Mathematics Questions and Answers August 24, 2018

A Statistical Analysis In the article Robbing Banks Reilly et al. studied several aspects of bank robberies. As these researchers state, Robbing a bank is the staple crime of thrillers, movies and newspapers. But . . . bank robbery is not all it is cracked up to be. The researchers concentrated on the factors that determine the amount of

Explain carefully the difference between the confidence interval and test of significance approaches to hypothesis testing

Write a corresponding null and alternative hypothesis for each research question below. Include clearly defined independent and dependent variables (measures) along with the expected relationship between them. What might be some potential confounds that you want to avoid with each research question/hypothesis in mind? How might you actively work

Pick 2 of the statistical tests that you applied to the quantitative data in your study. Paste the tables with the results from the two tests and discuss how the limitations of the study or the assumptions that you made could have impacted the results from the two tests that you have selected. See below and defined the standard deviation: Table 1:

Independent Variable X1 Education X2 Culture X3 Gender Mean 4.18 4.05 3.11 X4 Socioeconomic 3.7 X5 EthnicRacial 4.05 Median st 3 4 Mode 5 5 2 4 5 Standard Deviation,Independent Variable X1 Education X2 Culture X3 Gender PValue X5 EthnicRacial 0.48 0.67 1.52 X4 Socioeconomic 0.03 0.67 Meaning Pvalue is 0.05 Pvalue is 0.05 Pvalue is 0.05 Pvalue

You are an undergraduate student who studies linear programming in your quantitative methods course. Your parents run an agriculture business and they manage 80 acres of farm land. The firm plants maize crop and vegetables on the farm. The firm earns a net profit of 5,000$ for each acre planted with maize crop and 3,000$ for every acre of land

The following data shows the amount of money (in dollars) spent by a sample of 24 customers at the local fast food restaurant. (a) Construct a stem-and-leaf diagram using this data. (b) The restaurant believes that the average spending of customers is usually less than $25. Using your answer in (a), comment on this statement (c) Recommend and draw

37 23 17 48 14 18 29 32 19 9 42 32 14 21 26 26 25 17 100 8 19 4 21 19 6 21 9 11 0311 18

The following data shows the share prices (in dollars) of BMW in the month of November 2015. (a) Calculate the mean and standard deviation for this data. (b) Calculate the Minimum, Q1, Median, Q3 and Maximum values for this data.

Date 23 Nov 2015 20 Nov 2015 19 Nov 2015 18 Nov 2015 17 Nov 2015 16 Nov 2015 13 Nov 2015 12 Nov 2015 11 Nov 2015 10 Nov 2015 9 Nov 2015 6 Nov 2015 5 Nov 2015 4 Nov 2015 3 Nov 2015 Prices (S) 98.45 99.17 98.73 97.45 97.26 94.71 94.54 94.46 96.18 95.93 94.96 96.03 92.78 92.45 93.57

(a) An operator for a telephone-answering service answers a large number of calls for two real estate agents. The two agents are charged the same monthly fee for this service and it is assumed that they will each receive approximately half the calls coming in. Based on this assumption, find the probability that in the next 150 calls 90 or more

Discuss the importance of selecting a sample that may be considered representative of the entire population. Consider these questions: What is the first step in the process of selecting a sample? are there occasions where the sample selected does not represent the entire population? then, post on how auditors evaluate risk in relation to sample

1. As scientists conducting an experiment, you need to have an experimental group and a control group for testing a hypothesis. If you were a scientist, and with the knowledge you have, what kind of hypothesis would you test? 2. Provide an example of an experiment you might conduct. Who would be in your control/experimental group?

Solve the mathematical problem: with quadratic formula

6X 3 5 X

Write a paper identifying and commenting on the ethical issues in developing descriptive statistics, especially how measures of central tendency and dispersion can be misleading. What can be done to deal properly with these issues? Use Biblical principles where appropriate.

