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Questions in mathematics

[Done] 3. [tex]\int(3x - 2)^6 dx[/tex] Ans: [tex](1/504)(3x - 2)^7 + C[/tex] 4. [tex]\int(x(x-4))/x dx[/tex] Ans: [tex](x^2 + 4x + 8)/x + C[/tex]

[Done] Which equations represent circles that have a diameter of 12 units and a center that lies on the $y$-axis? Select two options. $x^2+(y-3)^2=36$ $x^2+(y-5)^2=6$ $(x-4)^2+y^2=36$ $(x+6)^2+y^2=144$ $x^2+(y+8)^2=36$

[Done] Complete the table. \begin{tabular}{|c|c|} \hline$x$ & $y=5 x$ \\ \hline-3 & 1 \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{tabular}

[Done] Giulia is playing a game with 6 cards: 4 kings, 1 queen, and 1 jack. She draws 1 card out of the stack of cards, replaces it, and then draws another card. What is the probability that she will draw a king and then a jack, [tex]P( king, then jack )[/tex] ? [tex] \frac{1}{36} [/tex] [tex] \frac{1}{24} [/tex] [tex] \frac{1}{9} [/tex] [tex] \frac{1}{6} [/tex]

[Done] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

[Done] Solve the equation on the interval [tex]$0 \leq 0\ \textless \ 2 \pi$[/tex]. [tex]$(\tan \theta+1)(\cos \theta-1)=0$[/tex]

[Done] A circle passes through points $A(1,2)$ and $B(3,4)$, and its center lies on the line $y=2 x-1$. What is the equation of this circle? Options: 1. $(x-2)^2+(y-3)^2=2$ 2. $(x-3)^2+(y-5)^2=10$ 3. $(x-1)^2+(y-1)^2=8$ 4. $(x-4)^2+(y-7)^2=26$ 5. $x^2+(y+1)^2=10

[Done] According to a poll, $30 \%$ of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth. $\begin{aligned} P(k \text { successes }) & ={ }_n C_k p^k(1-p)^{n-k} \\ { }_n C_k & =\frac{n!}{(n-k)|\cdot k|} \end{aligned}$ A. 0.024 B. 0.031 C. 0.132 D. 0.309

[Done] $\left[\begin{array}{lllllllll}43 & 45 & 50 & 47 & 51 & 58 & 52 & 47 & 0 \\ 61 & 50 & 45 & 55 & 57 & 41 & 46 & 49 & 31 \\ 59 & 44 & 53 & 57 & 49 & 40 & 48 & 52 & 51\end{array}\right]\\Using the class intervals of 43-44, 45-49 ... a) construct the frequency table b) draw a histogram for the distribution. c) draw a frequency polygon for it.

[Done] Calculate $1 \div \frac{5}{7}$. Give your answer as a fraction in its lowest terms.