Math - Others Questions

A random variate has the following triangular density f x 1 16 min x 8 x 0 x 8 Develop algorithms to generate this variate using Inverse transformation 1 Write the density function f x in two parts 2 Find f 4 f 8 3 Find the expectation of x 4 Draw f x 5 Find CDF F x 6 Draw F x 7 Find F 4 F 8 and F 10 8 Find the inverse of F x 9 Find the random variate 10 Find the value of the random variate for U 0 0 5 8 and 1

Choose which reasoning process is shown in the following example Explain your answer An HMO does a follow up study on 1329 randomly selected patients given a flu shot None of these people became seriously ill with the flu The study concludes that all HMO patients be urged to get a flu shot in order to prevent a serious case of the flu B Choose the correct answer below OA It is deductive reasoning because additional information may prove that other patients may not have taken the flu shot and still did not catch a serious case of the flu B It is deductive reasoning because a general conclusion is drawn based on specific observations C It is inductive reasoning because a general conclusion is drawn based on specific observations D It is inductive reasoning because the flu is epidemic If someone does not take the flu shot there is a great possibility for that person to catch a serious case of the flu

4 A stereo is marked down 75 If this is a 15 decrease find the sale price

A SCHOLARSHIPS FOUR OF EIGHT FINALISTS WILL BE SELECTED AND AWARDED 10 000 SCHOLARSHIPS IN HOW MANY WAYS CAN THIS SELECTION BE MADE B PRIZES A TEACHER DECIDES TO GIVE SIX DIFFERENT PRIZES TO SIX OF THE 30 STUDENTS IN HER CLASS IN HOW MANY WAYS CAN SHE DO SO

According to a census bureau from 2000 to 2016 the population of a certain region grew from 276 million to 309 million What was the percent of increase The percent of increase is Round to one decimal place as needed

Last year Charlie had 30 000 to Invest He Invested some of it in an account that paid 8 simple Interest per year and he Invested the rest in an account that paid 5 simple Interest per year After one year he received a total of 1710 in Interest How much did he invest in each account

Rewrite this number in appropriate scientific notation 905

Betsy a recent retiree requires 6 000 per year in extra income She has 70 000 to invest and can invest in B rat bonds paying 15 per year or in a certificate of deposit CD paying 7 per year How much money should be invested in each to realize exactly 6 000 in interest per year The amount of money invested at 15 The amount of money invested at 7

What percent of 200 is 190

1 Using the common denominator what is an equivalent fraction for 5

What is the probability that either event A or event B will occur Start by finding the probability of event A 4 19 3 19 A 10 19 P A B 2 19 19

The impulse response of the discrete causal system is y n 2y n 1 3x n 1 is 01 h n 3 2n 2u n 2 O 2 h n 32 22n 1u n 1 O 3 None of the answers 4 h n 3 2 1u n 1 h n Ek 2 1u n 1 O 5

The impulse response of the discrete causal system is y n 2y n 1 3x n 1 is 01 h n 3 2 2u n 2 O 2 h n 32 22n 1u n 1 O 3 None of the answers 4 h n 3 2 lu n 1 h n 2 u n 1 05

The total average power of the sum of two orthogonal signals can be always computed as the sum of these signals average powers O True O False

The minimum sampling rate necessary to reconstruct the sampled version of the signal 10 cos 60nt 5 sin 120nt 7 is x t O 1 60 samples sec O 2 None of the answers O 3 180 samples sec O 4 240 samples sec O 5 120 samples sec

5 The integration 10 cos 4nt t 1 dt 5 8 O 1 10 O 2 40 O 3 None of the answers O 4 40pi O 5 20pi

The discrete system with transfer function H z O 1 BIBO stable if the system zero at 2 is canceled O 2 Unstable O 3 Asymptotically stable O 4 None of the answers O 5 BIBO stable Z 2 Z 0 8 2 z 0 8 is

dy The response of the system 5y t 4x t with x t 8 t is dt O 1 None of the answers O2 03 O 4 05 y t 5e 5tu t 48 t y t 5e 5tu t y t 4e 5tu t y t 20e 5tu t 48 t 4

t 2 8n t 6 8n The signal x t 4 A 6 has 811 O 1 Has real Fourier series coefficients with the even indexed terms equal zero O 2 Has complex Fourier series coefficients with the odd indexed terms equal zero O 3 None of the answers O 4 Has complex Fourier series coefficients with no symmetry O 5 Has imaginary Fourier series coefficients with the even indexed terms equal zero

The sinusoidal steady state response of a discrete linear shift invariant system is also sinusoidal and have the same frequency of the discrete input sinusoid O True O False

8 The Fourier series coefficients X of the signal x t E co 106 2t 0 5n is 01 10 8f 0 5n 02 20 008 f 4n O 3 10 8f 0 25n O 4 None of the answers O 5 2 5 8f 4n

