Let f be a continuous function on [a, b] which is differentiable on (a,b). Then f is non-decreasing on [a,b] if and only if f′(x) ≥ 0 for all x ∈ (a,b), while if f is non-increasing on [a,b] if and only if f′(x) ≤ 0 for all x ∈ (a, b).

can you please prove this theorem? thank you!

78. Different states and counties are in the process of relaxing non-pharmaceutical interventions (i.e. social distancing) for the COVID-19 response. Please explain how you would setup a natural experiment to measure the effectiveness of different non-pharmaceutical interventions. Please write a hypothesis and how you would test the hypothesis. explain briefly

Using your text or online resources, what is the difference between communicable and non-communicable disease? What are the differences in the way we treat or prevent these two types of disease? What do you think is the most threatening communicable Disease? What do you think is the most threatening non-communicable disease

Every linear programming problem involves optimizing a:

Select one:

a. linear function subject to several linear constraints

b. linear regression model subject to several linear constraints

c. linear function subject to several non-linear constraints

d. non-linear function subject to several linear constraints

How can you describe the molecule CO2 in terms of polarity?

A client is 36 weeks’ gestation. The doctor has ordered a non-stress test to be performed. Her obstetrician provided her with no information about the test. The client is anxious and concerned about the test.

1. How will you explain the test to her?

2. Draw and label a reactive and draw a non-reactive NST strip

I have been told that a quick way to get the Feynman rules from a Lagrangian is to take an interaction term, forget about the fields and multiply an i. This works perfectly for example for QED but I wonder if there is an analogous non rigorous quick way to obtain the feynman rules of for example non abelian gauge theories.

A survey of 100,000 college graduates and 100,000 non-college graduates is conducted to determine how many of them own stock. 49,781 of the non-college graduates own stock vs. 50,219 for the college graduates. Analyze for a relationship between education and owning stock using a chi-square hypothesis test with alpha=1%.

Slotted non-persistent CSMA: Use the TWO-state Markov chain we discussed in class

to derive the throughput of non-persistent CSMA when nodes are required to transmit at the beginning of

a time slot, the length of a time slot is one propagation delay, and ideal acknowledgments are sent in 0

seconds over a secondary channel.

Does your employer offer an accountable or non-accountable plans for employee business expenses? Do you agree with the method? Provide support four your rationale.   If you are unsure of the type of plan your company has, would you suggest an accountable or non-accountable plan. Provide support for your rationale.