Examine how movement preparation is influenced by the number of response choices. Condition 1: Simple Reaction Time (One Ruler) The experimenter will hold one ruler vertically in the hand of his or her choosing at its highest point so that the 30 cm line is closer to the holding point (see Figure). The participant will place the thumb and

Partner dropping he ruler 30cm line on the ruler You trying to catch the ruler,Trial 1 2 4 5 6 7 8 9 10 MEAN Simple RT Choice RT

Answer T (true) or F (false) to the following: 1. For a normally distributed population of heights of 10,000 women, m = 63 inches and s = 5 inches. The number of heights in the population that fall between 66 and 68 inches is 1156. 2. In a normal distribution, approximately 91.31% of the area under the curve is found to the right of point 1.36

Define the following terms: Moving Average & Nave Weighted Moving Average Exponential Smoothing Trend Adjusted Exponential Smoothing Trend Projection Simple Linear Regression/Least Squares Multiple Regression Multiplicative Seasonal Model Regression Projector Error Analysis p Chart x-bar and R Charts c charts Average Outgoing Quality Process

Marcus has won a 8,000,000 state lottery. He can take his prize as either 25 yearly payments of 320,000 or a lump sum of 3,415,000. Which is the better option Assume an interest rate of 8. ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Round to the nearest dollar as needed.) A. The present

Lowes sells a snow shovel for 39.90. The dollar amount of markup on the shovel is 7.98. Round all dollar values to two decimal places and percentages to two decimals (i.e. 34.56). a. What is the cost to Lowes Answer A b. What is the markup on selling percentage A

A certain piece of machinery was purchased 4 yr ago by Garland Mills for 500,000. Its present resale value is 240,000. Assuming that the machines resale value decreases exponentially, what will it be 5 yr from now (Round your answer to the nearest dollar.) 133407 Need Help Master It

Consider the following quadratic equation 3x4x3 1082311 Step 1 of 2 Find the values of a, b, and c that should be used in the quadratic formula to determine the solution of the quadratic equation.

Solve the equation (x 10) (3x1) 7x 118 x

f(x) 9x 21x 5x 25 W Entry tip Enter the zeros (exact values, not decimal approximations) separated by commas. Question Help VIDEO Message instructor Submit Question Jump to Answer

Solve the following by factoring. x 2 + 4 x 2 1 = 0 List the answers separated by a comma. For example, if you found solutions x = 1 and x = 2 , you would enter 1 , 2 .

The blood types of 300 people are quoted as follows: 75 have type A blood, 90 have B blood type, 95 have O blood type and 40 have type AB blood. If someone is selected at random, what is the probability that this person has O blood type?

(a). (5 points) Consider f(x) tan x, for x (1, 117). Prove that f is strictly increasing. (b). (5 points) Consider its inverse, g(x) (). Prove that arctan x, defined as a function 9 R 1 g(x) 1x2 xR.,(c). (5 points) Prove that arctan is uniformly continuous in R.

g R R R R defined g(x, y) (3x2y, x) determine whether or not it is injective, surjective Fully justify your answers. Check g(x) is injective or not. Check g(x) is surjective or not.

3. Find the angles asked for from the following picture. Note that parts a, b and c are completely separate questions. That is, dont carry forward information from one question to another. a. If mAB 66, find mPAB. b. If mADB 35, find mPAB. 1 C. If MAD 130 and mAB 64, find mLAPD. a) Angle PAB b) Angle PAB c) Angle APD P B

Rewrite each dividend using compatible numbers. Then find the quotient. (a) 6414 79 (b) 74858 (c) 25575 (d) 16832

2 0 1. a. Given A compute the following, 4 1 i. A b. ii. A3 iii. A 2AI If a polynomial p(x) can be factored as a product of two lower degree polynomials p1(x) and p2(x) as p(x) P1(x)p2(x) then it can be proved that p(A) p (A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) x9, P(x) x3, P2(x) x 3.

Solve the equation. 180x3 144x25x40

Mr. and Mrs smith plan to open an RESP sinking fund for their child. They figure they need to have $121,000 till their son is 18 years old. if their sinking fund has a semiannual interest rate of 5.5%, how much do they have to contribute to the fund at the beginning of every quarter?

Given no change to the 0.8 percent chance that any women have breast cancer, and given that positive mammogram effectiveness is increased from 90% , and given that the false positive rate is decreased from 7%, what is the end result for the for the actual probability that the patient has breast cancer? Using Bayes's theorem, Please show all your

1. If 5,000 earns Php86.00 interest in 15 months, how much is the rate of interest 2. If the interest rate is 7.5 per year and the principal is Php2,500, determine the amount of interest for 20 months including the full amount. 3. How long will it take to accumulate Php3,200 to Php4,800 if money is worth 6.5 4. At what simple interest rate is

