Basic Math question and answers for September 26, 2024
- Q Let the matrix below be the augmented matrix [A|B] of a linear system Ax = b. Write the most general solution (the sum of a particular one and the general...
- Q Write the augmented matrix for the given system. The rows of the augmented matrix should be in the same order as the equations in the given system.x=5y= -(1/9)z=4
- Q (a) Show that the vectors v1 = (1,2,1,0), v2 = (2,6,0,2) and v3 = (3,7,2,2) form a linearly independent set in R^4.(b) Find a fourth vector v4 in R^4 such...
- Q Use Gaussian elimination to solve.The Burkes pay their babysitter $5 per hour before 11 P.M. and $7.50 after 11 P.M. One evening they went out for 5 hr and paid...
- Q Use a graphing utility that gives a matrix in a row-echelon form or a matrix in a reduced row-echelon form, if available, to solve the system of equations given to...
- Q Solve the system using Cramer's Rule.-2x - 4y = -22-x+3y = 14Find the determinant D (denominator).D=Find the determinant D, associated with z.DzFind the determinant Dy associated with y.Dy =
- Q Use Cramer's rule to solve for y.2x + 5y + 5z = -153x+4y-5z = 174x-3y-2z= -21
- Q Solve the system of equations, using a matrix or otherwise. If the system has an infinite number of solutions, express them in terms of the parameter z.{5x - 4y +8z...
- Q Solve the System. Give answer as (x, y, z).{-1x+5y-5z= -5{-2x-5y-6z=-6{4x-5y+2z=2No solutionInfinite number of solutions
- Q Given the matrix A, determine the matrix represented by 2A.A= -5 -2-7 8
- Q Use Cramer's rule to find the solution to the following system of linear equations.5x-4y=-83x+y=3
- Q Use Cramer's rule and the calculator provided to find the value of x that satisfies the system of linear equations.-4x-4y+5z=-2-4x+2y+ 5z = -55x-3y-2z=1Note that the ALEKS graphing calculator can be...
- Q Let A be a non-singular matrix of order 3 suchthat det. (A) = 5 and B is also a non-singularmatrix satisfying A-B+ AB = 0. The value ofdet. (A6- 2A4B...
- Q Consider the following system of linear equations.4x-16y=-4-4x+21y=-11Solve the system by completing the steps below to produce a reduced row-echelon form. R, and R? denote the first and second rows, respectively....
- Q Given the system of equations2x - 3y - 9z = -15x + 3z = -3- 3x + y - 4z = 12(a) determine whether the system is inconsistent or dependent;Your...
- Q Let A be an n x n matrix. Suppose that there exists an invertible matrix P such thatP-AP = D, where D is a diagonal matrix. Consider the following statements.(i)...
- Q Solve the following system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so.X + y - z = 62x - y +...
- Q Consider the system of equations.x+2y=8-3x-2y=12How do you solve the system of equations with Cramer's rule?Drag a value or determinant expression into each box to correctly solve the system using Cramer's...
- Q Solve the system by any method. Use the infinity symbol if the system has infinitely many solutions, or enter DNE if there are no solutions.- 3x + 4y = -26x...
- Q Solve the system using addition/elimination method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.- 3x - 4y = 114x...
- Q Solve the system of equations:-5/4 x + 5/2 y = 5/64/3 x + 1/4 y = -17/6
- Q 2. Given the system below, do the following:(x-2y+3z=02xy + 5z = 5x + y + 4z = 7a. Write the augmented matrix that represents this system below. Then enter this...
- Q Find the inverse of the given matrix.Select the correct choice below and, if necessary, fill in the answer box to coA. A=B. The matrix is not invertible.
- Q [SolveLancer Test] A, B and C are both N-order matrices, E is the identity matrix and satis-fies ABC-E, then which of the following options is true: [SolveLancer Test](a) ACB =...
- Q Use a matrix equation to solve the system of linear equations.x + 2y =.54x+10y = 11What is the inverse matrix?A. A-1B. The inverse matrix does not exist.(Type an integer or...
- Q A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. (a) Show that I - A is also idempotent. (b) Show...
- Q Solve the system of equations using matrices. Use Gauss-Jordan elimination.-4x - y - 3z = -397x + 8y - 4z = 353x - 2y + z = -4{(2, 8, -1)}{(1,9,...
- Q 10.045You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice...
- Q A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 5%, some at 6.5%, and some at 7.5%. Use...
- Q Use Cramer's rule to solve the system.4x + 3y - z = 31x - 3y + 2z = -54x + y + z = 29O {(7, 6, 7)}O {(4, -7,...
- Q Determine whether the following inequality is true or false.When graphing 2x ? 8y ? 16, to determine which side of the line to shade, choose a test point on 2x...
- Q x+2y=12-3x - 2y = 4How do you solve the system of equations with Cramer's rule?Drag a value or determinant expression into each box to correctly solve the system using Cramer's...
- Q Costumes have been designed for the school musical. Costume A requires 5 yards of fabric, 4 yards of ribbon, and 3 packets of sequins. Costume B requires 7 yards of...
- Q For what value(s) of k will the following system of linear equations have no solution? infinitely many solutions?x-3y = 5- 6x + 18y = k...Select the correct choice below and,...
- Q Mark each statement True or False. Justify each answer. a. A row replacement operation does not affect the determinant of a matrix. b. The determinant of A is the product...
- Q Solve each system analytically. If the equations are dependent, write the solutions set in terms of the variable z.3x+6y-z = 62x-3y + 5z = -108x+9y-2z= 12
- Q Solve the system analytically. If the equations are dependent, write the solution set in terms of the variable z.x+y+z= -22x+y-z = -14x-y+z= -4Select the correct choice below and, if necessary,...
