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Questions in mathematics

[Done] Find each limit. Use $-\infty$ or $\infty$ when appropriate. $f(x)=-\frac{2 x-2}{(x-2)^4}$ (A) $\lim_{x \rightarrow 2^{-}} f(x)$ (B) $\lim_{x \rightarrow 2^{+}} f(x)$ (C) $\lim_{x \rightarrow 2} f(x)$

[Done] A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches. Which of the following could be used to calculate the volume of water in the vase? [tex]$\pi(3 i n)^2(12 i n)-1.5(\frac{4}{3} \pi(9 i n)^3)$[/tex] [tex]$\pi(3 i n)^2(12 i n)-9(\frac{4}{3} \pi(1.5 i n)^3)$[/tex] [tex]$\pi(12 i n)^2(3 i n)-1.5(\frac{4}{3} \pi(9 i n)^3)$[/tex] [tex]$\pi(12 i n)^2(3 i n)-9(\frac{4}{3} \pi(1.5 i n)^3)$[/tex]

[Done] $\begin{array}{c} y=-\frac{1}{3} x+3 \\ 3 x-y=7 \end{array}$ Plot two lines by clicking the graph. Click a line to delete it.

[Done] What is the radius of a circle whose equation is $x^2+y^2+8 x-6 y+21=0$? A. 2 units B. 3 units C. 4 units D. 5 units

[Done] A number, w, is decreased by 6 and the result is multiplied by 4. The final result is greater than the original number. Write and solve an inequality for w.

[Done] The vertex of the graph of $y=(x-1)^2-5$ is ($\square$, $\square$).

[Done] A sequence is defined by the rule [tex]x_n=7 n+13[/tex]. Work out the value of [tex]x_{10}[/tex]. (Hint: [tex]x_{10}[/tex] is the [tex]10^{\text {th }}[/tex] term in the sequence.)

[Done] Use the distributive law to calculate $19 \times 6+19 \times 4$

[Done] Simplify the following: $\left[-(2 x-4 y)^6(2 x+4 y)^4\right]^3(2 x-4 y)^3(2 x+4 y)^6$ A. $(2 x-4 y)^{21}(2 x+4 y)^{18}$ B. $(2 x-4 y)^{12}(2 x+4 y)^{13}$ C. $-(2 x-4 y)^{21}(2 x+4 y)^{18}$ D. $-(2 x-4 y)^{12}(2 x+4 y)^{13}$

[Done] A firm will promote two employees out of a group of six men and three women. What probability concept would be used to assign probabilities to the outcomes? Multiple Choice A. Classical B. Empirical