Questions

5 10 A 50 meter tunnel must be constructed as part of a new aqueduct system for a city Two alternatives are being considered One is to build a full capacity tunnel now for 500 000 The other alternative is to build a half capacity tunnel now for 300 000 and then to build a second parallel half capacity tunnel 20 years hence for 400 000 The cost of repair of the tunnel lining at the end of every 10 years is estimated to be 20 000 for the full capacity tunnel and 16 000 for each half capacity tunnel Determine whether the full capacity tunnel or the half capacity tunnel should be constructed now Solve the problem by B C ratio analysis using a 5 interest rate and a 50 year analysis period There will be no tunnel lining repair at the end of the 50 years

A tunnel is being constructed through a mountain range where the tunnel is being constructed from both ends at the same time One end of tunnel starts at the point A 354 310 299 and s constructed in a straight line in the direction 71 61 6k whilst the other end of tunnel starts at the point B 156 150 81 and is constructed in a straight line in the direction 81 8j 4k The starting points and the direction vectors of both ends of the tunnel are measured in metres Verify that the tunnels being constructed from both ends meet by first finding the vector form of the equations of both tunnels and then finding their intersection point P 25 marks

You may need to use the appropriate appendix table or technology to answer this question A population has a standard deviation of 12 If a sample of size 36 is selected from this population what is the probability that the sample mean will be within 2 of the population mean O 0 6827 0 3413 0 6827 Since the mean is not given there is no answer to this question

Sampling distribution of x is the O probability distribution of the sample proportion O mean of the population O probability distribution of the sample mean mean of the sample

The 79 employees of your company are listed alphabetically and assigned two digit numbers from 01 to 79 To select five employees for a simple random sample you use pairs of digits from random number table below moving horizontally across the table 91244 62400 39878 89035 98424 12521 The employees that would be included in the sample would be those corresponding to the numbers 24 46 24 00 39 91 24 46 24 00 24 46 39 35 42 O 91 24 46 24 39

olve me following equation forx Let x 2x tx X 2 20 2 64 0 X

Differentiate the following function dx 16 X in 16 x x mx

Solve the following Equation for x 2x 5 2 772 2 X

xp Ap x 2ex 2x

Differentiate the function v Inf5x 6x 5 Y

solve the following equating fork 3 2 2x 1 3 2 7 X

Differentiate the following function x x ex Y dy

solve the following equation for X 10 108x 0

y In x 5 3x 8 1 8 axin x 5 3x 81 x

Find the derivative of the function y 4 cot ne y

Find an equation of the tangent line to the curve at the given point y sin sin x 0

Write the composite function in the form f g x Identify the inner function u g x and the outer function y f u y 1 7x g x f u Find the derivative dy dx dy dx

WAGE Assume that the accounting and actuarial industries employ people with similar skills Suppose a decrease in the their wages while the demand for accountants remains the same The following graph shows the labor market for accountants in the United States Show the effect of the fall in demand for actuaries on the U S labor market for accountants by shifting the labor demand curve the labor supply curve or both Supply Demand Demand Supply

1 Let w x represent the weight of the sand on a scale minutes after we started to unload the sand If the rate at which the weight of the sand changes with respect to time is x in pounds per minutes the expression that gives the total weight of the sand in pounds on the scale z minutes after we started to unload the sand is x 20 S 0 w t dt We assume that there was 20 lbs of sand on the scale when we started What is the meaning and measurement of w 6 OA the average weigth of sand unloaded each minute during the first 6 minutes in pounds OB the total weigth of sand on the scale after 6 minutes in pounds C the total weigth of sand unloaded during the first 6 minutes in pounds OD the average weigth of sand unloaded each minute during the first 6 minutes in pounds per minutes OE the average rate at which the weight of the sand is unloaded each minute during the first 6 minutes in pounds per minutes F the total weigth of sand unloaded during the 6th minute in pounds Let w 2 represent the weight of the sand on a scale z minutes after we started to unload the sand If the rate at which the weight of the sand changes with respect to time is a in pounds per minutes the expression that gives the total weight of the sand in pounds on the scale z minutes after we started to unload the sand is x 20 w t dt We assume that there was 20 lbs of sand on the scale when we started What is the meaning and measurement of 0 6 Lw t dt A the total weigth of sand unloaded during the first 6 minutes in pounds B the average weigth of sand unloaded each minute during the first 6 minutes in pounds C the total weigth of sand on the scale after 6 minutes in pounds D the average weigth of sand unloaded each minute during the first 6 minutes in pounds per minutes E the total weigth of sand unloaded during the 6th minute in pounds

The following represents the probability distribution for the daily demand of computers at a local store Demand Probability 0 0 05 1 0 20 2 0 35 3 0 25 0 15 What is the expected daily demand 01 1 65 2 2 25

