Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Textbook Question
Chapter 10.3, Problem 65E
Factor each trinomial completely:
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2. You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1.
400
Port 2
110
Port 3
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form).
(b) Suppose now that all is as in the previous question but that only 320L of
Important Chemical A are now required at Warehouse 1. Any excess chemical
can be transported to either Warehouse 1 or 2 for storage, in which case the
company must pay only the relevant transportation costs, or can be disposed
of at the…
choose true options in these from given question
a) always full and always crossing.
b) always full and sometimes crossing.
c) always full and never crossing.
d) sometimes full and always crossing.
e) sometimes full and sometimes crossing.
f) sometimes full and never crossing.
g) never full and always crossing.
h) never full and sometimes crossing.
i) never full and never crossing.
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.49. Find the probability that in a sample of 13 customers, at least 7 will order a nonalcoholic beverage
Chapter 10 Solutions
Elementary Technical Mathematics
Ch. 10.1 - Factor: 4a+4Ch. 10.1 - Factor: 3x6Ch. 10.1 - Factor: bx+byCh. 10.1 - Factor: 918yCh. 10.1 - Factor: 15b20Ch. 10.1 - Factor: 12ab+30acCh. 10.1 - Factor: x27xCh. 10.1 - Factor: 3x26xCh. 10.1 - Factor: a24aCh. 10.1 - Factor: 7xy21y
Ch. 10.1 - Factor: 4n28nCh. 10.1 - Factor: 10x2+5xCh. 10.1 - Factor: 10x2+25xCh. 10.1 - Factor: y28yCh. 10.1 - Factor: 3r26rCh. 10.1 - Factor: x3+13x2+25xCh. 10.1 - Factor: 4x4+8x3+12x2Ch. 10.1 - Factor: 9x415x218xCh. 10.1 - Factor: 9a29ax2Ch. 10.1 - Factor: aa3Ch. 10.1 - Factor: 10x+10y10zCh. 10.1 - Factor: 2x22xCh. 10.1 - Factor: 3y6Ch. 10.1 - Factor: y3y2Ch. 10.1 - Factor: 14xy7x2y2Ch. 10.1 - Factor: 25a225b2Ch. 10.1 - Factor: 12x2m7mCh. 10.1 - Factor: 90r210R2Ch. 10.1 - Factor: 60ax12aCh. 10.1 - Factor: 2x2100x3Ch. 10.1 - Factor: 52m2n213mnCh. 10.1 - Factor: 40x8x3+4x4Ch. 10.1 - Factor: 52m214m+2Ch. 10.1 - Factor: 27x354xCh. 10.1 - Factor: 36y218y3+54y4Ch. 10.1 - Factor: 20y310y2+5yCh. 10.1 - Factor: 6m612m2+3mCh. 10.1 - Factor: 16x332x216xCh. 10.1 - Factor: 4x2y36x2y410x2y5Ch. 10.1 - Factor: 18x3y30x4y+48xyCh. 10.1 - Factor: 3a2b2c2+27a3b3c381abcCh. 10.1 - Factor: 15x2yz420x3y2z2+25x2y3z2Ch. 10.1 - Factor: 4x3z48x2y2z3+12xyz2Ch. 10.1 - Factor: 18a2b2c2+24ab2c230a2c2Ch. 10.2 - Find each product mentally: (x+5)(x+2)Ch. 10.2 - Find each product mentally: (x+3)(2x+7)Ch. 10.2 - Find each product mentally: (2x+3)(3x+4)Ch. 10.2 - Find each product mentally: (x+3)(x+18)Ch. 10.2 - Find each product mentally: (x5)(x6)Ch. 10.2 - Find each product mentally: (x9)(x8)Ch. 10.2 - Find each product mentally: (x12)(x2)Ch. 10.2 - Find each product mentally: (x9)(x4)Ch. 10.2 - Find each product mentally: (x+8)(2x+3)Ch. 10.2 - Find each product mentally: (3x7)(2x5)Ch. 10.2 - Find each product mentally: (x+6)(x2)Ch. 10.2 - Find each product mentally: (x7)(x3)Ch. 10.2 - Find each product mentally: (x9)(x10)Ch. 10.2 - Find each product mentally: (x9)(x+10)Ch. 10.2 - Find each product mentally: (x12)(x+6)Ch. 10.2 - Find each product mentally: (2x+7)(4x5)Ch. 10.2 - Find each product mentally: (2x7)(4x+5)Ch. 10.2 - Prob. 18ECh. 10.2 - Find each product mentally: (2x+5)(4x7)Ch. 10.2 - Find each product mentally: (6x+5)(5x1)Ch. 10.2 - Find each product mentally: (7x+3)(2x+5)Ch. 10.2 - Find each product mentally: (5x7)(2x+1)Ch. 10.2 - Find each product mentally: (x9)(3x+8)Ch. 10.2 - Find each product mentally: (x8)(2x+9)Ch. 10.2 - Find each product mentally: (6x+5)(x+7)Ch. 10.2 - Find each product mentally: (16x+3)(x1)Ch. 10.2 - Find each product mentally: (13x4)(13x4)Ch. 10.2 - Find each product mentally: (12x+1)(12x+5)Ch. 10.2 - Find each product mentally: (10x+7)(12x3)Ch. 10.2 - Find each product mentally: (10x7)(12x+3)Ch. 10.2 - Find each product mentally: (10x7)(10x3)Ch. 10.2 - Find each product mentally: (10x+7)(10x+3)Ch. 10.2 - Find each product mentally: (2x3)(2x5)Ch. 10.2 - Find each product mentally: (2x+3)(2x+5)Ch. 10.2 - Find each product mentally: (2x3)(2x+5)Ch. 10.2 - Find each product mentally: (2x+3)(2x5)Ch. 10.2 - Find each product mentally: (3x8)(2x+7)Ch. 10.2 - Prob. 38ECh. 10.2 - Find each product mentally: (3x+8)(2x+7)Ch. 10.2 - Find each product mentally: (3x8)(2x7)Ch. 10.2 - Find each product mentally: (8x5)(2x+3)Ch. 10.2 - Find each product mentally: (x7)(x+5)Ch. 10.2 - Find each product mentally: (y7)(2y+3)Ch. 10.2 - Find each product mentally: (m9)(m+2)Ch. 10.2 - Find each product mentally: (3n6y)(2n+5y)Ch. 10.2 - Find each product mentally: (6ab)(2a+3b)Ch. 10.2 - Find each product mentally: (4xy)(2x+7y)Ch. 10.2 - Find each product mentally: (8x12)(2x+3)Ch. 10.2 - Find each product mentally: (12x8)(14x6)Ch. 10.2 - Find each product mentally: (23x6)(13x+9)Ch. 10.3 - Factor each trinomial completely: x2+6x+8Ch. 10.3 - Factor each trinomial completely: x2+8x+15Ch. 10.3 - Factor each trinomial completely: y2+9y+20Ch. 10.3 - Factor each trinomial completely: 2w2+20w+32Ch. 10.3 - Factor each trinomial completely: 3r2+30r+75Ch. 10.3 - Factor each trinomial completely: a2+14a+24Ch. 10.3 - Factor each trinomial completely: b2+11b+30Ch. 10.3 - Factor each trinomial completely: c2+21c+54Ch. 10.3 - Factor each trinomial completely: x2+17x+72Ch. 10.3 - Factor each trinomial completely: y2+18y+81Ch. 10.3 - Factor each trinomial completely: 5a2+35a+60Ch. 10.3 - Factor each trinomial completely: r2+12r+27Ch. 10.3 - Factor each trinomial completely: x27x+12Ch. 10.3 - Factor each trinomial completely: y26y+9Ch. 10.3 - Factor each trinomial completely: 2a218a+28Ch. 10.3 - Factor each trinomial completely: c29c+18Ch. 10.3 - Factor each trinomial completely: 3x230x+63Ch. 10.3 - Factor each trinomial completely: r212r+35Ch. 10.3 - Factor each trinomial completely: w213w+42Ch. 10.3 - Factor each trinomial completely: x214x+49Ch. 10.3 - Factor each trinomial completely: x219x+90Ch. 10.3 - Factor each trinomial completely: 4x284x+80Ch. 10.3 - Factor each trinomial completely: t212t+20Ch. 10.3 - Factor each trinomial completely: b215b+54Ch. 10.3 - Factor each trinomial completely: x2+2x8Ch. 10.3 - Factor each trinomial completely: x22x15Ch. 10.3 - Factor each trinomial completely: y2+y20Ch. 10.3 - Prob. 28ECh. 10.3 - Factor each trinomial completely: a2+5a24Ch. 10.3 - Factor each trinomial completely: b2+b30Ch. 10.3 - Factor each trinomial completely: c215c54Ch. 10.3 - Factor each trinomial completely: b26b72Ch. 10.3 - Factor each trinomial completely: 3x23x36Ch. 10.3 - Factor each trinomial completely: a2+5a14Ch. 10.3 - Factor each trinomial completely: c2+3c18Ch. 10.3 - Factor each trinomial completely: x24x21Ch. 10.3 - Factor each trinomial completely: y2+17y+42Ch. 10.3 - Factor each trinomial completely: m218m+72Ch. 10.3 - Factor each trinomial completely: r22r35Ch. 10.3 - Factor each trinomial completely: x2+11x42Ch. 10.3 - Factor each trinomial completely: m222m+40Ch. 10.3 - Factor each trinomial completely: y2+17y+70Ch. 10.3 - Factor each trinomial completely: x29x90Ch. 10.3 - Factor each trinomial completely: x28x+15Ch. 10.3 - Factor each trinomial completely: a2+27a+92Ch. 10.3 - Factor each trinomial completely: x2+17x110Ch. 10.3 - Factor each trinomial completely: 2a212a110Ch. 10.3 - Factor each trinomial completely: y214y+40Ch. 10.3 - Factor each trinomial completely: a2+29a+100Ch. 10.3 - Factor each trinomial completely: y2+14y120Ch. 10.3 - Factor each trinomial completely: y214y95Ch. 10.3 - Factor each trinomial completely: b2+20b+36Ch. 10.3 - Factor each trinomial completely: y218y+32Ch. 10.3 - Factor each trinomial completely: x28x128Ch. 10.3 - Factor each trinomial completely: 7x2+7x14Ch. 10.3 - Factor each trinomial completely: 2x26x36Ch. 10.3 - Factor each trinomial completely: 6x2+12x6Ch. 10.3 - Factor each trinomial completely: 4x2+16x+16Ch. 10.3 - Factor each trinomial completely: y212y+35Ch. 10.3 - Factor each trinomial completely: a2+16a+63Ch. 10.3 - Factor each trinomial completely: a2+2a63Ch. 10.3 - Factor each trinomial completely: y2y42Ch. 10.3 - Factor each trinomial completely: x2+18x+56Ch. 10.3 - Factor each trinomial completely: x2+11x26Ch. 10.3 - Factor each trinomial completely: 2y236y+90Ch. 10.3 - Factor each trinomial completely: ax2+2ax+aCh. 10.3 - Factor each trinomial completely: 3xy218xy+27xCh. 10.3 - Factor each trinomial completely: x3x2156xCh. 10.3 - Factor each trinomial completely: x2+30x+225Ch. 10.3 - Factor each trinomial completely: x22x360Ch. 10.3 - Factor each trinomial completely: x226x+153Ch. 10.3 - Factor each trinomial completely: x2+8x384Ch. 10.3 - Factor each trinomial completely: x2+28x+192Ch. 10.3 - Factor each trinomial completely: x2+3x154Ch. 10.3 - Factor each trinomial completely: x2+14x176Ch. 10.3 - Factor each trinomial completely: x259x+798Ch. 10.3 - Factor each trinomial completely: 2a2b+4ab48bCh. 10.3 - Factor each trinomial completely: ax215ax+44aCh. 10.3 - Factor each trinomial completely: y2y72Ch. 10.3 - Factor each trinomial completely: x2+19x+60Ch. 10.4 - Find each product: (x+3)(x3)Ch. 10.4 - Find each product: (x+3)2Ch. 10.4 - Find each product: (a+5)(a5)Ch. 10.4 - Find each product: (y2+9)(y29)Ch. 10.4 - Find each product: (2b+11)(2b11)Ch. 10.4 - Find each product: (x6)2Ch. 10.4 - Find each product: (100+3)(1003)Ch. 10.4 - Find each