College Math - Others Questions

3 22 0 5 4 3 2 1 1 2 3 4 5 6 2 H 3 Identify the function whose graph appears above f x

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

8 Your parents give you 700 to spend on books and supplies for this semester Your math book is 114 your biology book is 132 your biology lab book is 50 your English books are 142 and your drama book is 44 After you buy your books how much is left for supplies 9 Which property is represented by the following equation 23 7 2 23 7 2 Associative property of addition b Commutative property of addition c Distributive property of multiplication over addition d Additive inverse and additive identity A 10 The endpoints of a diameter of a circle C on the Cartesian plane are 5 2 and 0 2 Find the circumference of the circle C 11 The scores for your math tests are 88 81 97 97 83 78 85 95 79 82 What is your average score 12 Write 30 as the product of two odd numbers and one even number each of which is greater than 1 13 On a scavenger hunt you are supposed to cover an area on a map represented by a 2 cm by 5 cm rectangle to find clues for your hunt If the scale drawing on the map is 1 cm equals 20 feet what is the area in square feet you are supposed to cover 14 Find the answer to the following 13 5x3 3x6 2 12 15 True or False a a a xa 0 b a a a a 0 c axa axa 1 d aa xa 0

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

If Rita receives 41 14 interest for a deposit earning 5 simple interest for 140 days what is the amount of her deposit Round your answer to the nearest cent X Suggested tutorial Learn It Calculate the Interest Rate the Present Value or the Time for an Investment Using the Simple Interest Formula Nood

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

2 Consider the function f x y y x 16 i Determine an equation for the tangent plane to the surface z f x y at input 3 2 ii Use part i to estimate the number 1 98 3 3 01 2 16 by hand For fun ask a machine what this number comes out to and compare to your estimate are you close

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

2 8 points Determine if T is a linear transformation T R R T x y x y x y

A matrix is give 18 9 01 a Determine whether the matrix is in row echelon form Yes No b Determine whether the matrix is in reduced row echelon form Yes No c Write the system of equations for which the given matrix is the augmented matrix Enter each answer in terms of x ar 9 7

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

The system of linear equations has a unique solution Find the solution using Gaussian elimination or Gauss Jordan elimination y z 8 x 2x 3y 2z 16 3z 4 x y z 4x y

State the dimension of the matrix 21 18

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

Find all solutions to each of the following triangles 7 A 38 a 41 feet b 54 feet 8 A 43 a 31 feet b 37 feet 9 A 112 2 a 43 centimeters b 22 centimeters 10 B 30 b 42 centimeters a 84 centimeters 11 B 118 b 68 centimeters a 92 centimeters 12 A 124 3 a 27 centimeters b 50 centimeters 13 A 142 b 2 9 yards a 1 4 yards 14 A 65 b 7 6 yards a 7 1 yards 15 C 26 8 c 36 8 kilometers b 36 8 kilometers

Problem 2 10 points Let f x x1 5 3x 22x 99 a Find the critical points of f x on 1 2

XYZ Corporation invests 6 000 into 91 day treasury bills with an interest rate of 1 6 If the broker charges a 30 commission what is the yield yield

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

Given the following voltage and current i t 5 sin 377t 57 A u t 10 cos 377t 41 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

Consider the function In 1 72 00 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms For example if the series were 3 you would write 1 322 32z 33 3z Also indicate the radius of convergence Partial Sum Radius of Convergence 7

1 Find c 0 such that the area of the region enclosed by the parabolas y x c and y c x is 90

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

A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where represents the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 What does this area represent total profit for 200 cell phones sold total profit for more than 200 cell phones sold total revenue for 200 cell phones sold for 200 cell phones cold

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

Sketch the region enclosed by y 5x y 7x and x 1 Find the area of the e region

ethane DDT pesticide in Lake Michigan has been declining exponentially for many years In 1971 the DDT concentration was 13 00 ppm parts per million In 1984 the DDT concentration was 2 22 ppm Q1 1 Part a 20 Points Use the data points provided in question 1 to determine the exponential decay function D f t Ce that models the DDT concentration in Lake Michigan in ppm as a function of t years since 1971 Define all variables Include units Round r to four decimal places Show all work Put a box around your answer Upload a PDF of your work in the correct orientation

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

Use properties of logarithms to solve for x 15 points log y 3 log 2y 2 log y A y 2 1 only B y 2 only C y 1 only D y 1 2 only E y 2 only

Use properties of logarithms to solve for x 15 points 0 log 4x 3 log7 x 2 The value of x is The value of x is A Less than 1 B Between 1 and 2 5 C Between 2 5 and 4 D Between 4 and 5 5 E More than 5 5

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

Use properties of logarithms to rewrite as a single logarithm in the form log P where P is an algebraic expression 10 points log3 x 3 log3 y 7log3 2 A logs 3x 3y 7 x B log C logs D log 1 3 x 3y 7

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

Exercise 5 13pt Find the maximal domain and all the asymptotes of the following function 2x 7 a f z 3 b f x 1612 9

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

Use the definition of the logarithmic function to find x A log5x 0 B logx 25 2 C log3 x 2 D logx 8

Evaluate the logarithmic expression by using the properties of logarithm 1 A log5 54 B logs 125 C log55 1 D logs 125 E logs 5 F 5logs 4

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

Given the following voltage and current i t 5 sin 377t 48 A u t 10 cos 377t 52 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer 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

With a mortgage of 48 000 for 15 years with a rate of 8 what are the total finance charges O 34 567 80 5 023 68 545 76 54 576 None of the