Mathematics Questions and Answers July 04, 2020

O Find the inverse Laplace transform, y(1) L(Y(s) for 5s2 19 Y(s) (s2 2s 5)(s 1)

Let X be a random variable which takes nonnegative values with EX 3 and EX 5. If Z X 4X 7, then find the value of m such that P(Z 48) m.

(c) Let Y be a random variable with mean 5 and standard deviation 2 and let Z 3Y 2. Then find the numbers a and b so that P(a 0.75

(b) Let Y be a random variable with EY 2 and E(2Y 1) 17. Then find the constant c satisfying P(Y 2 c)

Suppose that if 0 ).

Let Y be a random variable with the following probability distribution y 4 2 1 1 2 3 f(y) 0.10 0.09 0.16 0.12 0.13 0.21 0.19 Find the standard deviation of Y.

If the joint probability of the random variables X and Y is for 0

Suppose the probability distribution of the random variables X and Y is given by x y 2 1 3 1 0.02 0.10 0.4 0.03 1 0.20 0.01 0.04 0.03 2 0.02 0.10 0.04 0.01 Compute EY2X 1

Determine the constant k so that the following function is a valid joint density of the random variables X and Y. 6kay e3x4y for x 0, y 2 0 f(x, y) elsewhere

Introduction Early one morning in March, Jordan Buford was preparing his daily work when his boss, Olivia Anton, approached him and announced, Little Annin Flagmakers (LAF) has submitted an application for a line of credit (LOC) for April through June. I want you to prepare budgeted financial statements similar to the ones you prepared for our

Exhibit 1. Excel Data Input Section A B A B 1 Input Data (USS) 30 Selling Administrative (SA) Costs 31 Variable SA cost per unit sold US1.25 3 Budgeted Sales xpected 32 Fixed SA cost per month US63,000 4. April (units) 2,500 33 Depreciation in fixed SA cost US10,000 May (units) 6,000 34 6. June (units) 3,000 35 Other Cash Outflows 7 July (units)

Find a real number r and a vector 7 such that 7 8 xa and 717. 3D Let 1 4 and 2 2 3

(a) Find conditions on b1, b2, b3 such that 6 E spanai, a2, as. (b) Find a vector b (b1, b2, b3)T such that spanat, a, a. Let 1 1 2 b af as and B b2 1 1 3 4 7 b3

Find a parametric equation for the line of intersection of the planes 2x 3y z 11 and 4x 9y z 31

Find the equation of the plane containing the line x 1t, y 1 t, z 3 2t and that is parallel to the line of intersection of x yz 1 and r 2y z 3.

Find x, y, A E (o,00) such that A is an eigenvalue of A and X 1 is an eigenvector of A corresponding to A, where 1 2 A 3 1 2

(a) 8 marks Find an invertible matrix P and a diagonal matrix D such that A PDP1. (b) 3 marks Find P1. (c) 3 marks Use your answers to parts and (b) to compute A. Note that if you compute A by computing the product A A, then you will get zero marks to (c) 1 1 Let A 3 2 0. 0. 1

The linear operator T R R is defined by the following equation Wi 2x1 2x2 3x3 W2 x1 x2x3 w3 3x1 2x2 x3 Which of the following is correct. (a) T is not one to one. (b) T is one to one but the standard matrix for T1 does not exist. 1 (c) T is one to one and its standard matrix for T1 is 2 3 (d) T is one to one and its standard matrix for T1

Find the volume of the parallelepiped determined by t (1,0,2), (2, 1, 1) and w (2, 1, 1). (a) 4 (b) 14 (c) 6 (d) 16 (e) None of these a bcde

Let S vi, o,., Tm C R. WVhich of the following is correct. .... (a) If m n, then S must be linearly independent (b) If m n, then S must be linearly dependent (c) If m n, then S must be linearly dependent (d) If m n, then S must be linearly independent (e) None of these

Assume that X 3 is an eigenvalue of an n x n matrix A. Which of the following is correct (a) 31 A is invertible (b) The eigenvector of A corresponding to1 2 is zero (c) 31 A 0 (d) The rank of 31 A is equal to n (e) None of these

Determine which of the following is incorrect. (a) If A is an invertible diagonal matrix, then A is invertible. (b) If both A and B are invertible, then A B is invertible. (c) If A is invertible, then (A)1 (A1). 3D (d) If A is invertible, then A 0 is not an eigenvalue of A. (e) None of these

Let z1 1i and z2 2 3i. Express 1 2 in x yi form. 21 3D 3D 21 22 (a) i (0) i (c) i (d)8i (e) None of these 11 (b) i (c) i (d) 5

Local bank does not know how much of its salaries related to cheque processing are fixed and how much are variable. However, total costs have been estimated at $750,000 for processing of 1,000,000 transactions and $850,000 for processing of 1,200,000 transactions. What are the variable costs per transaction? Select one: a. $2.00 b. $0.75 c. $0.71

Orthogonally diagonalize the matrix 4 3 1 1 3 4 1 1 A I 1 4 3 1 3 4 knowing that its eigenvalues are 1, 5 and 9.

