En la clase de gimnasia, se realizan los movimientos de las siguientes imágenes. Cada uno de ellos muestra un arco que se ha formado. Si se sabe que el largo de la pierna de la estudiante es de \( r=60 \mathrm{~cm} \), responder: En cada caso, dibuja el arco y el área de la región circular. ¿Cuál es el tamaño del arco formado si el ángulo en el primer caso es de \( \alpha=120^{\circ} \) y en el segundo es de \( \alpha=170^{\circ} \) ? ¿Cuál es el área de cada región?

Multiple Select Questlon Select all that apply Select inputs into the production process. (More than one answer may be correct) \( \square \) services \( \square \) goods \( \square \) capital \( \square \) labor \( \square \) land

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of \( \mu=1.1 \mathrm{~kg} \) and a standard deviation of \( \sigma=4.9 \mathrm{~kg} \). Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is 0.2397 . (Round to four decimal places as needed.) b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg . The probability is (Round to four decimal places as needed.)

Reflect: Summarize your findings. Describe how to determine the \( x \)-intercepts and vertex of \( y=a(x-H(x-s) \).

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 7.8 cm . a. Find the probability that an individual distance is greater than 207.50 cm . b. Find the probability that the mean for 25 randomly selected distances is greater than 196.20 cm . c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ?

A surplus store gives a scratch-off ticket to 2000 customers as they leave with their groceries. Can we expect t customers' average winnings to be close to the average winnings for the entire population of the scratch-off tic holders?