09. Consider a study published January 2023 by Dunfort et. al. in the Journal of the Academy of Nutrition and Dietetics. The study found that \( 59.5 \% \) of food products purchased by US households contained additives. (a) Describe the sampling distribution of the sample proportion of food products containing additives for samples of size 60 products. (b) Find the probability that at least half of the sample of 60 products have additives. (c) Describe the sampling distribution of the sample proportion of food products containing additives for samples of size 100 . (d) Find the probability that between \( 25 \% \) and \( 50 \% \) of the sample of 100 products have additives.

A Su un treno sono presenti 122 passeggeri nella prima carrozza e 56 nella seconda. Quanti passeggeri in tutto? Se alla prima fermati scendono 45 passeggeri, quanti ne restano sul treno?

What do prosecutors who act vindictively run the chance of doing? Threatening the defendant's due process rights Losing their cases badly Endangering the sentencing process Denying their own prosecutorial discretion

Find the values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point. \( (\sqrt{6},-\sqrt{2}) \) sin \( \alpha=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

\begin{tabular}{l} Exercise 2.5 \\ \( \begin{array}{lll}\text { 1. Express each of the following numbers as prime factorization form. } \\ \begin{array}{lll}\text { a. } 21 & \text { b. } 70 & \text { c. } 105\end{array} \\ \begin{array}{lll}\text { d. } 252 & \text { e. } 360 & \text { f. } 1,848\end{array} \\ \text { 2. } 180 \text { can be written as } 2^{a} \times 3^{b} \times 5^{c} \text {. Then, find the value of } a, b \text { and } c \text {. } \\ \text { 3. Find the four prime numbers whose product is } 462 .\end{array} \) \\ \hline\end{tabular}

Find all solutions of the equation in the interval \( [0,2 \pi) \). \[ (\csc \theta-\sqrt{2})(\sec \theta+\sqrt{2})=0 \] Write your answer in radians in terms of \( \pi \). If there is more than one solution, separate them with commas. \( \theta=\square \)