3. a. b. Solve the system by inverting the coefficient matrix and using Theorem 1.6.2 of the textbook. x2y32 0 wx4y4z 7 w3x7y9z 4 w2x4y 6z 6 Determine conditions on the bs, if any, in order to guarantee that the linear system is consistent. x12x2 x3 b 4x15x2 2x3 b2 4x17x2 4x3 b3

Graph the following function. g(x) (x 10)

1. In August 2013, a bank was offering 0.62% interest on its savings account, with interest reinvested daily. Assuming this rate of return continued for six years, how much would a deposit of $4,000 in August 2013 be worth in August 2019? (Round your answer to the nearest cent.) 2. Make An exponential model to represent the value after t years of

2 JP 2. GivenA 30, B 51 Is AB defined Calculate AB. Can you calculate BA Why (20 pts)

Let f RR satisfy (0) 1, f(1) 2, f(1) 1, (3) 0 and f(3) 0. (a) Approximate f(2) using a Hermite interpolating polynomial. (b) If C5 (R) and (5) is bounded by 4 estimate the error in (a).

Solve 4x2 11x 200 by factoring.

The order states: Give antihistamine elixir 2.5mg/kg/dose PO q4h. The patient weighs 143lbs. The drug is available as Antihistamine Elixir 200mg in every 8mL. Answer each of the following questions. a. The patient weighs kg. b. The patient will receive mg per dose? c. The patient will receive mg per day? d. The volume the nurse will administer in

There is a function f of the form .12 f(x) ax x 13 for which f(0.1) 6.06 10 and (0.9) 0.03577. Determine a and B, and assess the sensitivity of these parameters to slight changes in the values of at the two indicated points.

If the local professional basketball team, the Sneakers, wins todays game, they have a 3 chance of winning their next game. If they lose this game, they have a chance of winning their next game. a) Make a markov chain for this problem give the transition matrix. b) If there is a 5050 chance of winning todays game, what are the chances that they

Jonas' current annual salary is $70,000. Ten years from now how much will he need to earn to retain his present purchasing power if the rate of inflation over that period is 2% /year compounded continuously?

Christopher and Janai have a new grandson. How much money should they invest now so that he will have 78,000 for his college education in 18 years The money is invested at 3.8 compounded quarterly. S

Refer to the following matrices. 8397 972 19 22 6 0 1 2 A B 4 03 9 3 89 3672 5 03 1 C 10442 8 D 9 0 What is the size of each matrix A B C D X X X X

Let f a, b R be a continuous function. Show that for any c d such that c, d C a, b, there exists c, d such that 1 rd () C d f(x) dr. Use this to prove that if F(x) (t) dt, a (2) (3),then F(x) f(x), V x a, b. (4)

Comet Halley is an irregularlyshaped comet which is visible from Earth every 7576 years. For the purposes of this question, we will assume that the comet is spherical. a) Taking the diameter of the comet to be 10.6km, find the approximate volume of the comet in cubic centimetres. You may use the fact that the volume of a sphere is 4 V3r where r is

5. Solve the following radical equation. Please show all work and verify the 3 points solution. Upload a PDF of your solution. 3. Add file 3c4 4c43, c0

Perform the multiplication shown below. 2.69 6y 3

Simplify.

2 x4)2x 0x 26x 24

5. Explain why in every graph, the sum of the degrees of each of the vertices is twice the amount of edges. 6. Is it possible to have a graph with an odd amount of odd degree vertices Explain.

2. Draw a connected graph, with 7 vertices such that 4 vertices have degree 3 and 3 vertices have degree 4. 3. A mail carrier must deliver mail to this subdivision. She must make 2 passes on streets with houses on both sides, but only one pass on blocks that have houses on only one side. Draw a graph model for this situation. 4. To the right, you

4. Find the minimum values of the function f(x, y) x 2y xy, subject to the constraint 2xy22.

The figure has permieter P56. Find the value of x. The value of x is (Type a whole number.) 2 A x6 (Figure is not to scale)

Find.

