Let 𝐺

be any undirected graph with positive edge weights, and 𝑇 be a

minimum 

The

prefix function π[q] in KMP represents:

A startup replaces a naive search algorithm (O(n²)) with an optimized algorithm (O(n log n)) without changing hardware. After deployment, performance improves significantly.

Which conclusion is MOST appropriate?

The Edison Electric Institute has published figures on the number of kilowatt hours

used annually by various home appliances. It is claimed that a vacuum cleaner uses

an average of 46 kilowatt hours per year. If a random sample of 12 homes included

in a planned study indicates that vacuum cleaners use an average of 42 kilowatt

hours per year with a standard deviation of 11.9 kilowatt hours, does this suggest

at the 0.05 level of significance that vacuum cleaners use, on average, less than 46

kilowatt hours annually? Assume the population of kilowatt hours to be normal. how much is critical region

A random sample of 100 recorded deaths in the United States during the past

year showed an average life span of 71.8 years. Assuming a population standard

deviation of 8.9 years, does this seem to indicate that the mean life span today is

greater than 70 years? Use a 0.05 level of significance.

Suppose that the characteristic polynomial of some matrix

A is found to be 

p(λ) = (λ − 1)(λ − 3)^2

(λ − 4)^3

. What is

the size of A?

A manufacturer of sports equipment has developed a new synthetic fishing line that

the company claims has a mean breaking strength of 8 kilograms with a standard

deviation of 0.5 kilogram. Test the hypothesis that μ = 8 kilograms against the

alternative that μ is not equal to 8 kilograms if a random sample of 50 lines is tested and found

to have a mean breaking strength of 7.8 kilograms. Use a 0.01 level of significance. What is critical region

Consider product of three matrices M1​,M2​ and M3​ having w rows and x columns, x rows and y columns, and y rows and z columns. Under what condition will it take less time to compute the product as (M1​M2​)M3​ than to compute M1​(M2​M3​) ?