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question:There are 20 students in a class, 9 of whom are girls and 11 of whom are boys. a) In how many ways can a committee of 5 students be formed? b) In how many ways can a committee of 5 students be formed if it must include 2 girls and 3 boys? c) If a committee of 5 students is formed randomly, what is the probability that it will include 2 girls and 3 boys?

answer:a) The number of ways to form a committee of 5 students from 20 is: begin{align} _{20}C_5&=dfrac{20!}{(20-5)!5!}[0.3cm] &=15,504[0.3cm] end{align} b) The number of ways to choose 2 girls from 9 is: begin{align} _{9}C_2&=dfrac{9!}{(9-2)!2!}[0.3cm] &=36[0.3cm] end{align} The number of ways to choose 3 boys from 11 is: begin{align} _{11}C_3&=dfrac{11!}{(11-3)!3!}[0.3cm] &=165[0.3cm] end{align} Therefore, the number of ways to form a committee with 2 girls and 3 boys is: begin{align} _{9}C_2cdot_{11}C_3&=36cdot165[0.3cm] &=5,940[0.3cm] end{align} c) The probability of forming a committee with 2 girls and 3 boys is: begin{align} P(text{2 girls, 3 boys})&=dfrac{5,940}{15,504}[0.3cm] &approx0.38[0.3cm] end{align}

question:Sort the following numbers in ascending order: 5.6, -5, -5, -2.

answer:To sort the numbers in ascending order, we need to arrange them from smallest to largest. The smallest number is -5, and there are two of them. The next smallest number is -2, followed by 5.6. Therefore, the sorted order of the numbers is -5, -5, -2, 5.6. The answer is -5, -5, -2, 5.6

question:Apex Corporation has budgeted credit sales of 30,000 in December, 40,000 in January, and 25,000 in February. Collection patterns indicate that 25% of sales are collected in the month of sale, 55% in the first month after sale, and 20% in the second month after sale. What is the expected cash collection in January?

answer:Cash collected in January: December: 30,000 x 55% = 16,500 January: 40,000 x 25% = 10,000 February: 25,000 x 20% = 5,000 Total cash collected in January: 16,500 + 10,000 + 5,000 = 31,500

question:Why is the volume of hydrogen produced in the electrolysis of brine often depicted as twice that of chlorine, despite both gases being produced in equivalent amounts?

answer:The confusion arises from the visualization of the gases produced during the electrolysis of brine. While it is true that the same number of moles of hydrogen (H2) and chlorine (Cl2) are produced due to the stoichiometry of the reaction, their volumes at a given temperature and pressure can differ. Chlorine gas is denser than hydrogen, leading to a smaller volume of the same mass of chlorine compared to hydrogen. In diagrams, this difference in density can be exaggerated, resulting in hydrogen appearing to occupy a volume twice that of chlorine. However, this visual discrepancy does not reflect a disparity in the amounts of the gases produced. The difference in solution levels between the cathode and anode chambers, as mentioned, can be attributed to the removal of the evolved hydrogen gas in the cathode chamber and the continuous addition of sodium chloride solution to the anode chamber to maintain the electrolyte's concentration.