1. A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 64 like Snickers, 125 like Twix, 141 like Reese's Peanut Butter Cups, 30 like Snickers and Twix, 61 like Twix and Reese's Peanut Butter Cups, 43 like Snickers and Reese's Peanut Butter Cups, and 18 like all three kinds of chocolate candy. How many students like Twix and Reese's Peanut Butter Cups only?

2. A survey of 391 children given at a local elementary school showed that 200 like chocolate ice cream, 175 like pistachio ice cream, and 141 do not like chocolate or pistachio ice cream. How many children like at most one kind of ice cream mentioned in the survey?

Given the function f(x,y)=2x^3 + 6xy^2 - 3y^2 - 150x. Find the local minimums, maximums and saddle points of f(x,y).

(a) What is the maximum degree of a vertex in a simple graph with n vertices?

(b) What is the maximum number of edges in a simple graph of n vertices?

(c) Given a natural number n, does there exist a simple graph with n vertices and the maximum number of edges?

Diagonalize the matrix (That is, find a diagonal matrix D and an invertible matrix P such that

A=PDP−1.

(Do not find the inverse of P). Describe all eigenspaces of A and state the geometric and algebraic multiplicity of each eigenvalue.

A=

Supply: logP= -15.00+1.50 logQ

Demand: logP=5020-0.75 logQ

1. Create a table as shown. The first column contains values of Q from 500 to 10,000, in intervals of 500

2. Plot the supply and demand on the diagram. Label right X and Y axes

New supply: logP=-15.00+1.50 logQ+0.90

1. Create 2 new columns of‘New supply (log P)’ and 'new supply (P) for the new supply

2. Add the new supply curve to the existing diagram. Label the new supply curve

Show that if G is a group of order np where p is prime and 1 < n < p, then G is not simple.

(Please do not use Sylow theorem)

Belden, Inc. acquires 30 percent of the outstanding voting shares of Sheffield, Inc. on January 1, 2017, for $306,000, which gives Belden the ability to significantly influence Sheffield. Sheffield has a net book value of $784,000 at January 1, 2017. Sheffield's asset and liability accounts showed carrying amounts considered equal to fair values except for a copyright whose value accounted for Belden's excess cost over book value in its 30 percent purchase. The copyright had a remaining life of 16 years at January 1, 2017. No goodwill resulted from Belden's share purchase. Sheffield reported net income of $182,000 in 2017 and $244,000 of net income during 2018. Dividends of $64,000 and $90,000 are declared and paid in 2017 and 2018, respectively. Belden uses the equity method. On its 2018 comparative income statements, how much income would Belden report for 2017 and 2018 in connection with the company's investment in Sheffield? If Belden sells its entire investment in Sheffield on January 1, 2019, for $412,000 cash, what is the impact on Belden's income? Assume that Belden sells inventory to Sheffield during 2017 and 2018 as follows. What amount of equity income should Belden recognize for the year 2018? Year Cost to Belden Price to Sheffield Year-End Balance (at Transfer Price) 2017 $36,000 $60,000 $20,000 (sold in following year) 2018 34,160 61,000 38,000 (sold in following year)

Let S = {x : x 3 < 1}.

(a) Find supS

(b) Is S bounded?

Thank you!

Convert from rectangular to polar form and vice versa:

a. ?6

b. 2√5∠135∘

c. −2 − ?2√3

d. √2∠45∘

Please show your steps because I need to understand how we reached the solution

Thank you

(a) Patty Stacey deposits $2200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 6%, compounded annually. (Round your answer to the nearest cent.) (b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $2200 deposits at the end of each of the next 15 years. If the interest rate is 6%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)

How many non-isomorphic 5-vertex connected planar graphs are there? Use Sage
to produce / depict them. Include your Sage code. A number alone will receive no
credit.

x' = -3x + 2y,

y' = -10x + 5y +2e^t/cos 2t

Solve the system by variation of parameters

Determine whether each set of vectors is linearly dependent or linearly independent.

a) (1,1,0,1), (1,0,1,1), (0,1,1,1)

b) (1,0,1,0), (0,1,0,1), (1,-1,1,-1), (1,-1,0,0)

Find the value of the digit indicated with a question mark . ISBN value 0-321-50230-?