Mathematics Questions and Answers May 03, 2023

Let T 2 1 1 0 2 3 0 3 Let w and denote I3 (c) Express an arbitrary vector v nation of eigenvectors of T. (a) i). Calculate det (TxI3) for any x to find the characteristic polynomial of T ii). Determine the eigenvalues of T. (b) Find an eigenvector of T associated with each of the eigenvalues of T. 6 1 0 0 0 1 0 01 1 (a) Show that ATWA

Find the area enclosed by the given parametric curve and the xaxis. 3 x t 1, y 2t t YA 0 x sin t, y sint cos t, 0 t 2 YA X 0 X

Find the derivative. f(x) 2ln(x 6) Samples for typing similar answers 8 For writing 3e. type 3ex8x X For writing. Question 2 8x x42 Find the derivative. In(x) f(x) 6x type 8x3(x42) Samples for typing similar answers 8 X For writing 3 ex. 8x x42 type 3ex8x For writing type 8x3(x42) For writing 2xIn (8x) type 2x3ln(8x) x42 For writing type

Find the velocity of the scooter between the following (a) t 0 and t 1 i (b) t 1 and t2 (c) t2 and t3 81 feet per second feet per second feet per second,The figure below shows the distance, s(t), in feet of a scooter from home at time t seconds. feet 3 3 12 s(t) (seconds) 3

Consider the function f(x) (x 1) ln(x). (a) Find a formula for the Taylor series of the function f(x) about the point c 1. (b) Compute the interval of convergence of the Taylor series. (c) Suppose p4(x) denotes the Taylor polynomial of degree 4 for f(x) about the point c 1. What is the error in approximation for p4(x) at the point x 2

Find the value by substituting the given value of x into the polynomial P(x)=3x^(3)+4x^(2)+x-1;P(-2)

Instructions Use the interactive tool to plot Lorenz curves for the information in the table. Cumulative of Population Cumulative of Income, United States, 2010 Cumulative of Income, Argentina, 2010 0 0 0 20 5 4 40 15 13 60 29 28 United States data from Census.gov, beforetax income, rounded to 1100ths. Data for Argentina from WorldBank.org,

The below equation defines a function of x. f(x)=7x-4 If (3,g) is an element of the function, what is the value of g?

Solve the below expression: (3 x 2 + x 3 + 6 + 5 x ) ( x + 1)

What are the roots of the below polynomial equation? x^(2)+x-72=0

Solve and simplify the below equation x^(2)-14x+65=0.

Consider the functions below. ((x)1 g(x) 7x Determine the domains of the following. Use a graphing utility to verify your results. (Enter your answers using interval notation.) (a) Domain of f (b) Domain of g x x (c) Domain of fog

Write the given function in the form y k (h(x)) for some function h(x). Do not modify h(x) from what is given in the function below. 17 5 1 y k h(x) p 10

a. Use the table of regression results to answer the questions below (12 point each) Lefthanded Age Agesquared Constant I D.V. Wages 1,030,250 (53,649) 76,100 (33,126) 2,420.654 (1625.030) 2,050,090 (701,025) 623 Observation Standard errors in parentheses II D.V. Log(wages) 0.065 (0.004) 0.016 (0.010) 0.002 (0.002) 0.105 (0.080) 623 i. What is the

Suppose that a 3x3 matrix A factors into a product 1 0 0 U11 U12 U13 (963) 121 1 0 0 422 423 131 132 1 00 133 Determine the value of det(A).

then 060 5 e det b 5 C 5 f a a det b P 2 d 12 e 0 f and 1 d a det b 1 e 1 f 4, and det a 1 d 62 e 1, 3 f

Divide below expression and give the answer in the form of quotient +( remainder )/( divisor ) (4x^(3)-4x^(2)-14x+22)/(2x^(2)-8).

