### At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]

### Which of the following is the nth taylor polynomial tn(x) for f(x)=ln(1−x) based at b=0?

Find the smallest value of $n$ such that Taylor’s inequality guarantees that $|ln⁡(x) − ln⁡(1 − x)| < 0.01$ for all $x$ in the interval $l = [dfrac {- 1}{2}, dfrac {1}{2} ]$ The aim of this question is to find the $n^{th}$ Taylor polynomial of the given expression. Furthermore, the smallest value […]

### Given the proportion a/b = 8/15, what “ratio” completes the equivalent proportion a/8.

This problem aims to familiarize us with fractions and their ratio and proportion. Basically, this problem is related to fundamental calculus. Ratio and Proportion are described mainly founded on fractions. When a fraction is expressed in the form of a:b, it is called a ratio, whereas a proportion declares that two ratios are equivalent. Here, […]

### Which equation could be used to calculate the sum of the geometric series?

[ text{Series}  = dfrac{1}{3}+ dfrac{2}{9}+ dfrac{4}{27}+ dfrac{8}{21}+ dfrac{16}{243} ] This problem aims to familiarize us with the arrangement of object in series and sequences. The concepts required to solve this problem include geometric series and geometric sequences. The main difference between a series and a sequence is that there exists an arithmetic operation in sequence whereas […]

### Compilers can have a profound impact on the performance of an application. Assume that for a program, compiler A results in a dynamic instruction count of 1.0E9 and has an execution time of 1.1 s, while compiler B results in a dynamic instruction count of 1.2E9 and an execution time of 1.5 s.

Given that the processor’s clock cycle time is 1 ns, calculate each program’s average CPI under this situation. Assume there are two processors being used to run the compiled programs. How much quicker is the clock on the processor executing compiler A’s code compared to the clock on the processor executing compiler B’s code if […]