- Q If the column space of a 3x3 matrix consists of all vectors b=[b? b2 b3] such that b?+ b2= 3b3 thenone of the following set of the vectors forms abasis...
- Q (10 points) Write the augmented matrix from the system of equa-tions. Then, solve the system using Gaussian elimination (elementaryrow operations).x - 3y + 2z = 122x5y + 5z = 14x...
- Q Write a matrix equation equivalent to the following system.2x - 3y = -14x + 5y = 9Find the inverse of the coefficient matrix, and use it to solve the system.
- Q In the vector space P2, of polynomials of degree at most two, the third column of the matrix offrom the transition basisB={e?=4-x, e ? = ?2 + 3x, e3=1+x} to...
- Q Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent,express your answer...
- Q Write the following system of equations as a matrix equation and solve the system by finding the inverse of the coefficient matrix.|3x-y+2z=-1|4x-2y+z=-7|-x+3y-2z=-1
- Q If A is an invertible square matrix of order less than 4 such that |A-AT|!=0 and B = adjA, then which of the following is/are always true -adj(BA-B-A) = Aadj(BA-B-A)...
- Q Prove that any Mbius transformation can be written in a form with determinant 1, and that this form is unique up to sign.How does the determinant of T(z) = (az+b)/(cz...
- Q Question 4 of 25 A study of immunizations among school age children in California found that some areas had rates of unvaccinated school age children as high as 13 5...
- Q Suppose the binomial expansion of (x - y)^n includes the term - 84x^6y^3. The x^5y^4 term in the expansion will be The x^6y^8 term in the expansion will be
- Q Consider the binomial expansion of (4x + 3y)^n. Suppose the expansion includes a x^4y^8 term. Then n = ___ Check ALL of the following which will NOT in the simplified...
- Q Use the Binomial Theorem and Pascal's Triangle to find the expanded form of the binomial expression.(2x+3y)A. (2x) +6(2x) (3y)+15(2x)*(3y) +20(2x) (3y) +15(2x) (3y)* +6(2x)(3y) +(3y)B. (2x)+7(2x) (3y)+21(2x)*(3y) +35(2x) (3y) +21(2x)(3y)*...
- Q The time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there is less than 1 breakdown on a given day?.9048.3679.0952.000
- Q Suppose the binomial expansion of (4x + 5y)^n includes the term 1400000xy?.(A) The xy? term in the expansion will be?(B) The x?y? term in the expansion will be?
- Q The polynomial (x + 9)? (x 5) (- 3x + 7x + 2) has degree?The leading term will be?
- Q Suppose the binomial expansion of (x - y)n includes the term 84x6y3The x5y4 term in the expansion will be ___The x6y8 term in the expansion will be ___
- Q Suppose the binomial expansion of (2x 3y)n includes the term 15120x4y3The x4y3 term in the expansion will be The x5y3 term in the expansion will be
- Q Suppose the binomial expansion of (x + y)^n includes the term 3003x?y?. The x?y? term in the expansion will be? The x?y term in the expansion will be?
- Q Find the coefficient of the ay term in the expansion of (a + y)?.In the expansion,(a + y)? = a? + ... +___________ ay + ... +y?(Enter ONLY the coefficient)
- Q Find the indicated terms in the expansion of(4x + x - 2)(4x + 5x 10) (5x + 4x + 3)The degree 5 term is ___The degree 1 term is ___
- Q Which one of the following options is true when considering the expansion ofthe binomial expression (x + y)5?A. The expansion of (x + y)5 will yield 5 terms.B. The first...
- Q Find the term of the binomial expansion containing y^12.(x^4+y)^21
- Q Which of the following terms appear in the expansion of (x+y)^10? The letter a in each term represents a real constant.A. ax^4y^6B. ax^5C. ax^6y^4D. axy^7
- Q A cat has a litter of 7 kittens. Find the probability that exactly 4 of the kittens are female. Assumethat male and female births are equally likely. Estimate the probability...
- Q Suppose 3 out of 10 game pieces reads "Free candy bar". Which answer below would correctly find the probability that you win exactly 1 free candy bar with 4 game...
- Q A member of the American Kennel Club is researching Irish Wolfhounds, and measures ninety of them to find a sample average height of 33.0 Inches, with a 90% confidence interval...
- Q Three boxes colored red, orange, and blue are to be randomly ordered from left to right. What is the probability that the end boxes will be orange and blue, in...
- Q Which of the following can be classified as a binomial probability experiment?A coin is tossed 10 times. The random variable X is the number of heads that appear.A bag contains...
- Q A new type of grass seed was developed by an agricultural research company. It was determined that the probability of a seed germinating Is 0.92 (given the correct soll conditions,...
- Q The average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. Do twenty-year-old have fewer cavities? The data show the results of a survey of 16...
- Q Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.n = 50, p=0.9The mean, , isThe variance, ?2, isThe standard deviation,...
- Q Magnetic resonance imaging (MRI) is a process that pro- duces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to...
- Q 11% of all Americans live in poverty. If 47 Americans are randomly selected, find the probability thata. Exactly 3 of them live in poverty.b. At most 4 of them live...
- Q The commute times for students from home to school varies according to a distribution thatis approximately Normal with mean 28 minutes and standard deviation 18 minutes. What percent of the...
- Q A study of immunizations among school-age children in California found that some areas had rates of unvaccinated school-age children as high as 13.5% in 2014. Imagine a classroom of 20...
- Q If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are notindependent. If sampling is done without replacement and the...
- Q About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees...
- Q Evaluate 9 C3.9C3=(Simplify your answer. Type an integer or a fraction.)
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