product: (90+2)(902)Ch. 10.4 - Find each product: (3y2+14)(3y214)Ch. 10.4 - Find each product: (y+8)2Ch. 10.4 - Find each product: (r12)2Ch. 10.4 - Find each product: (t+10)2Ch. 10.4 - Find each product: (4y+5)(4y5)Ch. 10.4 - Find each product: (200+5)(2005)Ch. 10.4 - Find each product: (xy4)2Ch. 10.4 - Find each product: (x2+y)(x2y)Ch. 10.4 - Find each product: (ab+d)2Ch. 10.4 - Find each product: (ab+c)(abc)Ch. 10.4 - Find each product: (z11)2Ch. 10.4 - Find each product: (x3+8)(x38)Ch. 10.4 - Find each product: (st7)2Ch. 10.4 - Find each product: (w+14)(w14)Ch. 10.4 - Find each product: (x+y2)(xy2)Ch. 10.4 - Find each product: (1x)2Ch. 10.4 - Find each product: (x+5)2Ch. 10.4 - Find each product: (x6)2Ch. 10.4 - Find each product: (x+7)(x7)Ch. 10.4 - Find each product: (y12)(y+12)Ch. 10.4 - Find each product: (x3)2Ch. 10.4 - Find each product: (x+4)2Ch. 10.4 - Find each product: (ab+2)(ab2)Ch. 10.4 - Find each product: (m3)(m+3)Ch. 10.4 - Find each product: (x2+2)(x22)Ch. 10.4 - Find each product: (m+15)(m15)Ch. 10.4 - Find each product: (r15)2Ch. 10.4 - Find each product: (t+7a)2Ch. 10.4 - Find each product: (y35)2Ch. 10.4 - Find each product: (4x2)2Ch. 10.4 - Find each product: (10x)(10+x)Ch. 10.4 - Find each product: (ay23)(ay2+3)Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Prob. 8ECh. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.5 - Factor completely. Check by multiplying the...Ch. 10.6 - Factor completely: 5x22812Ch. 10.6 - Factor completely: 4x24x3Ch. 10.6 - Factor completely: 10x229x+21Ch. 10.6 - Factor completely: 4x2+4x+1Ch. 10.6 - Factor completely: 12x228x+15Ch. 10.6 - Factor completely: 9x236x+32Ch. 10.6 - Factor completely: 8x2+26x45Ch. 10.6 - Factor completely: 4x2+15x4Ch. 10.6 - Factor completely: 16x211x5Ch. 10.6 - Factor completely: 6x2+3x3Ch. 10.6 - Factor completely: 12x216x16Ch. 10.6 - Factor completely: 10x235x+15Ch. 10.6 - Factor completely: 15y2y6Ch. 10.6 - Factor completely: 6y2+y2Ch. 10.6 - Factor completely: 8m210m3Ch. 10.6 - Factor completely: 2m27m30Ch. 10.6 - Factor completely: 35a22a1Ch. 10.6 - Factor completely: 12a228a+15Ch. 10.6 - Factor completely: 16y28y+1Ch. 10.6 - Factor completely: 25y2+20y+4Ch. 10.6 - Factor completely: 3x2+20x63Ch. 10.6 - Factor completely: 4x2+7x15Ch. 10.6 - Factor completely: 12b2+5b2Ch. 10.6 - Factor completely: 10b27b12Ch. 10.6 - Factor completely: 15y214y8Ch. 10.6 - Factor completely: 5y2+11y+2Ch. 10.6 - Factor completely: 90+17c3c2Ch. 10.6 - Prob. 28ECh. 10.6 - Factor completely: 6x213x+5Ch. 10.6 - Factor completely: 56229x+3Ch. 10.6 - Factor completely: 2y4+9y235Ch. 10.6 - Factor completely: 2y2+7y99Ch. 10.6 - Factor completely: 4b2+52b+169Ch. 10.6 - Factor completely: 6x219x+15Ch. 10.6 - Factor completely: 14x251x+40Ch. 10.6 - Factor completely: 42x413x240Ch. 10.6 - Factor completely: 28x3+140x2+175xCh. 10.6 - Factor completely: 24x354x221xCh. 10.6 - Factor completely: 10ab215ab175aCh. 10.6 - Factor completely: 40bx272bx70bCh. 10 - Prob. 1RCh. 10 - Find each product mentally: (x6)(x+6)Ch. 10 - Find each product mentally: (y+7)(y4)Ch. 10 - Find each product mentally: (2x+5)(2x9)Ch. 10 - Find each product