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Is the word problem a chef needed 32 plates away in the kitchen. She broke 4 of the plates. How many plates does she have left? A conclusion of 32%4=8?

prove that ((x+y+z)/3)^(x+y+x) <=x^x.y^y.z^z<=((x²+y²+z²)/(x+y+z))^(x+y+z) where x,y,z bleongs to N

For any two subsets A and B of a set U , we define their symmetric difference to
be A ∆ B = (A \ B) ∪ (B \ A)
i) Check whether ∆ distributes over ∩ .
ii) Show that A ∆(fi)=A.
iii) Prove that A∆B= (A∩ B' ) U (A' ∩B)

Let A, B and C be subsets of a set. Prove that , A ∩ B ⊆ C iff A ⊆ B' U C

Use the Cauchy-Schwarz inequality to solve x³-25x²- 4x+ 100= 0 if we know that all its roots are rational.

2. ten person were appointed in a clerical position in an office. Their performance was noted by giving a test and marks recorded out of 50. They were given 6 months training and and again they were given a test marks were recorded out of 50.
Employees
A
B
C
D
E
F
G
H
I
J
Before training
25
20
35
15
42
28
26
44
35
48
After training
26
20
34
13
43
40
29
41
36
46
Apply the t.test can you conclude that the employees benefitted by the training.you are given ᾳ 5 %.

The set of all the points (x, y,z) satisfying the equation x−z = z−y represents a
line.

Sam purchased 500 company shares at $3.20 per share. Brokerage fees were 1.5% of the purchase price. Sam is paid a dividend of 26 cents per share, then immediately sells the shares for $4.80 each. If he pays no further brokerage fees, what is Sam’s total profit?

Use the Cauchy-Schwarz inequality to solve x³-25x²-4x+100=0, if we know
that all its roots are rational.

Find the orthogonal canonical reduction of the quadratic form
-x²+y²+z²+xy+xz-6yz
. Also, find its principal axes.