Sue earns £8.30 per hour for a 35 hour week and time and a half after that. How much would she earn in a 42-hour week? (To nearest 5 pence)

Q: Prove that Z ⨁ Z is not cyclic. Does your proof work for Z ⨁ Gwhere G is any group with more than…

A: To Do: Z⊕Z is not cyclic. Does the proof work for Z⊕G where G is any group with more than one…

Q: Compute Aa and Ay A: (-6, -1) and B: so Ax= The instantaneous slope of f(x) when f(x) is rational…

A:

Q: Five deposits are made at the EOYs 2021–2025. If the interest rate is 8% compounded annually, what…

A: Sol:- To calculate the amount in the account at the end of 2029, we need to find the future value of…

Q: (a) Tell about the convergence (conditionally/absolutely) of alternative series, which for an=1/n…

A: (a)   Alternative series ,for which an=1n                          ∑n=1∞(-1)nan≡ ∑n=1∞(-1)nn…

Q: Consider the ODE y = f(u), where the graph of f(y) is given below: f(y) Use the above picture to…

A:

Q: Find the equation of the straight line that (1).makes equal intercepts on the axes and passes…

A: (1) Let the equation of the line bexa+yb=1Since it makes equal intercepts on the coordinates axes,we…

Q: 1. Let R be a commutative ring with unity a. Let ✅ be a collection of ideals in R. Prove that ea is…

A:

Q: In Problems 59-66, use the price-demand equation to find the values of p for which demand is elastic…

A: Price-demand equation f(p)=2,400-6p2 The elasticity of demand, E at price p is defined by…

Q: (a) lim f(x) x--2 (b) lim f(x) x--1+ lim f(x) x--1- (d) lim f(x) (f) (e) (-1) lim f(x) X-+00

A:

Q: Given y = x+8x³ - 30x², find all points of inflection and interval(s) of concavity. Concave up:…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given, x=23y, x=0, y=7 ;  To find the volume V about y-axis.

Q: O Using Convolution Theorem b.) F(s) = 1 (s²+4) (s²+4s+8)

A:

Q: for the curve defined by =(t) = (e¹, 6t, e) ind the unit tangent vector, unit normal vector, normal…

A: We know that u.v'=u'v+vu' . And if a→=<a1,a2,a3> then a→=a12+a22+a32 .

Q: 6-1) with T defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is…

A:

Q: Compute the volume occupied by revolving a circle of radius 3 m from the axis about 10 m radius away…

A: Sol:- To find the volume of the solid generated by revolving a circle of radius 3 m about an axis 10…

Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: b) in the answer provided, we see the systems S1 and S3 satisfy the closure property.      For…

Q: 3 3) The Sequence of real function f(x) = x²+³ converges over a interval [1,1], dotally from th…

A:

Q: Modulo Rules. Find the remainders. a= 3³1; ; b = 17

A: Given: a=331, b=17. We have to find the remainder using modulo rules.

Q: In how many ways can an investor select five mutual funds for his investment portfolio from a…

A: Given: Number of mutual funds = 8. Number of mutual funds to be selected = 5. To find: The number of…

Q: Given the matrix find A³. Write A³ as input your answer below: -1 a 11 a12 = 8 a21 = 0 a22 = -27 A…

A:

Q: What size payments should occur when $8,000 is borrowed at 8% per year compounded quarterly and the…

A: Given: The present value of the loan, PV=$ 8,000           Number of payment periods, n=8…

Q: The equations for free fall at the surfaces of Venus and Jupiter (s in meters, t in seconds) are s =…

A:

Q: A company is planning to manufacture wheelchairs that are light, fast, and beautiful. The fixed…

A: (a) To find: The cost function. Given information: The fixed cost is $500,000 and variable cost is…

Q: Suppose f(x) = 8 - x². (a) Find the slope of the tangent line to the graph y = f(x) when x = −1. - f…

A:

Q: Note: NOT WRONSKIAN 9 Use variation of parameters. (D²+1) y = sec ² x

A:

Q: The graph of a function is given. Choose the answer that represents the graph of its derivative. -15…

A:

Q: A line 4x+y=1 through the point A(2,-7) meets the line BC whose equation is 3x-4y+1=0 at the point…

A:

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 1000t 180t2, where t is…

A:

Q: Determine the Laplace transform of the ODE: y' (t) = 6y' (t)- 4y (t) + 6x (t)

A: Given: Ordinary differential equation : y"t=6y't-4yt+6xtTo find: The Laplace transform of given…

Q: Virginia Osterman bought a television set on a 12-month installment plan that included a $70.20…

A: Interest refund is defined as the percentage of the interest collected on the loans which refunded…

Q: Give the domain and range of the function. W 2 12345 OA. Domain: (-5,5) Range: [-2,8) OB. Domain:…

A: A graph of the function is given, we have to find its domain and range.

Q: Prove that exactly one of the non-abelian groups of order 8 is isomorphic to a semidirect product C4…

A:

Q: Lagrange multipliers Each function ƒ has an absolute maximum value and absolute minimum value…

A: The given function fx, y=x2+y2 subject to the constraints 2x2+3xy+2y2=7. We have to find the maximum…

Q: Find the Annihilator of the given function(s) f(x)=x+xcos(2x) a. D²(D²+4) b. D²(D²+4)² C. D(D²+4) d.…

A: Sol:- To find the annihilator of the given function using differential operators, we need to find a…

Q: The monthly sales of Sunny Electronics' new sound system are given by q(t) = 2,000t - 60t² units per…

A:

Q: Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as…

A: The given graph shows the depth of water W in a reservoir over a one-year period as a function of…

Q: (Schr¨oder–Bernstein Theorem). Assume there exists a1–1 function f : X → Y and another 1–1 function…

A: Given: The existence of 1-1 functions f: X→Y and g: Y→X To prove: X~Y

Q: Problem #4: Consider the following matrix. Problem #4: A = 2 -1 8 2 -6 -3 -5 4 1 Let B = adj(A).…

A:

Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: Let S = {-2, -1, 0, 2, 1, √2, 2, 4). Determine which elements of S satisfy the inequality. ( 2-1 2x

A:

Q: y(x) = y = 2y + x² + 7 Give the largest interval over which the general solution is defined. (Think…

A:

Q: If H is a Hilbert space and SCH, show that S = S¹¹¹. When S is the same as S++ ? Justify.

A: Answer:If H is Hilbert space and SCH, show that S⊥=S⊥⊥⊥.when  S is same as S⊥⊥? Justfy.These…

Q: Let S\index{1} be a circle passing through A(0,1) and B(-2,2) and S\index{2} be a circle of radius…

A: The equation of line AB is             y-2=2-1-2-0(x+2)                 =-12(x+2)or       x+2y-2=0…

Q: The economic dimension (diameter and height) of a cylindrical overhead storage tank for a capacity…

A: The capacity of a cylindrical tank is 125,000 gallons. Firstly convert the capacity into ft3. It is…

Q: Decompose A = 1-2 4 Yor 6 0 7 3 -2 into product of lower triangular matrix and upper triangular…

A:

Q: 5. Give an example of a family {Un new} of open subsets of R, with usual metric, such that new Un is…

A:

Q: Solve the following differential equation by using integrating factors. xy=9y-8x²

A: xy' =9y-8x2A first order linear ODE has the form of y'x+pxy=qxRewrite in the form of a first order…

Q: d) Surveys of EV owners show that they charge at home 70% of the time. Let us assume that for the…

A: Sol:- d) To determine the ratio between the installation of fast charging stations to gasoline pumps…

Q: (a) find the function’s domain, (b) find the function’srange, (c) describe the function’s level…

A: The given function is f(x,y)=y-x. (a) To find: the function’s domain, (b) To find the function’s…

Q: A GIVEN: The three points in R³: B = C = - (-1,2,0) (1,0,1) (0,1,-2) FIND: a) the measure of ZABC,…

A: