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Questions in mathematics

📝 Answered - a. A tray of eggs contains 16 large sized eggs and 14 small sized eggs. An egg is selected at random. Find the probability of selecting either a small sized or large-sized egg. b. If [tex]$T^2=4 \pi^2 \frac{\left(h^2+k^2\right)}{h g}$[/tex] make 'k' the subject of the formula.

📝 Answered - $y=\frac{\left(x^2+x\right)\left(x^{-2}+1\right)}{x^2}$

📝 Answered - Solve $5 n-9>47-2 n$

📝 Answered - Simplify $\left(\frac{3}{8}\right)^{-2}\left(\frac{1}{3} \cdot \frac{3}{8}\right)^3\left(\frac{1}{3}\right)^4$.

📝 Answered - During the summer vacation, 35 students out of 100 took up music classes, 45 students took up dance classes, and 30 students did not take up either music or dance classes. If a student is chosen at random, what is the probability that the student took both music AND dance classes? $\frac{3}{10}$ $\frac{3}{4}$ $\frac{9}{10}$ $\frac{1}{10}$

📝 Answered - An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

📝 Answered - $\frac{5 \times 2^m-4 \times 2^{m-2}}{3 \times 2^{m+2}-5 \times 2^{m+1}}$

📝 Answered - What is the following sum? $2\left(\sqrt[3]{16 x^3 y}\right)+4\left(\sqrt[3]{54 x^6 y^5}\right)$

📝 Answered - 2. (1.9) True or False: To factor [tex]$x^2-13 x+30$[/tex], you need to find two integers that multiply to -13 and add to 30. Explain your answer. 3. (1.10) a. State the difference of squares pattern b. Use the difference of squares pattern to factor [tex]$x^2-36$[/tex] 4. (1.10) a. State the two binomial squares patterns. b. Use the binomial squares pattern to factor [tex]$x^2-12 x+36$[/tex]. 5. (1.10) The sum of cubes pattern [tex]$a^3+b^3$[/tex] factors to [tex]$(a+b)(a^2-a b+b^2)$[/tex]. Which of the polynomials below would be a sum of cubes? Factor it. i. [tex]$x^2+25$[/tex] ii. [tex]$y^3+125$[/tex] iii. [tex]$x^3+x^2+8$[/tex]

📝 Answered - In a class of 50 students, 28 take Mathematics, 20 take Computer Science, and 12 take both. Using the principle of inclusion-exclusion, find the number of students who take either Mathematics or Computer Science.