Pre-Algebra • Algebra • Trigonometry • Statistics • Solid Geometry • Calculus
I embarked on my academic journey as a sports enthusiast, prior to enrolling in my undergraduate studies. My enthusiasm for mathematics had always been muted, largely owing to the seemingly endless and purposeless calculations it often involved. However, a transformative experience awaited me during my time in college. It was there that I encountered a teacher who, in our very first class, presented a simple yet profound exercise: to complete the sentence "Mathematics is _______" with a single word that encapsulated our immediate perception of the subject. I hesitated briefly before filling the blank space with the word "boring." To my surprise, my teacher chose the word "beautiful." This striking contrast sparked my curiosity and set the stage for a remarkable journey of discovery. Guided by her teaching and insights, it took me a span of two to three months to truly grasp the hidden allure of mathematics. What I once considered mere calculations revealed themselves to be the building blocks of exquisite mathematical and geometric forms. This revelation marked the turning point in my relationship with mathematics. I came to realize that nothing in the realm of mathematics is devoid of purpose or significance. Behind every calculation lies a tapestry of captivating patterns and shapes. As I delved deeper into the core concepts, my appreciation for the elegance and depth of mathematics grew exponentially. This newfound passion became the bedrock of my academic pursuits. It paved the way for my entrance into the world of mathematical exploration, ultimately leading me to pursue a PhD in mathematics. The journey has brought me under the mentorship of an esteemed 80-year-old supervisor, a venerable professor renowned for his wisdom, at Jacobs University in Germany. Looking back, I can trace the evolution of my perspective from skepticism to fascination, all catalyzed by a single teacher's belief in the beauty that mathematics holds. With each step I take in my academic journey, I am reminded that the seeds of interest and passion can be sown in the most unexpected of places, transforming the trajectory of one's life in ways that are both profound and deeply fulfilling.
A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?
(24, -7) is on the terminal arm of an angle in standard position. Determine the exact values of the primary trigonometric functions.
If the midpoint of point A on the x=3 line and point B on the y=-2 line is C(-2,0), what is the sum of the ordinate of point A and the abscissa of point B?
Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places
6. Among 100 of products there are 20 rejects. We will randomly select 10 of products. The random variable X indicates the number of rejects among the selected products. Determine its distribution.
5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.
Given that y = ×(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.