The sample space for rolling a sixsided die is S 1, 2, 3, 4, 5, 6. To answer the following questions, enter your answer in each box in the form of a simplified fraction such as 12, 23, and so on. a) What is the probability of obtaining 4 b) What is the probability of an outcome larger than 3 c) What is the probability of an outcome that is no

The sample space for tossing a coin three times is SHHH, HHT, HTH, THH, TTT, TTH, THT, HTT Note 1 In your answer that is to be entered in the box below, please do not omit the 0 that comes before the decimal point that is, enter decimal values as 0.561, not 561 Note 2 Enter your answer without rounding it. a) What is the probability of obtaining

The data a11 4, a12 3, a13 19, a21 231, a22164, 023 283 which is represented in the following table, were derived from a study of the effectiveness of a flu vaccine. the value in each cell of the table represents the number of individuals in that category. Some participants in the study were given no vaccine, some were given one injection, and

A college sends a survey to selected members of the class of 2019. Of the 2,156 people who graduated that year, 652 were women, of whom 172 went on to graduate school. Of the male graduates, 129 went on to graduate school. An alumni member is selected at random. What is the probability that the alumni is female Note For any final answer that has

Evaluating (68w)(2w therefore dp (68w)(2w 3w 7)dw 3w 7)dw we make the substitution p . The integral later transforms to 2 C. dp. Hence

(a) If a and b are odd integers, Prove that a4 64 is divisible by 16.,2. Use induction to show that n k1 k 3 k(k 1)(k2) n(5n11) 4(n 1)(n2) for all positive integers n.

Use synthetic division to divide x^(3)-3x^(2)+x-8 by x-1. What are the quotient and the remainder?

Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?

Melanie's bedroom walls are 45% painted. The area of her walls totals 420 square feet. What is the number of square feet of Melanie's walls that still need to be painted?

Find the range of the below quadratic function. y=2x^(2)+8x+9

A cylindrical vase has a circumference of about 62.8 centimetres and a height of 33 centimetres. To the nearest cubic centimetre, How much water will the vase hold?

For the below expression: (12x^(2)+7x+12)-:(4x-3) (a) Use long division to divide. (b) Identify the dividend, divisor, quotient, and remainder

You are knitting a blanket. You want the area of the blanket to be 24f^(2). You want the length of the blanket to be 2ft longer than its width. What should the dimensions of the blanket be?

The average depreciation rate of a new boat is approximately 8% per year. If a new boat is purchased at a price of $75,000, which model is a recursive formula representing the value of the boat n years after it was purchased?

Shakira went bowling with her friends. She paid $3 to rent shoes and then $4.50 for each game of bowling. If she spent a total of $21, then How many games did Shakira bowl?

Abdoulaye has 66m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 272 square meters. Solve for the dimensions (length and width ) of the field.

Blake and Anthony have a snail race. Blake's snail move 1.5*10^(-3) centimetres per minute. Anthony snail moves 3.5*10^(-4) centimetres per minute. How much faster is Blake's snail racing than Anthony?

Duhail Complex averages about 15% of Bananas spoil before they can be sold. The manager purchases 200kg of bananas for 2.03QR per kilogram. What is the selling price if there is a 45% markup on the selling price?

Gregory can buy 4 pounds of wheat flour for $8 and 5 pounds of rye flour for $20. He has $12 to spend on a flour mixture. What linear equation in standard form can Gregory use to model the situation?

A twin-engined aircraft can fly 672 miles from city A to city B in 3 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

A baseball is hit in the Rogers Centre. After traveling a horizontal distance of 400 feet, it barely clears the centre field wall, which has a height of 10 feet before hitting the ground 420 feet from where it was hit. Considering the ground to be the x-axis, and the height of the ball to be on the y-axis, Determine the equation of a quadratic

Yolanda's assignment is to read at least 45 pages of a novel. Yolanda has read 28 pages. How many pages p does Yolanda have left to read? Write an inequality that represents this situation. Then solve the inequality.

The tip jar at a sandwich shop has been found to have a dollar value 0.65h+1.25, where h is the number of hours since the shop opened. a. By how much is the value of the tip jar increasing per hour?

Find the speed of each biker, then order from slowest to fastest. This equation relates the time, t, in hours to the distance travelled, d, in miles for Chris's bike ride: d=13.75t Dakota bikes 90 miles every 7 hours.

The chess club consist of 6 junior secondary students and 8 senior secondary students. Three junior and four senior secondary students are chosen for the inter school competition. In how many ways can this be done?

The Saad family is setting up for their annual New Year's party. There will be 143 adults and 62 children coming in th evening. Each table holds 15 people. How many tables will they need for all guests?

Two joggers, one averaging 9mph and one averaging 6mph, start from a designated initial point. The slower jogger arrives at the end of the run 40 minutes after the other jogger. Find the distance of the run.

Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?

