Question

1. Let D1 and D2 be two open disks in R^2 whose closures D1 and D2 intersect in exactly one point, so the boundary circles of the two disks are tangent. Determine which of the following subspaces of R 2 are connected: (a) D1 ∪ D2 . (b) D1 ∪ D2 . (c) D1 ∪ D2 .

Answer #1

1. Suppose two linear demand curves D1 and D2 have the same
vertical intercept and D1 is steeper than D2:
i. At any given P, which demand is more elastic?
ii. At any given Q, which demand is more elastic?
2 Suppose two linear demand curves D1 and D2 are parallel to
each other and D1 is higher than D2:
i. At any given P, which demand is more elastic?
ii. At any given Q, which demand is more elastic?...

Let d1 = 2, d2 = 3, and dn = dn−1 · dn−2. Find an explicit
formula for dn in terms of n and prove that it works.

i) Show how you would create two dummy variables,
d1 and d2, for when a person started smoking,
if we wanted never smokers to be the referent level.
D1={ 1; if smoking as an adult, 0; if
otherwise
D2={ 1; if smoking as a child, 0; if
otherwise
ii) Using the dummy variables from part (i), suppose you decide
to do the analysis using a multiple regression model:
Y = b0
+ b1d1 + b2d2 +
b3age + b4(d1)(age) +
b5(d2)(age) +...

1. Let S and R be two relations below.
R = {(1, 3), (1, 2), (8, 0), (6, 9)}
S = {(7, 5), (1, 6), (3, 1), (0, 3), (9, 4), (8, 6)}
Please find S◦R and R◦S.
Given two relations S and R on Z below, please determine the
following relations.
R = {(a, b) |a + 2 = b}
S = {(a, b) |3a > b}
(a) R−1
(b) R
(c) R◦R
(d) R−1 ◦ R
(e) R−1...

Consider the following axiomatic system: 1. Each point is
contained by precisely two lines. 2. Each line is a set of four
points. 3. Two distinct lines that intersect do so in exactly one
point.
True or false? There exists a model with no parallel lines.

(1 point) Which of the following subsets of {R}^{3x3} are
subspaces of {R}^{3x3}?
A. The 3x3 matrices with determinant 0
B. The 3x3 matrices with all zeros in the first row
C. The symmetric 3x3 matrices
D. The 3x3 matrices whose entries are all integers
E. The invertible 3x3 matrices
F. The diagonal 3x3 matrices

Two parallel, coaxial circular disks 1 and 2, each of area 21.8
cm^2, are separated by a small distance 0.8 mm. The disks 1 and 2
are charged uniformly with charge -4 nC and 1 nC, respectively. How
much work is required for an external force to move a proton
located between and far from the edges of the disks very slowly
from a point very close to disk 1 to one very close to disk 2?

Choose the correct answer:
1) The curve r = 2 + cos(2θ) is symmetric about Select one:
A_ all of these answers.
B_ the x-axis with vertical tangent at θ= π
C_ the origin with vertical tangent at θ = 2π
D_ the y-axis with vertical tangent at θ = 0.
2) The equation 3x^2 - 6x - 2y + 1= 0 is Select one:
A- a parabola open up with vertex (-1 , 1) and p = 1/6
B-...

1, Let f be a function such that f′′(x) =x(x+ 1)(x−2)^2. Find
the open intervals on which is concave up/down.
2. An inflection point is an x-value at which the concavity of a
function changes. For example, if f is concave up to the left of
x=c and f is concave down to the right of x=c, then x=c is an
inflection point. Find all inflection points in the function from
Problem 1.

Simultaneously roll two fair 3-sided dice whose sides are
numbered 1, 2, and 3. Let random variable K be the sum of the two
dice.
a) Calculate and plot the PMF of K.
b) Determine the expected value of K.
c) Calculate the variance of K.
d) Determine the expected value of K2 .
e) Determine the variance of K2 .

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