Questions 96 and 97 refer to the following information. rorle Juan worked as a waiter on Saturday nights to supplement his income. He kept a list of the tips he received for 8 weeks and the number of hours he worked each Saturday night. Week amo1 8. Tips $98 $75.25 $84 n $92 $60 $86.50 $90.60 W $77 Hours 6. re.s 6. 6. AL lar lea ree 96. What was the median amount of Juan's weekly tips? A. $60 B. $85.25 C. $92 culsv o D. $84 Sx noleupe orts ni 201 те E. $663 97. In addition to his tips, Juan's employer paid him $3 per hour. How much did he actually earn per hour, including his wages and his tips during week 3? argaret, garet A. $15.00 B. $16.80 no bi as u as nuch otal alue a C. $19.80 of the D. $87 as E. $99

Q: 1. Find the maximum value of r+y subject to the constraint r + y? = 18.

A:

Q: min flx,,x) = (x, - 1)*+ (n,- 1)² Subrected to 」+Z2コ4 X,ーュ-2 き6 Hint : Convert to standard fom and…

A:

Q: Evaluate the following integrals using Cauchy Residue Theory. All closed contours are traversed CCw.…

A:

Q: A company has 30,000 employees in three cities as shown in the table below. It wishes to give…

A:

Q: If the sum of eigenvalues of matrix 9. 7 16 A -9 k2 3 is 29, then the possible - 16 9 values of k…

A: We want to find the value of k

Q: Define a bijective map g : x2/3--->R.

A: Sol

Q: - Suppose that A and B arenxn matrices and A is invertible. Invent and prove a theorem that…

A: Solution

Q: The length in meters of the four sides of a building are 3x, 6x - 5, 9x, and 4x + 1. (a) Calculate…

A: (a). Add 3x, 6x-5, 9x and 4x+1 to calculate the total length around the building.…

Q: Prove by contradiction that if a sum of three real numbers is less than 30, th at least one of the…

A: We have to prove by contradiction that if a sum of three real number is less than 30, then at least…

Q: 4. Find the absolute extrema of the function f(r, y) = ry -I-3y on the triangular region with…

A:

Q: II. Solve each equation by completing the square: 4. x2 + 12x – 2 = 0 5. x(x – 1) = 30 6. 2y? + 7y –…

A: Solving Quadratic Equations usingCompleting the Square we follow the step given below : 1. Divide…

Q: Let X be the graph of f(x) = r²/3 given below that is, X is the subset of R x R satisfying the given…

A: Sol

Q: 3. Solve the initial value problem y" – 3y' + 2y = 10 sin x with y(0) = 1, y'(0) = -6 by using both…

A: The given initial value problem is                                          y''-3y'+2y=10sinx,…

Q: Find the angle a, in radians, between the vectors -5 and 3

A: Use the formula of angle between the vectors to solve the question.

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

Q: 'ind the standard matrix of the linear transformation T : R² → R³ that satisfies T(1,1) = (2, 1, 0)…

A: Linear transformation and matrix

Q: A coin is loaded so that the probability of a head occurring on a single toss is 5/6. In three…

A:

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim f (x)= 21 b) lim x-x+1=-5 x3 c) limx =8 x→2

A:

Q: Find the centroid of the given region. y = 2-r y=r

A: Introduction: The formula of the mass of the solid of the density function k is given by,…

Q: 3. Supply the missing integrand and limits of integration 62*y drdy = dy (b) L"62y dydr = L dr

A: Introduction: The double integral is most commonly used to calculate the surface area of a…

Q: Test for exactness, if it is exact then find the general solution, if NOT USE USE THE INTEGRATING…

A:

Q: N-1 N, k-r = mN, m an integer | Se-i(27/N)(k-r)n n=0 0, otherwise

A: To prove: ∑n=0N-1e-j2πNk-rn=N,k-r=mN, m is an integer0,otherwise

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: y= cos(2r) The initial interval is [0.8,

A: Follow the python script.

Q: 1. Let f : Z6 → Z6 be such that f(a) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 3. LetR be the region shown in the accompanying figure. Fill in the missing limits of integration…

A: We have to fill the missing limit of integration .

Q: If dįd2dzdądzded7ds is 1 4 0 5 7 3 2 3, let n = 100 + dzds and a = dzdg. n 3D Find d e Z, such that…

A: The solution follows from the Generalized Euclidean Algorithm for finding GCD.

Q: Use false position methodto find the solution to the following within 10−6

A:

Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Q: x3 – 2x? – 5 = 0, [1,4]

A: f(x) = x³ - 2 x ² - 5 , [1,4] f(1) = -6 <0,  f(2) = -5 <0, f(3) = 4 >0, f(4) = 27 >0…

Q: SET-UP the double integral that solves for the volume of the solid

A: To set up a double integral to find the volume of the solid.

Q: Suppose that (Sn) and (t„) are convergent sequences with lim s, = s and lim t, = t. Then b) lim…

A:

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

A:

Q: Suppose that the function f is defined on the interval -2, 2) as follows. -2 if-25x<-1 -1 if -1Sx<0…

A: Function value at a given point

Q: Use disk's (washer's) method to set up the integral finds the volume of the solid obtained by…

A: This is a problem of the volume of rotation.

Q: For an n × n matrix A, we can similarly define the matrix exponential aseA = I + A + (1/2!)A^2 +…

A:

Q: 2. An international airline has a regulation that each passenger can carry a suitcase having the sum…

A: Denote the width, length, and height by W, L, and H, respectively  We may as well assume that W + L…

Q: (a) Find the partial derivative of f with respect to x. fx(x, y) = (b) Find the partial derivative…

A:

Q: Find the volume of the pyramid with base in the plane z = -9 and sides formed by the three planes y…

A:

Q: di t. + 4 i - 5 Si dt = 2 u (t– 2) dt

A:

Q: Let X be the graph of f(x) = r2/3 given below %3D that is, X is the subset of R x R satisfying the…

A: Sol

Q: 1. Let u and v be vectors in R". Suppose ||u||2 = 2, ||v||² = 1, and u·v = 1. Compute

A:

Q: A closed rectangular box with a volume of 16 ft is made from two kinds of materials. The top and…

A: We will use Lagrange Multiplier method to  maximize / minimize a function f(x,,y,z) subject to…

Q: Find the orthogonal projection of -14 = -14 onto the subspace W of Rª spanned by and -2 projw(v) = 2…

A: To find The orthogonal projection of v onto the subspace of W of R^4 spanned by the given vectors.

Q: 5 et L be the line given by the span of in R³. Find a basis for the orthogonal complement Lt -7 -9…

A:

Q: Answer the following problems using the specified method up to four (4) iterations only. Round off…

A: In part (a) we will use the Bisection method in which if root lies between a    and b then root is…

Q: Let A be a m x n matrix whose columns are vectors of R™. What is the smallest n must be so that…

A: Let A be the m×n matrix A=a11a12…a1na21a22…a2n⋮⋮⋱⋮am1am2…amnm×n that is the transformation matrix…

Q: Bossing bought two bags, one for P700,000 and the other for P300,000. He sold the first at a gain of…

A: Given that Bossing bought two bags, one for P700,000 and the other for P300,000. He sold the first…

Q: Describe the graph of the equation: r = 4ti – 5j + (1 + 2r)k. [Choose the correct answer.] O The…

A: Introduction: In three dimensional Euclidean space, a line can also be represented. An equation of a…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.

A: Given,          ∫-aa∫-a2-x2a2-x2dydx