Emmas Onthe Go, a large convenience store, has to decide where in the store to put its magazine rack. The manager at Ermmas experiments with a selection of different locations, choosing a sample of days at each location. Each day, the manager records the amount of money brought in from the sale of magazines. Its possible to test whether there is a

Evaluate the limit. (If you need to use o or o, enter INFINITY or INFINITY.) sin (8 r) lim 10 tan (9 a)

Check whether the distributions D, and D2 are integrable (i) D, on R is spanned by the following vector fields W I1 e, (ii) D2 on the special linear group SL(R) A M2x2 det(A) 1 R R is generated by sin 0 V sin 8 cos e) cos 0 U

A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 2.9 hours, with a variance of 0.35. A government group conducts an independent study on the new pill, claiming that the actual variance, o of increase in sleeping time is different from the advertised variance. The government group tests 18

Chang is studying the growth of a particular type of plant. He is testing the effects of three growth factors lighting, age, and temperature. Here are the levels hes testing for each. Growth factor Levels Lighting Low, Medium, High, Very high Age 1 month, 2 months, 3 months, 4 months Temperature 20 C, 22 C He wants to find the number of ways of

It is estimated that 26 of all California adults are college graduates and that 32 of Califorria adults are regular internet users. It is also estirmated that 20 of Califomia adults are both college graduates and regular internet users. Answer the questions below. (If necessary, consult a list of formadas.) (a) What is the probability that a

Suppose that X, F, and Z are jointly.dntributed randum.vatiables, that is, they are defined on the same sample space. Suppose that we also have the following ELX) 4 E(Y) 2 E(Z) 9 Var (X)26 ar (Y)45 Var(Z) 39 Compute the values of the expressions below. 2(4 21) 0 Tar(ar) 0

A recent study at a local college claimed that the proportion, p, of students who commute more than fifteen miles to school is no more than 25. If a random sample of 260 students at this college is selected, and it is found that 75 commute more than fifteen miles to school, can we reject the colleges claim at the 0.01 level of significance Perform

Fundamental attribution error (FAE) is the terminology psychologists use to refer to the tendency of a person to overemphasize dispositional factors and to underemphasize situational factors when attributing reasons for other peoples behavior. Were interested in seeing if theres a difference in indlination to commit the FAE among groups that

Might we be able to predict life expectancies from birthrates Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter

For major league baseball teams, is there a relationship between player payrolls and gate money Here are data for each of the National League teams for the year 2000. The variable x denotes the 2000 player payroll (in millions of dollars), and the variable y denotes the mean attendance (in thousands of fans) for the 81 home games that year. The

In ongoing economic analyses, the U.S. federal government compares per capita incomes not only among different states but also for the same state at different times. For the 50 states, the sample correlation coefficient relating the 1980 per capita income and the 1999 per capita income is approximately 0.20 (source U.S. Bureau of Economic

For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. Here are the items to choose from. Choice Possible items Appetizer Buffalo wings, Cheese sticks, Chicken strips, Nachos Salad Caesar, Southwest Entree Grilled chicken, Salmon, Pot roast Side dish Corn, Pinto beans, Rice

It is estimated that 29 of all adults in the United States invest in stocks and that 84 of U.S. adults have investments in fixed income instruments (savings accounts, bonds, etc.), It is also estimated that 26 of U.S. adults have investments in both stocks and fixed income instruments. Answer the questions below. (If necessary, consult a list ot

Suppose that X, Y, wnd Z ure ontly dstrbuted randum yariables, that is, they are detined on the same sample space. Suppose that we also have the following. EX) 4 E(Z) 9 E(Y)2 Var (X)26 lar(Y)45 Var (2) 39 Compute the values of the expressions below. E(4 r) 0 For(a) 0

A fair die is rolled 4 times. What is the probabilitY of having no 3 and no 6 among the rolls? Round your answer to three decimal places. (if necessary, consult a list of formulas) n

Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, u. The managers plan to choose a random sample of completion times and estimate ju via the sample. Assuming that the standard deviation of the population of completion times is 10.1 minutes, what is the minimum sample size

