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Questions in mathematics

[Answered] Are there rational numbers between $\frac{5}{7}$ and $\frac{6}{7}$?

[Answered] In a survey of 100 people it was found that 65 read magazine [tex]$A$[/tex], 45 read magazine [tex]$B$[/tex], 40 read magazine [tex]$C$[/tex], 25 read magazine [tex]$A$[/tex] as well as [tex]$B$[/tex]; 20 read magazine [tex]$A$[/tex] as well as [tex]$C$[/tex], 15 read magazine [tex]$B$[/tex] as well as [tex]$C$[/tex]; 5 read all three magazines and 5 don't read any of them. i) Find the value of [tex]$n(A \cap B \cap C)$[/tex] ii) Show the information in a Venn diagram. iii) Find the value of [tex]$n(A \cup B \cup C)$[/tex] iv) In every 20 people, one does not read all three magazines. Justify it.

[Answered] A box contains different-colored marbles. If [tex]P(blue) = \frac{1}{4}[/tex], [tex]P(green) = \frac{1}{4}[/tex], and [tex]P(blue and green) = \frac{1}{16}[/tex], which statement is true? A. The events are independent because [tex]P(blue) \cdot P(green) = P(blue and green)[/tex]. B. The events are independent because [tex]P(blue) \cdot P(green) \neq P(blue and green)[/tex]. C. The events are dependent because [tex]P(blue) \cdot P(green) = P(blue and green)[/tex]. D. The events are dependent because [tex]P(blue) \cdot P(green) \neq P(blue and green)[/tex].

[Answered] What is the domain of the step function [tex]f(x)=\lceil 2 x\rceil-1[/tex]? A. [tex] \{x \mid x \geq-1\} [/tex] B. [tex] \{x \mid x \geq 1\} [/tex] C. [tex] \{x \mid x \text{ is an integer }\} [/tex] D. [tex] \{x \mid x \text{ is a real number }\} [/tex]

[Answered] Which is equivalent to [tex]$80^{\frac{1}{4} x}$[/tex]? A. [tex]$\left(\frac{80}{4}\right)^x$[/tex] B. [tex]$\sqrt[4]{80}^x$[/tex] C. [tex]$\sqrt[x]{80^4}$[/tex] D. [tex]$\left(\frac{80}{x}\right)^4$[/tex]

[Answered] This circle is centered at the origin, and the length of its radius is 6. What is the circle's equation? A. $x^6+y^6=1$ B. $x+y=36$ C. $x^2+y^2=6$ D. $x^2+y^2=36$

[Answered] Solve for $x$. $\frac{x}{2}=\frac{3 x+4}{2 x}$ A) $x=4,-1$ B) $x=4,1 / 2$ C) $x=4,-1 / 2$

[Answered] Which line is perpendicular to a line that has a slope of $-\frac{5}{6}$? line JK line LM line NO line PQ

[Answered] Simplify: [tex]$\frac{a^2}{a-3}-\frac{9-6 a}{3-a}$[/tex]

[Answered] (h) [tex]\frac{a^4}{4(a+3)^2}+\frac{81-18 a^2}{4(a+3)^2}[/tex]