A linear time invariant system with the four imaginary poles j2 j2 j4 and 14 is BIBO stable O True O False

The discrete time system y n ex n 2 is O 1 None of the answers O 2 None linear and causal O 3 None linear and none causal O 4 Linear and none causal O 5 Linear and time invariant

An FIR system direct Form l realization has direct input sequence and feedback output sequence branches O True O False

The convolution sum of two time limited discrete signals is time limited O True O False

The energy signals 10x t and 10 x 1 5 have the same energy O True O False

The mapping between the z transform and Laplace transform maps circles from s domain to circles in z domain O True O False

The sampler is a linear device used to transform a continuous signal to a discrete one O True O False

The spectral representation of a periodic signal can be computed using the Fourier transfor O True O False

The trigonometric Fourier series represents a single sided spectral representation O True O False

Ali is a Lead Engineer working on a new oil rig drilling project The project is located outskirts of Kuwait and has no cellular phone service Ali has a two way radio that allows him to transmit messages to other Engineers on the ground His device has a range of 8 miles in all directions The other Engineers have similar devices that can pick up Ali s messages when they are in range of his two way radio On a particular day Ali is in the project head office at the center of the project His co worker Mahmoud is doing a survey of the land by driving along a straight road through the project area The road that Mahmoud is on starts 12 miles west and 12 miles south of the project s head office and ends 14 miles north and 8 miles east of the project s head office A Construct a model on a coordinate plane of the scenario described B Approximately how many miles of road will Mahmoud be able to receive Ali s messages C Suppose that Mahmoud drives at an average rate of 14 miles per hour If Mahmoud starts his trip at 9 A M at what time should Ali expect him to first be able to receive his messages

1 A landscaper planted 7 flats of impatiens 12 8 3 flats of snapdragons and 13 flats of phlox 1 6 How many flats did she plant altogether She plant altogether flats Simplify your answer Type a mixed numeral if possible C

As of June 30 Year 2 the bank statement showed an ending balance of 17 811 The unadjusted Cash account balance was 17 479 The following information is available 1 Deposit in transit 2 745 2 Credit memo in bank statement for interest earned in June 22 3 Outstanding check 3 062 4 Debit memo for service charge 7 Required Determine the true cash balance by preparing a bank reconciliation as of June 30 Year 2 using the preceding information Note Negative amounts should be indicated with minus sign Bank Reconciliation Unadjusted bank balance 6 30 Year 2 Add Deposit in transit Less Outstanding check True cash balance 6 30 Year 2 Unadjusted book balance 6 30 Year 2 Less Outstanding check True cash balance 6 30 Year 2 S 17 479 2 745 3 062 17 162 17 479 17 479

1 Draw the logical circuit for F AB B C 2 Draw a diagram for F ABC ABC a For the original form b For the most possible simplified form 3 Find a logical equation for the following circuit A

Use the revenue and cost functions below to answer parts A B and C R x 75x 3x 1 x 20 C x 125 14x 1 x 20 C 0 75 OD 0 175 B Complete the table x Millions 1 4 8 12 16 20 Profit Profit P x Millions 67

The following data apply to Pro Beauty Supply Incorporated for May Year 2 1 Balance per the bank on May 31 11 995 2 Deposits in transit not recorded by the bank 1 800 3 Bank error check written by Best Beauty Supply was charged to Pro Beauty Supply s account 800 4 The following checks written and recorded by Pro Beauty Supply were not included in the bank statement 3013 3054 3056 240 520 1 520 5 Note collected by the bank 600 6 Service charge for collection of note 13 7 The bookkeeper recorded a check written for 688 to pay for the May utilities expense as 598 in the cash disbursements journal 8 Bank service charge in addition to the note collection fee 40 9 Customer checks returned by the bank as NSF 144 Required Determine the amount of the unadjusted cash balance per Pro Beauty Supply s books Answer is complete but not entirely correct 17 100

Enter an ordering on the atomic subformulae of the following formula P P V Q Enter an ordering

5 For the project work points x y shown in the figure the bearing of point R is due West The coordinate for point R is most nearly A 6392 82 6380 78 B 6380 78 6392 82 C 6392 82 11187 21 D 11187 21 6380 78 R N50 45 42 North 9250 43 7380 78 8790 01 5400 55

4 What is the minimum time Critical path that the project can be completed by for the following CPM network diagram A 4 days 3 days B 8 days D 4 days Professor Dr M G Attara PE PhD E 9 days 6 days G 7 days

2 An embankment having a volume of 420 000 yd3 is to be constructed from local borrow The dry unit weight and moisture content of the borrow material were determined to be 200 pcf and 20 respectively The embankment material has a total unit weight of 300 pcf and a moisture content of 15 The volume of borrow yd3 needed to construct the embankment is most nearly

