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Questions in mathematics

[Answered] What is 18,000 expressed in scientific notation? A. $1.8 \times 10^{-4}$ B. $1.8 \times 10^4$ C. $1.8 \times 10^{-5}$ D. $1.8 \times 10^5$

[Answered] Solve $(\sqrt{6})^{8 x}=216^{x-3}$.

[Answered] Select the correct answer from each drop-down menu. When [tex]p^2-4 p[/tex] is subtracted from [tex]p^2+p-6[/tex], the result is [ ] To get [tex]p-9[/tex], subtract [ ] from this result.

[Answered] The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density. \begin{tabular}{|r|r|r|} \hline & Land Area $\left( mi ^2\right)$ & Seismic Activity Density \\ \hline State A & 163,696 & 0.0299 \\ \hline State B & 10,931 & 0.1402 \\ \hline \end{tabular} Which statement about the number of earthquakes the states had for the given time span is true? A. State $A$ had approximately 1,533 more earthquakes than State B. B. State $B$ had approximately 1,533 more earthquakes than State A. C. State $A$ had approximately 3,362 more earthquakes than State B. D. State $B$ had approximately 3,362 more earthquakes than State A.

[Answered] Find the value of $a$ and $Y Z$ if $Y$ is between $X$ and $Z$. $X Y=7 a, Y Z=5 a, X Z=6 a+24$ $a=\square$ $Y Z=$ $\square$

[Answered] In Pitcher's ERA, the number of innings pitched, [tex]$I$[/tex], is measured by the formula [tex]$I=\frac{9 R}{A}$[/tex], where [tex]$R=$[/tex] runs allowed and [tex]$A=$[/tex] earned run average. Solve the formula for [tex]$A$[/tex].

[Answered] Determine if the function [tex]f(x)=\sqrt[5]{x^4}[/tex] is differentiable at [tex]x=0[/tex]. If not, identify why. a.) [tex]f(x)=\sqrt[5]{x^4}[/tex] is not differentiable at [tex]x=0[/tex] because [tex]f(0)[/tex] is not defined. b.) [tex]f(x)=\sqrt[5]{x^4}[/tex] is not differentiable at [tex]x=0[/tex] because [tex]\lim _{x \rightarrow 0} \sqrt[5]{x^4}[/tex] does not exist. c.) [tex]f(x)=\sqrt[5]{x^4}[/tex] is not differentiable at [tex]x=0[/tex] because [tex]f^{\prime}(0)[/tex] is not defined. d.) [tex]f(x)=\sqrt[5]{x^4}[/tex] is differentiable at [tex]x=0[/tex].

[Answered] Richard has $652 in his account and is planning a road trip. He looks at how expensive hotels and sightseeing costs are in certain cities, planning accordingly: \begin{tabular}{|c|r|} \hline City & Cost ($) \\ \hline Detroit & 196.87 \\ \hline Pittsburgh & 180.32 \\ \hline St. Paul & 102.87 \\ \hline Cincinnati & 155.81 \\ \hline Richmond & 211.86 \\ \hline \end{tabular} When Richard makes the calculations, he finds he does not have enough money to visit each city. What is the cheapest city that Richard can drop to avoid overdrawing his account? A. Richmond B. Detroit C. Pittsburgh D. Cincinnati

[Answered] The frequency table was made using a box containing slips of paper. Each slip of paper was numbered [tex]$0,1,2,3$[/tex], or 4. | [tex]$x$[/tex] | [tex]$f$[/tex] | |---|---| | 0 | 15 | | 1 | 20 | | 2 | 5 | | 3 | 5 | | 4 | 5 | Create a bar graph by dragging the sliders on the horizontal axis to represent the probability distribution.

[Answered] The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year. Which equation can be used to find [tex]$y$[/tex], the year in which both bodies of water have the same amount of mercury? A. [tex]$0.05-0.1 y=0.12-0.06 y$[/tex] B. [tex]$0.05 y+0.1=0.12 y+0.06$[/tex] C. [tex]$0.05+0.1 y=0.12+0.06 y$[/tex] D. [tex]$0.05 y-0.1=0.12 y-0.06$[/tex]