Mathematics problem solving

1. (a) (2 points) In a round-robin tennis tournament with n players, every tenni

1. (a) (2 points) In a round-robin tennis tournament with n players, every tennis player plays against every other player. Let T(n) be the total number of tennis matches taking pl…

1. (a) (2 points) In a round-robin tennis tournament with n players, every tenni

1. (a) (2 points) In a round-robin tennis tournament with n players, every tennis player plays against every other player. Let T(n) be the total number of tennis matches taking pl…

1. (a) (8 marks) Find the general solution of the following system of linear equ

1. (a) (8 marks) Find the general solution of the following system of linear equations using elementary row operations on the augmented matrix 2r 572 6x3 + 2x4 = 3r 4r2 8x3 4 (b) …

1. (a) 4 squared to the third power base= exponent= (b) (-3) to the fifth power

1. (a) 4 squared to the third power            base=                           exponent= (b) (-3) to the fifth power                         base=                           expone…

1. (a) 4 squared to the third power base= exponent= (b) (-3) to the fifth power

1. (a) 4 squared to the third power base= exponent= (b) (-3) to the fifth power  base= exponent= (c) (2/3) to the fourth power base= exponent= (d) X y squared base= exponent= (e) …

1. (a) All the female students who take part in our online class can be describe

1. (a) All the female students who take part in our online class can be described as what (select the best response)? A. A Sample B. A Portion C. A Level of Measurement D. A Popul…

1. (a) By reading values from the given graph of f, use four rectangles to find

1. (a) By reading values from the given graph of f, use four rectangles to find a lower estimate and an upper estimate for the area under the given graph f from x=0 to x=8. In eac…

1. (a) By reading values from the given graph of f, use four rectangles to find

1. (a) By reading values from the given graph of f, use four rectangles to find a lower estimate and an upper estimate for the area under the given graph f from x=0 to x=8. In eac…

1. (a) Calculate the probability generating function for a random variable whose

1. (a) Calculate the probability generating function for a random variable whose value is determined by the face shown after a roll of a fair six-sided die. Simplify this using th…

1. (a) Determine the digital resolution of a 12 ppm proton spectrum collected on

1. (a) Determine the digital resolution of a 12 ppm proton spectrum collected on a 300 MHz NMR instrument. Number of data points collected for this spectrum was 1K (1024 bytes). […

1. (a) Estimate the population proportion p where a random sample of 1000 is dra

1. (a) Estimate the population proportion p where a random sample of 1000 is drawn with sample proportion .65. Find a 90% confidence interval and a 95% confidence interval Comment…

1. (a) Estimate the volume of the solid that lies below the surface z = 9 x + 4

1. (a) Estimate the volume of the solid that lies below the surface z = 9x + 4y2 and above the rectangleR = [0, 2] × [0, 4]. Use a Riemann sum with m = n = 2 and choose the sample…

1. (a) Find parametric equations for the tangent line to the curve r(t) = ti + R

1. (a) Find parametric equations for the tangent line to the curve r(t) = ti + R cos((pi)t)j + R sin((pi)t)k at the point (1, -R,0). (b) Sketch both the curve and the tangent line…

1. (a) Find the six complex solutions of the equation -240 in modulus-principal

1. (a) Find the six complex solutions of the equation -240 in modulus-principal argument form and plot them on an Argand diagram. (b) Show that (1 + cos2+ isin 2)os* 1 for n a pos…

1. (a) Form an ungrouped frequency distribution of the following data. 1, 1, 0,

1. (a) Form an ungrouped frequency distribution of the following data. 1, 1, 0, 2, 3, 2, 2, 3, 0, 2, 3, 3 Referring to the preceding distribution, answer the following questions. …

1. (a) How many ternary strings (strings of [0, 1,2)) of length 5 are there? (b)

1. (a) How many ternary strings (strings of [0, 1,2)) of length 5 are there? (b) How many ternary strings of length 5 are there that does not contain the substring 012? (Thus 2012…

