Math - Others Questions

Find the line of best fit for the given data 4 2 5 9 7 12 8 13 The equation of the line of best fit is y x Round to the nearest tenth as needed

Make a scatter plot for the given data Use the scatter plot to describe whether or not the variables appear to be related Graph the point 1 10 Graph the point 4 7 Graph the point 2 9 Graph the point 5 5 Graph the point 6 3 Graph the point 7 3 Do the variables appear to be related No O Yes X y 1 10 4 7 2 5 9 5 6 3 7 3 CZE

Given a railroad curve with the following parameters D 2 00 00 18 00 00 PI Station 25 50 00 ft Compute the curve parameters the station PT O 34 78 12 O 47 69 42 O 65 43 21

Use a standard normal distribution table to find the percent of the total area under the standard normal curve between the following z scores z 0 8 and z 1 Click the icon to view the standard normal distribution table The percent of the total area between z 0 8 and z 1 is Round to the nearest integer

Given a railroad curve with the following parameters Dc 2 00 00 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Long Chord LC O 900 04 O896 35 O 148 72

Given a railroad curve with the following parameters Dc 2 00 00 18 00 00 PI Station 25 50 00 ft Compute the curve parameter Tangent length T 587 69 O872 65 420 00

Given a railroad curve with the following parameters Dc 2 00 00 C 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Length of the arc L O 1014 56 O452 71 900 04

Given a railroad curve with the following parameters Dc 2 00 00 C I 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Radius R O 2864 93 O 2546 32 O2798 65

A normal distribution has a mean of 13 and a standard deviation of 3 Use the 68 95 99 7 rule to find the percentage of values in the distribution below 4 What is the percentage of values in the distribution below 4 Type an integer or a decimal

Given a railroad curve with the following parameters Dc 18 00 00 2 00 00 PI Station 25 50 00 ft Compute the curve parameters the stations of the PC O 20 96 24 O 32 15 42 O 30 42 35

Click the icon to view the area under the standard normal curve table What problem solving method should be used OA The Analogies Principle B Draw Pictures OC Relate a New Problem to an Older One OD Be Systematic The area under the standard normal curve from 0 to 2 00 is Round to four decimal places as 0 Normal Curve Areas 79 Z 1 2 3 45 0 00 0000 0398 0793 1179 1554 1915 2257 2580 2881 3159 3413 3643 3849 4032 4192 4332 4452 4554 4641 4713 4772 4821 4861 z 01 0040 0832 1217 1591 1950 2291 2611 2910 3186 3438 3665 3869 4049 4207 4345 4463 4564 4649 4719 4778 4826 4864 02 0080 0478 0871 1255 1628 1985 2324 2642 2939 3212 3461 3686 3888 4066 4222 4357 4474 4573 4656 4726 4783 4830 4868 03 0120 0517 0910 1293 1664 POIO 2019 2357 2673 2967 3238 3485 3708 3907 4082 4236 4370 4484 4582 4664 4732 4788 4834 4871 04 0160 0557 0948 1331 1700 2054 2389 2704 2995 3264 3508 3729 3925 4099 4251 4382 4495 4591 4671 4738 4793 4838 4875 1 05 0199 0596 0987 1368 1736 2088 2422 2734 3289 3531 3749 3944 4115 4265 4394 06 0239 0636 1026 1406 1772 2123 4608 4686 4750 4803 4846 4881 07 0279 0675 1064 1443 1808 2157 4525 4616 08 0319 0714 1103 1480 1844 2190 2517 3599 3810 3997 4162 4306 4429 4535 4625 4699 4761 4812 4854 4887 09 0359 0753 1141 1517 1879 2224 2549 2852 3133 3389 3621 3830 4015 4177 4319 4441 4545 4633 4706 4767 4817 4857 4890

The cyclists X and Y leave town Q at the same time Cyclist X travels at the rate of 5km h on a bearing of 049 and Cyclist Y travels at the rate of 9km h on a bearing of 319 a Illustrate the information on a diagram b After travelling for two hours calculate correct to the nearest whole number the i distance between cyclists X and Y ii bearing of Cyclist X from Y c find the average speed at which cyclist X will get to Yin 4 hours

