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The geometric mean of a group of 15 observations was calculated as 12. It was later found that one observation was wrongly read as 19 instead of the correct value 9. Obtain the correct geometric mean of the data.
A BASKET CONTAINS 5 WHITE BALL (W) AND 5 BLACK BALL (B). WHAT IS THE POSSIBLE RESULT IF YOU DRAW 3 BALLS IN RANDOM FROM THE BASKET. LET X BE THE RANDOM VARIABLE REPRESENTING THE NUMBER OF BALCK BALL THAT OCCUR.
Ayana has $2.35 in nickels and dimes. If she has 33 coins in all, find the number of nickels and dimes
The production cost, represent by y, of smart phone devices are equal to the product of computing components (a) and the square of the number of devices (x), added to the product of labour (b) and number of devices (x); after which savings on reusable material (c) are subtracted
Write down an equation to represent the production cost (y) in terms of a, x, b and c
1. Solve the following LPP by graphical method
Maximize: 30X1 + 40X2
Subject to: 3X1 + 2X2 ≤ 600
3X1 + 5X2 ≤ 800
5X1 + 6X2 ≤ 1100 X1 ≥ 0, X2 ≥ 0
2. Solve the following LPP by Simplex method
Maximize: X1 + 4X2+5 X3
Subject to: 3X1 + 6X2 +3X3≤ 22
3X1 + 2X2+3X3 ≤ 14
3X1 + 2X2 ≤ 14 X1 ≥ 0, X2 ≥ 0, X3 ≥ 0
3. Solve the following LPP by Big M method
Maximize: 4X1 + X2
Subject to: 3X1 + X2 = 3
4X1 + 3X2 ≥6
X1 + 2X2 ≤ 3 X1 ≥ 0, X2 ≥ 0
4. Solve the following LPP by Two phase method
Maximize: -2X1 - X2
Subject to: X1 + X2 ≥ 2
X1 + X2≤ 4
X1 ≥ 0, X2 ≥ 0
5. Find the dual of the following
Maximize: 2X1 + X2
Subject to: X1 +5 X2 ≤ 10
X1 + 3X2≤ 6
X1 is unrestricted, X2 ≥ 0
Let φ : V → W be a linear transformation of vector spaces over the field F. The kernel of φ is by definition
the set ker(φ) ⊂ V of vectors v in V such that φ(v) = 0. The image of φ is the subset im(φ) of vectors w ∈ W
for which there exists some v ∈ V such that φ(v) = w.
(1) Show that the kernel of φ is a subspace of V .
(2) Show that the image of φ is a subspace of W.
(3) Show that φ is injective if and only if the kernel is 0.
(4) Show that φ is surjective if and only if the image is W.
Refer to Example 8. How large a sample will we need
in order to assert with probability 0.95 that the sample
mean will not differ from the true mean by more than
1.5. (replacing σ by s is reasonable here because the
estimate is based on a sample of size eighteen.)
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Below is the example 8
95% confidence interval for the mean of a normal population We know that silk fibers are very tough but in short supply. Engineers are making breakthroughs to create synthetic silk fibers that can improve everything from car bumpers to bullet-proof vests or to make artificial blood vessels . One research group reports the summary statistics1 n = 18 x = 22.6 s = 15.7 for the toughness (MJ/m3) of processed fibers. Construct a 95% confidence interval for the mean toughness of these fibers. Assume that the population is normal.
Reference book :- PROBABILITY AND STATISTICS FOR ENGINEERS (MILLER & FREUND’S) 9th edition. Page number :- 231
Number pattern: Investigate the difference between (the sum of the first and the third terms) and (two times the second/middle term) of any consecutive numbers of a quadratic sequence
1. 1;3;6;........
2. 2;4;8;......
(D^4 +13D^2 + 36)y = 0
The product cost, represented by y, of smart phone devices are equal to the product of computing componets(a) and the square of the number of divices(x) added to the product of labour(b) and number of devices(x), after which savings on reusable material(c) are subtracted. write down an equation to represent the production cost(y) in terms of a,x,b and c