Four scientists want to estimate the mean weight of fish in the same lake. To do this, each scientist randomly chose 5 fish from the lake and recorded their weights. The samples are shown in the table. (a) Fill in the sample means in the table. Do not round your answers. Sample weight (in pounds) Sample mean 1 3, 6, 6, 5, 3 2. 5, 6, 3, 4, 5 3. 6,

A toy company is going to issue new ID codes to its employees. Each code will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used. Assume that the digits can be repeated. How marny employee ID codes can be generated employee ID codes

Suppose we want to choose 2 objects, without replacement, from the 5 objects penci, eraser, desk, chair, and lamp. (if necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters (b) How many wiys can this be done, if the order of the choices does not matter

At a schools open house, Tshirts and sweatshirts were sold. Each item was purchased by either a student or a parent. The twoway frequency table summarizes a random sample of 60 items sold that night. Student Parent Tshirt 11 27 Sweatshirt 13 Let sweatshirt be the event that an item randomly chosen from among those sold was a sweatshirt. Let parent

Milan is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this Milan rolls the number cube once. He wins 1 if a 1 is rolled, 2 if a 2 is rolled, 3 if a 3 is rolled, and 4 if a 4 is rolled. He loses 2.75 if a 5 or 6 is rolled. (If

When a certain drug is administered intramuscularly the concentration in the blood at time t can be approximated by the function C(t) 50(e0.07t e0.42t) where the time t is measured in hours and C is measured in ugmL. Find the value of t at which this function reaches its maximum value. hours

Suppoe each icense platena certan state has one dut, followed by four letters, tolowed by onn digit. The letters F.O,S, and X and the dit are not used. So, there are 22 ettes and 9 digits that are used, Assume that the letters and digits can be repeated How many icense plates can be genersted useng this formar ticense plates

Suppose we want to choose 3 colors, without replacement, from the 4 colors red, blue, green, and purple. (If necessary, consult a list of formulas.) How many ways can this be done, if the order of the choices is taken into consideration (a) How many ways can this be done, if the order of the choices is not taken into consideration (b)

Melissa has a deck of 10 cards numbered 1 through 10. She is playing a game of chance. This game is this Melissa chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses 5.50 if an odd numbered card is drawn. (If necessary, consult a list of formulas.) (a)

Suppose we want to choose 2 letters, without replacement, from the 3 letters A, B, and C. (If necessary, consult a list of.formulas.) (a) How many ways can this be done, if the order of the choices matters (b) How many ways can this be done, if the order of the choices does not matter

A fair die is rolled 4 times. What is the probability of having no 3 and no 6 among the rols Round your answer to three decimal places. (If necessary, consult a list of formulas) 0.197

A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, u, of babies born during the 24 week of the gestation period. She plans to select a random sample of birth weights of such babies and use the mean of the sample to estimate p. Assuming that the population of birth weights of babies born during

Suppose we want to choose 2 objects, without replacement, trom the 4 objects pencil, eraser, desk, and chair. (If necessary, consult a list.of formulas) (a) How many ways can this be done, if the order of the choices is relevant (b) How many ways can this be done, if the order of the choices is not relevant

Choose the dependent variable (the response variable to be explained) and the independent variable (the predictor or explanatory variable). Dependent Variable Speed O Power independent Variable O Power O Speed Obtain the regression equation. (Round your answers to 3 decimal places.) Y X Calculate R. (Round your answer to 3 decimal places.) Using

Refer to the ANOVA table for this regression. d.f. 3 1,178,712 392,904 305,032 22 1,483,744 Source MS Regression Error Total 19 16,054 (a) State the degrees of freedom for the Ftest for overall significance. The degrees of freedom for regression are and for error (b) Use Appendix E to look up the critical value of Ffor a .05. (Round your answer

Consider the following data on 20 chemical reactions, with Y chromatographic retention time (seconds) and X molecular weight (gmmole). Retention Time and Molecular Weight (n 20) Retention Molecular Weight 136.24 Name Time alphapinene cyclopentene pdiethyl benzene decane 234.50 95.27 68.12 284.00 250.60 134.22 142.29 toluene 174.00 92.14 benzene

All the students in a school took a physical fitness test. Three students want to estimate the mean score for the school. To do this, they each randomly chose 5 schoolmates and recorded their scores. The samples are shown in the table. (a) Fill in the sample means in the table. Do not round your answers. Sample Score (out of 100) Sample mean 1 60,

Birth Rates and Characteristics of Nations (n = 153, k = 5) Nation BirthRate LifeExp InfMort Density GDPCap Literate Afghanistan 41.03 46.6 144.8 42.87 800 36 Albania 18.59 72.1 38.6 123.31 3800 93 Algeria 22.34 70.2 39.2 13.56 5600 62 Angola 46.18 38.9 191.7 8.50 1330 42 Argentina 18.23 75.5 17.2 13.82 12000 96 Armenia 12.00 66.6 41.1 111.75 3350

A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors LifeExp (life expectancy in years). InfMort (infant mortality rate). Density (population density per square kilometer). GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.