David and Keith are route drivers for a fast-photo company. David's route is 80 miles, and Keith's is 100 miles. Keith averages 10mph more than David and finishes his route 10 minutes before David. What is David's speed?

Question Nancy has two daughthers, namely Nia and Cia. Cia is 5 times as old as Nia now. Nancy is 4 times as old as Cia now. In 5 years, Nancy will be 3 times as old as Cia. How old is Nia and Cia now?

The cost of a ticket to the circus is $14.00 for children and $38.00 for adults. On a certain day, attendance at the circus was 1,200 and the total gate revenue was $36,000. How many children and how many adults bought tickets?

Vincent is charged a late fee of $0.90 for returning a DVD 6 days late to the library. The late fee is directly proportional to the number of days the DVD is late. How much would Vincent be charged for returning a DVD 11 days late?

Christina is trying to save money in her bank account. She decides that she can deposit $1000 each month into the account. The account earns 2.3% interest each month. How much money will be in the account after one year?

Company A has three times as many customers as company B. Company C has 10 customers more than company B. Let x represent the number of customers held by company B. What is the expression that represents the total number of customers held by all three companies?

A clothing retailer sells 120 jackets when the selling price is $76 per jacket. Research indicates that for every $2 decrease in selling price, they will sell 5 additional jackets. What selling price will maximise the revenue? What is the maximum revenue?

David is selling floral arrangements. Each arrangement uses 1 vase and 12 roses. Each vase costs David $2.00. Let C be the total cost of the arrangement and r be the cost of 1 rose. Which equation should David use to find the total cost of each arrangement?

During the period 2010 to 2013 there was a mean number of 3600 patients waiting on a heart transplant with a standard deviation 365 patients. What is the approximate percentage of people waiting for a heart between 2505 and 4695 patients?

Suppose that a random variable Z has a standard normal distribution. Use a standard normal table such as this one to determine the probability that Z is between 0.67 and 1.67. Give your answer in decimal form, precise to at least three decimal places. P(0.67 Z 1.67)

a. How many portfolios are possible? b. How many of these portfolios contain MRK but not PFE? c. How many of these portfolios contain at most one stock priced above $60? Dogs of the Dow The Dogs of the Dow refer to the stocks listed on the Dow with the highest dividend yield. Exercises are based on the following table, which shows the top 10

Symbol T VZ MRK PFE JNJ INTC KFT DD CVX MCD Company ATT Verizon Merck Pfizer Johnson Johnson Intel Kraft DuPont Chevron McDonalds Price 29.46 37.52 34.47 20.08 64.86 24.75 35.48 49.81 108.86 94.60 Yield 5.84 5.20 4.41 3.98 3.52 3.39 3.27 3.29 2.87 2.58

Design two number cubes so that the sum of the cubes will certainly be greater than 6, and about 70% of the outcomes will have an even sum. a. Generate all the possible outcomes. b. Find the percentage that generate an even sum. c. Explain how your design satisfies both conditions.

Let F2 0, 1 with the usual arithmetic modulo 2. The set F2 0,1 consisting of all nbit vectors (vectors of length n with entries 0 or 1) is an ndimensional vector space over F2, with the standard basis for example. Linear algebra in F2 as a vector space over F2 works just like linear algebra in R as a vector space over R, except that linear

a.Identify the class width, the class midpoints, and the class boundaries for the class 150 - 199. b.Construct a corresponding histogram for the weights of eggs (title and labels). c.Describe the shape of the distribution of the histogram for the weights of the eggs. d.If a relative frequency distribution were constructed for the weights of the

1) A power supply manufacturer claims the output voltage of one of its products has a mean value of 300 V with a standard deviation of 2.0 V, normallydistributed. A particular application demands that any power supply whose voltage is less than 297 V or greater than 303 V be rejected. Determine the probability of rejecting a power supply from this

What is the 5% VaR over a 2-month horizon of $5 million invested in a fund whose annual returns in excess of the risk-free rate are assumed to be normally distributed with (annual) mean 7% and volatility 20%?

If bar (CS)=x, bar (DS)=10, bar (RS)=x+1 and bar (AS)=3, Determine the lengths of bar (SR) and bar (CR).

