Suppose that a bacterial count satisfies the logistic hypothesis. The initial count is 450 organisms / mL and the maximum sustainable count is 10,000 organisms / mL. The count is found to increase 18% in the first 12 hours. Establish and solve an Initial Value Problem to express the count as a function of time, graph this function and calculate how long the count reaches 8,000 organisms / mL.

1. expand each function in a Taylor Series and determine radius of convergence.

a) f(x) = 1/(1-x) at x0 = 0

b) f(x) = e^(-x) at x0 = ln(2)

c) f(x) = sqrt(1+x) at x0 = 0

* Space travel is expensive! For their trip to the Moon, the Apollo astronauts’ living quarters were only 213 cubic feet (that’s smaller than a typical bathroom in a house). How many dollar bills could fit in there?

@ Would a stack of dollar bills in the amount of the U.S. national debt reach from the Earth to the Moon? Show your calculations to receive any credit!

@ Pluto has been hard to measure from Earth because of its atmosphere. In 2007 Young, Young, and Buie measured Pluto as having a diameter of 2322 km. The New Horizons probe traveled to Pluto and measured it up close and we now know the actual size is 2372 km. What was the percent error of the 2007 measurement?

Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)2 = x^2 + y^2, and let (x0, y0, z0) be a point
in their intersection. Show that the surfaces are tangent at this point, that is, show that the
have a common tangent plane at (x0, y0, z0).

Let k be an integer satisfying k ≥ 2. Let G be a connected graph with no cycles and k vertices. Prove that G has at least 2 vertices of degree equal to 1.

Show that the following two vector fields are conservative and find associated scalar potentials.
(a) F = 2ρsin(2φ) ρ + 2ρcos(2φ) φ + k
(b) F = (2r cos2 φ + sinθ cosφ) r + cosθ cosφ θ − [r(sin(2φ)/sinθ) + sinφ] φ

Question 3(a):
When customers arrive at Cool's Ice Cream Shop, they take a number and wait to be called to purchase ice cream from one of the counter servers. From experience in past summers, the store's staff knows that customers arrive at a rate of 150 per hour on summer days between 3:00 p.m. and 10:00 p.m., and a server can serve 1 customer in 1 minute on average. Cool's wants to make sure that customers wait no longer than 10 minutes for service. Cool's is contemplating keeping three servers behind the ice cream counter during the peak summer hours.
(i) Will this number be adequate to meet the waiting time policy?
(ii) What will be the probability that 3 to 4 customers in Shop?
(iii) In winter season, arrival rate of customer is reduced to half from 3:00 p.m. and 10:00 p.m. What decision should be taken by the owner according to cost cutting point of view?
Question 3(b):
Analysis of arrivals at a PSO gas station with a single pump (filler) has shown the time between arrivals with a mean of 10 minutes. Service times were observed with a mean time of 6 minutes.
(i) What is the probability that a car will have to wait?
(ii) What is the mean number of customers at the station?
(iii) What is the mean number of customers waiting to be served?
(iv) PSO is willing to install a second pump when convinced that an arrival would expect to wait at least twelve minutes for the gas. By how much the flow of arrivals is increased in order to justify a second booth?

Explain Fishers Exact Test ?

Difference between BLUE and BLUP ? Different properties of BLUP

Do I need to know where on the dart board the 3, 1, 5 cm darts landed to obtain precision and accuracy?

For the data and calculation for this lab report assume that a dart was thrown at bullseye 3 times with the aim of hitting the middle, the 3 distance from the middle obtain where 3cm, 1cm, and 5cm. Calculate the average, the percent error and discuss in your lab report and emphasize on the accuracy vs precision part

1. Evaluate the double integral for the function f(x,y) and the given region R.

R is the rectangle defined by -2  x  3 and 1   y  e⁴

2. Evaluate the double integral

for the function f(x, y) and the region R.

f(x, y) =

; R is bounded by the lines

x = 1, y = 0, and y = x.

3. Find the average value of the function f(x,y) over the plane region R.

f(x, y) = xy; R is the triangle bounded by y = x, y = 2 - x, and y = 0

4. Verify that y is a general solution of the differential equation and find a particular solution of the differential equation satisfying the initial condition.

y =

;  

= −2xy²;  y(0) = 7

A volume is described as follows:

1. the base is the region bounded by x = − y 2 + 16 y + 5 and x = y 2 − 30 y + 245 ;

2. every cross section perpendicular to the y-axis is a semi-circle. Find the volume of this object.

Prove: Let A be an mxm nonnegative definite matrix with rank(A)=r Then there exists an mxr matrix B having rank of r, such that A=BB^T

1. (15 pts) Is the matrix A =   1 0 1 0 1 1 1 1 2   diagonalizable? If yes, find an invertible matrix P and a diagonal matrix Λ such that P −1AP = Λ.

Verify that V in the previous example satisfies the axioms for a vector space.