Choose the dependent variable (the response variable to be explained) and the independent variable (the predictor or explanatory variable). (a1) Dependent Variable Website Hits Weekly Revenue (a2) Independent Variable Weekly Revenue Website Hits O (b) Obtain the regression equation. (Negative values should be indicated by a minus sign. Round your

Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodies Company restaurants. Annual Sales Growth () and Loyalty Card Usage ( of Net Sales) (n 74 restaurants) Loyalty Growth Store Growth Loyalty 1.6 Store 2.1 7.1 7.4 7.7 7.9 8.3 38 4.0 2.5 39 1.8 3.9 1.7 40 2.2 3.4 41 2.1 2.5 2.2 2.8 3.3 42 8.1

A fair die is rolled 6 times. What is the probability that a 3 is obtained on at least one of the rolls Round your answer to three decimal places. (If necessary, consult a list of formulas.)

hIVD4E3wOMXRKjq1oBw7QYjlbavbSPXtxYCjsh O CHISQUARE TESTS, INFERENCES FOR REGRESSION, AND ANOVA Hypothesis tests for the correlation coefficient and the slope of... Emmanuel V Based on uns information, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B,. (Assume that the

Fastfood restaurants may be able to save substantial amounts of money simply by decreasing the size of the paper napkins they provide to patrons. Papel Paper Products, a major paper company hoping to infiltrate the restaurant supply market, is considering pitching the smallernapkin idea to potential restaurant Clients. To determine the

Let a be a given constant. Consider the matrix 2 a 1 3D 3 3 3 7 5 (a) Find all values of a such that det(A) 0. D (b) Find all values of a such that A is invertible.

2. Find the solution of f (x) x2 10 Cos (x) by using the fixedpoint iteration method accurate to within 104.

Let S be the universal set, where S 1,2, 3, ..., 18, 19, 20 Let sets A and B be subsets of S, where Set A 3, 6, 7, 13, 15, 17, 18, 20 Set B 3,7, 10, 16 3D Set C 1,4, 14, 15, 18, 20 LIST the elements in the set (AUBUC) (AUBUC) Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the

A partnership has the following account balances: Cash, $86,000; Other Assets, $620,000; Liabilities, $364,000; Nixon (50 percent of profits and losses), $160,000; Cleveland (30 percent), $110,000; Pierce (20 percent), $72,000. The company liquidates, and $16,000 becomes available to the partners. Who gets the $16,000? Determine how much of this

(c) Calculate the area of a region bounded by the curves y x and y x2, the line y 3, and y 2. (5 marks)

Given these points on the XY plane: (3, 4), (5, -1) (-3,-5), (-5, 3), (-1,5), find a radius of a circle centered at the origin which minimizes the sum of squared distances between each point and the circle. The distance between a point and the circle is defined as the minimal distance between the point and any point on the circle.

The loan default rate at a certain bank is 1. The bank has developed a model to try to predict which loans will default. The models predicted positive rate is 3 99 of the loans that default are predicted as such by the model. If a model predicts that a loan will default, what is the probability that it will actually default Submit the answer as a

i) Find the permutation matrix ii) Find the solution of the PA using the LU decomposition. ,X1 X24 X3 4 x4 1 2 x1 2 x2 4 x32 x4 2 2 x1 2 x2 X3 X42 6 xi 2 x2 2 x3 5 x4 4

Calculate Il, I2, 13, 14, 15, 16, I7, 18 and I9 currents in the following circuit as an application of solving systems of linear equations.(Y9) 17 13 11 V 15 V 3 2 2 13 V 10 V 16 14 5 6. 8 18 7 V 8 V 9 V 9 19 12 V 15

The governing equation for a projectile shot vertically upward is dy dt2 mg CVV y(0) 0 and y(0) V, where m is the mass of the projectile (kg), y(t) is the height (m), g is the acceleration of gravity (9.80665 ms2). C is an aerodynamie drag parameter, and Vdyidt is the velocity. For m 10.0kg, C0.INsm, and Vo 500.0 ms, calculate (a) the maximum

Develop the explicit Euler approximation of the linear firstorder ODE, y xy F(t). Derive the corresponding modified differential equation (MDE), including the leading trunca error term. Investigate consistency and order.

