Five cards are selected from a 52-card deck for a poker hand. (a) How many simple events are in the sample space? (b) A royal flush is a hand that contains the A, K, Q, J, and 10, all in the same suit. How many ways are there to get a royal flush? (c) What is the probability of being dealt a royal flush? Correct answers with explanations please 🙏🏻

a) \( 51 / 2= \)

Find all solutions of the equation in the interval \( [0,2 \pi) \). \( -\cot x-1=\csc x \) Write your answer(s) in radians in terms of \( \pi \). If there is more than one solution, separate them with commas. \( x=\square \)

QUESTION 5 5.1 Determine the are length over the interval \( 0 \leq \theta \leq \frac{\pi}{2} \) for the curve with the following parametric equations:- \( \begin{array}{l}x=5 \cos ^{3} \theta \\ y=5 \sin ^{3} \theta\end{array} \)

1. Dada las funciones: \( f(\boldsymbol{x})=\boldsymbol{x}^{2}-4 \quad y \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}+2 \). Determina las operaciones de funciones. Traza las grafficas. a) \( (f+g)(x) \) b) \( (f-g)(x) \) c) \( (f . g)(x) \) d) \( \left(\frac{f}{g}\right)(x) \)

Choose the correct word/phrase from the selection provided in the box below. Choose an answer that best matches the statements given below. Write only the word next to the question number. E.g. 2.11 . Persuasive Message. Respect; Application letter; Templates; Free riders; Blog; Neat hairstyles; Sample; Networking; Vocal characteristics; Mention accomplishments 1.1. Used to collect primary information from a large sample 1.2. A technological tool used to develop a report 1.3. Building your credibility 1.4. Read news sites, blogs and other online sources 1.5. Accompanying curriculum vitae to tell the reader why you are sending it and how they can benerit 1.6. Important aspect to consider for interviews 1.7. A disadvantage of teamwork 1.8. A type of nonverbal communication 1.9. A rule of etiquette 1.10 A type of electronic media that can be used by anyone