13) log2 14) log0.25 4 15) log3 16) logg 4

1. Find the zeros (aka roots) of the polynomial function and state the multiplicity of each (a) (x1) (b) (x3)2(x1) (c) (x5)(x4)(x1) (d) (x5)2(x4)(x1) (e) (x5)3(x4)(x 1) (f) x(x1)(x1) (g) r2(x1)( 3) (h) (2x1) (3x4) (i) (2x1)2(3x4) (j) (2x3)2(3x 7)

The cost to produce x items is given by C (x)4x1 10 x (a) Find the marginal cost when x 10. (b) Find the average cost when x 10. (c) Find the marginal average cost when x 10. (d) Find the marginal revenue when x 10. (e) Find the marginal profit when x 10. 100 and the demand is given by p(x)log,(x1) (Round answers to the neares cent)

Simplify (3yc)3. Provide your answer below

Give the primepower factorization of each of these numbers. (a) 15 (b) 3375 (a) The primepower factorization of 15 is (c) 37,000

Find the zeros and fully factor f(x) x 5xx7, including factors for irrational and nonreal zeros. Use radicals, not decimal approximations.

a. Determine the primepower factorizations of both 105 and 189. b. Determine the set of all positive divisors (factors) of 105. c. Determine the set of all positive divisors of 189. d. Determine the greatest positive divisor of both 105 and 189. a. The primepower factorization of 105 is

The following graph shows the temperature in Nellies dorm room over a 24 h period. Temperature (C) T 25 20. 15 10 10 225 5 0 5 10 15 20 25 Time (h) Determine the equation of this sinusoidal function.

Solve for y in the equation In(54)In3 3 Solve for y in the equation 2 logy logs logly 10)

For the following function find (a) f(4), (b) f (c) f(a), (d) f and (e) any values of x such that f(x) 1. f(x)5x50x121 (a) Find the value of f(4). 1(4) (b) Find the value of f (2)(Type an integer or a decimal.) (c) Find the value of f(a). f(a) (d) Find the value of f (2)0 (e) Find the values of x such that f(x)1. x (Use a comma to separate

Evaluate the function k (x)3x 2x for the given value of x. Simplify your answer.

a) List the first 10 positive multiples of 9, starting with 1.99. b) List the first 10 positive multiples of 15, starting with 1.1515. c) Use parts a) and b) to determine the least natural number that is a multiple of both 9 and 15. a) The first 10 positive multiples of 9 are (Use a comma to separate answers as needed.)

(3) Suppose you have a loan of 196511 with annual interest rate 7.57 compounded monthly, and are making monthly payments to amortize this loan over 25 years. (a) Find the monthly payment. Use R1 (1 i)n P i (b) Find the unpaid balance of the loan after 5 years. Use y R1 (1 i)(nx),(4) Find the present value of each ordinary annuity. Payments

Let p(A) a a1 1, with companion matrix A Cnxn, show that roots of p(x) 0 are eigenvalues of A. A An1 an2 a1 ao 1 1 1 0

Let and Determine the domain of the composite function and then find the composite function. Domain Composite function () C

Consider the matrix A 231 1 0 2 0 3 3 1 0 1 6 and the vector b 2 1. Construct the augmented matrix Ab and use elementary row operations to transform it to reduced row echelon form. 2. Find a basis for the column space of A. 3. Find a basis for the null space of A. 4. Find the general solution to the linear system Ax b. 5. Can you find a vector

Let r(t) (et cost, et, et sint). Show that as t increases without bound, the curvature increases without bound, while the normal acceleration approaches zero.

Rewrite without parentheses and simplify. (3u8w) 2

Given f(x) 2x5 and g(x) x 3 find,c) f (9 ())

Solve for x. log2()log2(x4)5 x (Separate answers by a comma.) If the answer is radical use sqrt(5) to denote 5 (use the correct radicand in the problem) If the answer is a fraction then write the answer as a reduced fraction. Add Work

9(x) 2 (x 1) 2 21(x1)2, using Given A), Create a graph of (x) transformations. Label some key points. a) State the domain b) State the Range

1. Find the chromatic number of the following graphs and give the colour classes (colour class is the set of vertices with the same colour) D B 6 5 3 G H 2. Use the formula Pc(k) Pc(k)PGe(k) to find the chromatic polynomial of the following graph (take e as shown). 3. Find the chromatic index of the following graphs and give the colour classes

A critical patient needs to be transported by ground to the trauma center which is three and a half hours away. The patient is currently on a 12 liter per minute oxygen nonrebreathing mask. The transport unit can only carry Etype oxygen tanks. How many E tanks will you need to take along to make the trip safely Now, for a challenge. A concept that

Approximately 28 million people worldwide had paid subscriptions for digital music services in 2013. This was an increase from 8 million people in 2010. 3.7 Data ifpi.org a) Graph the data and determine an equation for the related line. Let d represent the number of people with paid digital music service subscrip tions and t the number of years

The high temperature for a certain day was 3 above zero and that nights low temperature was 24 below zero. Use this information to answer the questions. a) By how much did the temperature change between the day and the night b) What computation does part a) illustrate a) The temperature fell

Graph the first inequality subject to the nonnegative restrictions. 18x60y 1800, x0, y 0 Use the graphing tool to graph 18x60y 1800 and the boundary lines representing the nonnegative constraints. Click to enlarge graph

How many years will it take for an initial investment of 30,000 to grow to 75,000 Assume a rate of interest of 14 compounded continuously. It will take about investment to grow years for the 75,000. (Round to two decimal places as needed.)

