Your job is to fully staff your facility at the lowest cost. The facility must have at least 2 people w working from 6am-8pm Monday thru Friday and at least 1 person working from 10am to 6 pm on Saturdays. Nobody works on Sundays. Full time staff must work 8 hours a day, five days a week. Part time staff work 4 hours a day, 5 days a week. Nobody is allowed to work overtime. All employees receive the same hourly rate. What is the number of part time and full time employees that fully staffs the operation with the smallest total labor cost?

"Find the retail cost of gasoline (per unit volume) in your area and find the cost of electricity for residential users in your area. (a) Compare the cost of energy (per MJ) from gasoline and from electricity (b) The efficiency of a gasoline automobile is about 20% and the efficiency of a battery electric vehicle is about 85%. Discuss the relative transportation costs for gasoline and electric vehicles."

a real sequence x_n is defined inductively by x₁ =1 and x_n+1 = sqrt(x_n +6) for every n belongs to N

a) prove by induction that x_n is increasing and x_n <3 for every n belongs to N

b) deduce that x_n converges and find its limit

1(a) If ut − kuxx = f, vt − kvxx = g, f ≤ g, and u ≤ v at x = 0, x = l and t = 0, prove that u ≤ v for 0 ≤ x ≤ l, 0 ≤ t < ∞.

(b) If vt − vxx ≥ cos x for −π/2 ≤ x ≤ π/2, 0 < t < ∞, and if v(−π/2, t) ≥ 0, v(π/2, t) ≥ 0 and v(x, 0) ≥ cos x, use part (a) to show that v(x, t) ≥ (1 − e −t ) cos x.

If you needed to compare two simulated scenarios, and in one of them a self-driving car is braking up to -3 meters per second squared, in another up to -8 meters per second squared (unit of acceleration), which one do you think is more risky? Please explain your answer or how you arrived to this conclusion.

Consider an algebra where the vector space is ℝ³ and the multiplication of vectors is the conventional cross product you learned as a beginning physics student. Find the structure constants of this algebra.

Find Taylor series expansion for sin^2(z)

Solve by reduction of order

xy" - xy' + y = 0

1. An experiment was conducted to test the effect of different lighting systems and the presence or absence of a watchman on the average number of car burglaries per month at a parking garage. The data are in the following table and also in the file GARAGE, where the variables are named BURGLAR, LIGHTING and WATCHMAN.

1. Using the Lenth procedure, find which effect(s) (if any) appear significant.

effects

2. Interpret all of these significant effects.
3. Permanently upgrading the lighting in the garage will cost $700 per month. Hiring awatchman will cost $3000 per month. It is estimated that lawsuits and loss of business cost on average $2000 per burglary. Is it worth it to hire a watchman, install lights or both?

Give a proof or counterexample, whichever is appropriate.

1. NOT (∃x, (P(x) OR Q(x) OR R(x))) is logically equivalent to ∀x, ((NOT P(x)) AND (NOT Q(x)) AND (NOT R(x))).

2. NOT (∃x, (P(x) AND Q(x) AND R(x))) is logically equivalent to ∀x, ((NOT P(x)) OR (NOT Q(x)) OR (NOT R(x))).

3. NOT (∃x, (P(x) ⇒ Q(x))) is logically equivalent to ∀x, (P(x)⇒ NOT Q(x)).

4. NOT (∃x, (P(x) ⇒ Q(x))) is logically equivalent to ∀x, (P(x) AND (NOT Q(x))).

5. ∃x, (P(x) OR Q(x)) is logically equivalent to (∃x, P(x)) OR (∃x, Q(x)).

6. ∃x, (P(x) AND Q(x)) is logically equivalent to (∃x, P(x)) AND (∃x, Q(x)).

7. ∀x, (P(x) OR Q(x)) is logically equivalent to (∀x, P(x)) OR (∀x, Q(x)).

8. ∀x, (P(x) AND Q(x)) is logically equivalent to (∀x, P(x)) AND (∀x, Q(x)).

9. ∀x, (P (x) ⇒ Q(x)) is logically equivalent to (∀x, (x)) ⇒ (∀x, Q(x)).

Want a SEIRS model with stochastic transmission project proposal under the following headings for a MSc student in Applied Mathematical Modelling :
1)Topic
2) introduction
3) Background to the study
4)problem statement
5)aims
6)objectives
7)methodology

describe through mathematics how the central concepts of convergence and continuity transform from the usual Euclidean distance on the real line, to the more abstract notion of distance as given by a metric on a metric space, to finally a description that only refers to open sets. It should also describe how the concept of topology emerges from metric spaces.