mentally: (x+8)(x3)Ch. 10 - Find each product mentally: (x4)(x9)Ch. 10 - Find each product mentally: (x3)2Ch. 10 - Find each product mentally: (2x6)2Ch. 10 - Find each product mentally: (15x2)2Ch. 10 - Factor each expression completely: 6a+6Ch. 10 - Factor each expression completely: 5x15Ch. 10 - Factor each expression completely: xy+2xzCh. 10 - Factor each expression completely: y4+17y318y2Ch. 10 - Factor each expression completely: y26y7Ch. 10 - Factor each expression completely: z2+18z+81Ch. 10 - Factor each expression completely: x2+10x+16Ch. 10 - Factor each expression completely: 4a2+4x2Ch. 10 - Factor each expression completely: x217x+72Ch. 10 - Factor each expression completely: x218x+81Ch. 10 - Factor each expression completely: x2+19x+60Ch. 10 - Factor each expression completely: y22y+1Ch. 10 - Factor each expression completely: x23x28Ch. 10 - Factor each expression completely: x24x96Ch. 10 - Factor each expression completely: x2+x110Ch. 10 - Factor each expression completely: x249Ch. 10 - Factor each expression completely: 16y29x2Ch. 10 - Factor each expression completely: x2144Ch. 10 - Factor each expression completely: 25x281y2Ch. 10 - Factor each expression completely: 4x224x364Ch. 10 - Factor each expression completely: 5x25x780Ch. 10 - Factor each expression completely: 2x2+11x+14Ch. 10 - Factor each expression completely: 12x219x+4Ch. 10 - Factor each expression completely: 30x2+7x15Ch. 10 - Factor each expression completely: 12x2+143x12Ch. 10 - Factor each expression completely: 4x26x+2Ch. 10 - Factor each expression completely: 36x249y2Ch. 10 - Factor each expression completely: 28x2+82x+30Ch. 10 - Factor each expression completely: 30x227x21Ch. 10 - Factor each expression completely: 4x34xCh. 10 - Factor each expression completely: 25y2100Ch. 10 - Find each product mentally: (x+8)(x3)Ch. 10 - Find each product mentally: (2x8)(5x6)Ch. 10 - Find each product mentally: (2x8)(2x+8)Ch. 10 - Find each product mentally: (3x5)2Ch. 10 - Find each product mentally: (4x7)(2x+3)Ch. 10 - Find each product mentally: (9x7)(5x+4)Ch. 10 - Factor each expression completely: x2+4x+3Ch. 10 - Factor each expression completely: x212x+35Ch. 10 - Factor each expression completely: 6x27x90Ch. 10 - Factor each expression completely: 9x2+24x+16Ch. 10 - Factor each expression completely: x2+7x18Ch. 10 - Factor each expression completely: 4x225Ch. 10 - Factor each expression completely: 6x2+13x+6Ch. 10 - Factor each expression completely: 3x2y218x2y+27x2Ch. 10 - Factor each expression completely: 3x211x4Ch. 10 - Factor each expression completely: 15x219x10Ch. 10 - Factor each expression completely: 5x2+7x6Ch. 10 - Factor each expression completely: 3x23x6Ch. 10 - Factor each expression completely: 9x2121Ch. 10 - Factor each expression completely: 9x230x+25Ch. 10 - Perform the indicated operations and simplify:...Ch. 10 - Round 746.83 to the a. nearest tenth and b....Ch. 10 - Do as indicated and simplify: 2315+23Ch. 10 - Write 0.000318 in a. scientific notation and b....Ch. 10 - Change 625 g to kg.Ch. 10 - Change 7 m2 to ft2.Ch. 10 - Read the voltmeter scale in Illustration 1....Ch. 10 - Use