Basic Math Questions and Answers

1 True or False a 4x 2y 4y 2x b 4x 1 4y 4y 1 4 x c x y y x d 4xy 4yx

There are 10 400 students at JSU If 40 percent of the students live on campus select the correct method to be used to calculate the number of students living on campus and find the answer a 40 x 10 400 b 1 40 x 10 400 C 2 5 x 10 400 d 5 x 10 400 4 The area of a rectangle is represented by A Lx W If the area is equal to 28 which expression represents W a 28L b 28 L C L 28 d A 28L F What is the additive inverse of 1 3x What is the multiplicative inverse of 1 3x You need to replace a board on your front porch which is 10 3 feet long If the board I you purchased is 12 feet long how much do you need to cut off in order to have the correct size for the replacement board 424 2 4 2 424 53 424 2 424 2 424 4 12 2

display results from a test of the claim that hall of us say that we should replace passwords with biometric security Use the normal distribution as an approximation to the binomial distribution Use the display and a 0 10 significance level to complete pers a through e a is the best two tailed bolt tailed or right bailed Choose the correct answer below leit tailed two tailed right tailed b What is the test statistic 21 27 Round to two decimal places as needed c What is the P value P value 0 205 Round to three decimal places as needed d What is the null hypothesis and what do you conclude about it The null hypothesis is Ho P 05 where p denotes the population proportion of people who say that we should replace passwords with biomeline security Fail to act the not hypothes Type an integer or a decimal Do not round

evenue Mo s HookNLadder is the only company selling fire engines in the fictional country of Alexandrina Mo initially produced eight trucks but then decided to increase production to nine trucks The following graph gives the demand curve faced by Mo s HookNLadder As the graph shows in order to sell the additional fire truck Mo must lower the price from 80 000 to 60 000 per truck Notice that Mo gains revenue from the sale of the additional engine but at the same time he loses revenue from the initial eight engines because they are all sold at the lower price Use the purple rectangle diamond symbols to shade the area representing the revenue lost from the initial eight engines by selling at 60 000 rather than 80 000 Then use the green rectangle triangle symbols to shade the area representing the revenue gained from selling an additional engine at 60 000 110 100 90 22 80 70 PRICE Thousands of dollars per fire engine 60 50 40 30 20 10 O Revenue Lost Demand 2 3 4 5 6 7 8 9 10 QUANTITY Fire engines Revenue Gained Mo increase production from 8 to 9 fire engines because the dominates in this scenario True or False If alternatively Mo s HookNLadder were a competitive firm and 80 000 were the market price for an engine decreasing its price from 80 000 to 60 000 would result in the same change in the production quantity and thus total revenue O True

b A paint company has developed a new paint formula which should have a faster drying time compared to the old formula Paint drying time is known to be normally distributed and from previous tests it is known that the original paint formula has a mean drying time of 45 min The company s R D scientists believe the new formula will have a mean drying time of 235 min that is they expect the new formula to dry an average of 10 min faster than the old formula or that 10 They aren t sure what the population variances are yet but the new formula is not expected to affect the variance in drying time A scientist takes 10 samples of each paint formula and determines the mean drying time for each batch to be X 45 min and X2 34 min with sample variances equal to s 6 5 min and s 4 4 min respectively Find a 95 confidence interval on the difference in average lifetime between the two populations

5 4 3 3 3 22 1 2 1 2 3 4 2 3 14 5 6 Identify the function whose graph appears above f x

K Use the results from a survey of a simple random sample of 1038 adults Among the 1038 respondents 88 rated themselves as above average drivers We want to test the claim that more than themselves as above average drivers Complete parts a through e 17 of adults ra 20 a Regardless of the conclusion reached from the hypothesis test is it possible that more than of adults can be above average drivers 20 A Yes Assuming quality of driving can be quantified a distribution that is extremely skewed to the left would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean B No Assuming quality of driving can be quantified half of all adults must have driving quality less than or equal to the mean OC Yes Assuming quality of driving can be quantified a distribution that is extremely skewed to the right would be the most promising scenario for more than this proportion of adults to have driving quality that is above the mean COD No It is impossible to compare the quality of different adults driving b If we use the same significance level to conduct the hypothesis test using the P value method the critical value method and a confidence interval which method is not always equivalent to the other two A The P value method is not always equivalent to the other two B The confidence interval method is not always equivalent to the other two CC The critical value method is not always equivalent to the other two OD All three methods are always equivalent to each other c It was stated that we can easily remember how to interpret P values with this If the P is low the null must go What does this mean This statement means that if the is low in relation to then one should

engineer takes a sample of 10 batteries and calculates a sample variance of 1 3 hr2 Find a 99 confidence interval on the population variance o 0 b A school district wants to evaluate the effectiveness of a new teaching method for improving students math scores A sample of 25 students is randomly selected and their math scores are measured before and after the new teaching method is implemented The sample standard deviation of the differences in math scores is 5 2 points Find a 90 confidence interval on the population variance o

