The following data have been collected for a dry food:
Water Activity Moisture Content
(g H2O / g product)
0.1 0.060
0.2 0.085
0.3 0.110
0.4 0.122
0.5 0.125
0.6 0.148
0.7 0.173
0.8 0.232
(4 Point) This product was stored in an environment where after 30 days of storage the
moisture content of the product (in dry basis), as measured in the laboratory, was 25%. If
you were responsible for the warehouse and the quality of this product, would you be
concerned about the product quality based on its water activity? If you were, what would
you be concerned about?

The following reaction is conducted, starting with 0.60 M BF3 and 0.60 M NH3.

BF3 (aq) + NH3 (aq) ⇌ BF3NH3 (aq)

Plot the value of Q for this reaction against the concentration of BF3NH3 on the axes provided, including adding value markers to the axes. To do this, calculate the value of Q at the following BF3NH3 concentrations: 0.0 M, 0.1 M, 0.2 M, 0.3 M, 0.4 M, and 0.5 M. If the value of Kc for this reaction is 22.8, use your plot to determine the equilibrium concentration of BF3NH3. This problem is trickier than you think! Be sure you are correctly calculating all relevant concentrations at each point!

An expensive watch is powered by a​ 3-volt lithium battery expected to last three years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed.a. Determine the probability that the​ watch's battery will last longer than 3.8 years.b. Calculate the probability that the​ watch's battery will last more than 2.15 years.c. Compute the​ length-of-life value for which 15​% of the​ watch's batteries last longer.

a. The probability that the battery will last longer than 3.8 years is​

b. The probability that the battery will last more than 2.15 years is

c. The​ length-of-life value for which 15​% of the batteries last longer is years.

A peanut can has the usual “can shape” of a circular cylinder. Its sides are made of cardboard, its bottom is made of thick plastic-coated aluminum foil, and its top lid is made of clear plastic. It must have a volume of 480 cubic centimeters. The cardboard material used for the sides costs 0.1 cents per square centimeter, the foil material used for the bottom costs 0.3 cents per square centimeter, and the plastic material used for the top lid costs 0.5 cents per square centimeter. What dimensions should the can have in order to minimize the cost of the materials from which it is made?

Consider an annuity for 10 years, whose payments vary in geometric progression. An annual effective interest rate of 6% is used. Obtain the financial value at t = 29/05/2010 of this annuity considering different cases:

1. Annual payments increasing 3% annually. First payment (€1,650; 29/05/2011).
2. Annual payments increasing 5% annually. First payment (€1,650; 29/05/2011).
3. Monthly payments increasing 0.3% monthly. First payment (€175; 29/06/2010).
4. Monthly payments, constant during the year and increasing 4% annually. First payment (€175; 29/06/2010).

A peanut can has the usual “can shape” of a circular cylinder. Its sides are made of cardboard, its bottom is made of thick plastic-coated aluminum foil, and its top lid is made of clear plastic. It must have a volume of 480 cubic centimeters. The cardboard material used for the sides costs 0.1 cents per square centimeter, the foil material used for the bottom costs 0.3 cents per square centimeter, and the plastic material used for the top lid costs 0.5 cents per square centimeter. What dimensions should the can have in order to minimize the cost of the materials from which it is made?

A block of mass m begins at rest at the top of a ramp at elevation h with whatever PE is associated with that height. The block slides down the ramp over a distance d until it reaches the bottom of the ramp. How much of its original total energy (in J) survives as KE when it reaches the ground? (In other words, the acceleration is not zero like it was in lab and friction does not remove 100% of the original PE. How much of that original energy is left over after the friction does work to remove some?) m = 8.5 kg h = 5.5 m d = 5 m μ = 0.3 θ = 36.87°

A car wash offers both a regular wash and a deluxe wash for their customers. They track their customers over time and determine that a customer orders the deluxe wash with a probability of 0.3. They also offer air fresheners for their customer for a nominal fee and find that regular wash customers get an air freshener with a probability of 0.45, and deluxe wash customers get an air freshener with probability 0.8. Assume that the car wash only offers the regular and deluxe packages.

a.) What is the probability that a customer gets an air freshener, regardless of the type of wash they ordered?

b.) What is the probability a customer ordered the deluxe package, provided that you know they purchased an air freshener?

Year   Percentage
2000   28
2001   32
2002   36
2003   40
2004   44
2005   51
2006   53
2007   57
2008   60
2009   66

Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment.

alpha= 0.3 and beta= 0.4. Then calculate MAD.

----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Quarter   Price
Q1 2017   186.3
Q2 2017   190.9
Q3 2017   195.2
Q4 2017   195.2
Q1 2018   198.7
Q2 2018   201.2

Forecast the price index for Q3 2018 using a​ three-period simple moving average. Then calculate MAD.

Consider an M / M / 1 queueing system with capacity N = 1, arrival rate λ = 0.2 customers per minute, and service rate µ =0.3 customers per minute. Let X(t) be the number of customers present at time t.

a) Suppose that X(0) =0. Calculate P{X(1) = 0} and P{X(10) = 0}

b) Suppose that X(0) =1. Calculate P{X(1) = 0} and P{X(10) = 0}

c) Could you have predicted the difference between the answers in part a, and part b by the general theory of limiting probabilities?