the rules of measurement to multiply:...Ch. 10 - Combine like terms and simplify: 3(x2)4(23x)Ch. 10 - Combine like terms and simplify: (6a3b+2c)(2a3b+c)Ch. 10 - Solve: x34=2x5Ch. 10 - A rectangle is 5 m longer than it is wide. Its...Ch. 10 - Solve the proportion and round the result to three...Ch. 10 - A pulley is 18 in. in diameter, is rotating at 125...Ch. 10 - Complete the ordered-pair solutions of the...Ch. 10 - Solve for y: 3xy=5Ch. 10 - Draw the graph of 3x+4y=24Ch. 10 - Draw the graphs of 2xy=4 and x+3y=5. Find the...Ch. 10 - Solve each pair of linear equation:...Ch. 10 - Solve each pair of linear equation: y=3x5x+3y=8Ch. 10 - Solve each pair of linear equation: xy=63x+y=2Ch. 10 - Solve each pair of linear equation: xy=63x+y=2Ch. 10 - Solve each pair of linear equation:...Ch. 10 - Two rental automobiles were leased for a total of...Ch. 10 - Find each product mentally: (2x5)(3x+8)Ch. 10 - Find each product mentally: (5x7y)2Ch. 10 - Find each product mentally: (3x5)(5x7)Ch. 10 - Factor each expression completely: 7x363xCh. 10 - Factor each expression completely: 4x3+12x2Ch. 10 - Factor each expression completely: 2x27x4
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- 10. In the general single period market model with = {W1, W2, W3}, one risky asset, S, and a money market account, we have So = 4 for the risky asset. Moreover, the effective rate of interest on the money market account is 5% and at time t = 1 we have W1 W2 W3 S₁ 100 50 40 21 21 21 (a) Calculate all risk-neutral probability measures for this model. [4 Marks] (b) State if the model is arbitrage-free. Give a brief reason for your answer. [2 Marks] (c) A large bank has designed an investment product with payoff X at time t = 1. Given W₁ W2 W3 X 0 1 1.5 show that X is an attainable contingent claim. [4 marks]arrow_forwardQuestion 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.arrow_forwardFor the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.arrow_forward
- added 2 imagesarrow_forwardQuestion 2: (10 points) Evaluate the definite integral. Use the following form of the definition of the integral to evaluate the integral: Theorem: Iff is integrable on [a, b], then where Ax = (ba)/n and x₂ = a + i^x. You might need the following formulas. IM³ L² (3x² (3x²+2x- 2x - 1)dx. n [f(z)dz lim f(x)Az a n→∞ i=1 n(n + 1) 2 n i=1 n(n+1)(2n+1) 6arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forward
- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forwardA movie studio wishes to determine the relationship between the revenue generated from the streaming of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Theater revenue, x Streaming revenue, y (in millions of (in millions of dollars) dollars) 13.2 10.3 62.6 10.4 20.8 5.1 36.7 13.3 44.6 7.2 65.9 10.3 49.4 15.7 31.5 4.5 14.6 2.5 26.0 8.8 28.1 11.5 26.1 7.7 28.2 2.8 60.7 16.4 6.7 1.9 Streaming revenue (in millions of dollars) 18+ 16+ 14 12+ xx 10+ 8+ 6+ 2- 0 10 20 30 40 50 60 70 Theater revenue (in millions of dollars) Figure 1 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope…arrow_forward
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