Basic Math Questions and Answers

Use properties of determinants to evaluate the given determinant by inspection 3 1 0 0 2 6 0 04

3 5 Calculate the moment about point A in Figure P3 5 A 800 lb 5 3 200 lb 4 1400 lb 7 3 FIGURE P3 5

Find the first six coefficients for which the following identity holds on some nonempty open interval including x 0 8x e 7 x Answers Co C1 C2 C3 C4 B B 8 n 0

Suppose the interval of convergence for the following power series is 7 11 Find the constants m and b Answers m b B mx b n log n n 2

Consider the power series n 1 Answer R 1 x 10 n 10 Find the radius of convergence R If R type inf Find the interval of convergence Answer in interval notation

Rewrite the following in plain terms a VxER En Z x n b 3s EQVqZq c Vn Z a Z n 2a 1 3b Z n 26

The function f x is one to one Find f1 analyticall 3 f x X

2x 4 lim x 2 x 41 desinin de eri ka t r 2 D 12 22 B 2 2x 4 4 E Yoktur

Approximate the solution s to x 4x 4 0 using a graphing utility to x 4x 4 0 is are The approximate solution s to x Type an integer or decimal rounded to the nearest hundredth as needed Use a comma to separate answers as needed

If 2 telephone poles are 100 feet apart and a wire that is also 100 feet connects them how much feet will the wire sag if we add 1 foot of slack to the wire between the 2 poles

Let 7 R R be the matrix transformation corresponding to A T v 000 ar and v 2 Find TA u and TA V where u 4 1 1 3 2

x 3 and y2 b on in order for the area betw

0 Jasmine and Eric Walton bought 280 shares of WEX stock They paid a total of 9 788 50 They sold at 23 00 per share They paid a 60 00 sales commission con

or Problems 3 8 compute a the net sale and b the profit or loss Total Selling Price Net Profit Sale or Loss Paid per Share 3 4 5 6 7 8 Stock Sargent Inc 5 200 Putman Co 10 000 Western Inc 6 760 St Clair Land 1 710 MetalCo 4 500 Harmony Inc 2 700 72 00 30 00 32 50 10 50 22 00 X 17 50 Number of Shares 100 400 200 150 300 X 110 Commission 30 00 50 00 20 00 15 00 40 00 15 00 Gemeen II a a a b b b a b a b b a

Complete the problems to find the profit or loss Check your answers in the back of the book 1 You paid 1 829 for 40 shares of JTT stock You sold the stock for 61 50 per share The commission you paid was 35 50 2 You paid 24 000 for 1 000 shares of EXO stock You sold the stock for 22 50 per share The commission you paid was 49 95

3 Bruce and Shelita Maron own 850 shares of a pizza chain s stock They originally paid 28 75 per share for the stock They needed cash so they sold at the current price of 23 40 per share They paid a 14 95 sales commission for each transaction What was the profit or loss

The function A s 6s is used to find the surface area of a cube when given the length of the sides s where s 0 What is the inverse of the area function A A s C for s 0 B A s CA s for s 0 for s for s 0

Find the Surface Area and Volume 2 8 M 3 1 M Surface Area 6 5 M 4M 3 M

Find the volume and surface area 21 ft 16 7 ft 16 2 ft Surface Area 21 ft 23 3 ft

Find the Surface Area and Volume 28 8 km 26 4 km 26 4 km Surface Area Volume 41 5 km 32 km

Find the volume and surface area of the Isosceles triangular prism 3 7 cm 3 cm Surface area Volume 4 cm 6 cm 1

Find the volume and surface area of the right triangular prism X 3 cm Surface area Volume 5 cm 4 cm 11 cm 0

The following function is one to one Find function and its inverse on the same set f x 2x 4

Find the surface area and Volume of the right triangular prism 16 cm 12 cm Surface area 20 cm 10 cm

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What scenario could be modeled by the graph of the function f t 150 1 02 A wolf population that has an initial population of 150 increases by 2 each year A wolf population that has an initial population of 150 decreases by 2 each year O A wolf population that has an initial population of 150 decreases by 0 2 each year A wolf population that has an initial population of 150 increases by 0 2 each year

