Which one of the following hypotheses is/are valid? 1. \( H_{0}: \mu \leq 100 ; H_{1}: \mu \geq 100 \) 2. \( H_{0}: \mu=120 ; H_{1}: \mu \neq 120 \) 3. \( H_{0}: \mu \neq 130 ; H_{1}: \mu=130 \) 4. \( H_{0}: \bar{X} \leq 210 ; H_{1}: \bar{X}>210 \) 5. \( H_{0}: p \neq 0.42 ; H_{1}: p=0.42 \)

Montren que: \( \frac{\left(9^{n+1}+9^{n}\right)^{8}}{\left(3^{2 n}-3^{2 n+1}\right)^{2}} \in \mathbb{Z} \)

Write a sentence to explain how Jacob could use estimate to tell that his answer is incorrect.

82. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally repre- sentative online poll of 2,015 American adults aged 18 and above. They found that \( 3.3 \% \) of the respondents identified as vegetarian. Food habits in India tend to have a large religious and social component. How does the popularity of the vegetarian diet differ in the United States and India? A 2014 survey conducted by the Registrar General of India found that \( 29 \% \) of Indians were vegetarian. Suppose the proportion was obtained from a random sample of 1,000 Indians. (a) Construct and interpret a \( 99 \% \) confidence interval for the difference in proportions of vege- tarians in India and the United States. (b) Based on the interval, what kind of evidence do you expect to have for the alternative in a two-sided hypothesis test? Explain.

Give a fully simplified expression for \( \cos \left(\sin ^{-1}\left(\frac{y}{9}\right)\right) \) Your answer should have no trigonometric functions.

Show Attempt History A cold \( \left(0.15^{\circ} \mathrm{C}\right) \) piece of copper \( (5.03 \mathrm{~g}) \) was placed into a beaker with 57 mL of water at \( 326^{\circ} \mathrm{C} \). Your Answer Correct Answer a) Does the he at flow from the copper or from the water?