61 sample problems. The new algorithm completes the sample problems with a mean time of 14.06 hours. The current algorithm completes the sample problems with a mean time of 16.43 hours. Assume the population standard deviation for the new algorithm is 3.004 hours, while the current algorithm has a population standard deviation of 4.568 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Le

There is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

Step-by-step explanation:

From the question we are told that

    The  sample size for each algorithm is

     The sample mean  for new algorithm is  

     The  standard deviation for new algorithm is  

     The  sample  mean for  the current algorithm is  

     The standard deviation for current algorithm is  

     The  level of significance is

The  null hypothesis is  

The  alternative  hypothesis is

Here   are population mean for  new and current algorithm

Generally the test statistics is mathematically represented as

=>    

=>    

Generally the p-value is mathematically represented as

From the  z-table  

=>    

From the calculated value  we see that    hence the null hypothesis is rejected

        Hence we can conclude that there is sufficient evidence to conclude that the new algorithm has a lower mean completion time than the current algorithm

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it