Question Solved1 Answer discrete mathematics a. Determine the validity of the following argument and explain your reasoning: All monkeys are animals. Some animals walk on two legs. Therefore some monkeys walk on two legs. (3 marks) I b. Determine the validity of the following argument and explain your reasoning Nothing mysterious scares him. Vampire bats scare him. Therefore vampire bats are not mysterious. (3 marks) a. Rewrite the statement " ne N, 3 an equilateral n-gon that is not equiangular" in English without using the symbol Vor 2. (2 marks) I b. Determine the negation of the statement "x € Ray 6 R such that x² + y2 = 1." (2 marks)

1 and X1 = -3, 12 = 2 1-171 -27 points) 71= 1 .72 = 2 ,73 = |-1| (-5) a) Show that 7, and 7, are not orthogonal. (b) Find an orthogonal basis for Span{T1, 12} * oon 00 (C) Let A be a 3 x 3 symmetric matrix whose eigenvalue 1, has the two linearly independent eigenvectors 71,72 and whose eigenvalue 1, has eigenspace spanned by 73. Find an orthogonal matrix P and a diagonal matrix D such that AP = PD. (d) What is P-1? T

# Statistics Null Hypothesis: # paired t-test # Pl ans carefully according to question Q-1 Q-2 Q-3 Q-4 #Pl ans all You have the following data on average number of cats per 1000 citizens in different cities in 2000 and 2020 years (all data is artificial). city 2000 2020 Moscow 300 350 New York 320 370 Beirut 200 240 Minsk 700 750 You want to answer the question: are there any statistically significant changes in the number of cats per 1000 citizens in these two years. Let us try two-sample t-test first. Consider values in columns 2000 and 2020 as two independent samples, apply two- sample t-test with symmetrical alternative and enter p-value obtained. Enter numeric value with 3 digits after the decimal point. Now let us consider difference between 2020 in 2000 for each city. city 2000 2020 diff Moscow 300 350 50 New York 320 370 50 Beirut 200 240 40 Minsk 700 750 50 Let us model numbers in the last column as an i.i.d. sample from some random variable X. Our null hypothesis is that there are no systematic changes between 2020 and 2000 and all the differences are just due to random flukes. What is the expected value of X provided that null hypothesis holds? Now let us use 1-sample t-test to test null hypothesis that values in column "diff" are obtained from population (random variable) with zero mean. Use symmetric alternative. Find p-value. Enter 4 digits after the decimal point. Now let us apply paired t-test to our initial samples. Use function scipy.stats.ttest_rel that do exactly this. Enter p-value (4 digits after the decimal point).

please do both please 3. When they work together, Jerry and Leo can do their weekly house chores in 58 minutes. When Leo works alone he can finish the chores in 12 minutes less time than Jerry. When Jerry works alone, how long will it take him to do the weekly chores in the house? 4. For each pair of functions determine where the zeros of the original function occur and state the equations of the vertical asymptotes of the reciprocal function. If no zeros exist, state so. a) 9(t)= 7 - 131+30 b) j(w) x2 + 1

4) The population of a town is modelled by P(t) = 25t2 + 150t + 25 000, where P(t) is the size of the population and t is the number of years since 1990. (a) Calculate the average rate of change of population with respect to time from 1990 to 1993. Include units. [3] [ (b) Estimate the instantaneous rate of change of population with respect to time in the year 1995. Include units. [3]

On July 1, 20Y1, Danzer Industries Inc. issued $60,000,000 of 10-year, 8% bonds at a market (effective) interest rate of 10%, receiving cash of $52,522,704. Interest on the bonds is payable semiannually on December 31 and June 30. The fiscal year of the company is the calendar year. Required: 1. Journalize the entry to record the amount of cash proceeds from the issuance of the bonds on July 1, 20Y1. 2. Journalize the entries to record the following: a. The first semiannual interest payment on December 31, 20Y1, and the amortization of the bond discount, using the straight-line method. b. The interest payment on June 30, 20Y2, and the amortization of the bond discount, using the straight-line method. 3. Determine the total interest expense for 20Y1. 4. Will the bond proceeds always be less than the face amount of the bonds when the contract rate is less than the market rate of interest? 5. Compute the price of $52,522,704 received for the bonds by using the present value tables.

An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, and C are defined as follows. A: Observe a number less than 4. B: Observe a number less than or equal to 2. C: Observe a number greater than 3. Find the probabilities associated with the following events using either the simple event approach or the rules and definitions from this section. (Enter your probabilities as fractions.) (a) S (b) AB (c) B (d) ABC (e) ANB (f) Anc (9) BNC (h) AUC (0) BUC