Members of a book club only read the following mysteries, graphic novels andor epic fiction. Denote the events of reading mysteries, graphic novels and epic fiction as M, G and E, respectively. Suppose P(M) 0.6, P(G) 0.4, P(E) 0.3, P(MNG) 0.2, and no one reads both graphic novels and epic fiction. (a) Find P(MUG) (b) Find P((MnG)U(MNE)) (c) Are

1. An integrated circuit factory has 3 machines, namely, A, B and C. One integrated circuit produced by each machine is tested, which is either pass or fail, denoted by P or F, respectively. An observation is a sequence of 3 test results corresponding to the circuits from A, B and C. For example, the observed sequence PPF means that the circuits

Find the shape of the surface in a horizontally accelerating fluid container Hint Assume a fluid static case (i.e. after a steady state is reached). Lets place the origin of the coordinate system at the location where water surface meets the side of the container on the left (see the figure below). Lets consider that the liquid surface is given by

For the spring assemblage shown in Figure 212, obtain (a) the global stiffness matrix, (b) the displacements of nodes 24, (c) the global nodal forces, and (d) the local element forces. Node 1 is fixed while node 5 is given a fixed, known displacement 8 20.0 mm. The spring constants are all equal to k 200 kNm. Prinsvinvinovnt Figure 212 Spring

A fixed-fixed beam is configured in a test setup in order to find out the principal strains using Rosetta strain gauges. 91 results are obtained under fixed test conditions yielding an average strain of E = 1040. A precision uncertainty pf P_e = 42 at 95% confidence level is found using the statistical analysis of the test data. The bias

An article of faith among Democratic Party strategists (and a source of apprehension among Republican strategists) is that high voter turnouts help Democratic candidates. Why should this be the case? According to the conventional wisdom, Democratic electorates are less likely to vote than are Republican voters. Thus, low turnouts favour Republican

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 51 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) What percentage of the widget

You measure 30 textbooks' weights, and find they have a mean weight of 72 ounces. Assume the population standard deviation is 4 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight . Give the answers as decimals, to two places

Political scientists use correlation analysis to better understand and measure multidimensional concepts. Consider, for example, why people prefer one political candidate to another. Agreement on issues is one factor, but we also prefer candidates with the right temperament, that we can relate to, and that we can trust. When it comes to measuring

For n 25 independent observations from a normal population whose true mean u and true standard deviation o are both unknown 1. How many degrees of freedom does the relevant Students t distribution have (1 point) 2. Construct a level C95 confidence interval for the unknown meanu (2 points) 3. Compute (as numbers) the endpoints of the confidence

The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 48 and a standard deviation of 11. Using the empirical rule what is the approximate percentage of light bulb replacement requests numbering

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with = 95.9 ft and = 33.6 ft. You intend to measure a random sample of n = 122 trees. Required: What is the mean of the distribution of sample means? = What is the standard deviation of the distribution of sample means (i.e., the

If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is aX aX. X mit O 0 a1 X 92 a. Suppose that X and X are independent rvs with means 2 and 4 kips, respectively, and standard devia tions .5 and 1.0 kip, respectively. If a 5 ft and a 10 ft, what is the expected bending

Express numbers as integers and simplify the below fractions. x=-(1)/(5)y+12 10x+2y=15

The quantity z varies jointly with x and y and inversely with w When x=-7, y=9, and w=-9,z=49. Find z when x=10,y=-12, and w=4.

Selling price per uint 50 Unit manufacturing cost 15 Sales commissions 10% Shipping cost per unit 1 What is the variable cost per unit?

A gardener has 43 feet of fencing to enclose a rectangular garden that has a 2-foot-wide border around it (see the figure). Use this information to answer the below questions. (a) If the length of the garden is to be twice its width, what will be the dimensions of the garden? Length = Width = (Round to the nearest tenth as necessary.) b. what is

Find the present value for a $80,000 investment for 13 years at a compounded continuously at 3.3%.

Two trains going in opposite directions leave at the same time. Train B travels 25 mph faster than train A. In 5 hours the trains are 575 miles apart. Find the speed of each The speed of train A is

Solve the below equation, x^(3)-7x^(2)-2x+8=0.