Consider the probability density curve with some areas indicated. Find a) The proportion of the population is between 0 and 1. b) The probability that a randomly selected value will be between 1 and 2. c) The proportion of the population is between 0 and 2. d) The probability that a randomly selected value will be greater than 2. 1.2 Relative

Determine if a,, 5 is a solution to the following recurrence relation. Be sure to check both the initial conditions and the recurrence. an4an15an2 a 1, a 5

Multiply and simplify the following rational expression. Give your answer as a reduced rational expression. r9x14 x3 xx6x8

T Let T R R be a linear map such that 1 2 and T 3 1 1 2 0 a) (3 pts) Compute T 3 without finding the matrix A, where Tx . Ax. b) (3 pts) Determine the matrix A such that Tx Ax, for all R. c) (2 pts) Write the linear map T of x and y. x in terms For full (or any) credit, show all of your work. . You may use Matlab to find the rref of any

A car manufacturer announced that next year the price of a certain model car would increase by 4.5. This year the price is 15,123. Find the increase and the new price

A30 Q31 A31 Big Blossom Greenhouse was commissioned to develop an extra large rose for the Rose Bowl Parade. A random sample of blossoms from Hybrid A bushes yielded the following diameters (in inches) for mature peak blooms. 23 3 8 10 10 Find the sample variance and standard deviation Suppose two pizza restaurants advertise a 20minute average

Determine an orthonormal basis for the 3dimensional vector space U Span 12 4 1 4 3 32 with respect to the inner product 3 4 21 (A, B) Trace(ATB) assuming the usual operations of matrix addition and scalar multiplication. Write final answer in the form C1, C2, C3 a2 b b2 C1 C2 as a4 a3 b5 b4 b3 C5 C4 C3 where the as, bis and cis are all

Consider the relation on Z given by mn if mn is the square of an integer. is transitive. Prove that is reflexive and symmetric. Determine whether 2

Show that if ST and g TU are both surjective functions, then the composition gof SU is surjective.

Solve For x

2x7 x8 3 5 7

First, write the value(s) that make the denominator(s) zero. Then solve the equation. 18 15 3x1

(b) Consider the following linear program, max (3,4,0,0,0)x 1 1 1 0 0 40 s.t. 1 1 0 1 0 X 60 3 500 1 200 X 0 Show that x (0, 40, 0, 20, 0) is an optimal solution to this linear program. (Hint Use the vector y (4,0,0), and appeal to a fact we discussed in Module 3.)

x Find domain for g(x) 2. x 16

Solve 35 9 11. Round to the nearest thousandth as needed.

Describe an algorithm using pseudocode as discussed in class that takes a list of n integers a1, a2,..., an, and returns the number of negative integers in the list. Hint the initial value of the counter should be 0. 2. (4 points) The bubble sort algorithm discussed in class is used to sort the following sequence of integers 11 6 18 48 15 12 How

(a) Let g Rm R be a convex function, A an m n matrix, and b a vector in Rm. Show that is a convex function. (b) f(x) g(Axb) Let h R R be a convex function, and let a ER, ER be scalars with a 0. Show that f(x) ah(x) B is a convex function. Hint Make use of composition (see Exercise 3.2).

(a) A 3rd order RungeKutta method for solving the differential equation y f(x, y) with initial condition x xo, y yo is given by, k hf (xn, yn) k2hf (xnh2, ynk12) k3hf (xnh, yn 2k2 k) Yn1 yn(k4k2 k3). Apply this method to calculate approximate solutions to the differential equation, yry x, with x 0, y 2 at the point where x 0.2, using h

find

3 x log(),x2 x

Given f(x) x 4x9. Find f(2). Simplify the answer. Use the Graphical Equation editor to show your work in the box below. select Equations and then Graphical Equation to open the Click on Graphical Equation editor.

Divide and simplify. 3(a b) (ab) 8 ba