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Questions in mathematics

📝 Answered - For all sets [tex]$A, B$[/tex], and [tex]$C$[/tex], construct an algebraic proof for the given statement. Cite a property from Theorem 6.22 for every step. 30. [tex]$(A \cap B) \cup C=(A \cup C) \cap(B \cup C)$[/tex] 31. For all sets [tex]$A$[/tex] and [tex]$B, A \cup(B-A)=A \cup B$[/tex].

📝 Answered - c) If $x y z=1$, prove that $\frac{1}{1+x+y^{-1}}+\frac{1}{1+y+z^{-1}}+$\nd) If $a+b+c=0$, prove that $\frac{1}{1+x^a+x^b}+\frac{1}{1+x^b}+$\n12. a) If $x=2^{\frac{1}{3}}+2^{-\frac{1}{3}}$, prove that $2 x^3-6 x=5$.\nb) If $a=p^{\frac{1}{3}}-p^{-\frac{1}{3}}$, prove that $a^3+3 a=p-\frac{1}{p}$.\nc) If $x-2=3^{\frac{1}{3}}+3^{\frac{2}{3}}$, show that $x\left(x^2-6 x+3\right)=2$.\nOBJECTIVE QUESTION\n\nLet's tick $(\sqrt{ })$ the correct alternative.

📝 Answered - Factorise $a^2+14 a+45$ fully

📝 Answered - The temperature measured in Kelvin (K) is the temperature measured in Celsius ($C$) increased by 273.15. This can be modeled by the equation $K=C+$ 273.15. When solved for $C$, the equation is A. $C=K-273.15$ B. $C=273.15-K$ C. $C=K+273.15$ D. $C=273.15 K$

📝 Answered - Select the correct answer. Jacob is leaving his house to go to work and is running 5 minutes late. In the past, when Jacob has been 5 minutes late for work, he has taken an alternate route to work a total of 16 times. Jacob has also taken his normal route to work 27 times when running 5 minutes late. The table shows the outcomes for taking each route. | | Alternate route | Normal route | | :-------- | :-------------- | :----------- | | Late | 8 | 9 | | On time | 3 | 12 | | Early | 5 | 6 | | Total | 16 | 27 | Based on the information in the table, if Jacob's goal is to be on time or early for work, should he take the alternate route or his normal route? A. Jacob should take his normal route to work. B. There is not enough information to determine if Jacob should take the alternate route or his normal route to work. C. Neither route has an advantage. D. Jacob should take the alternate route to work.

📝 Answered - What is $2.56 \times 10^{-5}$ in standard form? A. 0.000256 B. $25,600,000$ C. 256,000 D. 0.0000256

📝 Answered - Solve the quadratic equation [tex]x^2+6 x-59=0[/tex] by completing the square. A) [tex]x=-3 \pm \sqrt{17}[/tex] B) [tex]x=3 \pm 2 \sqrt{17}[/tex] C) [tex]x=-3 \pm 2 \sqrt{17}[/tex] D) [tex]x=-2 \pm 3 \sqrt{17}[/tex]

📝 Answered - The ageing year up so teachers. $\begin{array}{cccccccccc} 21 & 37 & 49 & 27 & 49 & 42 & 26 & 33 & 246 & 40 \\ 50 & 29 & 23 & 24 & 29 & 31 & 36 & 22 & 27 & 38 \\ 31 & 26 & 42 & 39 & 34 & 23 & 21 & 32 & 41 & 46 \\ 46 & 21 & 33 & 29 & 28 & 43 & 47 & 40 & 34 & 44 \\ 26 & 38 & 34 & 49 & 45 & 27 & 25 & 33 & 39 & 40 \end{array}$ a. Form a frequency distribution table for the data using the interval of $21=25,26-30.31-35 \ldots$ b. Calculate the mode, mean, and median. c. Calculate the variance and standard deviation.

📝 Answered - Solve the equation: [tex]$\sqrt{x+11}=x+5$[/tex]

📝 Answered - Anna gets an overdraft fee if her balance at the end of the day is negative. On which day or days does Anna get an overdraft fee? I. Wednesday II. Thursday III. Friday A. I only B. I and II C. II and III D. III only