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Question 1. The current ratio for Potz and Pans has been calculated as 5.00:1 whereas the current ratio for WannaBees has been calculated as 1.76:1. Based on these results, it is prudent to assume that Potz and Pans is most likely to get the loan, although WannaBees also has good results. This is because the ratio is a measure of a company's capacity to meet its financial obligations. Both companies have current ratio figures greater than 1 to indicate that their assets are greater than the liabilities. Given that Potz and Pans has the highest ratio, it can be inferred that this is an indication that the company is financially well off. Still, the figures must be approached with caution since the...
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Question 4 b. n3+(n+1)3+(n+2)3Is divisible by 9 for all n≥1Proof The base case in this situation is n=0 which implies that n3+(n+1)3+(n+2)3=03+13+23=9 This is divisible by 9. Therefore, the basis holds true for n=0The inductive hypothesis becomes n=k≥0, k3+k+13+(k+2)3 is also divisible by 9 → k3+k+13+(k+2)3=9p…(i)By inductionn=k+1, equation (i) becomes (k+1)3+(k+2)2+(k+3)3=9p-k3+k+33…(ii) Simplifying (ii) we have =9p-k3+k+33=9p-k3+k3+9k2+9k+27=9p+9k2+k+3=9(p+k2+k+3)This implies that (k+1)3+(k+2)2+(k+3)3 is also divisible by 9 therefore, n3+(n+1)3+(n+2)3is divisible by 9 for all n≥1 d. 83 – 3n Is divisible by 5 for all n≥1Proof If n=1 then, 8n-3n= 81+31=5 this can be divided by 5....
Students name: Instructor: Course: Date: Light microscope 1. When a light microscope with an objective lens of 40X and its ocular lens is 10X, what is the total magnification of the image? The total magnification of an object viewed under a light microscope is the product of the objective lens and ocular lens magnification. Therefore total magnification is 40*10=400X 2. A revolving nose piece is the part of a light microscope positioned right above the stage and holds in position the low power, medium power, and the high power objective lens. Usually, these objective lenses are held in a manner that the revolving nose piece rotates allowing for the required...
Question 1The determination of the median height can be arrived at by taking the functional value of f (48). The value x should be substituted for 48. This should look like follows: F(48)= 3.1√(48)+19 =3.1(6.928)+19 =21.47+19 =40.5 Question 2 The calculation obtained above indicates a median height of 40.5 inches. However, the actual height is said to be 40.2 inches. The meaning of this analysis is that the model has overestimated the height by the difference of 40.5-40.2 which is 0.3 inches. Question 3 It is appropriate to determine the height of the girl during birth, considered as month zero. Once this has been achieved, it is good to substitute 0 in place of x. The function looks like...
Question 1 Activity Normal Time Crash Time Normal Cost Crash Cost Predecessor Max red NT-CT Cost to Crash per period CC-NC A 10 8 50 150 10-8=2 150-50=100 B 4 2 40 200 4-2=2 200-40=160 C 7 6 70 160 B 7-6=1 160-70=90 D 2 1 20 50 A,C 2-1=1 50-20=30 E 3 3 30 30 A,C 3-3=0 30-30=0 F 8 5 80 290 B 8-5=3 290-80=210 G 5 4 50 180 D 5-4=1 180-50=130 H 6 3 60 180 E,F 6-3=3 180-60=120 CC-NC/NT-CT(COST TO Crash Per Period) 150-50/10-8= 100/2=50 200-40/4-2=160/2=80 160-70/7-6=90/1=90 50-20/2-1=30/1=30 30-30/3-3=0 290-80/8-5=210/3=70 180-50/5-4=30/1=30 180-60/6-3=120/3=40 Project cost without crashing is 13 days(add the sum of Max Red) Normal cost is 400 Crash cost is 1040 Production cost is...
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Question 1) F(x) = -x2-4x +3For x= -2 then the f(x) = -(-2)2-4(-2)+3=7Question 2) 3(x-2)=-4(x+8)+103x-6= -4x-32+107x=-16X=-167Question 3) F(x) = xx-4All values would be real except when the value of x=4 hence the domain is D: allR: x≠4Question 4 Slope (m) = -3/7, y-intercept(c) =-4Y=mx+cHence, y=-37x -4Question 5 Slope(m) = -2, passes through (-1,6) hence the y intercept is Taking a point (x,y) where the line passes then Gradient is ∆y/∆x = y-6x-(-1)=-2y-6x+1=-2Hence y=-2x+4Question 6 (2x-7)(x+4)=02x(x+4)-7(x+4)=02x(x+4)=7(x+4)2x2+8x=7x+28 hence 2x2+x-28=0Using the factor method the values of X=7/2 , -4Question 7 Vertex f(x) =3x2-6x+8f(x) = a(x - h)2 + k, where (h, k) is the vertex hence f(x)...