Which expression is equivalent to 52 2 3 2x 3 C 4 13 4 2 2x 3 4 20 4x 6 4 132

Here are the scores of 13 students on a history test 59 60 61 61 64 66 67 69 73 76 78 83 89 Notice that the scores are ordered from least to greatest Give the five number summary and the interquartile range for the data set Five number summary Minimum Lower quartile Median Upper quartile Maximum Interquartile range Espanol 0 0 Aa

A bowl contains 6 yellow tickets and 4 green tickets Theree tickets are chosen at random from the bowl after replacing it a second tickets is chosen What is the probability of getting 2 yellow tickets on the first draw and 2 green ticket on the second draw

Problem 4 35 points Let x1 y1 x2 y2 X3 3 x12 y12 be a simple random sample from a population of bivariate data The variable X is x1 x2 x3 X12 The variable Y is y y2 3 12 The values of the terms in the sample are presented in the table below 7 is not given and you may need to find it The coefficient of determination is 0 9187 i Xi 112345 3 11 14 5 6 4 2 3 4 32 66 44 76 8 17 7 8 9 10 11 12 3 A What is the sample size n B Compute the correlation coefficient C Find the value of y7 91 y 23 54 45 49 62 89 17 33 65 81 D Hand draw the scatter plot of the sample E Calculate the least squares coefficients for the least squares line for the sample Then write down the equation for the least squares line F Predict the value of Y when the value of X is 32 i e x4 What is the residual when X is 32 G Briefly explain why we should not extrapolate a least squares line

If f x is a linear function f 5 2 and f 4 5 find an equation for f x f x

Compute the Euclidean distance between the sets of points below a 2 4 and 9 3 b 11 3 30 and 17 15 49 a The Euclidean distance between 2 4 and 9 3 is 7 07 Type an integer or decimal rounded to two decimal places as needed b The Euclidean distance between 11 3 30 and 17 15 49 is Type an integer or decimal rounded to two decimal places as needed

The lengths of adult males hands are normally distributed with mean 190 mm and standard deviation is 7 2 mm Suppose that 43 individuals are randomly chosen Round all answers to 4 where possible a What is the distribution of x N b For the group of 43 find the probability that the average hand length is less than 188 c Find the third quartile for the average adult male hand length for this sample size d For part b is the assumption that the distribution is normal necessary Yes No

Use the graph to complete problems 1 3 8 7 6 T T 8 7 9 5 3 2 7 3 2 1 0 1 2 w 5 6 7 8 y b What could be the ordered pair of point F E 1 2 3 4 5 6 7 8 C D Consider the line segment with endpoints E and F What could be the ordered pair of point E F X C What is the length of the line segment with endpoints E and F