1 LM X 72 X 4 2 2 2x y 4xy 2y 6 2 3 x 4x 4 x 2 4 4 4 x 4x 4 x 2

k ces Sofia Gomez runs a mobile pet grooming service She charges 30 direct labor per grooming hour She applies overhead to jobs on the basis of grooming hours She predicts 1 000 grooming hours for the year Her estimated overhead costs for the year follow Van depreciation Van maintenance 9 700 Van insurance expense 1 600 Indirect materials 1 Predetermined overhead rate 2 Total job cost 3 Price quote 1 200 Tool depreciation 800 Other overhead 550 1 150 1 Compute the predetermined overhead rate using estimated grooming hours 2 Sof a has been asked to groom 3 large dogs She expects this job to require a total of 9 direct labor grooming hours Compute her total cost direct labor plus applied overhead for this job 3 If Sof a targets a markup of 20 on the total cost for each job what price should she quote for the job in part 2 Check my w

In a dinner party of 290 persons in attendance 181 of them drink malt 142 drink wine and 117 drink fruit juice and each drink at least one of the three drinks If 75 drink Malt and wine 60 drink malt and juice and 54 drink wine and juice i ii Draw a Venn diagram to illustrate this information How many people drink a b C d e f All the three items exactly two of the drinks exactly one of the drinks wine alone at most two of the drinks at least two of the drinks

In a road worthiness test on 240 cars 60 passed The number that failed had faults in Clutch Brakes and Steering as follows Clutch only 28 Clutch and Steering 14 Clutch Steering and Brakes 8 Clutch and Brakes 20 Brakes and Steering only 6 The numbers of cars with faults in Steering only is twice the number of cars with faults in Brakes only a Draw a Venn diagram to illustrate this information b How many cars had i faulty Brakes ii only one fault

Estimate the error if P2 x 1 is used to estimate the value of cos x at x 0 1 2 Error Simplify your answer Round to seven decimal places as needed

Use the logarithm change of base formula to convert each of the following logarithms to the specified base Then use a calculator to approximate the logarithm Round approximations to four decimal places Convert log20 13 from base 20 to base 5 log20 13 which is approximately equal to Convert logg 10 from base 8 to base 10 logg 10 2 which is approximately equal to Convert log15 6 from base 15 to base e log156 which is approximately equal to

Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or decimal rounded to the nearest hundre as needed OA For the time period between and not inclusive of OB For the time period between and inclusive of sec and sec and sec the ball will be at least 41 ft above the ground sec the ball will be at least 41 ft above the ground

6 Using a sign chart and the graph provided sketch the polynomial function P x x 2 x 4 x 6

a Sketch the curves y x 1 and y 7 x on the same axes Find the area enclosed between the curves b

2 of the function f x 2x 37 12x 4 using the second derivative and sketch the graph

9 Suppose the interest rate on a 1 year T bond is 4 0 and that on a 2 year T bill is 7 0 Assuming the pure expectations theory is correct what is the market s forecast for 1 year rate 1 year from now

Using LEIBNIE S RULL find the 4th derivative U 3x 4xt Wxes10

The upper fixed and lower fixed point of a certain thermometer are marked 110 and 10 respectively What temperature on a centigrade thermometer will be four times that on this thermometer

Using a ruler and a pair of compasses only construct i a AABC with AB 7 5cm AC 13 5cm and LABC 120 B locus I of points equidistant from A and B Y locus I of points equidistant from B and C Using N the point of intersection of I and I as centre draw a circle to pass throug points A B and C

Prove the Adiabatic expression 1 and isothermal

30 0cm hydrochloric acid of concentration 6 4 dm neutralized 25 0cm of an unknown alkali XOH whose concentration was 4 85 g dm Calculate a the molar concentration of XOH b the relative atomic mass of the element X Name the element HCl 36 5

1 A 0 Smole of gas at temperature 300K expand Isothermally from an initial volume of 2 Lifes to 6 Litres what is the work done by the gas b Estimate the heat added to gas what is the final Pressure of the gas if the gas constant is said to be 8 31J molk

5 Kara starts tying a baby quilt at the local community center Each quilt takes 200 ties to complete Ten minutes later Julie joins Kara and both stay to finish the quilt Kara ties 6 per minute and Julie can tie 11 per minute a Write an expression to show the number of ties Kara has completed after m minutes b Using the same variable m write an expression for the number of ties Julie has completed c If you know they finished the quilt write an equation to model the situation d How many minutes did it take them to finish the quilt e How many did each of them tie f Suppose they tied the same amount How long would it take g How many did each of them tie h The next week Julie couldn t make it so her friend Susan came to help Susan can tie the ties as fast as Kara Using the same variable m write an expression for the number of ties Susan has completed 1 If you know they finished a quilt write an equation to model the situation 2h How many minutes did it take them to finish the quilt 2h How many did each of them tie