In a study of 809 randomly selected medical malpractice lawsuits them were dropped or dismissed Use a 0 01 significance level to test the claim that mos medical malpractice lawsuits are dropped or dismissed Which of the following is the hypothesis test to be conducted OA Ho p 0 5 H p 0 5 c Ho p 0 5 H p 0 5 E Ho p 0 5 H p 0 5 What is the test statistic Z B Ho p 0 5 H p 0 5 OD Ho p 0 5 H p 0 5 OF Ho p 0 5 p H p 0 5

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line about the line x 6 209 Volume TC 3 y x x y

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSISTENT x 2y 3z 8 2x 4y6z 16 3x 7y 2z 31 x y z

Solve the system of linear equations If the system is dependent express your answer in terms of t where x x t y y t and z t If the system is inconsistent enter INCONSIS 2x y 3z x y z x 17 7z 18 3x 2y z 20

State the dimension of the matrix 612

A matrix is given in row echelon form 1 0 2 4 1 2 5 14 0 0 1 4 a Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x y and z 5 14 b Use back substitution to solve the system x y z

1 to 2 2 to 5 3 to 1 1 to 1 5 to 1 5 1 52 8 11 5 4 3 2 1 1 2 5 2 2 figure The points of each preimage are represented by circles and the points of each image are represented by squares

8 Determine the scale factor of the geometric figure The points of each preimage are represented by circles and the points of each image are represented by squares 1 to 1 Sto 2 2 5 to 0 2 to 1 1 25 201

4 A reporter from the Sacramento Bee claims that more than 14 of California workers say it is likely they will quit working this year In a simple random sample of 250 California workers 18 said it is likely they will quit working this year At the significance level of 5 is there enough statistical evidence to support the report s claim Simple Random Sample Requirements 1 2 3 P 14 P214 Step 1 State the hypothesis Ho P 14 P 14 Tall Ha n 250 Step 2 Draw your distribution and find critical number s Step 3 Compute the test statistics Step 4 Make a Decision Step 5 Summarize the result Restate the level of significance and discuss the claim

There is a line through the origin that divides the region bounded by the parabola y 8x 3x and the x axis into two regions with equal area What is the slope of that line

m Determine the power output of a certain speaker if the intensity is approximately 0 0782 and the distance from the center of the sphere is 5 meters Round your answer to 3 decimal places Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Provide units

A portable boombox advertises a sound output power of 50 Watts W Determine the intensity in W m and in decibels for a person who is standing 4 meters from the boombox Round your answer to 3 decimal places Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work

Exercise 6 6pt Detrmine derivatives of the following functions a f x x e b f x ln 5x 2 COS I c f z d f x sin f x 9 x I

5 Rewrite each expression as a single logarithm a 5 log x log 2y 3 4log 3z 2 b 4lnx ln x 3 3 log x 1 c logx log 4x 3 2 log 5x 1

Determine the phase angle by which v1 t leads i2 t where v1 t 4 sin 377t 21 V i2 t 0 1 sin 377t 79 A Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degrees Do not include units in your answer Make sure your final answer is between 180deg and 180deg ex 5 is entered as 5

Calculate the current across the capacitor shown in Fig P8 6 if the voltage input is v2 t 22 sin 159t 245 V i t v t C 1 F Figure P8 6 For a current i t C cos wt P enter the value of the phase angle P be sure that your answer is between 180deg to 180deg Notes on entering solution Enter your solution in degree Have your current in cosine format Do not include units in your answer ex 5 is entered as 5

Find the volume of the solid whose base is the region bounded by y x y 1 and the y axis and whose cross sections perpendicular to the y axis are equilateral triangles 3 3 Volume

Tiffany purchased a 10 000 13 week Treasury bill that is paying 2 25 What is the effective rate on this T bill 2 2 2 7 2 26 2 0 None of these

With a mortgage of 48 000 for 15 years with a rate of 8 what are the total finance charges 34 567 80 5 023 68 545 76 54 576

On March 12 Bill Jones accepted a 12 000 note in granting a time extension of a bill for goods purchased by Ron Prentice Terms of the note were 13 for 90 days On April 24 Bill could no longer wait for the money and discounted the note at Able Bank at a discount rate of 14 The proceeds to Bill is O 12 047 90 12 163 54 12 390 00 12 048 90

The graph below shows a transformation of y 2 7 6 5 4 3 2 1 5 4 3 2 1 t 2 3 4 5 6 Write an equation of the form y a 2 c for the graph above f x

Given a mortgage of 48 000 for 15 years with a rate of 7 what are the total finance charges 29 659 20 5 023 68 545 76 54 576

The infinitely long region bounded by the graphs of y 0 x 0 and y e axis 6x is rotated around the x The volume of the resulting solid is

The graph shows a unit circle with point Pat O X P 13 13 Enter the exact values or DNE if the value is undefined Secant of XOP Cosecant of XOP Cotangent of ZXOP