38 42 Sylvester files as a single taxpayer during 2023 He itemizes deductions for regular tax purposes He paid charitable contributions of 7 700 real estate taxes of 1 100 state income taxes of 6 450 and mortgage interest of 2 900 on 30 450 of acquisition indebtedness on his home Sylvester s regular taxable income is 132 000 What is Sylvester s AMTI Answer is complete but not entirely correct

The probability density function for a uniform distribution ranging between 3 and 8 is undefined any positive value 0 2 5

Stephanie owns a gas station whose sales are uniformly distributed If the probability of selling between 3 000 to 7 000 gallons of gas on any given day is 25 and the minimum quantity she sells on any given day is 2 700 gallons what is the maximum amount of gasoline she sells on any day 16 000 gallons 17 350 gallons 18 700 gallons 20 050 gallons

You may need to use the appropriate technology to answer this question The probability that Pete will catch fish when he goes fishing is 0 84 Pete is going to fish 3 days next week Define the random variable x to be the number of days Pete catches fish What is the probability that Pete will catch fish on one day or less 0 065 0 069 0 840 0 935

You may need to use the appropriate appendix table or technology to answer this question The student body of a large university consists of 60 self identifying female students A random sample of 7 students is selected What is the probability that among the students in the sample at least 6 do not identify as female 0 0280 0 0774 0 1586 0 9720

You may need to use the appropriate appendix table or technology to answer this question Professor Avanti s Stats test scores distributed normally had a mean of 74 He says anyone scoring below 60 will fail the class This grading scheme failed 6 9 of the class What was the standard deviation of the test scores 1 48 7 70 9 44 12 85

Four percent of the customers of a mortgage company default on their payments A sample of nine customers is selected What is the probability that exactly two customers in the sample will default on their payments 0 0012 0 0368 0 0433 0 0866

A value of 0 5 that is added to or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called a probability density factor continuity approximation factor O continuity correction factor factor of conversion

The variance Var x for the binomial distribution is given by which equation np n 1 n 1 p np 1 p np 1 np

12 Forty percent of the students in a class of 600 are planning to go to graduate school What is the standard deviation of this binomial distribution 0 40 60 144

Which of the following is a required condition for a discrete probability function f x 0 for all values of x Of x 0 for all values of x f x 1 for all values of x f x 1 for all values of x

If F x f xf xf x where f 1 3 f 3 5 f 1 3 f 3 4 and f 5 5 find F 1 F 1

A probability distribution showing the probability of x successes in n trials where the probability of success does not change from trial to trial is termed a uniform probability distribution normal probability distribution binomial probability distribution hypergeometric probability distribution

are the functions whose graphs are shown let u x f g x v x g f x and w x g g x Find each derivative if it exists If it does not exist explain why If an answer does not exist ent 0 f 9 a u 1 It does exist Ou 1 does not exist because f 1 does not exist Ou 1 does not exist because g 1 does not exist Ou 1 does not exist because f 3 does not exist Ou 1 does not exist because g 2 does not exist b v 1 It does exist O v 1 does not exist because f 1 does not exist Ov 1 does not exist because g 1 does not exist Ov 1 does not exist because f 3 does not exist v 1 does not exist because g 2 does not exist c w 1 It does exist Ow 1 does not exist because f 1 does not exist w 1 does not exist because g 1 does not exist w 1 does not exist because f 3 does not exist Ow 1 does not exist because g 2 does not exist

It takes 9 hours to fill a pool with the inlet pipe A full pool can be emptied in 11 hours with the outlet pipe How long will it take to fill the pool if the pool starts out empty and both pipes are open

Evaluate the following definite integrals using a net area interpretation a b C 3 x 3 dx 6 3 x 3 d 6 a x 3 dx

a Suppose that a cyclist is riding on a straight road and the velocity of the bike at various times is recorded in the following table t in hours 0 4 0 8 1 2 1 6 2 0 v t in km h 20 18 15 19 18 14 Calculate L5 for v t over 0 2 and explain its physical meaning b A group takes a road trip from Kelowna to Radium Hot Springs 451 km away according to their map To pass the time the passengers note the speed of the car every few minutes using the odometer and find that the velocity of the car in km h at time t in hours can be approximated by the following continuous curve V 100 95 90 85 80 0 3 Approximate R10 and L10 of v t over 0 5 and interpret their meaning physically

3 Approximate the definite integral f x dx using the Riemann sums R4 L4 and M4 in turn Use sketches to determine which of R4 L4 and M4 is a lower bound for the integral an upper bound for the integral the best approximation for the integral