Question 6 A body at rest is given an initial uniform acceleration of 6 0ms2 for 25s after which the acceleration is reduced to 4 0ms for the next 15s The body maintains the speed attained for 40s after which it is bought to rest in 20s a Draw the velocity time graph of the motion b Using the graph calculate the i 11 111 iv average speed during the same interval as in iii maximum speed attained during the motion average retardation as the body is being brought to rest total distance travelled during the first 80s

IJ Exerc Expand the following logarithms Use either the power rule product rule or quotient rule 1 log 95 2 log 21 3 l gs 5 log xy 7 log3 5y Expand 2 9 logs 2 11 log x y 13 log 15 log 2x5 4a 4 log2 6a 6 logs A 8 log 10 log 12 logs E 8 16 109 14 log 9x3 9x 18 Ion 3 2

A woman bought 130kg of tomatoes for N52 000 00 She sold half of the tomatoes at a profit of 30 The rest of the tomatoes began to go bad she then reduced the selling price per kg by 12 Calculate a b the new selling price per kg the percentage profit on the entire sales if she threw away 5kg of bad tomatoes

In the following problems you will fill in the details for various proofs On exams you are expected to write out the entire proof so you should practice by writing out the proof of each statement then comparing your work with the proofs given in the problem set In this problem you will complete the details of the proof of a direct proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n is odd then n 5n is even Proof Suppose that n is odd By definition n 2k 1 for some integer k So n 5n 2k 1 5 2k 1 2m where m Since Z is closed under addition and multiplication me Z Since n 5n 2m this means that n 5n is even

Tess needs to buy shredded rubber for her children s playground The shredded rubber costs 15 per ton and there is a delivery cost of 40 with each order What types of numbers are possible in the domain O All positive rational numbers less than 40 O All rational numbers greater than 15 O All positive rational numbers All rational numbers

10 A company s 10 year bonds are yielding 7 5 percent per year Treasury bonds with the same maturity are yielding 5 2 percent per year and the real risk free rate r is 2 1 percent The average inflation premium is 2 4 percent and the maturity risk premium is estimated to be 0 1 t 1 where t number of years to maturity If the liquidity premium is 0 2 percent what is the default risk premium on the corporate bonds

In this problem you will complete the details of the proof of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial involving the variables k and p Prove Let m n be integers If mn is even then m is even or n is even Proof Suppose that mn is even Assume for the sake of contradiction that it s not true that m is even or n is even By DeMorgan s Law this means that m is odd and n is odd By definition of odd m 2k 1 and n 2p 1 for some integers k and p This means that mn 2k 1 2p 1 2N 1 where N Since Z is closed under addition and multiplication NE Z Since mn 2N 1 this means that mn is odd This contradicts the fact that mn is even Therefore it must be true that m is even or n is even O

In this problem you will complete the details of an indirect proof Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer If n 17 is even then n is odd Proof Suppose that n 17 is even Assume for the sake of contradiction that n is even By definition n 2k for some integer k So n 17 2k 17 2m 1 where m Since Z is closed under addition and multiplication m e Z Since n 17 2m 1 this means that n 17 is odd However this contradicts the fact that n 17 is even Therefore n must be odd

Let T D R be sets contained in a universe U a Using the distributive law which of the following is equal to the set TU DNR OA TUD n DURC OB TND U TOR OC TUD n R OD TUD n TUR OE None of the above b Using the DeMorgan s law which of the following is equal to the set TU D n R OA TU DNR OB TU DUR OC TUD n R OD TUD U TUR

Let P n be the following proposition over P the set of positive integers a Which of the following is P 5 5 5 1 2 5 1 6 OA 12 22 52 OB 5 5 1 2 5 1 6 OC 12 22 5 OD 12 22 52 55 OE None of the above 12 2 n b Is P 5 true or false and why O A P 5 is true because 5 5 1 2 5 1 is a correct expression O B P 5 is true because both sides of the equation equal 55 OC P 5 is true because P 5 equals 55 OD P 5 is false because one side equals 55 but the other side does not equal 55 OE None of the above n n 1 2n 1 6 c Let k be a positive integer Consider P k and P k 1 What can you add to the left hand side of P k to get to the left hand side of P x 1 Enter an expression involving k

