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Questions in mathematics

[Done] Identify the values of $a, b$, and $c$ that make the statement below true. [tex] $\log _2 64=6$ if and only if $a^b=c$. [/tex] [tex] a=\square b=\square c=\square [/tex]

[Done] Write the expression $a^{15}$ as a product of two exponents with the same base, one of which equals $a^6$.

[Done] A 10-item statistics quiz was given to 30 students. The table below gives the scores received along with the corresponding frequencies. \begin{tabular}{|c|c|c|c|c|c|c|}\ \hline Score & 5 & 6 & 7 & 8 & 9 & 10 \ \hline Frequency & 1 & 2 & 5 & 5 & 7 & 10 \ \hline \end{tabular} What was the mean score on the quiz?

[Done] $181.93 \div(-11.3) A) $-2,055.809$ B) 16.1 C) -16.1 D) -0.062

[Done] 7.) $-15-x=-2x-2x$ 8.) $-5x+5x+10=x+2$

[Done] [tex]\frac{x^2-25}{x^2+8 x+15} \cdot \frac{x^2+3 x}{x-5}[/tex]

[Done] Use a calculator to find the common logarithm. $\log (-83)$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The answer is $\square$ . (Round to four decimal places as needed.) B. The answer does not exist.

[Done] Write $\frac{2}{5}, \frac{3}{5}$ and $\frac{5}{10}$ in order from smallest to largest.

[Done] Three-fifths of the members of the Spanish club are girls. There are a total of 30 girls in the Spanish club. Which statements can be used to solve for [tex]$x$[/tex], the total number of members in the Spanish club? Select three options. [tex]$\frac{3}{5} x=30$[/tex] [tex]$\frac{3}{5}=\frac{x}{30}$[/tex] [tex]$\left(\frac{5}{3}\right) \frac{3}{5} x=30\left(\frac{3}{5}\right)$[/tex] [tex]$\left(\frac{5}{3}\right) \frac{3}{5} x=30\left(\frac{5}{3}\right)$[/tex] [tex]$x=50$[/tex]

[Done] Is $(4,2)$ a solution to the system $y-x=2$ and $-3x-2y=-8$? A. Yes, because $(4,2)$ is a solution to both equations. B. Yes, because $(4,2)$ is a solution to one equation. C. No, because $(4,2)$ is a solution to only one equation. D. No, because $(4,2)$ is a solution to neither equation.