Ken played golf yesterday and shot 107. Considering that he normally shoots in the low 80’s or high 70’s, this round of golf really frustrated him. It was so frustrating that he decided to buy new golf clubs. But first he had to give his old golf clubs away. He gave half of his golf clubs, plus half a club more, to Daniel. Then he gave half of his remaining golf clubs to Gary. Then he gave half of his remaining golf clubs and half a club more to Will. This left Ken with one club (his putter), which he decided to keep. How many golf clubs did Ken start with before giving them away?

Must be answered by working backwards. No algebra.

Problem 7-19 (Algo) A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.5 per minute. In serving themselves, customers take about 16 seconds, exponentially distributed.

a. How many customers would you expect to see, on average, at the coffee urn? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. How long would you expect it to take to get a cup of coffee? (Round your answer to 2 decimal places.)

c. What percentage of time is the urn being used? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

d. What is the probability that three or more people are in the cafeteria? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 16 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

f. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 16 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

A ball is thrown vertically upward from the top of a building 112 feet tall with an initial velocity of 96 feet per second. The distance s  (in feet) of the ball from the ground after t seconds is s (t) = 112 + 96t - 16t2 Complete the table and discuss the interpretation of each point. t s(t) Interpretation 0 0.5 1 2 100 100 200 200 Answer these questions. After how many seconds does the ball strike the ground? After how many seconds will the ball pass the top of the building on its way down? How long will it take the ball to reach the maximum height? What is the maximum height?

The question is to use Matlab to find the clamped cubic spline v(x) that interpolates a function f(x) that satisfies: f(0)=0, f(1)=0.5, f(2)=2, f(3)=1.5, f'(0)=0.2, f'(3)=-1 and then plot v(x).

This is my code so far:

x = [0 1 2 3];

y = [0 0.5 2 1.5];

cs = spline(x,[0 y 0]);

xx = linspace(0,3,101);

figure()

plot(x,y,'o',xx,ppval(cs,xx),'-');

IS THIS RIGHT? HOW CAN I GET MATLAB TO GIVE ME THE EQUATION OF v(x)?

1) Give parametrizations of the following circles with the indicated centers C(a, b) and radius R, and any other indicated properties.

a) C(1, 1), R = 2, traversed once counter clockwise.
b) C(1, 1), R = 2, traversed once clockwise.
c) C(0, 0), R = 1, starts at (0, 1).
d) C(0, 0), R = 1, starts at (−1, 0), traversed once clockwise.
e) C(0, 0), R = 1, traverses the circle twice on the domain 0 ≤ t ≤ 1.

The solution to the Initial value problem x′′+2x′+17x=2cos(6t),x(0)=0,x′(0)=0 is the sum of the steady periodic solution xsp and the transient solution xtr. Find both xsp and xtr.

Abstract algebra:

Deduce the main theorem of Galois theory from Artin's lemma.

1. Let V = { S, A, B, a, b, λ} and T = { a, b }, Find the languages generated by the grammar G = ( V, T, S, P } when the set of productions consists of:
   1. S → AB, A → aba, B → bab.
   2. S → AB, S → bA, A → bb, B → aa.
   3. S → AB, S → AA, A → Ab, A → a, B → b.
   4. S → A, S → B, A → abA, A → a, B → baB, B → b.
   5. S → AB, A → aBb, B → bAa, A → λ, B → λ.

Consider the mathematical system with the single element {1} under the operation of multiplication. Answer and explain the following:

a)      Is the system closed?

b)      Does the system have an identity element?

c)      Does 1 have an inverse?

d)     Does the associative property hold?

e)      Does the commutative property hold?

f)       Is {1} under the operation of multiplication a commutative group?

The selling prices of all stocks listed on the CDNX stock exchange are known to be normally distributed with a mean of $20 and a standard deviation of $4. (a) What percentage of stocks have a selling price between $20 and $40? (b) If 167 of the stocks sell for $26 or higher, how many stocks sell on the CDNX exchange? (c) What is the minimum selling price of the most expensive 5% of stocks? (d) 2 out of every 3 stocks sells for higher than what price? (e) The prices of the middle 80% of stocks are between what two values?

There exists a group G of order 8 having the following presentation: G=〈i,j,k | ij=k, jk=I, ki=j, i^2 =j^2 =k^2〉. Denotei2 bym. Showthat every element of G can be written in the form e, i, j, k, m, mi, mj, mk, and hence that these are precisely the distinct elements of G. Furthermore, write out the multiplication table for G (really, this should be going on while you do the first part of the problem).

Suppose we had defined some bijection f : N → Q +.

(a) Discuss how you could use f to prove that Q − is countably infinite. That is, define a new function h : N → Q − that uses f in some way. Discuss why using f makes h itself a bijection.

(b) Discuss how you could show that Q is countably infinite.

1. Find the volume of the solid using triple integrals. The solid bounded below by the cone

z= sqr x2+y2 and bounded above by the sphere x2+y2+z2=8.(Figure)

1. Find and sketch the region of integration R.
2. Setup the triple integral in Cartesian coordinates.
3. Setup the triple integral in Spherical coordinates.
4. Setup the triple integral in Cylindrical coordinates.
5. Evaluate the triple integral in Cylindrical coordinates.