Consider the production function ? = ? 1 3? 2 3. Let r and w
denote the prices of K (capital) and L (labor). Suppose ?̅ = 27
(fixed) and L is variable.
a. Write down the expression for the short-run production
function.
b. Compute the marginal product of labor (??? ) and the average
product of labor (??? ). Is the ??? increasing or decreasing? Is
??? >, <, or = ????
c. Find expressions for fixed cost [F],...
Determine if the following set forms a subspace in R^2.
The set is (x1,x2)^t ,in other words the column vector [x1,x2].
Can you go through each axiom and show your work?, I have a lot of
difficulty with these types of questions and I want to make sure I
understand.Thank you in advance.
Determine which of these sets spans R^3
q) (1,0,1) , (3,1,0), (-1,0,0),(2,1,5)
x) (2,1,2) , (1,1,1), (-3,0,-3)
y) (-1,2,1),(4,1,-3),(-6,3,5)
z) (1,0,0),(0,2,0),(1,2,0),(0,-1,1)
a) only q
b)q and x
c) q and z
d) only z
Given the following set of keys: {1, 2, 3} determine the number
of distinct left-leaning red-black trees that can be constructed
with those keys. Draw the tree for each possible key-insertion
order, showing the transformations involved at each step.
True or False.
1. If the set {v1,v2} is a basis of R^2, then the set {v1,v1+v2}
is also a basis of R^2.
2.If W be a vector space and V1,V2 are subspaces of W, then V1 u
V2 is also a subspace of W. V1 u V2 denotes the union of V1 and V2,
i.e. the set of vectors which belong to either V1 or V2 (or to
both).
3.If W be a vector space and V1,V2 are subspaces...
Determine if the following subsets are subspaces:
1. The set of grade 7 polynomials
2. The set of polynomials of degree 5 such that P (0) = 0
3. The set of continuous functions such that f (0) = 2
For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4,
3, 5, 3, 7] please compute the following
1. measures of central tendency (3 points)
2. standard deviation ( 5 points)
3. is 18 an outlier? (5 points)
4. describe the shape of the distribution (2 points)
3. For each of the following relations on the set Z of integers,
determine if it is reflexive, symmetric, antisymmetric, or
transitive. On the basis of these properties, state whether or not
it is an equivalence relation or a partial order.
(a) R = {(a, b) ∈ Z 2 ∶ a 2 = b 2 }.
(b) S = {(a, b) ∈ Z 2 ∶ ∣a − b∣ ≤ 1}.
Consider the following two sample data sets.
Set 1:
5
3
2
8
6
Set 2:
3
12
13
2
7
a. Calculate the coefficient of variation for each data set.
b. Which data set has more variability?
a. The coefficient of variation for set 1 is
nothing
%.
(Round to one decimal place as needed.)