4x "It is emphatically the province and duty of the judicial department to say what the law is. Those who apply the rule to particular cases, must of necessity expound and interpret that rule. If two laws conflict with each other, the courts must decide on the operation of each." -Chief Justice John Marshall 1803 Which conclusion can be drawn from this excerpt of the Supreme Court's decision in Marbury v.Madison? A The junsdiction granted to the judicial branch is limited to federal and constitutional laws This decision established the concept of judicial review and strengthened the role of the Judicial branch B C This decision gave Congress the authority to charter the National Bank, which angored the Anti-Federalists This decision strengthened the "Elastic Clause" of the U.S. Constitution and oxpanded the powers of Congress D

What threshold p value would you use to ascribe significant to the results of your inferential statistics, briefly explain your reasoning

Solve this system of equations, show all the calculations.  0.6 * x^-0.4 * y^0.4 - 50λ = 0  0.4 * x^0.6 * y^-0.6 - 20λ = 0 200 - 50x - 20y = 0

You borrow £10,000 from a friend and agree that you will repay the loan by four equal end-of-year instalments. Your friend will charge you a constant annual interest rate of 8%. What will be your annual repayments?

Use the Fourier-Poisson formula to find the limit as t → ∞ of the solution to the problem Ut = κUxx, x ∈ R, t > 0, U(x, 0) = 3 x < 0                   1 x > 0 .  Plot the solutions at several instants of time and describe in qualitative terms the behaviour of the solution to as t → ∞. What is limt→∞ U(x, t)?

EXPLAIN THE MAIN REASONS OF HYPOTHESIS TESTING IN STATISTICAL ANALYSIS? 1

A general insurance company offers policies for three different kinds of rowing boat: A Type, B Type and C Type. For A Type boats, the number of claims per boat per year follows a Poisson distribution with parameter 𝜇. The following data is available for the past five years: Year 1 2 3 4 5 Number of A Type boats insured 80 98 145 158 166 Number of claims 12 21 26 38 52 (i) Derive the maximum likelihood estimate of 𝜇 based on the data above.

The number of signicant gures in 0.00150 is: A. 2 B. 3 C. 4 D. 5 E. 6

A common way to represent a game in which two players have two strategies to choose from and play simultaneously or without knowing what the other has chosen to do, is:

A machine X costs rs. 5000. its maintenance cost is Rs. 1000 in each of first four years and then it increases by Rs. 200 every year. Assuming that the machine has no salvage value and the maintenance cost incurred in the beginning of each year , determine the optimal replacement time for the machine assuming that the time value of money is 10% pa.

Think about Frost’s poem “Mending Wall.” What does “Good fences make good neighbors” mean? Why does the speaker disagree with his neighbor about the fence?