1. (a) If W = the set of all days of the week, and Y is the set of all words or

1. (a) If W = the set of all days of the week, and Y is the set of all words or names that end in the letter y, how many elements are in the intersection of W and Y? (b) If B = th…

1. (a) If f(2)=2 and f(x) 5 for all x>2, then explain why f(4) 8. (b) Use the Me

1. (a) If f(2)=2 and f(x) 5 for all x>2, then explain why f(4) 8. (b) Use the Mean Value Theorem to demonstrate that if f(a) = b and f(x) d for all x > a, then f(x) d(x a) +…

1. (a) Let Y = X^3 + u where X and u are independent standard normals. Compute E

1. (a) Let Y = X^3 + u where X and u are independent standard normals. Compute E (Y | X = x): (b) Suppose we have iid observations (Xi; Yi) i=1 to n from the above model. We run t…

1. (a) Show that 0.1 and 1/3 can be written as the following binary forms: 0.1 =

1. (a) Show that 0.1 and 1/3 can be written as the following binary forms: 0.1 = (0.00011001100110011...)2 1 = (0.010101010...)2 3 (Hint: You can write the right hand binary numbe…

1. (a) State whethereach of these statements is true or false, giving brief reas

1. (a) State whethereach of these statements is true or false, giving brief reasons whythis is so (Note that no markswill be awarded for a simple true/false reply). i. When using …

1. (a) Suppose that you formulate a Linear Programme (LP) with: three deci 0 sio

1. (a) Suppose that you formulate a Linear Programme (LP) with: three deci 0 sion variables b, s and g; objective to maximise 30b +50s+80g; and ten constraints. On solving the LP,…

1. (a) Take a well-shuffled deck of 52 playing cards and start opening cards one

1. (a) Take a well-shuffled deck of 52 playing cards and start opening cards one by one from the top. How long is the expected wait till the first ace? (b) Now instead of opening …

1. (a) Tay-Sachs disease is a rare but fatal genetic disease. If a couple are bo

1. (a) Tay-Sachs disease is a rare but fatal genetic disease. If a couple are both carriers, then a child born to them has a probability 0.25 of having the disease. If such a coup…

1. (a) The Fibonacci numbers are the numbers in the following integer sequence,

1. (a) The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and are characterised by the fact that every number after the first …

1. (a) Translate the following into a mathematical statement: “For an ideal gas

1. (a) Translate the following into a mathematical statement: “For an ideal gas at constant pressure, it is known that the volume of the gas V, is directly proportional to the tem…

1. (a) Use Newton\'s Method to approximate the fixed point of the function f(e t

1. (a) Use Newton's Method to approximate the fixed point of the function f(e to an accuracy of 10-4. Choose any starting value for x0 that gives convergence. Recall, a function h…

1. (a) Use interval notation to indicate where (in that interval) the graph of g

1. (a) Use interval notation to indicate where (in that interval) the graph of g is concave up: ? (b) Use interval notation to indicate where (in that interval) the graph of g is …

1. (a) write 0.0000242 in scientific notation (b) write 5.61 x 10 -6 (ten to the

1. (a) write 0.0000242 in scientific notation (b) write 5.61 x 10 -6 (ten to the negative 6) 2. (a)Write eight ten-thousandths in scientific notation (b) Write 4.8 x 10-2 (ten to …

1. (adapted from Ross, 1.1) California has a license plate system for cars (not

1. (adapted from Ross, 1.1) California has a license plate system for cars (not including trucks) where the license plate consists of 7-places. The first place is a number; the ne…

1. (apply total probability and Bayes’ rules) A large industrial firm uses three

1. (apply total probability and Bayes’ rules) A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known…

1. (b) Use the data in the following table, which summarizes results from 985 pe

1. (b) Use the data in the following table, which summarizes results from 985 pedestrian deaths that were d aus by accidents (based on data from the National Highway Traffic Safet…

1. (based on 6.52) Write a short paragraph explaining what is wrong in each situ

1. (based on 6.52) Write a short paragraph explaining what is wrong in each situation and why it is wrong. (a) A researcher tests the following null hypothesis: H0: Xbar=23 . (b) …