Marsha Terban bought a home for 119 000 with a down payment of 19 000 Her rate of interest is 5 1 2 for 30 years The balance of the mortgage at the end of the first month is 3 33 98 944 99 669 76 99 890 54 None of these

Dan Miller bought a new Toyota truck for 28 000 Dan made a down payment of 6 000 and paid 390 monthly for 70 months The total finance charge was 13 300 5 300 11 300 27 300 None of these

Graduated payments result in the borrower paying More at the beginning of the mortgage Less at the beginning of the mortgage Less at the end of the mortgage The mortgage at 1 2 the standard rate O None of these

Amanda Chin purchased a home for 296 000 she put 20 down with a mortgage rate of 6 for 30 years What is Amanda s monthly payment 1 776 1 402 1 240 80 1 419 74

An amortization schedule shows Balance of interest outstanding The increase to principal Increase in loan outstanding Portion of payment broken down to interest and principal None of these

A simple discount note results in Lower interest costs than a simple interest note Same interest costs as a simple interest note Interest deducted when note is paid back Interest deducted in advance None of these

A 120 000 5 200 day note dated June 6 is discounted on October 8 The discount period is 124 days 76 days 142 days 67 days None of these

A credit card company claims that the mean credit card debt for individuals is greater than 4 900 You want to test this claim You find that a random sample of 37 cardholders has a mean credit card balance of 5 046 and a standa deviation of 650 At a 0 01 can you support the claim Complete parts a through e below Assume the population is normally distributed Use a comma to separate answers as needed Round to three decimal places as needed Determine the rejection region s Select the correct choice below and fill in the answer box es within your choice Round to three decimal places as needed OA t t and t U OC t 2 435 c Find the standardized test statistic t t 1 37 Round to two decimal places as needed d Decide whether to reject or fail to reject the null hypothesis OA Reject Ho because the test statistic is not in the rejection region OB Fail to reject Ho because the test statistic is not in the rejection region OC Fail to reject Ho because the test statistic is in the rejection region n Reject Ho because the test statistic is in the rejection region B

Keith needs 5040 for a future project He can invest 3000 now at an annual rate of 6 2 compounded semiannually Assuming that no withdrawals are made how long will it take for him to have enough money for his project Do not round any intermediate computations and round your answer to the nearest hundredth

2 Consider the language L amb2mc m n 0 m odd n even Is this language context free If it is give a GRAMMAR that accepts it else prove it s not a CFL

5 The order is Ampicillin 500 mg in 100 mL of 0 9 Normal Saline IVPB The order is to administer the IVPB over 45 minutes Your tubing delivers 12 gtts mL How many mL hour should the IV pump be set 60mix 9 m2 125 100 me mt What is the correct rate of the infusion in gtts minute 45 The 72000 IL 00 mL

Complete the following table Use Table 15 1 Note Round your intermediate calculations and final answer to the nearest cent First Payment Broken Down Into Selling price Down payment Amount mortgage Rate Years Monthly payment Balance at end of month Interest Principal 120 000 5 000 6 50 30

Joan of Arc helped to relieve the siege of Orleans Paris Agincourt Reims

Translate each of the following sentences about the beans in the bowl using the given translation key Domain The world and everything in it J x x is a jellybean i e one of those in the pictured bowl R x x is red G x x is green B x x is black NOTE Click here for info on typing symbols and formulae in activities Question 8 If some of the jellybeans are black then none are red Question 9 Some of the jellybeans are not black Question 10 4 points 4 points

Twenty sections of bilingual math courses taught in both English and Spanish are to be offered in introductory algebra intermediate algebra and liberal arts math The preregistration figures for the number of students planning to enroll in these bilingual sections are given in the following table Use Webster s method with d 29 6 to determine how many bilingual sections of each course should be offered Course Enrollment Introductory Algebra 120 Intermediate Algebra 282 Liberal Arts Math 186 Course Number of Apportioned Sections Introductory Algebra

A large hotel chain needs to apportion 28 new staff members among three hotels based on the numbers of rooms in each hotel as shown below Use the table to answer parts a and b Hotel A B C Total Number of rooms 308 218 286 812 a What is the standard divisor 29 Type an integer or a decimal rounded to the nearest hundredth as needed b Find each hotel s standard quota The standard quota for hotel A is 10 62 Type an integer or a decimal rounded to the nearest hundredth as needed The standard quota for hotel B is

A resort management company plans to apportion 58 new beach umbrellas among four resorts based on the number of rooms in each resort as shown in the table Determine each resort s apportionment using Jefferson s method Hint Some divisors between 10 and 11 will work Resort A B C D Total Number of Rooms 93 105 137 265 600 Resort A Number of Umbrellas 9 Type an integer Resort B Number of Umbrellas

7 Ana and Baker are on opposite sides of a tall tree Anna is closer and measures the angle of elevation to the top of the tree to be 74 and Baker measures an angle of elevation of 43 If Ana and Baker are 50 meters apart how tall is the tree to the nearest meter