Consider the following differential equation with exact solution y(t) t(ee) 3y y t1, 0

2. Solve the differential equation xy 2xy 5y3

Iz 1. Let fU C be holomorphic. Suppose every point in the image of f lies on the curve y e x sin x if we identify C with R. 1. Let D Prove f is constant. Hint Show that we must have that f(z) 0.

sin z 2. Let f(z) Find the radius of convergence of the Taylor series of f(z) z416 at zo 1 i.

3. Let U C a,., ax . Let fU C be holomorphic. Suppose Res(f, a) 0 for all a, E a, .,ar. Prove that there is a holomorphic function FU C such that F f.

4. Find cos dx. You can assume without proof that this integral converges. 1 Indicate the contour you use to evaluate this integral.

1 elz 5. Find 2 JIzl1 z(22) dz for any natural n 2 1. Your answer should be written in closed form.

Solve the Differential Equations by Inspection (40xy21y)dx (35xy20x20xy14xy)dy3D0

Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables. (a) Calculate the tstatistic for each slope, at significance level 0.01.

Using data set E, answer the questions given below. DATA SET E Microprocessor Speed (MHz) and Power Dissipation (watts) (n 14 chips) Speed (MHz) Chip 1989 Intel 88486 Power (watts) 20 1993 Pentium 100 10 233 300 600 1997 Pentium II 35 1998 Intel Celeron 1999 Pentium III 20 42 1999 AMD Athlon 600 50 2000 Pentium 4 1300 51 2004 Celeron D 2100 73

A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors LifeExp (life expectancy in years), InfMort (infant mortality rate). Density (population density per square kilometer). GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.

Use the inverse trigonometric keys on a calculator to find the measure 37 m 30 m of angle A. C. A (Round the answer to the nearest whole number.)

This series of questions are focusing on the Debt Ratio 1 The Debt Ratio for Company A is For every 1 dollar of assets Company A purchased, equity was used to complete the purchase. The Debt Ratio for Company B is cents of debt was used and For every 1 dollar of assets Company B purchased. equity was used to complete the purchase. Which company

10 animals at a local shelter. There are 4 dogs, 5 cats, and 1 penguin. One animal is adopted to its forever home (does not return), and a second animal is adopted. Let C be the number of cats adopted. Construct a probability distribution of C. Find PrC 1.

Here is a set of data points (minus 2, minus 2), (minus 1, 0), (0, 1), (2, 2) Find the normal equation matching the set of the given data. D C Answer E ao G F H where C ,D , E ,F G , H are all integers.

1. a) Show that A (3, 0, 2), B (4, 3, 0) and C (8, 1, 1) are vertices of a right triangle. b) At which vertex is the right angle 1. 1.b 2.a 2b 3 4 5.a 5.b G 10 5 15 15 20 20 5 10

The college is planning to add a food vender in the student union and would like to know what type of food service the students would prefer. A sample of 120 students is obtained and each student is asked to select hisher preference from a coffee shop, a pizza place, or a hamburger grill. The resulting frequency data are as follows coffee pizza

2. a) Find the equation of the plane through (2, 1, 7) that is perpendicular to the line x 4 2t, y 2 3t, z 5t. 3D b) Find the vectors parallel to the plane 2x yz 4 and orthogonal to the vector i j k.

3. The total surface area S of a right circular cylinder related to the base radius r and height h by the equation S2nr2 2arh. How is ds related to dt dr if h is dt ds related to dt dr when r is halved. dt constant Find the equation of

4. Solve the following system of linear equations using the inverse matrix method. x 4 y 2z 1 3 x y z 5 3 x y 2z 6

4 3 5. a) Is 2 an eigenvector of A 3 2 If so, find the eigenvalue. 1 2. b) Find the eigenvalues and eigenvectors of 3 4 21 B 0 1 Verify that the trace equals the sum of the eigenvalues, and the determinant equals their product.

If X1, X2,.....X9 N(20, 16) P(20 X 22) then a. 0.4987 b. 0.4878 c. 0.2734 d. 0.4332

Suppose that the root are p and q (axp) (axq) 2 axbxc axbxc axbxc a(pq)x pq a ax bx c ax (p q)x pq 2 a axapxaqxpq a ax 2 Explanation Please refer to solution in this step. B

Find the value of COS given that sin a 4 6 11 b 4 6 5 6 TT and ta

a b of 27 x 2 3 dx La x 9 2 3 dx 1 x 9 C S 10 0 dx