Question

Let

U={1,2, 3, ...,3200}.

Let S be the subset of the numbers in U that are multiples of 4, and let T be the subset of U that are multiples of 9. Since 3200 divided by 4 equals it follows that n(S)=n({4*1,4*2,...,4*800})=800

(a) Find n(T) using a method similar to the one that showed that n(S)=800

(b) Find n(S∩T).

(c) Label the number of elements in each region of a two-loop Venn diagram with the universe U and subsets S and T.

Answer #1

4. Let set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20}
set A = numbers in U that divide into 12 with no remainder,
set B = numbers in U that divide into 16 with no remainder, and set
C = the numbers in U that divide into 20 with no remainder.
a. Made a Venn diagram showing the elements of the sets U, A,...

1. Consider the following situation: The universal set U
is given by: U = {?|? ? ? , ? ≤ 12}
A is a proper subset of U, with those numbers that are
divisible by 4.
B is a proper subset of U, with those numbers that are
divisible by 3.
C is a proper subset of U, with those numbers that are
divisible by 2
a) Using Roster Notation, list the elements of sets U, A, B and
C....

2. There is a famous problem in computation called Subset Sum:
Given a set S of n integers S = {a1, a2, a3, · · · , an} and a
target value T, is it possible to find a subset of S that adds up
to T? Consider the following example: S = {−17, −11, 22, 59} and
the target is T = 65. (a) What are all the possible subsets I can
make with S = {−17, −11, 22,...

Given the set S = {(u,v): 0<= u<=4 and 0<= v<=3} and
the transformation T(u, v) = (x(u, v), y(u, v)) where x(u, v) = 4u
+ 5v and y(u, v) = 2u -3v,
graph the image R of S under the transformation T in the
xy-plan
and find the area of region R

1)
a) Let z=x4 +x2y, x=s+2t−u, y=stu2:
Find:
( I ) ∂z ∂s
( ii ) ∂z ∂t
( iii ) ∂z ∂u
when s = 4, t = 2 and u = 1
1) b> Let ⃗v = 〈3, 4〉 and w⃗ = 〈5, −12〉. Find a
vector (there’s more than one!) that bisects the angle between ⃗v
and w⃗.

1. Let u(x) and v(x) be functions such that
u(1)=2,u′(1)=3,v(1)=6,v′(1)=−1
If f(x)=u(x)v(x), what is f′(1). Explain how you arrive at your
answer.
2. If f(x) is a function such that f(5)=9 and f′(5)=−4, what is the
equation of the tangent line to the graph of y=f(x) at the point
x=5? Explain how you arrive at your answer.
3. Find the equation of the tangent line to the function
g(x)=xx−2 at the point (3,3). Explain how you arrive at your
answer....

THIS IS THE GENERAL EQUILIBRIUM PROBLEM THAT I PROMISED. YOU
FIRST SOLVE FOR THE INITIAL EQUILIBRIUM AS POINT A. WE CONSIDER TWO
DIFFERENT AND SEPARATE SHOCKS (I CALL THEM SCENARIOS). THE FIRST
SHOCK IS TO THE IS CURVE, THE SECOND SHOCK IS A ‘LM’ SHOCK. AGAIN,
WE CONSIDER THESE SHOCKS SEPARATELY SO THAT AFTER YOU COMPLETE
SCENARIO 1 (THE IS SHOCK), WE GO BACK TO THE ORIGINAL CONDITIONS
AND CONSIDER THE SECOND SCENARIO WHICH IS THE ‘LM’ SHOCK.
Consider the...

Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
of the athletic shoe industry? Is this likely to be favorable or
unfavorable for New Balance?
2- What issues does New Balance management need to address?
3-What recommendations would you make to New Balance Management?
What does New Balance need to do to continue to be successful?
Should management continue to invest...

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