The area between 2 0 and 2 1 79 under the standard normal curve is Area under the standard normal distribution to the left of Z page 1 O AN 3 4 33 12 3 1 10 29 28 MY 06 2002 2001 2000 4000 DOG www PORT boto 2010 HOOD 1000 2014 2014 A100 23 4000 26 00M 35 0046 34 www A900 500 Click here to view page 1 of the standerd normal table Click here to view peac 2 of the standard normal table 8500 1900 2 0 13 14 13 14 0455 0445 13 0571 14 D DY 0140 0184 1000 0004 5000 000 0411 00 00 0021 0027 2025 0000 004 0044 0006 0044 www 2015 1 23 0004 0047 23 DIND OTES 21 2143 0136 218 0110 0233 4219 0044 82944 1000 000 Core 030 030 0675 2104 90 WW 0001 0004 0004 0006 wwww www 0011 100 2021 00 29 4400 SLED 8154 0197 05 0475 0485 1000 MA 9000 005 0054 0000 Dov 0006 2011 2016 0033 0010 004 1 000 0094 trie KLIG 0200 250 0114 0322 0392 0401 19500 seve 060 4796 3721 O w 04 43 3003 0001 0004 0004 0006 100009 0012 0017 9000 BOOK 41000 0012 WIL VIDO Senza 1200 1000 0041 500 9400 0125 0163 0207 8363 3329 0409 wwwww 0023 DAX 9000 2000 0073 0015 00 6400 0129 9000 000 0166 0312 DOM 0418 0516 06180630 02 0001 000 2011 0041 0044 0017 0009 1900 T 6000 www 001 100 10 0001 0001 4000 www 0013 0016 0024 0033 0034 0041 0056 0060 01 04 0136 0174 8121 0281 www 0100 0132 0170 0017 0274 0344 0427 0435 0526 0643 4550 00 0025 0026 www 0035 0047 0062 0417 0655 1000 5000 2000 0010 www 0013 Pla 0019 0062 0107 0139 0179 0220 0267 0159 046 0546 www Area under the standard normal distribution to the left of Z p D T 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1 1 2 CL 1 3 2 0 21 2 2 2 3 2 4 2 5 26 2 7 24 2 9 01 03 04 05 04 09 5160 3219 5359 5714 3753 5000 5040 5060 5120 5199 5239 3394 5438 5478 3517 557 556 3636 5793 5832 3671 5910 349 3987 5026 6064 4103 6141 6579 6217 6255 6293 6331 6368 6406 644 6460 1064 6700 4736 6774 6608 8544 7019 7054 7008 7123 7324 7357 7349 6517 6679 7224 3257 7500 7611 2642 2673 3704 3734 7764 7501 7910 2919 7967 2995 3023 2152 7190 3454 2450 2517 2794 7823 159 3413 3106 8212 8238 8364 4504 8299 8436 0461 2465 8531 A554 264 w 4706 4749 8770 890 00 6554 AVIS 8849 www 9012 9192 www 9312 www 3412 Fo ESSAY 1996 1601 9914 1459 6050 3066 1620 1990 LOVE 2006 100 9641 9649 9713 9719 www 8712 9801 9821 9826 www 930 19046 1950 to 9066 9049 www www 9222 9996 9953 9920 9940 9955 1965 196 9974 0975 9982 9981 1994 6299 509 www wwww pleas m 9857 3573 959 9776 4283 9830 2008 3000 we WHA 9474 5484 5434 9042 IMG www 32346 wie Bots V 2 9726 9712 768 9824 9671 9901 www 2266 VOOR 8729 4925 www 3231 3251 9582 9495 9922 9925 9943 9945 1921 9956 9467 9967 9968 9976 9962 Lese the 300 9115 245 3104 2005 50542 0416 MAY 4738 9744 9793 9790 98039 9642 98 5 9878 www 9904 619 www www 4051 Fire 9331 9279 ww 901 wwwww HOW www wwww 90 9803 9929 19946 9959 9960 www 3970 9971 9977 3979 279 9964 9964 1966 5666 6025 195 2074 416 8790 2000 9147 07 2600 www 9446 9001 9584 www 9906 9909 9911 Cose 9418 9429 9525 www 9535 M 9028 4106 AMS 8590 DIRE 2016 3625 eces 2007 9015 9163 REF 9306 9319 Spe 3767 1817 1457 9647 490 1993 9916 9931 P932 MAA 9948 9949 9962 9972 9973 9979 9960 3901 2941 9934 1936 395 9952 9964 1974 www 3761 9812 MIOK 9950 h 3954 How 7549 7852 1965 8133 8107 ww 9699 3706 www LZW www LIVE www 0545 302 M631

abisbrale T 2387 LRA BAM Talk About It A classmate let w epresent the unknown hole and set up the quivalent ratios 60 Is this 100 ethod valid Why ght this method not the most antageous one to in this case back from 60 to 10 Then scale forward from 10 to 100 x10 Number of Students 19 Percent 10 banquet namun san Number of Students Percent 6 6 114 60 Number of Students Percent WTO 10 M 190 100 por cor Method 3 Use a double number line Step 1 Draw a double number line Draw a double number line The bottom number line represents the percent so use increments of 10 to draw tick marks and label the percents The top number line represents the part of the whole that corresponds with each percent so label the tick mark that corresponds with 60 on the bottom number line with 114 0 114 Because 60 6 10 divide 114 by 6 to obtain 19 Because scale 10 x 10 100 multiply 19 by 10 to obtain 190 So 60 of 190 is 114 0 10 20 30 40 50 60 70 80 90 100 Step 2 Find the whole Since there are 6 increments before 114 the value of each tick mark on the top number line increases by 114 6 or 19 units 0 19 38 57 76 95 114 133 152 171 190 0 10 20 30 40 50 60 70 80 90 100 The double number line shows that 100 or the whole is 190 So using any method the whole is 190 In other words 60 of 190 students is 114 students