Let S T be sets in a universe U and let x y U a Use the definition of set subtraction to complete the following statement ES T if and only QA ES and x T OB x S and x E T OC ES or x T OD x Sorr ET OE None of the above b Use the negation of the previous answer to finish the following statement x S T if and only OA ES or x T OB x S and x T OC x Sor x E T OD ES and x T OE None of the above

Let P n be the following proposition over P the set of positive integers a Which of the following is P 14 OA 2 22 2 4 215 1 OB 20 2 22 23 2 4 2 5 1 OC 20 2 2 23 2 4 OD 2 22 23 2 4 214 1 1 OE 214 1 1 20 2 22 2 2 1 1 b Let k be a positive integer Consider P k and P k 1 What can you add to the left hand side of P k to get to the left hand side of P k 1 Enter an expression involving k

In this problem you will complete the details of the proof of an if and only if statement Fill in the blanks below Each blank should be filled with a polynomial in the variable k Prove Let n be an integer Then n is even if and only if n is even We will prove the following two statements 1 If n is even then n is even 2 If n is even then n is even Direct proof of 1 Suppose that n is even By definition n 2k for some integer k So n 2k 2m where m Since Z is closed under addition and multiplication me Z Since n 2m this means that n is even Indirect proof of 2 Suppose that n is even Assume for the sake of contradiction that n is odd Since n is odd n 2k 1 for some integer k This means that n 2k 1 4k 4k 1 2p 1 where p 8 Since Z is closed under addition and multiplication p E Z Since n is of the form 2p 1 for some integer p this means that n is odd However this contradicts the fact that n is even Therefore n must be even O

In this problem we prove the following statement Let A B be sets in a universe U Then An Bc C AUB Your task is to provide justification for some of the steps Possible answers are given below Put a number into each blank with no parentheses 1 definition of union 2 definition of intersection 3 definition of subset 4 definition of set subtraction i e S T 5 definition of complement 6 DeMorgan s law of logic Proof Let a A n B Then x E A and x E B by justification Since a A this means that x A by justification Using the same reasoning a E B means that a B so x EB is true Combining these facts A EB is true Therefore EA V EB is true using justification In other words E AUB is true using justification Since AUB this means that a E AUB using justification 9 I So x A is true which is equivalent to x AUB

Let S A be sets in a universe U and suppose z S satisfies z A Which of the following statements must be true DA ZE AC OB ZE S A OC ZE A S OD 2 2 E SXS 4

Suppose that R C are sets so that RC C Also let tERand z E C Which of the following statements must be true OA te C OB z t E C x R OC t z E R x C OD ZER A

This problem covers more laws of set theory Let B be a set contained in a universe U Each set below is equal to B or U Select the correct set from the drop down menu Try using a Venn diagram if the answer isn t immediately clear Involution Law B Null Laws BUU Bn Idempotent Laws BUB BnB Identity Laws BU BOU Complement Laws BUB

Micromedia offers computer training seminars on a variety of topics In the seminars each student works at a personal computer practicing the particular activity that the instructor is presenting Micromedia is currently planning a two day seminar on the use of Microsoft Excel in statistical analysis The projected fee for the seminar is 675 per student The cost for the conference room instructor compensation lab assistants and promotion is 9600 per 2 days Micromedia rents computers for its seminars at a cost of 115 per computer per day a Develop a model for the total cost to put on the seminar Let x represent the number of students who enroll in the seminar Round your answers to the nearest whole number For subtractive or negative num use a minus sign even if there is a sign before the blank Example 300 Total cost 9 600 b Develop a model for the total profit if x students enroll in the seminar Round your answers to the nearest whole number For subtractive or negative number use a minus sign even if there is a sign before blank Example 300 Total profit Total profit 230 X 615 X X 9 600 c Micromedia has forecasted an enrollment of 30 students for the seminar How much profit will be earned if their forecast is accurate Round your answer to the nearest dollar 8 850 X d Compute the breakeven point Round your answer to the nearest whole number The breakeven point is 15 X students

A farmer wishes to enclose two identical adjoining rectangular pens against the side of a large barn both pens touch the barn She wants each pen to have an area of 600 square feet and will use the barn as one side of the enclosure What is the least amount of fencing needed in feet to create the two pens The least amount of fence required is ft NOTE enter an answer that is correct to at least three decimal places or an exact value

Sean Lee purchases 20 000 worth of supplies for his restaurant by making a 3 000 down payment and amortizing the remaining cost with quarterly payments over the next 4 years The interest rate on the debt is 16 compounded quarterly what is the size of each payment what is the total amount paid for the purchase what is the total interest paid over the life of the loan