7 elevation of BM2 is most nearly a 109 53 ft b 117 85 ft c 124 47 ft d 24 47 ft BS Based on the information provided in Figure 1 the BS FS 10 88 2 56 T LILI 7 64 BM Elev 300 00 FS 3 11 TP BS 9 72 FS TP 3 10 not to scale BM

6 The average production of the excavator is the controlling factor in a highway ditch cleanin contract Excavators with four different bucket sizes are available as rental units The hourly renta rate is directly proportional to the bucket capacity of the excavator Assume that productio loose yd hr is equal to excavator cycles per hour x average bucket payload in LCY per cycle The excavator characteristics are as follows 0 0 0 0 Excavator O A B C D 1 2 3 4 Minimum Cycle Average Bucket Payload Time min LCY 0 50 1 00 1 75 2 00 The optimally efficient excavator is Excavator 1 Excavator 2 Excavator 3 Excavator 4 0 25 0 33 0 50 0 98

3 A work task has a current cost of 6 000 with a budget cost at this same point of 4 000 The total budget or this task is 9 000 The estimated cost at completion for this task is most nearly

Listed below are the numbers of unprovoked shark attacks worldwide for the last several years Why is it that a dotplot of these data would not be very effective in helping us understand the data Which of the following graphs would be most effective for these data dotplot stemplot time series graph Pareto chart pie chart frequency polygon 70 54 68 82 79 83 76 73 98 81 0 Why is it that a dotplot of these data would not be very effective in helping us understand the data OA Even though the data are numeric they are actually categorical data because each value is discrete B The data set is too small for a dotplot to reveal important characteristics of the data OC The spread of the data is very small so it would be nearly impossible to see any differences when represented graphically OD There are several duplicate values in the data and most graphical methods cannot accurately show duplicate values Which of the following graphs would be most effective for these data dotplot stemplot time series graph Pareto chart pie chart frequency polygon OA A dotplot would be most effective since it is important to be able to recreate the original list of values OB A Pareto chart would be most effective since the data are categorical data OC A stemplot would be most effective since it is important to be able to recreate the original list of values D A time series graph would be most effective since the data are listed in order over a period of several years OE A pie chart would be most effective since the data are categorical data OF A frequency polygon would be most effective since the data are listed in order over a period of several years 4

what is the elevation of the highest contour line shown on the map below x 10 788 10 500 O a 10000m O b 10688m C 10799m 10 000

1 A loader has a full bucket capacity of 10 yd3 and the average time required to place one bucketload of soil into a truck is 1 min The loader is supported by four trucks with a volume of 50 yd3 each and a cycle time of 12 min plus the time to load the truck The ideal productivity yd3 hr of this system is most nearly

dy t dt Given the system 2 2cos 2t is O 4 3y t 10x t the steady state response of the system O 1 The system does not have a steady state response 2 y t 10cos 0 5t tan 4 O 3 TE y t 20cos 2t 4 tan tan TT y t 4cos 2t 05 y t 20cos 2t 1 2 tan

Southern Environmental Consulting SEC Inc designs plans and specifications for asbestos abatement removal projects in public private and government buildings Currently SEC must conduct an air test before allowing the occupancy of a building after the asbestos has been removed SEC subcontracts air test samples to a laboratory for analysis by transmission electron microscopy TEM To offset the cost of TEM analysis SEC charges its clients 125 more than the subcontractor s fee The only expenses in this system are the costs of shipping the air test samples to th subcontractor and the labor involved in shipping the samples With the growth of the business SEC must consider eith continuing to subcontract the TEM analysis to outside companies or developing its own TEM laboratory Because of the passage of the Asbestos Hazard Emergency Response Act AHERA by the U S Congress SEC expects about 1 000 air sample tests per year over eight years The firm s MARR is known to be 7 Click the icon to view the description of alternatives Click the icon to view the interest factors for discrete compounding when MARR 7 per year a Determine the cost of an air sample test by the TEM laboratory in house

Washington Air Company is considering the purchase of a helicopter for connecting services between the company s base airport and the new intercounty airport being built about 30 miles away It is believed that the chopper will be needed only for six years until the Rapid Transit Connection is phased in The estimates on two types of helicopters under consideration the Whirl 2B and the ROT 8 are given in the table below Assuming that the Whirl 2B will be available in the future with identical costs what is the annual cost advantage of selecting the ROT 8 Use an interest rate of 8 Click the icon to view the estimates on two types of helicopters under consideration Click the icon to view the interest factors for discrete compounding when i 8 per year

You are considering purchasing a dump truck The truck will cost 74 000 and have operating and maintenance cos that start at 15 000 the first year and increases by 1 000 per year Assume that the salvage value at the end of fiv years is 17 000 and interest rate is 15 What is the equivalent annual cost of owning and operating the truck for five years Click the icon to view the interest factors for discrete compounding when i 15 per year The equivalent annual cost of owning and operating the truck is Round to the nearest dollar