ary The part is 90 country music songs The percent is 75 The whole the number of songs he has in his fibrary is the unknown Method 1 Use a bar diagram Draw a bar diagram with 4 equal size sections of 25 each Shade 3 sections to represent 75 Label the shaded sections as 90 songs 90 songs Percent 0 Method 2 Use equivalent ratios Let w represent the whole part whole now work How many songs are represented by each section Label each section on the bar diagram How many songs are represented by the whole 90 W 90 x30 90 120 x30 25 75 100 3 percent 50 75 Simplify 100 as 4 O using either method Landon has 75 Because 3 x 30 90 multiply 4 by 30 to obtain 120 So w 120 100 songs in his music library neck the first year of ownership a new car lost 20 of its value If the lost 4 200 of its value how much did the car originally cost e any strategy 4 200 An Think About It A classmate claims that because 75 is less than 100 Landon should have more than 90 music songs in his library Do you think this reasoning is correct Why or why not Talk About It Explain why setting up the equation relating the equivalent ratios was advantageous to use in this example

ework Represent the map to the right as a graph Use the abbreviatio Determine whether the graph in part a has an Euler circuit I a Choose the correct answer below OA MT ID WY b OR

Duante is wrapping a present that is 1 foot wide 10 inches long and 8 inche high What is the minimum amount of wrapping paper he will need

Click here to watch the video Use Euler s Theorem to determine whether an Euler path Euler circuit neither or both exist A W M OA Euler Circuit OB Euler Path OC Both OD Neither WY Choose the correct answer below

mework Determine an Euler circuit that begins and ends wi Choose a possible Euler circuit that begins and en O A A E D F E C D B F A B A E D F E D B F A E

A partial path has been provided Co B E D B A D

Find the margin of error for 96 confidence interval with standard error 5 0 4 for simple random sample size of 100 Formula 1 The margin of error m Critical Value Standard Error 2 Find critical value using step to question No 15 3 Find population Standard error using relation 5 Check Your Understanding An IQ test was given to a simple random sample of 75 students at a certain college The sample mean score was 105 2 Scores on this test are known to have a standard deviation of o 10 Construct a 90 confidence interval for the mean IQ score of students at this college Formula 1 Confident Interval of population meanu x m u X m Where margin of error m Critical Value Population Standard

5 Example 3 Finding z Scores TI 84 Plus Find the z scores that bound the middle 96 d Area A 0

Which of the following is a negation of the statement below There is a horse that can t swim O Any horse can swim O All horses can not swim O Some horses can swim Some horses can not swim

Let s R x is x is a rabbit and H x is x hops and the domain consists of all animals Which of the following is an English translation of the statement below Vx R x H x All animals are hopping rabbits O Some rabbits hop O All rabbits hop If an animal hops then it is a rabbit

Which of the following is the negation of the statemen All Americans eat cheeseburgers There is an American who eats cheeseburgers Some Americans don t each cheeseburger None of the above All Americans don t each cheeseburger

Determine which of the statements below are universal and which are existential quantifications A student in your class has a cat and a dog Everyone studies discrete mathematics All comedians are funny Some people in New York have never been to France H A Existential quantification B Universal quantification

From the list below select ALL predicates When a 2 a 2 0 O x y 1 City x is capital of y x is a positive number x 20 if x is an integer a b b a for all real a and b

From the list below choose domains for which the given statement is true Everyone is studying discrete mathematics Choose ALL that applies All students of LaGuardia All students of New York City All students in this class All people enrolled in MAT231 classes at the LaGCC All students of the Computer Science program at LaGuardia All people in the world