406 The following results for a wastewater sample were determined at 20C. For a sample (to be selected by instructor) determine the ultimate carbonaceous oxygen demand, the ultimate nitrogenous oxygen demand (NOD), the carbonaceous BOD reactionrate constant (k), and the nitrogenous NOD reactionrate constant (k). Determine k(0 1.05) and k,(0

Considering the Newman projections shown, choose the number corresponding to the correct energy level of each conformer AC. 3 C A B A H H H Br CH3 CH3 B H3C H H Br CH3 FH C H H H3C Br CH3 FH 2 60 5 w 6 4 120 180 240 300 360

The speed of the rivers current is 6 mph. If a boat travels 22 miles downstream in the same time that it takes to travel 10 miles upstream, find the speed of the boat in still water. The speed of the boat in still water is

The demand equation for a certain product is given by p 112 0.085, where p is the unit price (in dollars) of the product and az is the number of units produced. The total revenue obtained by producing and selling z units is given by R zp. Determine prices p that would yield a revenue of 7020 dollars. Note Round the prices to two decimal places.

The sound level b in decibels is given by b = 10 log (I / Io), where I is the intensity of a given sound and Io is the minimum detectable intensity. How many times more intense is the sound of a typical food processor at 86 decibels compared to that of a typical alarm clock at 70 decibels?

A movie theater has a seating capacity of 197. The theater charges 5.00 for children, 7.00 for students, and 12.00 for adults. There are half as many adults as there are children. If the total ticket sales was 1428, How many children, students, and adults attended children attended. students attended. adults attended.

Let 1, 2, 3 be a given positively oriented ON base in space. Define a new basis f1, f2, f3 by e e2 z e3, f2 ze ze2 z e3 f the conditions f3 3. Show that f1, f2, f3 is also an ON basis. (This reasoning does not need to be submitted). Further calculate the determinant of the transition matrix T. det(T) ( ). Is this base positively or

Consider the below data set. Round your answers to the nearest hundredth as needed. 124 124 119 107 124 98 101 96 86 105 Mean = Median = Mode = Range =

Determine the mean, median, and mode of below data set: 111.8 135.4 116.4 135.4 117.6 100.6 97.7 105.8 135.4 124.1 Mean = Median = Mode =

Please help me with this problem -4 (1 point) Find the LU factorization of A = a 12 0 -3 -4 2 A = -3 0 . 4 -1 -2 -1 0 -4 To solve the system -3 -4 2 9 9 8 X= -12 6 12 -7 -21 using the LU factorization, you would first solve 9 Ly = 12 -21 and then solve UX = Find the solution X =

Assume that you have a balance of $2000on your MasterCard and that you make no more charges. Assume that MasterCard charges12% APRand that each month you make only the minimum payment of 5% of the balance. Find a formula for the balance B after t monthly payments.

The regression equation relating attitude rating (x) and job performance rating (y) for ten randomly selected employees of a company is y=11.7+1.02x. Predict the job performance rating for an employee whose attitude rating is 67. 80.1 12.6 80.0 78.9

How many poker hands consist of one club and four cards that are notclubs? a) C(13,1) x C(49,4) b) C(52,1) x C(49,4) c) C(13,1) x C(39,4) d) C(52,1) x C(39,4) e) none

Determine the equation of the line passing through each point below having the conrreesponding slope. Linear Functions, Determining The Equation Determine the equation of the line passing through the each point below having the corresponding slope. Ordered Pair Slope Equation of the line ( - 3, 3) m = 0 (1, - 4) The slope does not exist ( - 5, -8)

A number added to the product of 20 and the reciprocal of the number equals 9. Find the two solutions. The difference between your solutions is?

You wish to invest $1,000, and you have two choices. One is a sure thing: You will make a 5% profit. The other is a riskier venture.If the riskier venture pays off, you will make a 25% profit; otherwise, you lose your $1,000. What is the minimum required probability of the riskier venture paying off in order for its expected value to equal or

I am stuck on these two questions when I working on these two, anyone know how to solve them? 1. + -/0 points WADiffEQTutBank1 5.3.008.Tut. Use the table of Laplace transforms to solve the initial value problem. y"(t) - 4y'(t) + 4y(t) = 92t, subject to y(0) = 2, y'(0) = 15 y(t) = Additional Materials Tutorial 2. + -/0 points WADiffEQTutBank1

a. Banff/Canmore splits one of the original arcs into two arcs. Which one? Report the node numbers for the two nodes that the original arc touched. b. Fort Macleod is connected to two other nodes. Which ones? Report the node numbers. c. Report the length of the longest arc and the node numbers for the two nodes that are connected by the arc. d.