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Questions in mathematics

[Done] Which represents the reflection of $f(x)=\sqrt{x}$ over the $y$-axis? \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline \end{tabular}

[Done] Simplify the expression: [tex]$\left(a^3\right)^2 \cdot a^5$[/tex]

[Done] Assume the random variable $X$ has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. $P(X \leq 3), n=6, p=0.3$

[Done] An arc on a circle measures $8^{\circ}$. The measure of the central angle, in radians, is within which range? A. 0 to $\frac{\pi}{2}$ radians B. $\frac{\pi}{2}$ to $\pi$ radians C. $\pi$ to $\frac{3 \pi}{2}$ radians D. $\frac{3 \pi}{2}$ to $2\pi$ radians

[Done] Which best describes the graph of [tex]f(x)=\log _2(x+3)+2[/tex] as a transformation of the graph of [tex]g(x)=\log _2 x[/tex]? A. a translation 3 units right and 2 units up B. a translation 3 units left and 2 units up C. a translation 3 units up and 2 units right D. a translation 3 units up and 2 units left

[Done] $10^8 \div 10^4=$ F $\quad 1^4$ G $\quad 10^2$ H $10^{12}$ J $100^4$ K None of these

[Done] Which of the following is a biconditional statement? A) If [tex]$x \neq 5$[/tex] then [tex]$x^2 \neq 25$[/tex] B) [tex]$x=5$[/tex] if and only if [tex]$x+5=10$[/tex] C) [tex]$x=5$[/tex] if [tex]$x^2=25$[/tex] D) If [tex]$x^2=25$[/tex], then [tex]$x=5$[/tex] or [tex]$x=-5$[/tex]

[Done] What is the amplitude of the sinusoid given by [tex]y=-3 \sin (5 x) [/tex]?

[Done] Which function has an inverse that is also a function? $\lbrace(-4,3),(-2,7),(-1,0),(4,-3),(11,-7)\rbrace$ $\lbrace(-4,6),(-2,2),(-1,6),(4,2),(11,2)\rbrace$ $\lbrace(-4,5),(-2,9),(-1,8),(4,8),(11,4)\rbrace$ $\lbrace(-4,4),(-2,-1),(-1,0),(4,1),(11,1)\rbrace$

[Done] Simplify the expression. $\frac{b^{-\frac{1}{2}} b^{\frac{5}{2}}}{b^{\frac{1}{3}}}$ Write your answer using only positive exponents. Assume that all variables are positive real numbers.