The critical value is 1 717 a 0 05 JF 22 0 05

A company looks to maximize its profits a The demand function relates the price of a product and the quantity sold Suppose that the company sells 1000 units when the price is 10 dollars and sells 20 fewer units every time the price is increased by one dollar selling the corresponding amount more due to price decreases Find a formula for f p the number of goods sold when the price is p dollars b The revenue is the money the company receives from sales Find a formula for R g p the revenue the company receives when the price is p dollars Hint revenue is the price times the quantity sold c The company can manufacturer goods for a cost of C 1000 2x dollars Find a formula for C h p the cost of producing the number of goods sold when the price is p dollars d The profit is revenue minus cost Find a formula for P j p the profit earned by the company when the price is p dollars What price is a critical number for profit Consider all positive prices p 0 as your domain e Classify the above critical number as corresponding to a local maximum by using a calculator to test nearby values Then argue why this must be the absolute maximum on the domain p 0

3 Given the sketch of a piecewise function f x over the interval 0 5 calculate the exact value of the integral al 5 f x dx f x

3 Please use Microsoft equation maker to write the formula for calculating d effect size for an independent samples t test d 2

X Y 1 1 2 3 4 5 6 6 8 3 9 6 6 8 5 8 4 9 3 9 2 8

1 Let w x represent the weight of the sand on a scale x minutes after we started to unload the sand If the rate at which the weight of the sand changes with respect to time is w x in pounds per minutes the expression that gives the total weight of the sand in pounds on the scale z minutes after we started to unload the sand is w x 20 w t dt We assume that there was 20 lbs of sand on the scale when we started What is the meaning and measurement of w 6 A the average weigth of sand unloaded each minute during the first 6 minutes in pounds OB the total weigth of sand on the scale after 6 minutes in pounds O C the total weigth of sand unloaded during the first 6 minutes in pounds OD the average weigth of sand unloaded each minute during the first 6 minutes in pounds per minutes OE the average rate at which the weight of the sand is unloaded each minute during the first 6 minutes in pounds per minutes OF the total weigth of sand unloaded during the 6th minute in pounds 1 Let w x represent the weight of the sand on a scale x minutes after we started to unload the sand If the rate at which the weight of the sand changes with respect to time is w in pounds per minutes the expression that gives the total weight of the sand in pounds on the scale z minutes after we started to unload the sand is w x 20 w t dt We assume that there was 20 lbs of sand on the scale when we started What is the meaning and measurement of w t dt OA the total weigth of sand unloaded during the first 6 minutes in pounds OB the average weigth of sand unloaded each minute during the first 6 minutes in pounds O C the total weigth of sand on the scale after 6 minutes in pounds D the average weigth of sand unloaded each minute during the first 6 minutes in pounds per minutes OE the total weigth of sand unloaded during the 6th minute in pounds F the average rate at which the weight of the sand is unloaded each minute during the first 6 minutes in pounds per minutes

The table gives temperatures in degrees Fahrenheit in a certain town on a given day The sinusoidal functioni F t 8 cos t c 30 models the data where F t is the temperature in F at time t in hours past 12 midnight and c is a constant Which of the following is true about the value of e A B D The value of cis 2 because this accounts for a phase shift of g t 8 cos t 30 that aligns a minimum value of the data set with a minimum value of g The value of cis 2 because this accounts for a vertical shift of g t 8 cos t 30 that aligns a minimum value of the data set with a minimum value of g The value of c is 14 because this accounts for a phase shift of g t 8 cos t 30 that aligns a maximum value of the data set with a maximum value of g The value of cis 14 because this accounts for a vertical shift of g t 8 cos t 30 that aligns a maximum value of the data set with a maximum value of g

Write a linear function f that has the indicated values Sketch the graph of f f 5 17 f 2 11 f x Simplify your answer Type an expression using x as the variable Type your answer in slope intercept form Use the graphing tool to graph the function Click to enlarge graph A

The graph of y f bx is a horizontal compression of the graph of y f x if b The graph of y f bx is a horizontal compression of the graph of y f x if b 1

Write an equation for a function whose graph fits the description given below The graph of f x x3 is shifted five units left stretched vertically by a factor of 2 reflected in the y axis and shifted six units up What is the equation of the described function g x

Specimen heating The fraction of the energy in the incident electron beam which reappears in the form of X rays light etc is small most being converted into heat in the target The temperature rise AT is expressed as AT 4 8Egl kd Eo is the incident electron energy keV the current A k the thermal conductivity Wcm K1 and d the beam diameter m Metals k 1 4 AT is negligible Mica k 6x103 Eo 20 keV 10 nA d 1 m T 160K

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval and approximate the solutions to four decimal places Enter your answers as a comma separated list 3 sin 9 sint 5 0 2 2