Search & Filtering
Suppose z is a function of x and y and tan(√x + y) = e^z^2. Determine ∂z/∂x and ∂z/∂y.
1.One-tailed test;variance is known,a=0.05,n=35
A dog owner wants to minimize the cost of buying dog food for his bullmastiffs. Two types of dog
food are available mixed with three kinds of minerals: calcium, phosphorous, and potassium. The per
kilo cost of dog food A and dog food B are P 20.00 and P 16.00, respectively, whereas the minimum
requirement of calcium, phosphorous and potassium are 75, 50, and 30 units, respectively. Also, in
one kilogram of dog food A, 5 units of calcium, 2 units of phosphorous, and 3 units of potassium are
mixed. Again, in one kilogram of dog food B, 4, 6, 3 units of calcium, phosphorous, and potassium,
respectively are mixed. How many of each type of dog food must be bought to minimize the cost?
2. Prove that a relation R on a set A is symmetric if R-1 = R.
3. Give an example of a relation that is reflexive but neither symmetric nor transitive.
4. Show that the relation ‘is perpendicular to’ over the set of all straight lines in the plane is symmetric but neither reflexive nor transitive.
5. Let S and T be sets with m and n element respectively. How many elements has S × T? How many relations are there in S × T?
6. If R and S are equivalence relations in the set X, prove that R ∩ S is an equivalence relation.
7. Show that the relation of congruence modulo m has m distinct equivalence classes.
8. Show that a partition of a set S deter- mines an equivalence relation in S.
9. Let S = {n: n ∈ N and n > 1}. If a, b ∈ S define a ~ b to mean that a and b have the same number of positive prime factors (distinct or identical). Show that ~ is an equivalence relation.
10. Prove that in the set N × N, the relation R defined by (a, b) R (c, d ) ⇔ ad = bc is an equivalence relation.
1.Prove that any graph (not necessarily a tree) withvvertices andeedges that satisfiesv>e+1v>e+1will NOT be connected.
1. We define a forest to be a graph with no cycles.
a) Explain why this is a good name. That is, explain why a forest is a union of trees.
b) Suppose FF is a forest consisting of mm trees and v vertices. How many edges does FF have? Explain.
c) Prove that any graph GG with v vertices and e edges that satisfies v<e+1 must contain a cycle (i.e., not be a forest).
A dog owner wants to minimize the cost of buying dog food for his bullmastiffs. Two types of dog
food are available mixed with three kinds of minerals: calcium, phosphorous, and potassium. The per
kilo cost of dog food A and dog food B are P 20.00 and P 16.00, respectively, whereas the minimum
requirement of calcium, phosphorous and potassium are 75, 50, and 30 units, respectively. Also, in
one kilogram of dog food A, 5 units of calcium, 2 units of phosphorous, and 3 units of potassium are
mixed. Again, in one kilogram of dog food B, 4, 6, 3 units of calcium, phosphorous, and potassium,
respectively are mixed. How many of each type of dog food must be bought to minimize the cost?
A. By adding 3 in each of the following in the set 6, 3, 5, 9, 7, 4 we obtain the set 9, 6, 8, 12, 10 and 7. Show how these 2 sets have the same standard deviations but different means.
B. After 3 months of training between these 2 employees, the proficiency test results were as follows:
Employee A: 58, 59, 60, 54, 65, 66, 52, 75, 69, 52
Employee B: 56, 87, 89, 78, 71, 73, 84, 65, 66, 48
Who do you consider more consistent? Show the statistical proof.
C. The following are the wages per hour of call center agents in a certain company:
Wages No.
P 60-61 12
P 62-63 18
P 64-65 27
P 66-67 20
P 68-69 25
P 70-71 22
P 72-73 17
P 74-75 15
P 76-77 10
Determine the following:
1. Quartile Deviations of their wages
2. Standard Deviation of their wages
B. Construct the frequency distribution of the following scores use 5 as class interval and
10 as the size of groupings. (20 points)
20 45 28 35 47 33 39
47 75 58 62 44 58 60
72 34 42 43 73 50 43
27 30 66 38 47 38 39
70 62 37 45 25 39 74
VIII. EVALUATION
Construct the following scores using frequency distribution.
88 77 72 68 66 60 55 51 47 37 26
85 77 71 68 64 58 54 50 45 36 25
81 75 71 67 63 57 53 50 45 35 24
80 75 76 67 63 57 52 49 44 33 23
79 74 70 56 62 57 52 49 40 29 19
79 74 69 66 61 56 51 48 39 27
74 64 74 46 54 64 58 66 51
76 72 62 74 72 53 64 72 50
76 66 60 35 69 40 72 38 48
45 45 33 48 55 21 32 48 66
50 55 49 40 48 47 45 54 34
(𝑥𝑦2+ 𝑦 − 𝑥)𝑑𝑥 + 𝑥(𝑥𝑦 + 1)𝑑𝑦 = 0