1. (continued) Suppose the price of a box of Graham crackers, the price of a 6-p

1. (continued) Suppose the price of a box of Graham crackers, the price of a 6-pack of Chocolate bars, and the price of a bag of jumbo Marshmallows (in rubles) (G, C, M) jointly f…

1. (continued) Suppose the price of a box of Graham crackers, the price of a 6-p

1. (continued) Suppose the price of a box of Graham crackers, the price of a 6-pack of Chocolate bars, and the price of a bag of jumbo Marshmallows (in rubles) (G, C, M) jointly f…

1. (la , uats) When thre friends go for coffee, they decide who will pay the che

1. (la , uats) When thre friends go for coffee, they decide who will pay the check by If all three having each person flip a coin and then having the "odd person out" pay. Hips pr…

1. (note: R.V. means random There are several scenarios described below. For eac

1. (note: R.V. means random There are several scenarios described below. For each of them, do the following variable) (1) Define the R.V. that means something like, "Let X be the …

1. )A researcher is testing the effect of marijuana use on reaction time. A samp

1. )A researcher is testing the effect of marijuana use on reaction time. A sample of n = 9 students is obtained and each student is given a dose of marijuana. Thirty minutes late…

1. )A researcher is testing the effect of marijuana use on reaction time. A samp

1. )A researcher is testing the effect of marijuana use on reaction time. A sample of n = 9 students is obtained and each student is given a dose of marijuana. Thirty minutes late…

1. * The human genome contains approximately 20,000 protein-coding genes, yet it

1. * The human genome contains approximately 20,000 protein-coding genes, yet it has the capacity to produce several hundred thousand gene products. What can account for the vast …

1. *For n 2 1, let f(n) count the number of binary strings of length n that do n

1. *For n 2 1, let f(n) count the number of binary strings of length n that do not contain 011 as a substring. Among these strings, let g(n) count those which do not end in 01. (a…

1. + -12 points SApCalcBr1 5.1.001 My Notes Ask Your Teacher The table shows the

1. + -12 points SApCalcBr1 5.1.001 My Notes Ask Your Teacher The table shows the marginal cost for a company's product at various production levels. Marginal cost Marginal cost Un…

1. + -133 points DevoreStat97,E.006 My Notes Ask Your Teacher On the basis of ex

1. + -133 points DevoreStat97,E.006 My Notes Ask Your Teacher On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be no…

1. + -14 points HoltLinAlg2 4.3.001 Consider the following matrices. (To make yo

1. + -14 points HoltLinAlg2 4.3.001 Consider the following matrices. (To make your job easier, an equivalent echelon form is given for the matrix.) 1-3 21 10-10 3 8-2 Find a basis…

1. + -15 points DevoreStat9 7.E.036 My Notes Ask Your Teacher A sample of 26 off

1. + -15 points DevoreStat9 7.E.036 My Notes Ask Your Teacher A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on t…

1. + 6 points Close SE EE There are 155 good football players in the state of Oh

1. + 6 points Close SE EE There are 155 good football players in the state of Ohio. The Bears and Packers have each made up a scouting list, but 90 of these players are not on are…

1. + n3 points l Previous Answers waneFMAC7 43.002. My Notes Ask Your Teac You o

1. + n3 points l Previous Answers waneFMAC7 43.002. My Notes Ask Your Teac You own a hamburger franchise and are planning to shut down operations for the day, but you are left wit…

1. +-15 points DevoreStatg2. E.030 My Notes Ask Your Teacher A friend of mine is

1. +-15 points DevoreStatg2. E.030 My Notes Ask Your Teacher A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and …

1. +-6 points DevoreStat9 1.E.019. The number of contaminating particles on a si

1. +-6 points DevoreStat9 1.E.019. The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample of size 10…

1. +0/3 points | Previous Answers SwokATG13 8.2.007 My Notes Solve AABC. (Round

1. +0/3 points | Previous Answers SwokATG13 8.2.007 My Notes Solve AABC. (Round your answers to the nearest whole number. If there is no solution, enter NO SOLUTIO =146", a=145, c…