SB B 4 Find b Find LC 12 Page 6 of 8 rounded to one decimal place A 2 marks rounded to the nearest degree A 2 marks K 2 marks

SHORT ANSWER FULL SOLUTION 39 MARKS show all work and proper form for full marks solutions as demonstrated in class no marks given for guess and check methods 4 x 2 10 on the same grid 4 x 2 10 2 1 a Graph and label the relations y x and y use a scale of 1 unit Draw and label the Axis of Symmetry for y Complete the information requested below y x 2 Axis of Symmetry Vertex Y intercept y 4 x 2 10 Direction of Opening Y intercept Optimal Value Solve for x 2x 3x 5 0 A 4 marks K mark each K 2

Find the area of the shaded region in square units y 13 12 11 11 60 10 9 8 7 16543 3 2 1 12 3 I square units fix 19 8 1 63 x L 4 5 6 7 8 9 10 11 X

Find the area of the shaded region in square units y 11 10 96 8 7 6 5 4 3 2 1 1 square units fix 10 2x 2 3 4 5 6 e

Find the area of the shaded region in square units y 8 7 6 5 4 3 2 1 fix 1 3 x 1 square units 2 3 4 5 6 X