# Learn ## Hypothesis Testing #1 (Statistics)

Hypothesis Testing #1 Question: A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 30.6. A random sampling of 25 scores obtained from individuals who …

## Unit Circle and Logarithm Problem #1 (Trigonometry)

Unit Circle and Logarithm #1 Question: The point $\left(log_b\left(\sqrt{b}\right),\:y\right)$ where $b>0,\:b=1$, is on the terminal arm of angle $\theta$ drawn in the standard position of the unit circle. Find the angle $\theta$ between 0 and $\pi$. Answer: For unit circle and logarithm #1 problem, we need to apply our knowledge on logarithm rules and on …

## Arithmetic Sequences #1 (Algebra)

Arithmetic Sequences #1 Question: Find the explicit formula for the following sequence: 1, 2/3, 3/5, 4/7. Answer: To get the explicit formula for the arithmetic sequences #1 question, we could express the first term 1 as $\frac{1}{1}$. By looking at the sequence as $$\frac{1}{1},\:\frac{2}{3},\:\frac{3}{5},\:\frac{4}{7}$$, the patterns could be distinguished from the numerator and from the …

## Sinusoidal Function Problem #1 (Trigonometry)

Sinusoidal Function #1 Question: A ferris wheel is 20 meters in diameter and boarded at ground level. The wheel makes one full rotation every 7 minutes, and at time t=0 you are at the 3 o’clock position and ascending. Let f(t) denote your height (in meters) above ground at t minutes. Find a formula for …